%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV790-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n029.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 21:53:18 EDT 2023

% Result   : Unsatisfiable 0.42s 0.81s
% Output   : Proof 0.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16  % Problem    : SWV790-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.18  % Command    : do_cvc5 %s %d
% 0.17/0.39  % Computer : n029.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit   : 300
% 0.17/0.39  % WCLimit    : 300
% 0.17/0.39  % DateTime   : Tue Aug 29 04:55:56 EDT 2023
% 0.17/0.39  % CPUTime    : 
% 0.24/0.57  %----Proving TF0_NAR, FOF, or CNF
% 0.24/0.57  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2IvBeUaZE2/cvc5---1.0.5_10970.p...
% 0.42/0.67  ------- get file name : TPTP file name is SWV790-1
% 0.42/0.68  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10970.smt2...
% 0.42/0.68  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.42/0.81  % SZS status Unsatisfiable for SWV790-1
% 0.42/0.81  % SZS output start Proof for SWV790-1
% 0.42/0.83  (
% 0.42/0.83  (let ((_let_1 (tptp.c_Message_Omsg_OCrypt tptp.v_K (tptp.c_Message_Omsg_ONonce tptp.v_Nb)))) (let ((_let_2 (tptp.c_Event_Oevent_OSays tptp.v_B tptp.v_A _let_1))) (let ((_let_3 (tptp.c_List_Orev tptp.v_evsf tptp.tc_Event_Oevent))) (let ((_let_4 (tptp.c_fequal tptp.tc_Event_Oevent))) (let ((_let_5 (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent))) (let ((_let_6 (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy tptp.v_Ba tptp.v_X))) (let ((_let_7 (= tptp.v_B tptp.c_Message_Oagent_OSpy))) (let ((_let_8 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evsf)))) (let ((_let_9 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_10 (tptp.c_in tptp.v_B tptp.c_Event_Obad tptp.tc_Message_Oagent))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.c_in tptp.c_Message_Oagent_OSpy tptp.c_Event_Obad tptp.tc_Message_Oagent))) (let ((_let_13 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) (let ((_let_14 (= tptp.c_Message_Oagent_OSpy tptp.v_B))) (let ((_let_15 (ASSUME :args (_let_12)))) (let ((_let_16 (ASSUME :args (_let_11)))) (let ((_let_17 (SYMM (ASSUME :args (_let_7))))) (let ((_let_18 (not _let_14))) (let ((_let_19 (not _let_12))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_15 _let_17 _let_16) :args (_let_12 _let_11 _let_14)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_16)) (CONG (SYMM _let_17) (REFL :args (tptp.c_Event_Obad)) (REFL :args (tptp.tc_Message_Oagent)) :args (APPLY_UF tptp.c_in)) (TRUE_INTRO _let_15))) :args (_let_12 _let_14 _let_11)) :args ((not (and _let_12 _let_11 _let_14)) SB_LITERAL))) (CONG (REFL :args (_let_19)) (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) (REFL :args (_let_18)) :args (or))) :args ((or _let_10 _let_19 _let_18))) _let_17 _let_16 _let_15 :args (false false _let_14 true _let_10 false _let_12)) :args ((forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_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_A $$unsorted) (V_b $$unsorted) (V_C $$unsorted)) (not (= (tptp.c_Public_OshrK V_A) (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_C))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) (forall ((V_K $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_C))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (not (tptp.c_in _let_2 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1 V_K V_NA V_evs) _let_2))) _let_1 tptp.tc_Event_Oevent) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OAgent V_A)))))))) _let_1 tptp.tc_Event_Oevent)))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_B $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_K_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (not (tptp.c_in _let_2 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1 V_K V_NA V_evs) _let_2))) _let_1 tptp.tc_Event_Oevent) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OAgent V_A))))) (or (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1 V_A V_B V_K V_evs) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 _let_2))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in _let_2 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))))) (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_A $$unsorted) (V_NA $$unsorted)) (let ((_let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_3 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (or (tptp.c_in (tptp.c_Event_Oevent_OSays (tptp.v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1 V_B V_X V_evs) V_B V_X) _let_3 tptp.tc_Event_Oevent) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_ONonce V_NB)) (tptp.c_Message_Oparts _let_1) tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_3 tptp.tc_Event_Oevent)) (tptp.c_in _let_2 (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (or (tptp.c_in V_X (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) _let_1 tptp.tc_Event_Oevent) (tptp.c_in (tptp.c_Event_Oevent_OGets V_A V_X) _let_1 tptp.tc_Event_Oevent) (tptp.c_in (tptp.c_Event_Oevent_OSays V_A (tptp.c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 V_A V_X V_evs) V_X) _let_1 tptp.tc_Event_Oevent) (= V_A tptp.c_Message_Oagent_OSpy) (not (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_3 (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_OMPair _let_2 _let_2)))) (let ((_let_4 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_5 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (or (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B _let_3) _let_5 tptp.tc_Event_Oevent) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__1 V_K V_evs) (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__2 V_K V_evs) _let_4))) _let_5 tptp.tc_Event_Oevent) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OAgent V_A))) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in _let_3 _let_1 tptp.tc_Message_Omsg))))))))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H) (tptp.c_Event_Oevent_OGets V_agent V_msg)))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_C $$unsorted)) (not (= (tptp.c_Public_OshrK V_A) (tptp.c_Public_OpublicKey