%------------------------------------------------------------------------------
% File     : SWV006-0 : TPTP v9.0.0. Released v3.2.0.
% Domain   : Software Verification
% Axioms   : Cryptographic protocol axioms for public
% Version  : [Pau06] axioms.
% English  :

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

% Status   : Satisfiable
% Syntax   : Number of clauses     :   79 (  31 unt;   6 nHn;  75 RR)
%            Number of literals    :  136 (  72 equ;  77 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-3 aty)
%            Number of functors    :   24 (  24 usr;   6 con; 0-3 aty)
%            Number of variables   :  229 ( 119 sgn)
% SPC      : 

% Comments : Requires MSC001-0.ax, MSC001-2.ax
%------------------------------------------------------------------------------
cnf(cls_Event_OServer_A_58_Abad_A_61_61_62_AR_0,axiom,
    ~ c_in(c_Message_Oagent_OServer,c_Event_Obad,tc_Message_Oagent) ).

cnf(cls_Event_OSpy_A_58_Abad_0,axiom,
    c_in(c_Message_Oagent_OSpy,c_Event_Obad,tc_Message_Oagent) ).

cnf(cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0,axiom,
    ( ~ c_in(V_c,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
    | c_in(V_c,c_Event_Oused(V_evs),tc_Message_Omsg) ) ).

cnf(cls_Event_Oevent_Odistinct__1__iff1_0,axiom,
    c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OGets(V_agent_H,V_msg_H) ).

cnf(cls_Event_Oevent_Odistinct__2__iff1_0,axiom,
    c_Event_Oevent_OGets(V_agent_H,V_msg_H) != c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) ).

cnf(cls_Event_Oevent_Odistinct__3__iff1_0,axiom,
    c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H) ).

cnf(cls_Event_Oevent_Odistinct__4__iff1_0,axiom,
    c_Event_Oevent_ONotes(V_agent_H,V_msg_H) != c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) ).

cnf(cls_Event_Oevent_Odistinct__5__iff1_0,axiom,
    c_Event_Oevent_OGets(V_agent,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H) ).

cnf(cls_Event_Oevent_Odistinct__6__iff1_0,axiom,
    c_Event_Oevent_ONotes(V_agent_H,V_msg_H) != c_Event_Oevent_OGets(V_agent,V_msg) ).

cnf(cls_Event_Oevent_Oinject__1__iff1_0,axiom,
    ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H)
    | V_agent1 = V_agent1_H ) ).

cnf(cls_Event_Oevent_Oinject__1__iff1_1,axiom,
    ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H)
    | V_agent2 = V_agent2_H ) ).

cnf(cls_Event_Oevent_Oinject__1__iff1_2,axiom,
    ( c_Event_Oevent_OSays(V_agent1,V_agent2,V_msg) != c_Event_Oevent_OSays(V_agent1_H,V_agent2_H,V_msg_H)
    | V_msg = V_msg_H ) ).

cnf(cls_Event_Oevent_Oinject__2__iff1_0,axiom,
    ( c_Event_Oevent_OGets(V_agent,V_msg) != c_Event_Oevent_OGets(V_agent_H,V_msg_H)
    | V_agent = V_agent_H ) ).

cnf(cls_Event_Oevent_Oinject__2__iff1_1,axiom,
    ( c_Event_Oevent_OGets(V_agent,V_msg) != c_Event_Oevent_OGets(V_agent_H,V_msg_H)
    | V_msg = V_msg_H ) ).

cnf(cls_Event_Oevent_Oinject__3__iff1_0,axiom,
    ( c_Event_Oevent_ONotes(V_agent,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H)
    | V_agent = V_agent_H ) ).

cnf(cls_Event_Oevent_Oinject__3__iff1_1,axiom,
    ( c_Event_Oevent_ONotes(V_agent,V_msg) != c_Event_Oevent_ONotes(V_agent_H,V_msg_H)
    | V_msg = V_msg_H ) ).

cnf(cls_Message_OCrypt__synth_0,axiom,
    ( ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg) ) ).

cnf(cls_Message_OCrypt__synth_1,axiom,
    ( ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg) ) ).

cnf(cls_Message_OHPair__eq__MPair__iff1_0,axiom,
    ( c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OMPair(V_X_H,V_Y_H)
    | V_X_H = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)) ) ).

cnf(cls_Message_OHPair__eq__MPair__iff1_1,axiom,
    ( c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OMPair(V_X_H,V_Y_H)
    | V_Y_H = V_Y ) ).

cnf(cls_Message_OHPair__eq__MPair__iff2_0,axiom,
    c_Message_OHPair(V_X,V_x) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_x)),V_x) ).

cnf(cls_Message_OHPair__eq__iff1_0,axiom,
    ( c_Message_OHPair(V_X_H,V_Y_H) != c_Message_OHPair(V_X,V_Y)
    | V_X_H = V_X ) ).

