TSTP Solution File: SWV731-1 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV731-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n028.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 21:53:05 EDT 2023

% Result   : Unsatisfiable 27.51s 27.77s
% Output   : Proof 27.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18  % Problem    : SWV731-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.20  % Command    : do_cvc5 %s %d
% 0.20/0.40  % Computer : n028.cluster.edu
% 0.20/0.40  % Model    : x86_64 x86_64
% 0.20/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.40  % Memory   : 8042.1875MB
% 0.20/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.40  % CPULimit   : 300
% 0.20/0.40  % WCLimit    : 300
% 0.20/0.41  % DateTime   : Tue Aug 29 09:30:26 EDT 2023
% 0.20/0.41  % CPUTime    : 
% 0.26/0.61  %----Proving TF0_NAR, FOF, or CNF
% 0.26/0.61  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.2ko3imvaro/cvc5---1.0.5_19854.p...
% 0.60/0.78  ------- get file name : TPTP file name is SWV731-1
% 0.60/0.79  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19854.smt2...
% 0.60/0.79  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.71/10.93  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.69/15.99  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.81/21.05  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.82/26.09  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.51/27.77  % SZS status Unsatisfiable for SWV731-1
% 27.51/27.77  % SZS output start Proof for SWV731-1
% 27.55/27.78  (
% 27.55/27.78  (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)))) (let ((_let_2 (tptp.c_Set_Oimage tptp.c_Public_OshrK _let_1 tptp.tc_Message_Oagent tptp.tc_nat))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) tptp.v_K) _let_2)))) (let ((_let_4 (tptp.hAPP tptp.c_Message_Omsg_OKey tptp.v_K))) (let ((_let_5 (= tptp.v_X (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OAgent tptp.v_A)))))) (let ((_let_6 (or (not _let_5) _let_3))) (let ((_let_7 (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_7 tptp.v_evs) tptp.c_NS__Shared__Mirabelle_Ons__shared)))) (let ((_let_9 (tptp.c_in tptp.tc_Message_Oagent))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_9 tptp.v_A) tptp.c_Event_Obad)))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.hAPP tptp.c_Public_OshrK tptp.v_A))) (let ((_let_13 (tptp.c_Message_Omsg_OCrypt _let_12 (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_4 tptp.v_X)))))) (let ((_let_14 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_15 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_14 _let_13) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs)))))) (let ((_let_16 (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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A _let_1)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)) V_evs) tptp.c_NS__Shared__Mirabelle_Ons__shared))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) _let_1) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))))))))) (let ((_let_17 (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_K_H $$unsorted) (V_N $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)) V_evs) tptp.c_NS__Shared__Mirabelle_Ons__shared))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))))))) (let ((_let_18 (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent))) (let ((_let_19 (forall ((V_X $$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.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)) V_evs) tptp.c_NS__Shared__Mirabelle_Ons__shared))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (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))))))))) (let ((_let_20 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_21 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_22 (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OSignature))) (let ((_let_23 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage _let_22 _let_1 tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg))) (let ((_let_24 (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OEncryption))) (let ((_let_25 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage _let_24 _let_1 tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg))) (let ((_let_26 (tptp.c_Orderings_Obot__class_Obot _let_21))) (let ((_let_27 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A _let_13)) (tptp.c_List_Oset tptp.v_evs tptp.tc_Event_Oevent))))) (let ((_let_28 (not _let_27))) (let ((_let_29 (not _let_8))) (let ((_let_30 (not _let_3))) (let ((_let_31 (or _let_30 _let_29 _let_28))) (let ((_let_32 (_let_17))) (let ((_let_33 (ASSUME :args _let_32))) (let ((_let_34 (not _let_31))) (let ((_let_35 (not _let_15))) (let ((_let_36 (or _let_27 _let_29 _let_10 _let_35))) (let ((_let_37 (_let_16))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (ASSUME :args (_let_8)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_10 _let_35 _let_29 _let_27 (not _let_36)))) (ASSUME :args (_let_11)) (ASSUME :args (_let_15)) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.v_A tptp.v_NA tptp.v_B tptp.v_K tptp.v_X tptp.v_evs QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP _let_14 (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)))))) :args _let_37)) _let_38 :args (_let_36 false _let_16)) :args (_let_27 true _let_10 false _let_15 false _let_8 false _let_36)))) (let ((_let_41 (or _let_5 _let_29 _let_28))) (let ((_let_42 (_let_19))) (let ((_let_43 (ASSUME :args _let_42))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (tptp.v_K tptp.v_evs tptp.v_A _let_12 tptp.v_NA tptp.v_B tptp.v_X QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_29 _let_30 _let_28 _let_34))) _let_39 (MACRO_RESOLUTION_TRUST (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_5 _let_29 _let_28 (not _let_41)))) _let_39 _let_40 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.v_X tptp.v_B tptp.v_K tptp.v_A tptp.v_evs _let_12 tptp.v_NA QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_42)) _let_43 :args (_let_41 false _let_19)) :args (_let_5 false _let_8 false _let_27 false _let_41)) :args (_let_3 false _let_5)) _let_40 :args (_let_34 false _let_8 false _let_3 false _let_27)) _let_33 :args (false true _let_31 false _let_17)) :args ((forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_2) tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oparts V_H) _let_2) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) _let_1))))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Event_Oused (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Event_Oused V_evs) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Event_Oused (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Event_Oused V_evs) _let_1)))) (forall ((V_c $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_3 (tptp.hAPP _let_2 V_c))) (let ((_let_4 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_4 (tptp.c_Message_Oparts V_H) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_4))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg))))))))))) (= (tptp.c_Message_Oparts _let_26) _let_26) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X _let_2 tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_Y _let_2 tptp.tc_Message_Omsg)) _let_1) (tptp.c_Message_Oparts V_H) _let_1))))) (= (tptp.c_Message_OkeysFor _let_26) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (= (tptp.c_Message_Oanalz _let_26) _let_26) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts V_H) _let_1)))) (forall ((V_X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Message_Oparts (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Event_Oknows V_A V_evs))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X _let_2 tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts _let_2) _let_1))))) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_evs))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_2) tptp.tc_Message_Omsg)) _let_1 _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) _let_1))))))) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X _let_2 tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts _let_2) _let_1))))) (not (= tptp.c_Public_Okeymode_OEncryption tptp.c_Public_Okeymode_OSignature)) (forall ((V_P $$unsorted) (V_keymode $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_keymode)) (not (tptp.hBOOL (tptp.hAPP V_P tptp.c_Public_Okeymode_OEncryption))) (not (tptp.hBOOL (tptp.hAPP V_P tptp.c_Public_Okeymode_OSignature))))) (not (= tptp.c_Public_Okeymode_OSignature tptp.c_Public_Okeymode_OEncryption)) (= (tptp.c_Event_OinitState tptp.c_Message_Oagent_OServer) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP _let_24 tptp.c_Message_Oagent_OServer))) (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP _let_22 tptp.c_Message_Oagent_OServer))) _let_26 tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) _let_25 _let_21) _let_23 _let_21) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey _let_2 tptp.tc_nat tptp.tc_Message_Omsg) _let_21)) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((V_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_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Osynth V_G) _let_2 _let_1)))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (tptp.c_lessequals (tptp.c_Message_Osynth V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBC V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_1))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_ONonce V_nat_H))) (= V_nat V_nat_H))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_H) _let_1) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_S $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_a T_b) (tptp.c_Set_Oimage V_f V_S T_a T_b) T_b T_a) V_S) (not (tptp.c_lessequals V_S V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_B T_b) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (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_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 ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((V_agent1 $$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_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) T_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a)))) (forall ((V_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 ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) _let_1))) (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_G T_a)) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (= (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oinsert V_K (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool)) tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_a))) (or (= _let_1 V_A) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (not (tptp.c_lessequals _let_1 V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_F T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_G T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Lattices_Oupper__semilattice__class_Osup V_F V_G (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.c_in tptp.t_a))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_COMBC _let_2 V_R tptp.t_a _let_1 tptp.tc_bool) (tptp.c_COMBC _let_2 V_S tptp.t_a _let_1 tptp.tc_bool) _let_1) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_2 tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S _let_1)))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_b T_a) V_B T_a T_b) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (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 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Osynth V_G) (tptp.c_Message_Osynth V_H) _let_1) (tptp.c_Message_Osynth (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_1))) (forall ((V_H $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_Message_Osynthp V_H (tptp.c_Message_Omsg_OHash V_X))) (not (tptp.hBOOL (tptp.c_Message_Osynthp V_H V_X))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) _let_2 _let_1)))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Osurj V_f T_a T_b) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_agent V_agent_H))) (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_in T_a))) (or (tptp.c_lessequals V_R V_S _let_1) (not (tptp.c_lessequals (tptp.c_COMBC _let_2 V_R T_a _let_1 tptp.tc_bool) (tptp.c_COMBC _let_2 V_S T_a _let_1 tptp.tc_bool) _let_1)))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_in T_a))) (or (tptp.c_lessequals (tptp.c_COMBC _let_2 V_R T_a _let_1 tptp.tc_bool) (tptp.c_COMBC _let_2 V_S T_a _let_1 tptp.tc_bool) _let_1) (not (tptp.c_lessequals V_R V_S _let_1)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_msg $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OHash V_msg) (tptp.c_Message_Omsg_OHash V_msg_H))) (= V_msg V_msg_H))) (forall ((V_A $$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 ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (= (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) T_b T_a) V_f) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (= (tptp.c_Event_OinitState tptp.c_Message_Oagent_OSpy) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage _let_24 tptp.c_Event_Obad tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage _let_22 tptp.c_Event_Obad tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg) _let_21) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage tptp.c_Public_OshrK tptp.c_Event_Obad tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg) _let_21) _let_25 _let_21) _let_23 _let_21)) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_H $$unsorted) (V_H_H $$unsorted) (V_G $$unsorted) (V_G_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (not (= (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H))) (not (= (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_G_H))) (= (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G_H V_H_H _let_1)))))) (forall ((V_A $$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 $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_A $$unsorted) (V_evs $$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_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg_H) (tptp.c_Message_Omsg_ONonce V_nat)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_B _let_2))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) V_A _let_1)))) (forall ((V_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 $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((V_agent_H $$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 ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oimage V_f V_A T_a T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_B T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((T_a $$unsorted) (V_t $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_t))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_in T_a))) (or (not (= (tptp.c_COMBC _let_2 V_R T_a _let_1 tptp.tc_bool) (tptp.c_COMBC _let_2 V_S T_a _let_1 tptp.tc_bool))) (= V_R V_S))))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_OHash V_msg)))) (forall ((V_msg $$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_nat $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_msg1_H $$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_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_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_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_h $$unsorted) (V_F $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_h V_F T_a T_b) T_b) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_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 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oparts V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oparts V_G) _let_2 _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a))) (forall ((T_a $$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)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_A $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_B _let_1) _let_2)))) (forall ((V_nat_H $$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_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat $$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_H $$unsorted) (V_msg_H $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OHash V_msg)))) (forall ((V_nat_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H) (tptp.c_Message_Omsg_ONonce V_nat)))) (forall ((V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H)))) (forall ((V_nat $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OHash V_msg_H)))) (forall ((V_msg_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_nat_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_agent $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_ONonce V_nat_H)))) (forall ((V_agent $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OHash V_msg_H)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oparts V_H) _let_2) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) _let_1))))))) (forall ((V_evs $$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_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_a T_c T_b) _let_1 T_b T_c) T_c) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_g _let_1 T_b T_a) T_a))))) (forall ((V_Y $$unsorted) (V_G $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (let 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(tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Set_Oimage (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) (tptp.c_Set_Oimage V_f V_X T_a T_b) T_b T_a) V_X) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.c_Set_Oimage (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b T_a) V_A) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_X $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G 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(tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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))))) (forall ((V_X $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.c_Fun_Osurj (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) T_b T_a) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_List_Oset V_xs T_a) T_a)) (forall ((V_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H) (tptp.c_Event_Oevent_OGets V_agent V_msg)))) (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Osynth V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (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 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_let_2)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Obij (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) T_b T_a) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((V_nat $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OHash V_msg_H)))) (forall ((V_G $$unsorted) (V_H $$unsorted) (V_G_H $$unsorted) (V_H_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G_H V_H_H _let_1)) _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H) _let_1)) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_G_H) _let_1))))) (forall ((T_a $$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))) (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp _let_18)) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) V_G)))))) (forall ((V_K $$unsorted) (V_KK $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_KK tptp.tc_nat tptp.tc_Message_Omsg) V_C _let_1) tptp.tc_Message_Omsg) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oinsert V_K V_KK tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg) V_C _let_1)))) (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_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_xa)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_b T_a) V_x)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a)))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (let ((_let_2 (tptp.c_in T_b))) (let ((_let_3 (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_a T_b))) (or (not (= (tptp.hAPP _let_3 V_x) (tptp.hAPP _let_3 V_y))) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1)))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))) (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_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (= (tptp.hAPP V_f (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_b T_a) V_y)) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) (tptp.c_Set_Oimage V_f V_A T_b T_a)))))) (= (tptp.hAPP _let_20 tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) tptp.v_x) _let_20)) (forall ((V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_aa $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_aa T_a)) (= (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into V_A V_f T_aa T_a) (tptp.hAPP V_f V_x)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals V_x (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (tptp.c_lessequals (tptp.c_List_Oset V_xs T_a) (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_List_Oset V_xs T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_List_Oset (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oset V_xs T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_c $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts V_H))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts V_G))) (not (tptp.hBOOL (tptp.hAPP _let_1 (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))))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (let ((_let_2 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (not (tptp.c_lessequals V_G _let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts V_G)))))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (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))))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_G))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (let ((_let_2 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (not (tptp.c_lessequals V_G _let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_G)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_b T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_n $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_ONonce V_n)))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_H)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Osynth V_H))))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_ONonce V_N)))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_H)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Osynth V_H))))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_ONonce V_N)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Osynth V_H))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_H)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OHash V_X)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_H)) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1)))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (not (tptp.c_lessequals V_G _let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Osynth V_G)))))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OHash V_X)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1))))))) (forall ((V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (not (tptp.c_Fun_Obij V_f T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_a T_b) (tptp.hAPP V_f V_x)) V_x) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (T_aa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (or (not (tptp.c_Fun_Oinj__on V_f _let_1 T_aa T_a)) (= (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into _let_1 V_f T_aa T_a) (tptp.hAPP V_f V_x)) V_x)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OHash 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 V_H) tptp.tc_Message_Omsg)))) (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_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 ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_G)))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_2)) _let_2) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) _let_1))))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (= (tptp.c_Message_Oparts _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_H) _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) (forall ((V_X $$unsorted) (V_K $$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_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)) (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_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 $$unsorted) (V_H $$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_K $$unsorted) (V_N $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$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_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 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_G))) (= (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_H _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_2 _let_1))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Osynth (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Message_OinvKey V_x)) (tptp.c_Set_Oimage tptp.c_Message_OinvKey V_A tptp.tc_nat tptp.tc_nat))))))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Message_OinvKey V_x)) (tptp.c_Set_Oimage tptp.c_Message_OinvKey V_A tptp.tc_nat tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (= (tptp.hAPP V_f (tptp.hAPP (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) V_y)) V_y) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_ONonce V_N) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OHash V_X) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_e $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons V_e V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oused (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Event_Oused V_evs))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Event_OinitState V_A) (tptp.c_Event_Oknows V_A V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Obij V_f T_a T_b) (not (tptp.c_Fun_Osurj V_f T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Obij V_f T_a T_b) (not (tptp.c_Fun_Osurj V_f T_a T_b)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_a) (not (tptp.c_Fun_Osurj V_f T_a T_a)) (not (tptp.c_Finite__Set_Ofinite _let_1 T_a))))) (forall ((V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.c_Fun_Osurj V_f T_a T_a) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_a)) (not (tptp.c_Finite__Set_Ofinite _let_1 T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on (tptp.c_Hilbert__Choice_Oinv__into (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_f T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((V_N $$unsorted) (V_B $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_ONonce V_N)) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)))))) (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))) (forall ((V_A $$unsorted) (V_B $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OEncryption) V_A)) (tptp.hAPP tptp.c_Public_OshrK V_B)))) (forall ((V_E $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_E tptp.tc_nat tptp.tc_Message_Omsg)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool)))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A_H V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_NS__Shared__Mirabelle_Ons__sharedp tptp.v_x) (tptp.hAPP (tptp.hAPP _let_7 tptp.v_x) tptp.c_NS__Shared__Mirabelle_Ons__shared)) (forall ((V_C $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_C))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool)))) (forall ((V_N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_ONonce V_N)) (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_NA $$unsorted) (V_evs1 $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) _let_1))) V_evs1 tptp.tc_Event_Oevent))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) _let_1) (tptp.c_Event_Oused V_evs1))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs1)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_y $$unsorted) (T_aa $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_y))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) _let_1) (tptp.c_Set_Oimage V_f _let_2 T_aa T_a)))) (not (tptp.c_Fun_Oinj__on V_f _let_2 T_aa T_a)) (= V_y (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 _let_1 V_f T_a T_aa)))))) (forall ((V_b $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (= V_b (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 V_b V_f T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.c_Set_Oimage V_f _let_1 T_a T_b)))) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP V_f V_x))) (or (not (= (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 _let_2 V_f V_x T_a T_aa) V_x)) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_aa T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) _let_2) (tptp.c_Set_Oimage V_f _let_1 T_aa T_a))))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 V_P V_f T_a T_b)) (tptp.c_Set_Oimage V_f _let_1 T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f _let_1 T_a T_b))))) (forall ((V_f $$unsorted) (T_aa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_x))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_aa tptp.tc_bool)))) (or (not (tptp.c_Fun_Oinj__on V_f _let_2 T_aa T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) _let_1) (tptp.c_Set_Oimage V_f _let_2 T_aa T_a))) (= _let_1 (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 _let_1 V_f V_x T_a T_aa))))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (let ((_let_3 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (or (tptp.hBOOL (tptp.hAPP _let_4 _let_2)) (not (tptp.hBOOL (tptp.hAPP _let_4 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_X) _let_2)))))))) (forall ((V_X $$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_in tptp.tc_Message_Omsg))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (or (tptp.hBOOL (tptp.hAPP _let_4 _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_4 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_X) _let_2)))))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (= (tptp.c_Message_Osynthp (tptp.c_COMBC _let_1 V_H tptp.tc_Message_Omsg (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool) tptp.tc_bool) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_1 tptp.v_x) (tptp.c_Message_Osynth V_H))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP _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))))))) (or _let_2 (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_H)))) _let_2)))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_H)))))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) _let_2 _let_2)))) (forall ((V_evs $$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_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OCrypt V_K V_X) V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_OinvKey V_K) (tptp.c_Message_OkeysFor V_H) tptp.tc_nat))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (= V_A tptp.c_Message_Oagent_OSpy))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_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_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (let ((_let_2 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_in tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Event_OinitState V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Event_Oevent_ONotes V_A V_X)) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Event_Oevent_OGets V_A V_X)) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (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_2)) (= V_A tptp.c_Message_Oagent_OSpy) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Event_Oknows V_A V_evs))))))))) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (let ((_let_2 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 V_X V_evs))) (let ((_let_4 (tptp.c_in tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Event_OinitState tptp.c_Message_Oagent_OSpy))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Event_Oevent_ONotes _let_3 V_X)) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Event_Oevent_OSays _let_3 (tptp.c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 V_X V_evs) V_X)) _let_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))))))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_AS $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AS tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_AS $$unsorted)) (or (= V_b V_c) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AS tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat)))))) (forall ((V_A $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OEncryption) V_A))) tptp.c_Message_OsymKeys)))) (forall ((V_Z $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_2 (tptp.hAPP _let_1 V_Z))) (let ((_let_3 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_3 (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_X) _let_3))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)))))))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)))) (not (tptp.hBOOL (tptp.hAPP _let_2 (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.hAPP (tptp.hAPP _let_1 V_X) (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H))))))))) (forall ((V_K $$unsorted) (V_G $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Oanalz V_G))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X 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.hAPP (tptp.hAPP _let_1 V_X) (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H))))))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) V_nE))))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) _let_1 _let_1))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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))))))) (or _let_1 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) V_nE))) _let_1))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) V_nE))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_H))))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)))) (or (tptp.hBOOL (tptp.hAPP _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))))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_H)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) V_nE)))))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))))) (tptp.hBOOL (tptp.hAPP _let_1 (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)))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs3 $$unsorted) (V_NA $$unsorted) (V_S $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NA))) (let ((_let_4 (tptp.c_in tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs3 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair _let_2 _let_3)))) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))))) _let_1))) (= V_A tptp.c_Message_Oagent_OServer) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs3))))))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Event_Oknows V_A V_evs))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OGets V_A V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))) (= V_A tptp.c_Message_Oagent_OSpy))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP tptp.c_Public_OshrK V_x)) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_b) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (V_AS $$unsorted)) (let ((_let_1 (tptp.c_Public_OpublicKey V_x))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP _let_1 V_A))) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage _let_1 V_AS tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) V_AS)))))) (forall ((V_A $$unsorted) (V_AS $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) V_AS)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AS tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat)))))) (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 $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs5 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_3 (tptp.c_in tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_OMPair _let_2 _let_2))) V_evs5 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_NA) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))))) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Event_Oevent_OSays V_B_H V_A (tptp.c_Message_Omsg_OCrypt V_K _let_2))) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) tptp.c_Message_OsymKeys))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs5)))))))) (forall ((V_K $$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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K))) (tptp.c_Message_Oanalz V_H))))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K))) (tptp.c_Message_Oanalz V_H))))))) (forall ((V_NA $$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.c_in tptp.tc_Event_Oevent))) (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_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_5 (tptp.c_Message_Omsg_OMPair _let_2 _let_4))) V_evso tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (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_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_2))) _let_1))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evso)))))))))) (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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (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)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) tptp.c_Message_OsymKeys))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) _let_1) (tptp.c_Event_Oused V_evs4))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs4)))))) (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf)))))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evsf))))) (forall ((V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_KAB $$unsorted) (V_evs2 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NA))) (let ((_let_3 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_4 (tptp.c_Message_Omsg_OAgent V_A))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 _let_4))))))) V_evs2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays V_A_H tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_3 _let_2)))) (tptp.c_List_Oset V_evs2 tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_KAB) tptp.c_Message_OsymKeys))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) _let_1) (tptp.c_Event_Oused V_evs2))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs2))))))))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_G $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K))) (tptp.c_Message_Oparts V_H))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H))))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)))))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_NA $$unsorted) (V_evs1 $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) _let_2))) V_evs1 tptp.tc_Event_Oevent)) tptp.c_NS__Shared__Mirabelle_Ons__shared)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) _let_2) (tptp.c_Event_Oused V_evs1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_evs1) tptp.c_NS__Shared__Mirabelle_Ons__shared))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs3 $$unsorted) (V_NA $$unsorted) (V_S $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_in (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))) (let ((_let_5 (tptp.c_in tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (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)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (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))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (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))) (= V_A tptp.c_Message_Oagent_OServer) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_evs3) tptp.c_NS__Shared__Mirabelle_Ons__shared)))))))))) (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 $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (let ((_let_2 (tptp.c_List_Oset V_evs5 tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_4 (tptp.c_in tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_OMPair _let_3 _let_3))) V_evs5 tptp.tc_Event_Oevent)) tptp.c_NS__Shared__Mirabelle_Ons__shared)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_NA) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))))) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Event_Oevent_OSays V_B_H V_A (tptp.c_Message_Omsg_OCrypt V_K _let_3))) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) tptp.c_Message_OsymKeys))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_evs5) tptp.c_NS__Shared__Mirabelle_Ons__shared))))))))) (forall ((V_NA $$unsorted) (V_NB $$unsorted) (V_K $$unsorted) (V_evso $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_in (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.c_in tptp.tc_Event_Oevent))) (let ((_let_5 