V_b V_C)))) (forall ((V_K $$unsorted)) (= (tptp.c_Message_OinvKey (tptp.c_Message_OinvKey V_K)) V_K)) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_in V_x V_B T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_f $$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_X $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Set_Oinsert (tptp.v_sko__NS__Shared__Mirabelle__XIssues__def__1 V_A V_B V_X V_evs) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (not (tptp.c_NS__Shared__Mirabelle_OIssues V_A V_B V_X V_evs)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ofilter V_P (tptp.c_List_Oreplicate V_n V_x T_a) T_a) (tptp.c_List_Olist_ONil T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_x $$unsorted) (V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Ofilter V_P V_xs T_a))) (or (= (tptp.c_List_Oremove1 V_x _let_1 T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_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_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_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_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 $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_agent V_agent_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Oremove1 V_x V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Public_OpublicKey V_b V_C) (tptp.c_Public_OshrK V_A)))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (or (= (tptp.c_List_Ofilter V_P _let_1 T_a) _let_1) (not (tptp.hBOOL (tptp.hAPP V_P V_x)))))) (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 $$unsorted) (V_Y $$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 $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Osynth (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_agent $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_X_H $$unsorted) (V_Y_H $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H))) (= V_Y_H V_Y))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_OdropWhile V_P V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_a $$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_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 ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) (tptp.c_Event_Oused V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_evs))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_2) tptp.tc_Message_Omsg)) _let_1 _let_2) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_m V_x T_a) (tptp.c_List_Oreplicate V_n V_y T_a))) (= V_m V_n))) (forall ((V_K $$unsorted) (V_K_H $$unsorted)) (or (not (= (tptp.c_Message_OinvKey V_K) (tptp.c_Message_OinvKey V_K_H))) (= V_K V_K_H))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) (forall ((V_A $$unsorted)) (let ((_let_1 (tptp.c_Public_OshrK V_A))) (= (tptp.c_Message_OinvKey _let_1) _let_1))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a) (not (tptp.c_in V_x V_A T_b)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (not (= (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Public_OpublicKey V_c V_A_H)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.c_Public_OpublicKey V_b V_A) (tptp.c_Public_OpublicKey V_c V_A_H))) (= V_A V_A_H))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.c_Public_OpublicKey V_b V_A) (tptp.c_Public_OpublicKey V_c V_A_H))) (= V_b V_c))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_Y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X_H V_Y))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_Y_H V_Y))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_X_H V_X))) (forall ((V_xa $$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_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A))) (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg)) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_List_Oset (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_C))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H))) (= V_msg1 V_msg1_H))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H))) (= V_msg2 V_msg2_H))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Orotate1 V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Orotate1 V_xs T_a) T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.c_in V_x V_xa T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.c_in V_x V_A T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OAgent V_agt))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((T_a $$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_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_List_Oset (tptp.c_List_Oremove1 V_x V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_Y_H V_Y))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Public_OshrK V_x) (tptp.c_Public_OshrK V_y))) (= V_x V_y))) (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_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A))) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_NA $$unsorted) (V_evs1 $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_NA))) (or (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.c_in _let_1 (tptp.c_Event_Oused V_evs1) tptp.tc_Message_Omsg) (not (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a) (not (tptp.c_in V_a V_A T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a) (not (tptp.c_in V_a V_B T_a)))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_t V_B T_a) (not (tptp.c_in V_t V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_A $$unsorted) (V_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 $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((V_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_C)) (tptp.c_Public_OshrK V_A)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_agent $$unsorted) (V_agent_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OAgent V_agent_H))) (= V_agent V_agent_H))) (forall ((V_c $$unsorted) (V_A_H $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Public_OpublicKey V_c V_A_H) (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_NA $$unsorted) (V_NB $$unsorted) (V_K $$unsorted) (V_evso $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evso tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_3 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_2 _let_3))) V_evso tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_3 V_X))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_2)) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evso)))))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= (tptp.c_List_Oappend (tptp.c_List_Obutlast V_xs T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Olast V_xs T_a) _let_1 T_a) T_a) V_xs) (= V_xs _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs3 $$unsorted) (V_NA $$unsorted) (V_S $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.