%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV750-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 21:53:09 EDT 2023

% Result   : Unsatisfiable 10.71s 11.11s
% Output   : Proof 10.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18  % Problem    : SWV750-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.19  % Command    : do_cvc5 %s %d
% 0.19/0.40  % Computer : n013.cluster.edu
% 0.19/0.40  % Model    : x86_64 x86_64
% 0.19/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40  % Memory   : 8042.1875MB
% 0.19/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40  % CPULimit   : 300
% 0.19/0.40  % WCLimit    : 300
% 0.19/0.40  % DateTime   : Tue Aug 29 07:25:32 EDT 2023
% 0.19/0.40  % CPUTime    : 
% 0.25/0.59  %----Proving TF0_NAR, FOF, or CNF
% 0.25/0.60  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.bsfyEHrNBo/cvc5---1.0.5_30728.p...
% 0.47/0.73  ------- get file name : TPTP file name is SWV750-1
% 0.47/0.73  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_30728.smt2...
% 0.47/0.73  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.69/10.88  --- Run --no-e-matching --full-saturate-quant at 5...
% 10.71/11.11  % SZS status Unsatisfiable for SWV750-1
% 10.71/11.11  % SZS output start Proof for SWV750-1
% 10.71/11.13  (
% 10.71/11.13  (let ((_let_1 (tptp.c_List_Oset tptp.v_evso tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey tptp.v_K))) (let ((_let_3 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OAgent tptp.v_A))))) (let ((_let_4 (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair _let_2 _let_3))))) _let_1 tptp.tc_Event_Oevent)))) (let ((_let_5 (not _let_4))) (let ((_let_6 (tptp.c_Message_Omsg_ONonce tptp.v_NAa))) (let ((_let_7 (= tptp.v_K tptp.v_Ka))) (let ((_let_8 (or (not _let_7) (not (= tptp.v_NA _let_6))))) (let ((_let_9 (tptp.c_Message_Omsg_OAgent tptp.v_Aa))) (let ((_let_10 (tptp.hAPP tptp.c_Message_Omsg_OKey tptp.v_Ka))) (let ((_let_11 (tptp.hAPP tptp.c_Public_OshrK tptp.v_Ba))) (let ((_let_12 (tptp.c_Message_Omsg_OCrypt _let_11 (tptp.c_Message_Omsg_OMPair _let_10 _let_9)))) (let ((_let_13 (= tptp.v_X _let_12))) (let ((_let_14 (tptp.c_Message_Omsg_OAgent tptp.v_Ba))) (let ((_let_15 (tptp.hAPP tptp.c_Public_OshrK tptp.v_Aa))) (let ((_let_16 (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OCrypt _let_15 (tptp.c_Message_Omsg_OMPair _let_6 (tptp.c_Message_Omsg_OMPair _let_14 (tptp.c_Message_Omsg_OMPair _let_10 _let_12))))) _let_1 tptp.tc_Event_Oevent)))) (let ((_let_17 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_18 (tptp.hBOOL (tptp.c_in tptp.v_evso tptp.c_NS__Shared__Mirabelle_Ons__shared _let_17)))) (let ((_let_19 (forall ((V_NA $$unsorted) (V_NA_H $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_NA V_NA_H) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent))))))))) (let ((_let_20 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_21 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)))) (let ((_let_22 (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OSignature))) (let ((_let_23 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage _let_22 _let_21 tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg))) (let ((_let_24 (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OEncryption))) (let ((_let_25 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage _let_24 _let_21 tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg))) (let ((_let_26 (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent))) (let ((_let_27 (tptp.c_Orderings_Obot__class_Obot _let_20))) (let ((_let_28 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_29 (tptp.c_Message_Omsg_OCrypt _let_11 (tptp.c_Message_Omsg_OMPair _let_2 _let_9)))) (let ((_let_30 (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OCrypt _let_15 (tptp.c_Message_Omsg_OMPair _let_6 (tptp.c_Message_Omsg_OMPair _let_14 (tptp.c_Message_Omsg_OMPair _let_2 _let_29))))) _let_1 tptp.tc_Event_Oevent)))) (let ((_let_31 (not _let_30))) (let ((_let_32 (not _let_18))) (let ((_let_33 (= _let_6 tptp.v_NA))) (let ((_let_34 (or _let_33 _let_32 _let_5 _let_31))) (let ((_let_35 (_let_19))) (let ((_let_36 (ASSUME :args _let_35))) (let ((_let_37 (not _let_34))) (let ((_let_38 (AND_INTRO (SYMM (ASSUME :args (_let_7))) (SYMM (SYMM (ASSUME :args (_let_13))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_6 tptp.v_NA tptp.v_evso tptp.v_A tptp.v_B tptp.v_K _let_3 tptp.v_Aa tptp.v_Ba _let_29 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_5 _let_33 _let_32 _let_31 _let_37))) (ASSUME :args (_let_4)) (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_38 :args ((or (not (= tptp.v_Ka tptp.v_K)) (not _let_33)) SB_DEFAULT SBA_FIXPOINT)))) (ASSUME :args (_let_18)) (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO _let_38 :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) :args (_let_37 false _let_4 true _let_33 false _let_18 false _let_30)) _let_36 :args (false true _let_34 false _let_19)) :args ((forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_2) tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oparts V_H) _let_2) _let_2) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Event_Oused (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Event_Oused V_evs) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Event_Oused (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Event_Oused V_evs) _let_1)))) (forall ((V_c $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 (tptp.c_Message_Oparts V_H) _let_1) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))))) (= (tptp.c_Message_Oanalz _let_27) _let_27) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_B _let_2))))) (= (tptp.c_Message_Oparts _let_27) _let_27) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((V_f $$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_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X _let_2 tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_Y _let_2 tptp.tc_Message_Omsg)) _let_1) (tptp.c_Message_Oparts V_H) _let_1))))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (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 ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 (tptp.c_HOL_Ouminus__class_Ouminus _let_2 _let_1) _let_1)))) (forall ((T_a $$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) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Otop__class_Otop T_a) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Obot__class_Obot T_a) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_List_Oset (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts V_H) _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_A (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1))))) (forall ((V_A $$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 ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_2 _let_1) _let_2)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oset V_xs T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (= (tptp.hAPP _let_28 tptp.v_x) (tptp.c_in tptp.v_x _let_28 tptp.t_a)) (forall ((V_X $$unsorted)) (not (tptp.hBOOL (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 $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Event_Oknows V_A V_evs))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X _let_2 tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts _let_2) _let_1))))) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_evs))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_2) tptp.tc_Message_Omsg)) _let_1 _let_2) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X _let_2 tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts _let_2) _let_1))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_G)))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_2)) _let_2) _let_2) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oremdups V_x T_a))) (= V_x _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$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))) (= (tptp.c_Event_OinitState tptp.c_Message_Oagent_OServer) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP _let_24 tptp.c_Message_Oagent_OServer))) (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP _let_22 tptp.c_Message_Oagent_OServer))) _let_27 tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) _let_25 _let_20) _let_23 _let_20) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage tptp.c_Public_OshrK _let_21 tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg) _let_20)) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Osynth V_G) _let_2 _let_1)))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (tptp.c_lessequals (tptp.c_Message_Osynth V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_X_H V_X))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_Y_H V_Y))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_1))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_X_H $$unsorted) (V_Y_H $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H))) (= V_X_H (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_OHPair V_X V_Y))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (not (= tptp.c_Public_Okeymode_OSignature tptp.c_Public_Okeymode_OEncryption)) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_H) _let_1) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a)))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (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 _let_1)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oparts V_H) _let_2) _let_2) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_ONonce V_N) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_xs T_a) (tptp.c_List_Oappend V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) (tptp.c_Event_Oused V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) T_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a)))) (forall ((V_P $$unsorted) (V_keymode $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_keymode)) (not (tptp.hBOOL (tptp.hAPP V_P tptp.c_Public_Okeymode_OEncryption))) (not (tptp.hBOOL (tptp.hAPP V_P tptp.c_Public_Okeymode_OSignature))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_A _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1) _let_1) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Osynth V_G) (tptp.c_Message_Osynth V_H) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((V_x $$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 $$unsorted)) (= V_xs (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Odistinct V_ys T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((T_a $$unsorted) (V_bs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__inter _let_1 V_bs T_a) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_B _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((V_Y $$unsorted) (V_G $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_Y (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_Y (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) _let_1))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((V_B $$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_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Osynth (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OHash V_X_H))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oremdups _let_1 T_a) _let_1))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_OHPair V_X V_Y))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_x V_y))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Oappend V_xs V_ys T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in V_ys _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in V_xs _let_2 _let_1))))))) (forall ((T_a $$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 ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((V_xs $$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_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (= tptp.c_Public_Okeymode_OEncryption tptp.c_Public_Okeymode_OSignature)) (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp _let_26)) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1)))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Osynth V_G) (tptp.c_Message_Osynth V_H) _let_1) (tptp.c_Message_Osynth (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_1))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OHash V_X))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1))) (= V_A V_B)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_A) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_B)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_List_Oset V_xs T_a) (tptp.c_List_Oset V_ys T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_Z $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_Z) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OHash V_X))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_msg $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OHash V_msg) (tptp.c_Message_Omsg_OHash V_msg_H))) (= V_msg V_msg_H))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a))) (forall ((T_b $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_HOL_Ouminus T_b)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP V_A tptp.v_x) T_b)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_x $$unsorted) (V_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_x $$unsorted)) (= (tptp.c_Message_OHPair