cnf(cls_Message_OHPair__eq__iff1_1,axiom,
    ( c_Message_OHPair(V_X_H,V_Y_H) != c_Message_OHPair(V_X,V_Y)
    | V_Y_H = V_Y ) ).

cnf(cls_Message_OHPair__neqs__1__iff1_0,axiom,
    c_Message_Omsg_OAgent(V_A) != c_Message_OHPair(V_X,V_Y) ).

cnf(cls_Message_OHPair__neqs__2__iff1_0,axiom,
    c_Message_Omsg_ONonce(V_N) != c_Message_OHPair(V_X,V_Y) ).

cnf(cls_Message_OHPair__neqs__3__iff1_0,axiom,
    c_Message_Omsg_ONumber(V_N) != c_Message_OHPair(V_X,V_Y) ).

cnf(cls_Message_OHPair__neqs__4__iff1_0,axiom,
    c_Message_Omsg_OKey(V_K) != c_Message_OHPair(V_X,V_Y) ).

cnf(cls_Message_OHPair__neqs__5__iff1_0,axiom,
    c_Message_Omsg_OHash(V_Z) != c_Message_OHPair(V_X,V_Y) ).

cnf(cls_Message_OHPair__neqs__6__iff1_0,axiom,
    c_Message_Omsg_OCrypt(V_K,V_X_H) != c_Message_OHPair(V_X,V_Y) ).

cnf(cls_Message_OHash_91X_93_AY_A_61_AAgent_AA_A_61_61_62_AR_0,axiom,
    c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OAgent(V_A) ).

cnf(cls_Message_OHash_91X_93_AY_A_61_ACrypt_AK_AX_H_A_61_61_62_AR_0,axiom,
    c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OCrypt(V_K,V_X_H) ).

cnf(cls_Message_OHash_91X_93_AY_A_61_AHash_AZ_A_61_61_62_AR_0,axiom,
    c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OHash(V_Z) ).

cnf(cls_Message_OHash_91X_93_AY_A_61_AKey_AK_A_61_61_62_AR_0,axiom,
    c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_OKey(V_K) ).

cnf(cls_Message_OHash_91X_93_AY_A_61_ANonce_AN_A_61_61_62_AR_0,axiom,
    c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_ONonce(V_N) ).

cnf(cls_Message_OHash_91X_93_AY_A_61_ANumber_AN_A_61_61_62_AR_0,axiom,
    c_Message_OHPair(V_X,V_Y) != c_Message_Omsg_ONumber(V_N) ).

cnf(cls_Message_OHash__synth_0,axiom,
    ( ~ c_in(c_Message_Omsg_OHash(V_X),c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(V_X),V_H,tc_Message_Omsg) ) ).

cnf(cls_Message_OKey__synth_0,axiom,
    ( ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg) ) ).

cnf(cls_Message_OMPair__analz_0,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
    | c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_OMPair__analz_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)
    | c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_OMPair__eq__HPair__iff1_0,axiom,
    ( c_Message_Omsg_OMPair(V_X_H,V_Y_H) != c_Message_OHPair(V_X,V_Y)
    | V_X_H = c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_Y)) ) ).

cnf(cls_Message_OMPair__eq__HPair__iff1_1,axiom,
    ( c_Message_Omsg_OMPair(V_X_H,V_Y_H) != c_Message_OHPair(V_X,V_Y)
    | V_Y_H = V_Y ) ).

cnf(cls_Message_OMPair__eq__HPair__iff2_0,axiom,
    c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_x)),V_x) = c_Message_OHPair(V_X,V_x) ).

cnf(cls_Message_OMPair__parts_0,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
    | c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_OMPair__parts_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
    | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_OMPair__synth_0,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(V_Y,c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg) ) ).

cnf(cls_Message_OMPair__synth_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg) ) ).

cnf(cls_Message_OMPair__synth__analz__iff1_0,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
    | c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ) ).

cnf(cls_Message_OMPair__synth__analz__iff1_1,axiom,
    ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
    | c_in(V_Y,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ) ).

cnf(cls_Message_OMPair__synth__analz__iff2_0,axiom,
    ( ~ c_in(V_Y,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
    | ~ c_in(V_X,c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(c_Message_Oanalz(V_H)),tc_Message_Omsg) ) ).

cnf(cls_Message_ONonce__synth_0,axiom,
    ( ~ c_in(c_Message_Omsg_ONonce(V_n),c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(c_Message_Omsg_ONonce(V_n),V_H,tc_Message_Omsg) ) ).

cnf(cls_Message_Oagent_Odistinct__1__iff1_0,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OFriend(V_nat_H) ).

cnf(cls_Message_Oagent_Odistinct__2__iff1_0,axiom,
    c_Message_Oagent_OFriend(V_nat_H) != c_Message_Oagent_OServer ).

cnf(cls_Message_Oagent_Odistinct__3__iff1_0,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy ).