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.c_in (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair _let_2 _let_3))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) _let_1 tptp.tc_Event_Oevent)) (= V_A tptp.c_Message_Oagent_OServer) (not (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs3))))))) (forall ((V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.c_Event_Oused V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (= V_A tptp.c_Message_Oagent_OSpy))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_NA $$unsorted) (V_evs1 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) _let_2))) V_evs1 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1) (tptp.c_in _let_2 (tptp.c_Event_Oused V_evs1) tptp.tc_Message_Omsg) (not (tptp.c_in V_evs1 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B (tptp.v_sko__NS__Shared__Mirabelle__XIssues__def__1 V_A V_B V_X V_evs)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) (not (tptp.c_NS__Shared__Mirabelle_OIssues V_A V_B V_X V_evs)))) (forall ((V_X $$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.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OAgent V_A)))) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_X_H $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_NA_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_X V_X_H) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent)))))) (forall ((V_B $$unsorted) (V_B_H $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_NA_H $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_B V_B_H) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent)))))) (forall ((V_NA $$unsorted) (V_NA_H $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_NA V_NA_H) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent)))))) (forall ((V_A $$unsorted) (V_A_H $$unsorted) (V_evs $$unsorted) (V_NA_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_A V_A_H) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent)))))) (forall ((V_K_H $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_N $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_X $$unsorted)) (or (= V_K_H (tptp.c_Public_OshrK V_A)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_Ofilter V_P V_xs T_a) V_xs)) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oremove1 V_y V_xs T_a) T_a) T_a)) (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oreplicate V_n V_y T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast V_xs T_a) T_a) T_a)))) (forall ((V_a $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_in V_a (tptp.c_List_Oset V_xs T_a) T_a) (not (tptp.c_in V_a (tptp.c_List_Oset (tptp.c_List_Oremove1 V_b V_xs T_a) T_a) T_a)) (= V_a V_b))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_List_Oset (tptp.c_List_Oremove1 V_b V_xs T_a) T_a) T_a) (not (tptp.c_in V_a (tptp.c_List_Oset V_xs T_a) T_a)) (= V_a V_b))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olast V_xs T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Obutlast (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) _let_1))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) V_x)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Obutlast (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Obutlast V_xs T_a) T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (tptp.c_lessequals (tptp.c_List_Oset V_xs T_a) (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_x $$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 ((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_X $$unsorted)) (not (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) _let_1) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_a V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg)))) (forall ((V_ys $$unsorted) (V_zs $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (not (= (tptp.c_List_Oappend V_ys V_zs T_a) _let_1)) (= (tptp.c_List_Oappend (tptp.c_List_Osko__List__Xappend__eq__Cons__conv__1__1 V_x V_xs V_ys V_zs T_a) V_zs T_a) V_xs) (= V_zs _let_1)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_ys V_zs T_a))) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Osko__List__XCons__eq__append__conv__1__1 V_x V_xs V_ys V_zs T_a) T_a) V_ys) (= _let_1 V_zs)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 V_P (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_xa V_xb T_a) T_a) T_a))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 V_P V_xb T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 V_P (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_xa V_xb T_a) T_a) T_a))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 V_P V_x T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))))) (forall ((V_ys $$unsorted) (V_zs $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (not (= (tptp.c_List_Oappend V_ys V_zs T_a) _let_1)) (= V_ys (tptp.c_List_Olist_OCons V_x (tptp.c_List_Osko__List__Xappend__eq__Cons__conv__1__1 V_x V_xs V_ys V_zs T_a) T_a)) (= V_zs _let_1)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_ys V_zs T_a))) (= V_xs (tptp.c_List_Oappend (tptp.c_List_Osko__List__XCons__eq__append__conv__1__1 V_x V_xs V_ys V_zs T_a) V_zs T_a)) (= _let_1 V_zs)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (= (tptp.c_List_Oappend _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend _let_1 V_xs T_a) T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Obutlast V_xs T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Olast V_ys T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Olast V_xs