%------------------------------------------------------------------------------
% File     : SWV005-3 : TPTP v7.2.0. Released v3.2.0.
% Domain   : Software Verification
% Axioms   : Cryptographic protocol axioms for public, simplified
% Version  : [Pau06] axioms.
% English  :

% Refs     : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source   : [Pau06]
% Names    : Public-simp.ax [Pau06]

% Status   : Satisfiable
% Syntax   : Number of clauses     :   42 (   0 non-Horn;  32 unit;  24 RR)
%            Number of atoms       :   52 (  24 equality)
%            Maximal clause size   :    2 (   1 average)
%            Number of predicates  :    2 (   0 propositional; 2-3 arity)
%            Number of functors    :   28 (  12 constant; 0-4 arity)
%            Number of variables   :   92 (  69 singleton)
%            Maximal term depth    :    4 (   2 average)
% SPC      : 

% Comments : Requires MSC001-0.ax, MSC001-1.ax, SWV005-0.ax, SWV005-2.ax
%------------------------------------------------------------------------------
cnf(cls_Public_OCrypt__notin__used__empty_0,axiom,
    ( ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg) )).

cnf(cls_Public_OMPair__used_0,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Event_Oused(V_H),tc_Message_Omsg)
    | c_in(V_Y,c_Event_Oused(V_H),tc_Message_Omsg) )).

cnf(cls_Public_OMPair__used_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Event_Oused(V_H),tc_Message_Omsg)
    | c_in(V_X,c_Event_Oused(V_H),tc_Message_Omsg) )).

cnf(cls_Public_ONonce__notin__initState_0,axiom,
    ( ~ c_in(c_Message_Omsg_ONonce(V_N),c_Message_Oparts(c_Event_OinitState(V_B)),tc_Message_Omsg) )).

cnf(cls_Public_ONonce__notin__used__empty_0,axiom,
    ( ~ c_in(c_Message_Omsg_ONonce(V_N),c_Event_Oused(c_List_Olist_ONil),tc_Message_Omsg) )).

cnf(cls_Public_OSpy__spies__bad__privateKey_0,axiom,
    ( ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent)
    | c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A))),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )).

cnf(cls_Public_OSpy__spies__bad__shrK_0,axiom,
    ( ~ c_in(V_A,c_Event_Obad,tc_Message_Oagent)
    | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )).

cnf(cls_Public_Oanalz__spies__pubK_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(V_b,V_A)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )).

cnf(cls_Public_OinvKey__K_0,axiom,
    ( ~ c_in(V_y,c_Message_OsymKeys,tc_nat)
    | c_Message_OinvKey(V_y) = V_y )).

cnf(cls_Public_OinvKey__shrK_0,axiom,
    ( c_Message_OinvKey(c_Public_OshrK(V_A)) = c_Public_OshrK(V_A) )).

cnf(cls_Public_Okeymode_Ocases__1_0,axiom,
    ( c_Public_Okeymode_Okeymode__case(V_y,V_f2,c_Public_Okeymode_OSignature,T_a) = V_y )).

cnf(cls_Public_Okeymode_Ocases__2_0,axiom,
    ( c_Public_Okeymode_Okeymode__case(V_f1,V_y,c_Public_Okeymode_OEncryption,T_a) = V_y )).

cnf(cls_Public_Okeymode_Odistinct__1_0,axiom,
    ( c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption )).

cnf(cls_Public_Okeymode_Odistinct__2_0,axiom,
    ( c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature )).

cnf(cls_Public_Okeymode_Orecs__1_0,axiom,
    ( c_Public_Okeymode_Okeymode__rec(V_y,V_f2,c_Public_Okeymode_OSignature,T_a) = V_y )).

cnf(cls_Public_Okeymode_Orecs__2_0,axiom,
    ( c_Public_Okeymode_Okeymode__rec(V_f1,V_y,c_Public_Okeymode_OEncryption,T_a) = V_y )).

cnf(cls_Public_Okeymode_Osize__1_0,axiom,
    ( c_Nat_Osize(c_Public_Okeymode_OSignature,tc_Public_Okeymode) = c_0 )).

cnf(cls_Public_Okeymode_Osize__2_0,axiom,
    ( c_Nat_Osize(c_Public_Okeymode_OEncryption,tc_Public_Okeymode) = c_0 )).