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_6 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair _let_6 (tptp.c_Message_Omsg_OMPair _let_3 _let_5))) V_evso tptp.tc_Event_Oevent)) tptp.c_NS__Shared__Mirabelle_Ons__shared)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (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_6 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_5 V_X)))))) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_3))) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_evso) tptp.c_NS__Shared__Mirabelle_Ons__shared))))))))))) (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_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (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)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (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)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) tptp.c_Message_OsymKeys))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) _let_2) (tptp.c_Event_Oused V_evs4))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_evs4) tptp.c_NS__Shared__Mirabelle_Ons__shared))))))) (forall ((V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_KAB $$unsorted) (V_evs2 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.c_in (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.hAPP (tptp.hAPP _let_1 (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)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (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)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_KAB) tptp.c_Message_OsymKeys))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) _let_2) (tptp.c_Event_Oused V_evs2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_evs2) tptp.c_NS__Shared__Mirabelle_Ons__shared)))))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_3 (tptp.c_Message_Osynth _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_3)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X)) _let_3))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K))) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) _let_1)))))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_x V_y))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays V_A V_B V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))))) (tptp.hBOOL (tptp.hAPP _let_1 (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)))))))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)))))))) (forall ((V_H $$unsorted) (V_agt $$unsorted)) (tptp.hBOOL (tptp.c_Message_Osynthp V_H (tptp.c_Message_Omsg_OAgent V_agt)))) (not (= tptp.c_Message_Oagent_OServer tptp.c_Message_Oagent_OSpy)) (not (= tptp.c_Message_Oagent_OSpy tptp.c_Message_Oagent_OServer)) (forall ((V_A $$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.hAPP tptp.c_Message_OinvKey _let_1) _let_1))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP 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))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays V_A V_B V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))))) (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent)) tptp.c_NS__Shared__Mirabelle_Ons__shared)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf)))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_evsf) tptp.c_NS__Shared__Mirabelle_Ons__shared)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K))) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X)) _let_1))))))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_OkeysFor V_H))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.c_Message_OsymKeys))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_OCrypt V_K V_X)) V_H)))))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP tptp.c_Message_OinvKey V_K)) (tptp.c_Message_OkeysFor V_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_OCrypt V_K V_X)) V_H))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad))))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x))) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_K) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (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)))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_ONotes V_A V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))))) (forall ((V_K_H $$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.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)) V_evs) tptp.c_NS__Shared__Mirabelle_Ons__shared))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (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)))))) _let_19 (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_Y) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1))))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_Y) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1))))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_Y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1))))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_Y) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_H)) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1)))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_H)) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1)))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_a V_G tptp.tc_Message_Omsg)))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts V_G))))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) _let_1)))))) (forall ((V_c $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_H)))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts V_H)))))) (forall ((V_c $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts V_H))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_H))))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts V_H))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_H))))))) (forall ((V_X $$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 $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_H)) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1)))))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_3 (tptp.c_Message_Osynth _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X)) _let_3)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_3))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K))) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) _let_1)))))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_2 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_2 _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K))) _let_1)))))) (forall ((V_K $$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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K))) (tptp.c_Message_Oanalz V_H))))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_OinitState V_B)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_Oused V_evs)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_H $$unsorted)) (= (tptp.c_Message_Oparts (tptp.c_Message_Oanalz V_H)) (tptp.c_Message_Oparts V_H))) (forall ((V_K $$unsorted) (V_X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_OCrypt V_K V_X)) (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_A T_c T_b) T_b T_a) (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_b T_a T_c) V_A T_c T_a))) (forall ((V_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (tptp.hBOOL (tptp.c_Message_Osynthp V_H (tptp.c_Message_Omsg_OMPair V_X V_Y))) (not (tptp.hBOOL (tptp.c_Message_Osynthp V_H V_Y))) (not (tptp.hBOOL (tptp.c_Message_Osynthp V_H V_X))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Event_Oused V_evs))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)))))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_Y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1))))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_Y) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1))))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (or (tptp.hBOOL (tptp.hAPP _let_2 _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Osynth _let_1)))))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Osynth V_H))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_H)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (or (tptp.hBOOL (tptp.hAPP _let_2 _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Oanalz _let_1)))))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_H))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_H)))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_A V_B)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x V_B T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Oinsert V_a V_B T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x V_A T_a)))) (forall ((V_Abs $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_Rep $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_in T_b))) (or (not (= (tptp.hAPP V_Abs V_x) (tptp.hAPP V_Abs V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)) (= V_x V_y)))) (forall ((V_Rep $$unsorted) (V_Abs $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_Rep (tptp.hAPP V_Abs V_y)) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_y) V_A))) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_A T_a))))))) (forall ((T_b $$unsorted) (V_Rep $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_Abs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_Rep V_x)) V_A)) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_B T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_A T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays V_A V_B V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)))) (tptp.c_Event_Oused V_evs)))) (forall ((V_X $$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 $$unsorted) (V_H $$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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) _let_1)))))) (forall ((V_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H) (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_a V_G tptp.tc_Message_Omsg)))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oanalz V_G))))))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) tptp.c_Message_OsymKeys)))) (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_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OAgent V_agt))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) _let_1)))))) (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_A $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OAgent V_A) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Event_Oknows V_A V_evs))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_ONotes V_A V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_y))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_List_Oset V_xs T_a))) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a))))))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)))) (tptp.c_Event_OinitState V_A)))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H))) (= V_b V_c))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H))) (= V_A V_A_H))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H)))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b)))) (forall ((V_K $$unsorted) (V_K_H $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Message_OinvKey V_K) (tptp.hAPP tptp.c_Message_OinvKey V_K_H))) (= V_K V_K_H))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_2 (tptp.hAPP _let_1 V_Y))) (let ((_let_3 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.hAPP _let_2 _let_3)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_X) _let_3))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Osynth (tptp.c_Set_Oinsert 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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Event_Oused V_evs))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays V_A V_B V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))))) (forall ((V_Rep $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_Abs $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_Rep V_x) (tptp.hAPP V_Rep V_y))) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)) (= V_x V_y))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_2 (tptp.hAPP _let_1 V_Y))) (let ((_let_3 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.hAPP _let_2 _let_3)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_X) _let_3))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)))))))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_K $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_K) tptp.c_Message_OsymKeys)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Message_OinvKey V_K)) tptp.c_Message_OsymKeys)))))) (forall ((V_K $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Message_OinvKey V_K)) tptp.c_Message_OsymKeys)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_K) tptp.c_Message_OsymKeys)))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_K $$unsorted)) (or (= (tptp.hAPP tptp.c_Message_OinvKey V_K) V_K) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) tptp.c_Message_OsymKeys))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg))) (forall ((V_N $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_N tptp.tc_nat tptp.tc_Message_Omsg))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_ONotes V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_ONotes V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H))) (= V_agent V_agent_H))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Event_Oused V_evs))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_ONotes V_A V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg))) (forall ((V_Abs $$unsorted) (V_Rep $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_Abs (tptp.hAPP V_Rep V_x)) V_x) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) (tptp.c_Message_OkeysFor _let_1))))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_K $$unsorted)) (= (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) V_K)) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_agent2 V_agent2_H))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_agent1 V_agent1_H))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) tptp.c_Message_OsymKeys)))) (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_A $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) (tptp.c_Event_OinitState V_A))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_H $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_Message_Osynthp V_H V_X)) (not (tptp.hBOOL (tptp.hAPP V_H V_X))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_C $$unsorted)) (not (= (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C))))) (forall ((V_H $$unsorted) (V_H_H $$unsorted) (V_X $$unsorted)) (or (not (= (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H_H tptp.tc_Message_Omsg))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Event_Oknows V_A V_evs))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays V_A V_B V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent)))))) (forall ((V_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C)) (tptp.hAPP tptp.c_Public_OshrK V_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.