T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Obutlast V_ys T_a) T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_a V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) _let_1) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_Y (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_2 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_2 _let_1 tptp.tc_Message_Omsg)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_N $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_N tptp.tc_nat tptp.tc_Message_Omsg))) (= (tptp.c_Message_Oparts _let_1) _let_1))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_H $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OAgent V_agt) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_Y (tptp.c_Message_Osynth (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Osynth V_G) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_K_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_X V_K_H))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_G $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg))))) (forall ((V_N $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_N tptp.tc_nat tptp.tc_Message_Omsg))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.c_in (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_G)) (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_N $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_N $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (tptp.c_in (tptp.c_List_Oappend V_xs V_ys T_a) _let_2 _let_1) (not (tptp.c_in V_ys _let_2 _let_1)) (not (tptp.c_in V_xs _let_2 _let_1)))))) (forall ((V_xs $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (tptp.c_in V_xs _let_2 _let_1) (not (tptp.c_in (tptp.c_List_Oappend V_xs V_ys T_a) _let_2 _let_1)))))) (forall ((V_ys $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (tptp.c_in V_ys _let_2 _let_1) (not (tptp.c_in (tptp.c_List_Oappend V_xs V_ys T_a) _let_2 _let_1)))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_OtakeWhile V_P V_xs T_a) (tptp.c_List_OdropWhile V_P V_xs T_a) T_a) V_xs)) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_OtakeWhile V_P V_ys T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__XtakeWhile__append2__1__1 V_P V_xs T_a)))))) (forall ((V_NA $$unsorted) (V_NB $$unsorted) (V_K $$unsorted) (V_evso $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_List_Oset V_evso tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_4 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_5 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair _let_3 _let_4))) V_evso tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_4 V_X))))) _let_2 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_3)) _let_2 tptp.tc_Event_Oevent)) (not (tptp.c_in V_evso tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1))))))))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_e $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons V_e V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in tptp.c_Message_Oagent_OServer tptp.c_Event_Obad tptp.tc_Message_Oagent)) (forall ((V_A $$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 $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs3 $$unsorted) (V_NA $$unsorted) (V_S $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_List_Oset V_evs3 tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs3 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair _let_3 _let_4))) _let_2 tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) _let_2 tptp.tc_Event_Oevent)) (= V_A tptp.c_Message_Oagent_OServer) (not (tptp.c_in V_evs3 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (tptp.c_in V_K (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair V_B (tptp.c_Message_Omsg_OMPair V_K V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)) (not (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_in V_x V_A T_a)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_in V_a V_A T_a) (= V_a V_b) (not (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a)) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a)) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a)) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.c_in V_x V_B T_a) (tptp.c_in V_x V_A T_a) (= V_A V_B))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.c_in V_a V_A T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_aa)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_b)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a) (not (tptp.c_in V_x V_A T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (not (tptp.c_in V_x V_A T_a)))) (forall ((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_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ofilter V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Ofilter V_P V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (or (= (tptp.c_List_OdropWhile V_P _let_1 T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OdropWhile V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_OdropWhile V_P V_xs T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Olist_OCons V_y V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Oremove1 V_x V_xs T_a) T_a)) (= V_x V_y))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_OdropWhile V_P V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_y))))) (forall ((V_P $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (or (not (= (tptp.c_List_Ofilter V_P V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ofilter V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Ofilter V_P V_xs T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_P $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Ofilter V_P V_ys T_a))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) V_xs)) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Obutlast _let_1 T_a) _let_1))) (forall ((T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_OdropWhile V_P _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orotate1 V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orotate1 _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Ofilter V_P _let_1 