V_X V_x) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_x)) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) V_Y))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) V_A _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_x T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((V_A $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OAgent V_A) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_x $$unsorted) (V_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 $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs1 V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs1 T_a) V_zs T_a))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_x $$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 $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_X_H (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_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_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((V_X $$unsorted) (V_x $$unsorted)) (= (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_x)) V_x) (tptp.c_Message_OHPair V_X V_x))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oremdups V_xs T_a) V_xs)) (tptp.c_List_Odistinct V_xs T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremdups V_xs T_a) V_xs) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= _let_1 (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OHash V_X))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a))) (forall ((V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_B T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (or (tptp.c_lessequals (tptp.c_Message_OkeysFor V_G) (tptp.c_Message_OkeysFor V_H) (tptp.tc_fun tptp.tc_nat tptp.tc_bool)) (not (tptp.c_lessequals V_G V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OMPair V_X V_Y) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((V_xs $$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_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_OHash V_msg)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_X_H $$unsorted) (V_Y_H $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H))) (= V_Y_H V_Y))) (forall ((V_msg $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_H $$unsorted) (V_Y $$unsorted) (V_X $$unsorted)) (or (tptp.c_Message_Oanalzp V_H V_Y) (not (tptp.c_Message_Oanalzp V_H (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (forall ((V_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (tptp.c_Message_Oanalzp V_H V_X) (not (tptp.c_Message_Oanalzp V_H (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_Y_H V_Y))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Oremdups V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a))) (forall ((V_X $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) (tptp.c_Message_Oanalz V_G)) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_K V_X_H) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OHash V_msg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) (forall ((V_H $$unsorted) (V_H_H $$unsorted) (V_X $$unsorted)) (or (not (= (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H_H tptp.tc_Message_Omsg))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_H) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (forall ((V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) _let_2 _let_1)))))) (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Oanalz V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz V_G) V_H _let_1)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1))))) (forall ((V_H $$unsorted) (V_H_H $$unsorted) (V_G $$unsorted) (V_G_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (not (= (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H))) (not (= (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_G_H))) (= (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G_H V_H_H _let_1)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_nat $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OHash V_msg_H)))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_msg_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_agent $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OHash V_msg_H)))) (or (not (tptp.class_HOL_Ouminus tptp.t_b)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus tptp.v_A (tptp.tc_fun tptp.t_a tptp.t_b)) tptp.v_x) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP tptp.v_A tptp.v_x) tptp.t_b))) (forall ((V_nat $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OHash V_msg_H)))) (forall ((V_N $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg_H) (tptp.c_Message_Omsg_ONonce V_nat)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oremdups V_x T_a) _let_1)) (= V_x _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_ys)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Oremdups V_xs T_a) T_a)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oremdups _let_1 T_a)))) (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Osynth V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_B V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (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_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_b tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) T_a T_b) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Set_Oimage V_f V_A T_a T_b) _let_2) _let_2) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop _let_1) T_a T_b)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OHash V_X) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) _let_1) (not (tptp.hBOOL (tptp.c_in V_X V_G tptp.tc_Message_Omsg)))))) (forall ((V_H $$unsorted) (V_X $$unsorted)) (or (tptp.c_Message_Oanalzp V_H V_X) (not (tptp.hBOOL (tptp.hAPP V_H V_X))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_OHPair V_X V_Y) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_xs V_ys)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_x V_y)))) (forall ((V_xs $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (tptp.hBOOL (tptp.c_in V_xs _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_List_Oappend V_xs V_ys T_a) _let_2 _let_1))))))) (forall ((V_ys $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (tptp.hBOOL (tptp.c_in V_ys _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_List_Oappend V_xs V_ys T_a) _let_2 _let_1))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oappend _let_1 _let_1 T_a) _let_1))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_G $$unsorted) (V_H $$unsorted) (V_G_H $$unsorted) (V_H_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G_H V_H_H _let_1)) _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H) _let_1)) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_G_H) _let_1))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_ys T_a) V_zs T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_ys V_zs T_a) T_a))) (forall ((V_xs $$unsorted) (V_xs1 $$unsorted) (V_us $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_xs1 V_us T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_xs1 T_a) V_us T_a))) (forall ((V_zs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_zs V_x T_a) V_ys T_a) (tptp.c_List_Oappend V_zs (tptp.c_List_Oappend V_x V_ys T_a) T_a))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_x V_ts T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_x T_a) V_ts T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_2 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_2 _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor _let_1) tptp.tc_nat)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_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 ((V_c $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) _let_1) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_a V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_Y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X_H V_Y))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_A V_B))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_a V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_G $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) _let_1) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_Y (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_Y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_OHPair V_X V_Y) _let_2 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_Y _let_2 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_OHPair V_X V_Y) _let_2 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg)))))) (forall ((V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_Z $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in V_Z (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_Z (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OHash V_X))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_Y (tptp.c_Message_Osynth (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth V_G) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OHash V_X) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_K_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_X V_K_H))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_G $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg))) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg)))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (= (tptp.c_Message_Oparts _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_H) _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OAgent V_agt))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_C))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_G)) (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (= (tptp.c_Message_Oanalz _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz V_H) _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_G))) (= (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_H _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_2 _let_1))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OAgent V_agt))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_C))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_N $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_N $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey V_x) (tptp.c_Set_Oimage tptp.c_Message_OinvKey V_A tptp.tc_nat tptp.tc_nat) tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey V_x) (tptp.c_Set_Oimage tptp.c_Message_OinvKey V_A tptp.tc_nat tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_x V_A tptp.tc_nat))))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_e $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons V_e V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.hBOOL (tptp.c_in _let_26 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_17)) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Event_OinitState V_A) (tptp.c_Event_Oknows V_A V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) (tptp.c_Event_OinitState V_A))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_G $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg))) tptp.tc_nat))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_KAB $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_KAB) _let_1 tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_KAB (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_KAB $$unsorted)) (let ((_let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg)) (= V_K V_KAB) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_KAB) _let_1 tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_KAB (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))))) (forall ((V_x $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_x))) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_evs $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) _let_1 tptp.tc_Event_Oevent)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OGets V_A V_X) _let_1 tptp.tc_Event_Oevent)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A (tptp.c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 V_A V_X V_evs) V_X) _let_1 tptp.tc_Event_Oevent)) (= V_A tptp.c_Message_Oagent_OSpy) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (V_AS $$unsorted)) (let ((_let_1 (tptp.c_Public_OpublicKey V_x))) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP _let_1 V_A)) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage _let_1 V_AS tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_A V_AS tptp.tc_Message_Oagent)))))) (forall ((V_A $$unsorted) (V_AS $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_A V_AS tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AS tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat) tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_b) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat) tptp.tc_nat)))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (not (tptp.hBOOL (tptp.c_in V_K V_nE tptp.tc_nat))))) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)) _let_1 _let_1))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)))) (or _let_1 (not (tptp.hBOOL (tptp.c_in V_K V_nE tptp.tc_nat))) _let_1))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_K V_nE tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_K V_nE tptp.tc_nat)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_2 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_2 _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_A $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OEncryption) V_A)) tptp.c_Message_OsymKeys tptp.tc_nat)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_AS $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AS tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat) tptp.tc_nat)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_AS $$unsorted)) (or (= V_b V_c) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AS tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat) tptp.tc_nat))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (= V_A tptp.c_Message_Oagent_OSpy))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 V_X V_evs))) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_OinitState tptp.c_Message_Oagent_OSpy) tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes _let_2 V_X) _let_1 tptp.tc_Event_Oevent)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays _let_2 (tptp.c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 V_X V_evs) V_X) _let_1 tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg))))))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_K $$unsorted) (V_KK $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_KK tptp.tc_nat tptp.tc_Message_Omsg) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_K V_KK tptp.tc_nat))) (not (tptp.c_lessequals V_KK (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) _let_1) _let_1)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_KK $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (let ((_let_2 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_3 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_3 (tptp.c_Message_Oanalz _let_2) tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in V_K V_KK tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in _let_3 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_KK tptp.tc_nat tptp.tc_Message_Omsg) _let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg))) (not (tptp.c_lessequals V_KK (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) _let_1) _let_1)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_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_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor V_H) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) V_H tptp.tc_Message_Omsg))))) (forall ((V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.c_Event_Oused V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)))) (or _let_2 (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) _let_2)))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)) _let_2 _let_2)))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey V_K) (tptp.c_Message_OkeysFor V_H) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) V_H tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_KK $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (let ((_let_2 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_3 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_3 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_KK tptp.tc_nat tptp.tc_Message_Omsg) _let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_3 (tptp.c_Message_Oanalz _let_2) tptp.tc_Message_Omsg))) (not (tptp.c_lessequals V_KK (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) _let_1) _let_1)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (let ((_let_3 (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)))) (or (tptp.hBOOL (tptp.c_in _let_3 _let_2 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_1 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg))))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (let ((_let_3 (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)))) (or (tptp.hBOOL (tptp.c_in _let_3 _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_2 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg))))))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A_H V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_evs $$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_B $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OEncryption) V_A)) (tptp.hAPP tptp.c_Public_OshrK V_B)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_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_evs $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.c_Public_Osko__Public__XNonce__supply1__1__1 V_evs)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)))) (forall ((V_N $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OHash V_X) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (forall ((V_H $$unsorted) (V_X $$unsorted) (V_K $$unsorted)) (or (tptp.c_Message_Oanalzp V_H V_X) (not (tptp.c_Message_Oanalzp V_H (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K)))) (not (tptp.c_Message_Oanalzp V_H (tptp.c_Message_Omsg_OCrypt V_K V_X))))) (forall ((V_K $$unsorted) (V_X $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) tptp.tc_Message_Omsg)))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_OHPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (= (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg))) _let_1) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (not (tptp.hBOOL (tptp.c_in V_xs (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a)))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)))) (forall ((V_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= V_b (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Set__XrangeE__1__1 V_b V_f T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremdups (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Oremdups V_xs T_a)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))))) (forall ((V_a $$unsorted) (V_as $$unsorted) (T_a $$unsorted) (V_bs $$unsorted)) (or (= (tptp.c_List_Olist__inter (tptp.c_List_Olist_OCons V_a V_as T_a) V_bs T_a) (tptp.c_List_Olist_OCons V_a (tptp.c_List_Olist__inter V_as V_bs T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_List_Oset V_bs T_a) T_a))))) (forall ((V_a $$unsorted) (V_as $$unsorted) (T_a $$unsorted) (V_bs $$unsorted)) (or (= (tptp.c_List_Olist__inter (tptp.c_List_Olist_OCons V_a V_as T_a) V_bs T_a) (tptp.c_List_Olist__inter V_as V_bs T_a)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_List_Oset V_bs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xa T_a) T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xb T_a) T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olength__unique (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olength__unique V_xs T_a)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (not (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremdups (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oremdups V_xs T_a) T_a)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (= (tptp.c_Event_OinitState tptp.c_Message_Oagent_OSpy) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage _let_24 tptp.c_Event_Obad tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage tptp.c_Message_OinvKey (tptp.c_Set_Oimage _let_22 tptp.c_Event_Obad tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg) _let_20) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey (tptp.c_Set_Oimage tptp.c_Public_OshrK tptp.c_Event_Obad tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat tptp.tc_Message_Omsg) _let_20) _let_25 _let_20) _let_23 _let_20)) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs5 $$unsorted) (V_S $$unsorted) (V_NA $$unsorted) (V_X $$unsorted) (V_B_H $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs5 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_OMPair _let_2 _let_2))) V_evs5 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_NA) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B_H V_A (tptp.c_Message_Omsg_OCrypt V_K _let_2)) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs5))))))) (forall ((V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_KAB $$unsorted) (V_evs2 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NA))) (let ((_let_3 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_4 (tptp.c_Message_Omsg_OAgent V_A))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 _let_4))))))) V_evs2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A_H tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_3 _let_2))) (tptp.c_List_Oset V_evs2 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_KAB tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Event_Oused V_evs2) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs2))))))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs4 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_NB))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_1)) V_evs4 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A_H V_B (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OAgent V_A)))) (tptp.c_List_Oset V_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Event_Oused V_evs4) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs4)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_NA $$unsorted) (V_evs1 $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) _let_1))) V_evs1 tptp.tc_Event_Oevent))) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Event_Oused V_evs1) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs1)))))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg)))) (forall ((V_n $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_n))) (or (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (or (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)))))) (forall ((V_N $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_N tptp.tc_nat tptp.tc_Message_Omsg))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_A $$unsorted) (V_H $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OAgent V_agt) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_2 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_2 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_y (tptp.c_List_Oset V_xs T_a) T_a)) (= V_y V_x) (not (tptp.hBOOL (tptp.c_in V_y (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) T_a))))) (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf))) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evsf))))) (forall ((V_c $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))) (forall ((V_x $$unsorted) (V_AA $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_AA tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_AA $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_x V_AA tptp.tc_Message_Oagent))))) (forall ((V_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 ((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 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Public_OshrK V_A))) (= (tptp.hAPP tptp.c_Message_OinvKey _let_1) _let_1))) (forall ((V_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C) (tptp.hAPP tptp.c_Public_OshrK V_A)))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_C $$unsorted)) (not (= (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C)))) (forall ((V_agent_H $$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_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H)))) (forall ((V_A $$unsorted) (V_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_N $$unsorted) (V_B $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_H $$unsorted)) (= (tptp.c_Message_Oparts (tptp.c_Message_Oanalz V_H)) (tptp.c_Message_Oparts V_H))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Event_OinitState V_B) tptp.tc_Message_Omsg))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_x) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_x) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_x V_A tptp.tc_nat))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_B $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth _let_1) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X V_H tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts _let_1) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X V_H tptp.tc_Message_Omsg))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_K $$unsorted) (V_evs $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_b) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg))))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) tptp.c_Message_OsymKeys tptp.tc_nat)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (= (tptp.c_Message_Osynth _let_1) _let_1))) (forall ((V_N $$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_b $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H))) (= V_b V_c))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H))) (= V_A V_A_H))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H)))) (forall ((V_K $$unsorted) (V_K_H $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Message_OinvKey V_K) (tptp.hAPP tptp.c_Message_OinvKey V_K_H))) (= V_K V_K_H))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (or (= V_b V_c) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_AA $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_AA tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_AA $$unsorted)) (let ((_let_1 (tptp.c_Public_OpublicKey V_x))) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP _let_1 V_xa) (tptp.c_Set_Oimage _let_1 V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_xa V_AA