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))))) (forall ((V_Rep $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_Abs $$unsorted)) (or (= (tptp.c_Set_Oimage V_Rep (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) V_A) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (forall ((V_Abs $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_Rep $$unsorted)) (or (= (tptp.c_Set_Oimage V_Abs V_A T_b T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Typedef_Otype__definition V_Rep V_Abs V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)))) (= (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_c T_a T_b) _let_1 T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g _let_1 T_b T_c) T_c T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Osurj V_f T_a T_b)))) (forall ((V_X $$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_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Osynth V_H))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_H)))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_H)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Osynth V_H))))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_Y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_N $$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_agt $$unsorted) (V_H $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_OAgent V_agt)) (tptp.c_Message_Osynth V_H)))) (forall ((V_A $$unsorted) (V_H $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_OAgent V_A)) (tptp.c_Message_Osynth V_H)))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) tptp.c_Message_OsymKeys))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X)) _let_1))))))) (forall ((V_H $$unsorted) (V_K $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_Message_Osynthp V_H (tptp.c_Message_Omsg_OCrypt V_K V_X))) (not (tptp.hBOOL (tptp.hAPP V_H (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)))) (not (tptp.hBOOL (tptp.c_Message_Osynthp V_H V_X))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_K_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_X V_K_H))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Event_Oevent) (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)))))) (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_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))))) (forall ((V_K $$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_X $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP tptp.c_Public_OshrK V_X)) tptp.c_Message_OsymKeys))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (or (= V_b V_c) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x)) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat)))))) (forall ((V_A $$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.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_7 _let_18) tptp.c_NS__Shared__Mirabelle_Ons__shared)) (tptp.c_Fun_Oinj__on tptp.c_Public_OshrK _let_1 tptp.tc_Message_Oagent tptp.tc_nat) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_9 tptp.c_Message_Oagent_OServer) tptp.c_Event_Obad))) _let_17 (forall ((V_K $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)) V_evs) tptp.c_NS__Shared__Mirabelle_Ons__shared))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.c_Message_OsymKeys))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) (tptp.c_Event_Oused V_evs)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) (tptp.c_Set_Oimage V_f V_A T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) (tptp.c_Set_Oimage V_f V_A T_a T_b)))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= V_b (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Set__XrangeE__1__1 V_b V_f T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_B $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.c_Message_Omsg_OCrypt V_K V_X)) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X)))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Osynth V_H))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_H))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) V_H)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X)))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_H)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Osynth V_H)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) V_H)))))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_in tptp.tc_Message_Omsg))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) V_H)) (tptp.hBOOL (tptp.hAPP _let_2 V_H)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Message_Osynth V_H)))))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) V_H))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1))))))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_x) V_A))))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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)))))) (forall ((V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A))) (tptp.c_Event_OinitState V_A)))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A))) (tptp.c_Event_Oused V_evs)))) (forall ((V_B $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_B))) (tptp.c_Event_Oused V_evs)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP 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))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad))))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x)) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (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))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_AA $$unsorted)) (let ((_let_1 (tptp.c_Public_OpublicKey V_x))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP _let_1 V_xa)) (tptp.c_Set_Oimage _let_1 V_AA tptp.tc_Message_Oagent tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_xa) V_AA)))))) (forall ((V_x $$unsorted) (V_AA $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_x) V_AA)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x)) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat)))))) _let_16 (forall ((V_X $$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))) (let ((_let_3 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_X) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP tptp.c_Message_Omsg_OKey _let_2)) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Message_Omsg_OCrypt _let_2 V_X)) _let_1)))))))) (forall ((V_c $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Event_Oused V_evs))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (forall ((V_K $$unsorted) (V_evs $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) V_K) (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (tptp.hAPP tptp.c_Message_Omsg_OKey V_K)) (tptp.c_Event_Oused V_evs))))) (forall ((V_X $$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)))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) V_X)) _let_1))))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)) V_evs) tptp.c_NS__Shared__Mirabelle_Ons__shared))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)) V_evs) tptp.c_NS__Shared__Mirabelle_Ons__shared))))) (forall ((V_agent $$unsorted) (V_agent_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OAgent V_agent_H))) (= V_agent V_agent_H))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_Y) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1))))))) (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_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) V_X))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Message_Oparts V_H))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_H)))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_9 tptp.c_Message_Oagent_OSpy) tptp.c_Event_Obad)) (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 ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (let ((_let_2 (tptp.c_in tptp.tc_Message_Omsg))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_X) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X)) _let_1))))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)) V_evs) tptp.c_NS__Shared__Mirabelle_Ons__shared))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Oagent) V_A) tptp.c_Event_Obad)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_Message_Omsg) (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))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_List_Olist tptp.tc_Event_Oevent)) V_evs) 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(tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (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)))) (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 (= 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(tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.tc_nat) (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)))))) (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_nat $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.hAPP tptp.c_Public_OshrK V_y))) (= V_x V_y))) (forall ((T_aa $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_aa T_a))))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_b T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) _let_15 _let_11 _let_8 _let_6 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.55/27.78  )
% 27.55/27.79  % SZS output end Proof for SWV731-1
% 27.55/27.79  % cvc5---1.0.5 exiting
% 27.55/27.79  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------