T_a) _let_1))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oremove1 V_x _let_1 T_a) _let_1))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Orotate1 V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((V_A $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg)) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Event_OinitState V_B) tptp.tc_Message_Omsg)) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((V_B $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_B)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (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 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (= (tptp.c_Message_Oparts _let_13) _let_13) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oparts V_H))) (or (tptp.c_lessequals (tptp.c_Message_Oparts V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oparts V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oparts V_G) _let_2 _let_1)))))) (forall ((V_X $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) (tptp.c_Message_Oanalz V_G)) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (let ((_let_2 (tptp.c_List_Oreplicate V_k V_x T_a))) (= (tptp.c_List_Oappend _let_1 _let_2 T_a) (tptp.c_List_Oappend _let_2 _let_1 T_a))))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Odistinct V_ys T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofilter V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Ofilter V_P V_xs T_a) (tptp.c_List_Ofilter V_P V_ys T_a) T_a))) (forall ((V_K $$unsorted) (V_X_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_K V_X_H) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_agent $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_msg1 $$unsorted) (V_msg2 $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) (forall ((V_agent $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H)))) (forall ((V_nat_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_nat $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_H $$unsorted) (V_H_H $$unsorted) (V_X $$unsorted)) (or (not (= (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H_H tptp.tc_Message_Omsg))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_H) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (= (tptp.c_Message_Oanalz _let_13) _let_13) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) _let_2 _let_1)))))) (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Oanalz V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Osynth V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Osynth V_G) (tptp.c_Message_Osynth V_H) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (tptp.c_lessequals (tptp.c_Message_Osynth V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Osynth V_G) _let_2 _let_1)))))) (not (= tptp.c_Message_Oagent_OServer tptp.c_Message_Oagent_OSpy)) (not (= tptp.c_Message_Oagent_OSpy tptp.c_Message_Oagent_OServer)) (forall ((V_N $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_nat_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_nat $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_agent $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_ONonce V_nat_H)))) (forall ((V_msg1_H $$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_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H)))) (forall ((V_agent1 $$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_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H) (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg)))) (forall ((V_agent_H $$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_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Ofilter V_P V_xs T_a) T_a) (tptp.c_List_Ofilter V_P (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Orev V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Orev V_xs T_a) T_a)))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A_H V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A_H V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P V_xs T_a) V_xs) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 V_P V_xs T_a)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_List_Osko__List__XtakeWhile__cong__1__1 V_P V_Q V_x T_a))) (or (= (tptp.c_List_OtakeWhile V_P V_x T_a) (tptp.c_List_OtakeWhile V_Q V_x T_a)) (not (tptp.hBOOL (tptp.hAPP V_Q _let_1))) (not (tptp.hBOOL (tptp.hAPP V_P _let_1)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_List_Osko__List__XtakeWhile__cong__1__1 V_P V_Q V_x T_a))) (or (= (tptp.c_List_OtakeWhile V_P V_x T_a) (tptp.c_List_OtakeWhile V_Q V_x T_a)) (tptp.hBOOL (tptp.hAPP V_Q _let_1)) (tptp.hBOOL (tptp.hAPP V_P _let_1))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (tptp.c_NS__Shared__Mirabelle_Ons__sharedp _let_5) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (or (= (tptp.c_List_OtakeWhile (tptp.c_COMBB tptp.c_Not (tptp.c_COMBC (tptp.c_fequal T_a) (tptp.c_List_Olast V_xs T_a) T_a T_a tptp.tc_bool) tptp.tc_bool tptp.tc_bool T_a) V_xs T_a) (tptp.c_List_Obutlast V_xs T_a)) (not (tptp.c_List_Odistinct V_xs T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_OdropWhile V_P V_xs T_a) (tptp.c_List_Olist_ONil T_a))) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_as $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_List_Olast V_as T_a) (tptp.c_List_Oset V_as T_a) T_a) (= V_as (tptp.c_List_Olist_ONil T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_Ofilter V_P V_xs T_a) (tptp.c_List_Olist_ONil T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Oremove1 V_x V_ys T_a) T_a)) (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast V_xs T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast V_ys T_a) T_a) T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_List_OdropWhile V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_OdropWhile V_P V_xs T_a) V_ys T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oremove1 V_x V_xs T_a) V_ys T_a)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_i V_x T_a))) (= (tptp.c_List_Oappend _let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_x _let_1 T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Orotate1 (tptp.c_List_Olist_OCons V_x V_xs