tptp.tc_Message_Oagent)))))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x)) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)))) (forall ((V_K $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey V_K) tptp.c_Message_OsymKeys tptp.tc_nat))))) (forall ((V_K $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey V_K) tptp.c_Message_OsymKeys tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))))) (forall ((V_K $$unsorted)) (or (= (tptp.hAPP tptp.c_Message_OinvKey V_K) V_K) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_agent V_agent_H))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (= (tptp.c_Message_Oparts _let_1) _let_1))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x)) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)))) (forall ((V_K $$unsorted)) (= (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) V_K)) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) tptp.c_Message_OsymKeys tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_C $$unsorted)) (not (= (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oused (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Event_Oused V_evs))) (forall ((V_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C)) (tptp.hAPP tptp.c_Public_OshrK V_A)))) (forall ((V_c $$unsorted) (V_A_H $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H) (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))))) (forall ((V_X $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_X) tptp.c_Message_OsymKeys tptp.tc_nat))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_ONonce V_x) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (forall ((V_A $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg))) (forall ((V_B $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_B)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg))) (forall ((V_B $$unsorted) (V_A $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs4 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_2)) V_evs4 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A_H V_B (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OAgent V_A)))) (tptp.c_List_Oset V_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Event_Oused V_evs4) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_evs4 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1))))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))))) (= (tptp.c_NS__Shared__Mirabelle_Ons__sharedp tptp.v_x) (tptp.c_in tptp.v_x tptp.c_NS__Shared__Mirabelle_Ons__shared _let_17)) (forall ((V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_KAB $$unsorted) (V_evs2 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_KAB))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NA))) (let ((_let_4 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_5 (tptp.c_Message_Omsg_OAgent V_A))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_2 _let_5))))))) V_evs2 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A_H tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair _let_4 _let_3))) (tptp.c_List_Oset V_evs2 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_KAB tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Event_Oused V_evs2) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_evs2 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))))))) (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf))) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_evsf tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs5 $$unsorted) (V_S $$unsorted) (V_NA $$unsorted) (V_X $$unsorted) (V_B_H $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_List_Oset V_evs5 tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NB))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_OMPair _let_3 _let_3))) V_evs5 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_NA) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B_H V_A (tptp.c_Message_Omsg_OCrypt V_K _let_3)) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs5 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_K_H $$unsorted) (V_N $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_NA $$unsorted) (V_evs1 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) _let_2))) V_evs1 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Event_Oused V_evs1) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_evs1 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1))))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg)))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_K $$unsorted) (V_S $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_NA) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs3 $$unsorted) (V_NA $$unsorted) (V_S $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs3 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair _let_2 _let_3))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) _let_1 tptp.tc_Event_Oevent))) (= V_A tptp.c_Message_Oagent_OServer) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs3)))))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OGets V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (= V_A tptp.c_Message_Oagent_OSpy))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))) (forall ((V_NA $$unsorted) (V_NB $$unsorted) (V_K $$unsorted) (V_evso $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evso tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_3 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_2 _let_3))) V_evso tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_3 V_X))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_2)) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evso))))))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_S $$unsorted) (V_A $$unsorted) (V_KA $$unsorted) (V_N $$unsorted) (V_B $$unsorted) (V_K $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt V_KA (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair V_B (tptp.c_Message_Omsg_OMPair V_K V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair V_B (tptp.c_Message_Omsg_OMPair V_K V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs3 $$unsorted) (V_NA $$unsorted) (V_S $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_List_Oset V_evs3 tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs3 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair _let_3 _let_4))) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) _let_2 tptp.tc_Event_Oevent))) (= V_A tptp.c_Message_Oagent_OServer) (not (tptp.hBOOL (tptp.c_in V_evs3 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1))))))))) (forall ((V_X $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_X (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OAgent V_A)))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 V_X)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))))) (forall ((V_NA $$unsorted) (V_NB $$unsorted) (V_K $$unsorted) (V_evso $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_List_Oset V_evso tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_4 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_5 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair _let_3 _let_4))) V_evso tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_4 V_X))))) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_3)) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_evso tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))))))) (forall ((V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A _let_1) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))))) (forall ((V_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_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_ONonce V_nat)))) (forall ((V_agent $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H)))) (forall ((V_nat_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H) (tptp.c_Message_Omsg_ONonce V_nat)))) (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.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X V_H tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (tptp.hBOOL (tptp.c_in tptp.c_Message_Oagent_OSpy tptp.c_Event_Obad tptp.tc_Message_Oagent)) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_ONotes V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H))) (= V_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_nat_H $$unsorted) (V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H)))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_K_H $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_N $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_X $$unsorted)) (or (= V_K_H (tptp.hAPP tptp.c_Public_OshrK V_A)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_nat_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.hAPP tptp.c_Public_OshrK V_A))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey _let_2) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_2 V_X) _let_1 tptp.tc_Message_Omsg))))))) (not (= tptp.c_Message_Oagent_OServer tptp.c_Message_Oagent_OSpy)) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_A_H $$unsorted) (V_evs $$unsorted) (V_NA_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_A V_A_H) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent))))))) _let_19 (forall ((V_B $$unsorted) (V_B_H $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_NA_H $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_B V_B_H) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent))))))) (forall ((V_X $$unsorted) (V_X_H $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_NA_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_X V_X_H) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent))))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H))) (= V_nat V_nat_H))) (forall ((V_agent $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))))) (forall ((V_agent $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H)))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg))) (forall ((V_nat_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg)))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_ONonce V_nat_H))) (= V_nat V_nat_H))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_S T_a)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_S T_a))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_nat V_nat_H))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_S $$unsorted) (V_NA $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (= V_X (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OAgent V_A)))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_NA) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_agent $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_ONonce V_nat_H)))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H))) (= V_msg1 V_msg1_H))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H))) (= V_msg2 V_msg2_H))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) V_X) _let_1 tptp.tc_Message_Omsg)))))) (not (= tptp.c_Message_Oagent_OSpy tptp.c_Message_Oagent_OServer)) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_ONonce V_nat)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_msg1 $$unsorted) (V_msg2 $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2)))) (forall ((V_X $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_K_H $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_X (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OAgent V_A)))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) (forall ((V_nat $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (not (tptp.hBOOL (tptp.c_in tptp.c_Message_Oagent_OServer tptp.c_Event_Obad tptp.tc_Message_Oagent))) (forall ((V_msg1_H $$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_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H) (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.hAPP tptp.c_Public_OshrK V_y))) (= V_x V_y))) (not (tptp.hBOOL (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (not (tptp.hBOOL (tptp.c_in tptp.v_B tptp.c_Event_Obad tptp.tc_Message_Oagent))) _let_18 (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.v_Ba tptp.v_Aa (tptp.c_Message_Omsg_OCrypt tptp.v_Ka (tptp.c_Message_Omsg_ONonce tptp.v_NB))) _let_1 tptp.tc_Event_Oevent)) _let_16 (forall ((V_x $$unsorted)) (not (= tptp.v_Ka (tptp.hAPP tptp.c_Public_OshrK V_x)))) _let_13 _let_4 (forall ((V_NBa $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair V_NBa (tptp.hAPP tptp.c_Message_Omsg_OKey tptp.v_K)))) (tptp.c_List_Oset tptp.v_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) _let_7 _let_8 (or (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evso)) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair tptp.v_x _let_2))) _let_1 tptp.tc_Event_Oevent)) _let_5) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Oboolean__algebra T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ouminus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ouminus T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Lattices_Oboolean__algebra tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Ouminus tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a)))))))))))))))))))))))))))))))))))))))))))))
% 10.71/11.13  )
% 10.71/11.13  % SZS output end Proof for SWV750-1
% 10.71/11.13  % cvc5---1.0.5 exiting
% 10.71/11.13  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------