cnf(cls_Message_Oagent_Odistinct__4__iff1_0,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer ).

cnf(cls_Message_Oagent_Odistinct__5__iff1_0,axiom,
    c_Message_Oagent_OFriend(V_nat) != c_Message_Oagent_OSpy ).

cnf(cls_Message_Oagent_Odistinct__6__iff1_0,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(V_nat) ).

cnf(cls_Message_Oagent_Oinject__iff1_0,axiom,
    ( c_Message_Oagent_OFriend(V_nat) != c_Message_Oagent_OFriend(V_nat_H)
    | V_nat = V_nat_H ) ).

cnf(cls_Message_Oanalz_OInj_0,axiom,
    ( ~ c_in(V_X,V_H,tc_Message_Omsg)
    | c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_Oanalz__analzD__dest_0,axiom,
    ( ~ c_in(V_X,c_Message_Oanalz(c_Message_Oanalz(V_H)),tc_Message_Omsg)
    | c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_Oin__parts__UnE_0,axiom,
    ( ~ c_in(V_c,c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),tc_Message_Omsg)
    | c_in(V_c,c_Message_Oparts(V_H),tc_Message_Omsg)
    | c_in(V_c,c_Message_Oparts(V_G),tc_Message_Omsg) ) ).

cnf(cls_Message_Omsg_Oinject__1__iff1_0,axiom,
    ( c_Message_Omsg_OAgent(V_agent) != c_Message_Omsg_OAgent(V_agent_H)
    | V_agent = V_agent_H ) ).

cnf(cls_Message_Omsg_Oinject__2__iff1_0,axiom,
    ( c_Message_Omsg_ONumber(V_nat) != c_Message_Omsg_ONumber(V_nat_H)
    | V_nat = V_nat_H ) ).

cnf(cls_Message_Omsg_Oinject__3__iff1_0,axiom,
    ( c_Message_Omsg_ONonce(V_nat) != c_Message_Omsg_ONonce(V_nat_H)
    | V_nat = V_nat_H ) ).

cnf(cls_Message_Omsg_Oinject__4__iff1_0,axiom,
    ( c_Message_Omsg_OKey(V_nat) != c_Message_Omsg_OKey(V_nat_H)
    | V_nat = V_nat_H ) ).

cnf(cls_Message_Omsg_Oinject__5__iff1_0,axiom,
    ( c_Message_Omsg_OHash(V_msg) != c_Message_Omsg_OHash(V_msg_H)
    | V_msg = V_msg_H ) ).

cnf(cls_Message_Omsg_Oinject__6__iff1_0,axiom,
    ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H)
    | V_msg1 = V_msg1_H ) ).

cnf(cls_Message_Omsg_Oinject__6__iff1_1,axiom,
    ( c_Message_Omsg_OMPair(V_msg1,V_msg2) != c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H)
    | V_msg2 = V_msg2_H ) ).

cnf(cls_Message_Omsg_Oinject__7__iff1_0,axiom,
    ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H)
    | V_nat = V_nat_H ) ).

cnf(cls_Message_Omsg_Oinject__7__iff1_1,axiom,
    ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H)
    | V_msg = V_msg_H ) ).

cnf(cls_Message_Oparts_OInj_0,axiom,
    ( ~ c_in(V_X,V_H,tc_Message_Omsg)
    | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_Oparts__emptyE_0,axiom,
    ~ c_in(V_X,c_Message_Oparts(c_emptyset),tc_Message_Omsg) ).

cnf(cls_Message_Oparts__partsD__dest_0,axiom,
    ( ~ c_in(V_X,c_Message_Oparts(c_Message_Oparts(V_H)),tc_Message_Omsg)
    | c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_Osynth_OAgent_0,axiom,
    c_in(c_Message_Omsg_OAgent(V_agt),c_Message_Osynth(V_H),tc_Message_Omsg) ).

cnf(cls_Message_Osynth_OCrypt_0,axiom,
    ( ~ c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
    | ~ c_in(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)
    | c_in(c_Message_Omsg_OCrypt(V_K,V_X),c_Message_Osynth(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_Osynth_OHash_0,axiom,
    ( ~ c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OHash(V_X),c_Message_Osynth(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_Osynth_OInj_0,axiom,
    ( ~ c_in(V_X,V_H,tc_Message_Omsg)
    | c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_Osynth_OMPair_0,axiom,
    ( ~ c_in(V_Y,c_Message_Osynth(V_H),tc_Message_Omsg)
    | ~ c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
    | c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ) ).

cnf(cls_Message_Osynth_ONumber_0,axiom,
    c_in(c_Message_Omsg_ONumber(V_n),c_Message_Osynth(V_H),tc_Message_Omsg) ).

cnf(cls_Message_Osynth__synthD__dest_0,axiom,
    ( ~ c_in(V_X,c_Message_Osynth(c_Message_Osynth(V_H)),tc_Message_Omsg)
    | c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg) ) ).

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