T_b) T_b) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_b) T_b) T_b))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Oappend V_ys V_zs T_a))) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Osko__List__XCons__eq__append__conv__1__1 V_x V_xs V_ys V_zs T_a) T_a) V_ys) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys $$unsorted) (V_zs $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_zs T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Osko__List__Xappend__eq__Cons__conv__1__1 V_x V_xs V_ys V_zs T_a) V_zs T_a) V_xs) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) V_xs)) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) V_x)) (forall ((V_ys $$unsorted) (V_zs $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_zs T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= V_ys (tptp.c_List_Olist_OCons V_x (tptp.c_List_Osko__List__Xappend__eq__Cons__conv__1__1 V_x V_xs V_ys V_zs T_a) T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Oappend V_ys V_zs T_a))) (= V_xs (tptp.c_List_Oappend (tptp.c_List_Osko__List__XCons__eq__append__conv__1__1 V_x V_xs V_ys V_zs T_a) V_zs T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_B $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_in V_x V_A T_a) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)) (not (tptp.c_in V_xs (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_A $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))) (forall ((V_B $$unsorted) (V_A $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_ONonce V_NB)))) (let ((_let_3 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_4 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (or (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A _let_2) _let_4 tptp.tc_Event_Oevent) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1 V_K V_NA V_evs) _let_3))) _let_4 tptp.tc_Event_Oevent) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_3 V_X)))) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg)))))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_Q $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P V_x T_a) (tptp.c_List_OtakeWhile V_Q V_x T_a)) (tptp.c_in (tptp.c_List_Osko__List__XtakeWhile__cong__1__1 V_P V_Q V_x T_a) (tptp.c_List_Oset V_x T_a) T_a))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P V_xs T_a) V_xs) (tptp.c_in (tptp.c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 V_P V_xs T_a) (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_N $$unsorted) (V_B $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (= (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg))) _let_1) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_OHPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (forall ((V_x $$unsorted) (V_A $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_x) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_ys T_a))) (or (not (= (tptp.c_List_OdropWhile V_P V_xs T_a) _let_1)) (= V_xs (tptp.c_List_Oappend (tptp.c_List_OtakeWhile V_P V_xs T_a) _let_1 T_a))))) (forall ((V_xs $$unsorted) (V_P $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_ys T_a))) (or (not (= V_xs (tptp.c_List_Oappend (tptp.c_List_OtakeWhile V_P V_xs T_a) _let_1 T_a))) (= (tptp.c_List_OdropWhile V_P V_xs T_a) _let_1) (tptp.hBOOL (tptp.hAPP V_P V_y))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.c_Public_OpublicKey V_b V_A))) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))) (forall ((V_A $$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 $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg))) (forall ((V_K $$unsorted) (V_X $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) tptp.tc_Message_Omsg))) (forall ((V_N $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) tptp.tc_Message_Omsg))) (forall ((V_B $$unsorted) (V_A $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_3 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_4 (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_ONonce V_NB)))) (or (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A _let_4) _let_3 tptp.tc_Event_Oevent) (not (tptp.c_in _let_4 (tptp.c_Message_Oparts _let_1) tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_3 tptp.tc_Event_Oevent)) (tptp.c_in _let_2 (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))))))) (forall ((V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))))) (or (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A _let_1) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in _let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_X (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OAgent V_A)))) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 V_X)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_COMBB tptp.c_Not (tptp.c_COMBC (tptp.c_fequal T_a) V_x T_a T_a tptp.tc_bool) tptp.tc_bool tptp.tc_bool T_a))) (or (= (tptp.c_List_OdropWhile _let_1 (tptp.c_List_Orev V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Orev (tptp.c_List_OtakeWhile _let_1 V_xs T_a) T_a) T_a)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)) (not (tptp.c_List_Odistinct V_xs T_a))))) (forall ((V_P $$unsorted) (V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_OtakeWhile V_P V_evs tptp.tc_Event_Oevent)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 V_P (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_xa V_xb T_a) T_a) T_a))) (tptp.c_in (tptp.c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 V_P V_x T_a) (tptp.c_List_Oset V_x T_a) T_a) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_xa V_xb T_a) T_a))) (or (tptp.c_in (tptp.c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 V_P _let_1 T_a) (tptp.c_List_Oset _let_1 T_a) T_a) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 V_P V_xb T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_xa V_xb T_a) T_a))) (or (tptp.c_in (tptp.c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 V_P _let_1 T_a) (tptp.c_List_Oset _let_1 T_a) T_a) (tptp.c_in (tptp.c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 V_P V_x T_a) (tptp.c_List_Oset V_x T_a) T_a) (not (tptp.hBOOL (tptp.hAPP V_P V_xa)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 V_P (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_xa V_xb T_a) T_a) T_a))) (tptp.c_in (tptp.c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 V_P V_xb T_a) (tptp.c_List_Oset V_xb T_a) T_a) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_xa V_xb T_a) T_a))) (or (tptp.c_in (tptp.c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 V_P _let_1 T_a) (tptp.c_List_Oset _let_1 T_a) T_a) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 V_P V_x T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_xa V_xb T_a) T_a))) (or (tptp.c_in (tptp.c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 V_P _let_1 T_a) (tptp.c_List_Oset _let_1 T_a) T_a) (tptp.c_in (tptp.c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 V_P V_xb T_a) (tptp.c_List_Oset V_xb T_a) T_a) (not (tptp.hBOOL (tptp.hAPP V_P V_xa)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted)) (let ((_let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_3 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_5 (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_OMPair _let_4 _let_4)))) (or (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B _let_5) _let_3 tptp.tc_Event_Oevent) (not (tptp.c_in _let_5 (tptp.c_Message_Oparts _let_1) tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OAgent V_A)))))))) _let_3 tptp.tc_Event_Oevent)) (tptp.c_in _let_2 (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent)))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Public_OshrK V_A))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey _let_2) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_2 V_X) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_OtakeWhile V_P V_ys T_a) T_a)) (tptp.c_in (tptp.c_List_Osko__List__XtakeWhile__append2__1__1 V_P V_xs T_a) (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_c $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in V_c (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_S $$unsorted) (V_NA $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg) (= V_X (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OAgent V_A)))) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_NA) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Oappend V_evs (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg))) (forall ((V_P $$unsorted) (V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_OtakeWhile V_P V_evs tptp.tc_Event_Oevent))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Orev V_evs tptp.tc_Event_Oevent))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Event_Oevent_OSays V_A V_B V_x))) (or (tptp.c_NS__Shared__Mirabelle_OIssues V_A V_B V_X V_evs) (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_OtakeWhile (tptp.c_COMBB tptp.c_Not (tptp.c_COMBC (tptp.c_fequal tptp.tc_Event_Oevent) _let_1 tptp.tc_Event_Oevent tptp.tc_Event_Oevent tptp.tc_bool) tptp.tc_bool tptp.tc_bool tptp.tc_Event_Oevent) (tptp.c_List_Orev V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_in _let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_2 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_2 tptp.tc_Message_Omsg) (not (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OpublicKey V_b V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_A tptp.c_Message_Oagent_OSpy))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Oappend V_evs (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_OtakeWhile (tptp.c_COMBB tptp.c_Not (tptp.c_COMBC (tptp.c_fequal tptp.tc_Event_Oevent) (tptp.c_Event_Oevent_OSays V_A V_B (tptp.v_sko__NS__Shared__Mirabelle__XIssues__def__1 V_A V_B V_X V_evs)) tptp.tc_Event_Oevent tptp.tc_Event_Oevent tptp.tc_bool) tptp.tc_bool tptp.tc_bool tptp.tc_Event_Oevent) (tptp.c_List_Orev V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg)) (not (tptp.c_NS__Shared__Mirabelle_OIssues V_A V_B V_X V_evs)))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Oappend V_evs (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) 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_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (or (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent)) (not (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf))) tptp.tc_Message_Omsg)) (not (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evsf)))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_S $$unsorted) (V_A $$unsorted) (V_KA $$unsorted) (V_N $$unsorted) (V_B $$unsorted) (V_K $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt V_KA (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair V_B (tptp.c_Message_Omsg_OMPair V_K V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Oappend V_evs (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))) (forall ((V_evs $$unsorted)) (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Orev V_evs tptp.tc_Event_Oevent)))) (forall ((V_a $$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 $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_OtakeWhile V_P V_xs T_a) V_xs)) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Orev _let_1 T_a)))) (tptp.c_in _let_5 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_9) (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_A $$unsorted) (V_evs $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_H $$unsorted)) (= (tptp.c_Message_Oparts (tptp.c_Message_Oanalz V_H)) (tptp.c_Message_Oparts V_H))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_xs V_ys)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_x V_y)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oappend _let_1 _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_ys T_a) V_zs T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_ys V_zs T_a) T_a))) (forall ((V_xs $$unsorted) (V_xs1 $$unsorted) (V_us $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_xs1 V_us T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_xs1 T_a) V_us T_a))) (forall ((V_zs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_zs V_x T_a) V_ys T_a) (tptp.c_List_Oappend V_zs (tptp.c_List_Oappend V_x V_ys T_a) T_a))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_x V_ts T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_x