cnf(cls_Public_OkeysFor__parts__initState_0,axiom,
    ( c_Message_OkeysFor(c_Message_Oparts(c_Event_OinitState(V_C))) = c_emptyset )).

cnf(cls_Public_Onot__symKeys__priK_0,axiom,
    ( ~ c_in(c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A)),c_Message_OsymKeys,tc_nat) )).

cnf(cls_Public_Onot__symKeys__pubK_0,axiom,
    ( ~ c_in(c_Public_OpublicKey(V_b,V_A),c_Message_OsymKeys,tc_nat) )).

cnf(cls_Public_OpriEK__noteq__shrK_0,axiom,
    ( c_Message_OinvKey(c_Public_OpublicKey(c_Public_Okeymode_OEncryption,V_A)) != c_Public_OshrK(V_B) )).

cnf(cls_Public_OpriK__in__initState_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A))),c_Event_OinitState(V_A),tc_Message_Omsg) )).

cnf(cls_Public_OpriK__neq__shrK_0,axiom,
    ( c_Public_OshrK(V_A) != c_Message_OinvKey(c_Public_OpublicKey(V_b,V_C)) )).

cnf(cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0,axiom,
    ( c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A)) != c_Public_OpublicKey(V_c,V_A_H) )).

cnf(cls_Public_OprivateKey__into__used_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A))),c_Event_Oused(V_evs),tc_Message_Omsg) )).

cnf(cls_Public_OpubK__neq__shrK_0,axiom,
    ( c_Public_OshrK(V_A) != c_Public_OpublicKey(V_b,V_C) )).

cnf(cls_Public_OpublicKey__in__initState_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(V_b,V_A)),c_Event_OinitState(V_B),tc_Message_Omsg) )).

cnf(cls_Public_OpublicKey__inject_0,axiom,
    ( c_Public_OpublicKey(V_b,V_A) != c_Public_OpublicKey(V_c,V_A_H)
    | V_b = V_c )).

cnf(cls_Public_OpublicKey__inject_1,axiom,
    ( c_Public_OpublicKey(V_b,V_A) != c_Public_OpublicKey(V_c,V_A_H)
    | V_A = V_A_H )).

cnf(cls_Public_OpublicKey__into__used_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(V_b,V_A)),c_Event_Oused(V_evs),tc_Message_Omsg) )).

cnf(cls_Public_OpublicKey__neq__privateKey_0,axiom,
    ( c_Public_OpublicKey(V_c,V_A_H) != c_Message_OinvKey(c_Public_OpublicKey(V_b,V_A)) )).

cnf(cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0,axiom,
    ( c_in(c_Public_OshrK(V_X),c_Message_OsymKeys,tc_nat) )).

cnf(cls_Public_OshrK__in__initState_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_OinitState(V_A),tc_Message_Omsg) )).

cnf(cls_Public_OshrK__in__knows_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oknows(V_A,V_evs),tc_Message_Omsg) )).

cnf(cls_Public_OshrK__in__used_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oused(V_evs),tc_Message_Omsg) )).

cnf(cls_Public_OshrK__injective_0,axiom,
    ( c_Public_OshrK(V_x) != c_Public_OshrK(V_y)
    | V_x = V_y )).

cnf(cls_Public_OshrK__neq__priK_0,axiom,
    ( c_Message_OinvKey(c_Public_OpublicKey(V_b,V_C)) != c_Public_OshrK(V_A) )).

cnf(cls_Public_OshrK__neq__pubK_0,axiom,
    ( c_Public_OpublicKey(V_b,V_C) != c_Public_OshrK(V_A) )).

cnf(cls_Public_Ospies__pubK_0,axiom,
    ( c_in(c_Message_Omsg_OKey(c_Public_OpublicKey(V_b,V_A)),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )).

cnf(cls_Public_OsymKeys__invKey__iff_0,axiom,
    ( ~ c_in(c_Message_OinvKey(V_K),c_Message_OsymKeys,tc_nat)
    | c_in(V_K,c_Message_OsymKeys,tc_nat) )).

cnf(cls_Public_OsymKeys__invKey__iff_1,axiom,
    ( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
    | c_in(c_Message_OinvKey(V_K),c_Message_OsymKeys,tc_nat) )).

%------------------------------------------------------------------------------