T_a) V_ts T_a))) (forall ((V_nat_H $$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_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_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_OtakeWhile V_P _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a) _let_1))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_ys)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_agent1 V_agent1_H))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_agent2 V_agent2_H))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_X V_H tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_X V_H tptp.tc_Message_Omsg)))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Orev V_xs T_a))) (= V_xs _let_1)))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Orev V_ys T_a))) (= V_xs V_ys))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) _let_12 (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (or (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1) (not (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf))) tptp.tc_Message_Omsg)) (not (tptp.c_in V_evsf tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1))))) (forall ((T_a $$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_nat_H $$unsorted) (V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (= (tptp.c_Message_Oparts _let_1) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Orev V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a))) (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_P $$unsorted) (V_xs $$unsorted) (V_x $$unsorted) (V_l $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x V_l T_a) T_a) T_a) (tptp.c_List_OtakeWhile V_P V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a) (tptp.c_in V_x (tptp.c_List_Oset V_xa T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a) (tptp.c_in V_x (tptp.c_List_Oset V_xb T_a) T_a))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs _let_1)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_OtakeWhile V_P V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a)) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oparts _let_1) tptp.tc_Message_Omsg))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H))) (= V_nat V_nat_H))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Orev V_xs T_a) T_a) V_xs)) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Orev V_ys T_a) T_a) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Orev (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= V_x (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_x T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_xs T_a) (tptp.c_List_Oappend V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_ONil T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (not (= _let_1 (tptp.c_List_Orev V_xs T_a))) (= V_xs _let_1)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_ONonce V_nat_H))) (= V_nat V_nat_H))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x V_S T_a) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.c_in V_x V_S T_a)))) (forall ((V_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_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_nat $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_nat V_nat_H))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a))) (forall ((V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_in V_y (tptp.c_List_Oset V_xs T_a) T_a) (= V_y V_x) (not (tptp.c_in V_y (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= V_xs (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Olist_ONil T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs T_a) V_ys T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs V_ys T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a))) (forall ((V_x $$unsorted) (V_xs1 $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs1 V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs1 T_a) V_zs T_a))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_X V_H tptp.tc_Message_Omsg)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Osynth _let_1) tptp.tc_Message_Omsg))))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (= (tptp.c_Message_Osynth _let_1) _let_1))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= _let_1 (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (= _let_1 (tptp.c_List_Orev _let_1 T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a) T_a)))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (or (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (or (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))))) (forall ((V_n $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_n))) (or (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a) T_a)))) (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) _let_11 (tptp.c_in tptp.v_evsf tptp.c_NS__Shared__Mirabelle_Ons__shared _let_9) (tptp.c_in tptp.v_X (tptp.c_Message_Osynth _let_8) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey tptp.v_K) _let_8 tptp.tc_Message_Omsg)) _let_7 (= tptp.v_A tptp.v_Ba) (= _let_1 tptp.v_X) (tptp.c_in tptp.v_X (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_OtakeWhile (tptp.c_COMBB tptp.c_Not (tptp.c_COMBC _let_4 _let_6 tptp.tc_Event_Oevent tptp.tc_Event_Oevent tptp.tc_bool) tptp.tc_bool tptp.tc_bool tptp.tc_Event_Oevent) (tptp.c_List_Oappend _let_3 (tptp.c_List_Olist_OCons _let_6 _let_5 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg) (or (not (tptp.c_in _let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_OtakeWhile (tptp.c_COMBB tptp.c_Not (tptp.c_COMBC _let_4 _let_2 tptp.tc_Event_Oevent tptp.tc_Event_Oevent tptp.tc_bool) tptp.tc_bool tptp.tc_bool tptp.tc_Event_Oevent) _let_3 tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg)) (not (tptp.c_in _let_2 (tptp.c_List_Oset tptp.v_evsf tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBC V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_x) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_fequal T_a) V_X) V_Y)))))))))))))))))))))))))))
% 0.42/0.83  )
% 0.42/0.83  % SZS output end Proof for SWV790-1
% 0.42/0.83  % cvc5---1.0.5 exiting
% 0.42/0.83  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------