%------------------------------------------------------------------------------
% File     : SWV005-0 : TPTP v7.2.0. Released v3.2.0.
% Domain   : Software Verification
% Axioms   : Cryptographic protocol axioms for messages
% Version  : [Pau06] axioms.
% English  :

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

% Status   : Satisfiable
% Syntax   : Number of clauses     :   44 (   0 non-Horn;  30 unit;  25 RR)
%            Number of atoms       :   58 (  51 equality)
%            Maximal clause size   :    2 (   1 average)
%            Number of predicates  :    2 (   0 propositional; 2-3 arity)
%            Number of functors    :   23 (   7 constant; 0-3 arity)
%            Number of variables   :   77 (  29 singleton)
%            Maximal term depth    :    4 (   2 average)
% SPC      : 

% Comments : Requires MSC001-0.ax, MSC001-1.ax
%------------------------------------------------------------------------------
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_Oagent_Odistinct__1_0,axiom,
    ( c_Message_Oagent_OServer != c_Message_Oagent_OFriend(V_nat_H) )).

cnf(cls_Message_Oagent_Odistinct__2_0,axiom,
    ( c_Message_Oagent_OFriend(V_nat_H) != c_Message_Oagent_OServer )).

cnf(cls_Message_Oagent_Odistinct__3_0,axiom,
    ( c_Message_Oagent_OServer != c_Message_Oagent_OSpy )).

cnf(cls_Message_Oagent_Odistinct__4_0,axiom,
    ( c_Message_Oagent_OSpy != c_Message_Oagent_OServer )).

cnf(cls_Message_Oagent_Odistinct__5_0,axiom,
    ( c_Message_Oagent_OFriend(V_nat) != c_Message_Oagent_OSpy )).

cnf(cls_Message_Oagent_Odistinct__6_0,axiom,
    ( c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(V_nat) )).

cnf(cls_Message_Oagent_Oinject_0,axiom,
    ( c_Message_Oagent_OFriend(V_nat) != c_Message_Oagent_OFriend(V_nat_H)
    | V_nat = V_nat_H )).

cnf(cls_Message_Oagent_Osize__1_0,axiom,
    ( c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) = c_0 )).

cnf(cls_Message_Oagent_Osize__2_0,axiom,
    ( c_Nat_Osize(c_Message_Oagent_OFriend(V_nat),tc_Message_Oagent) = c_0 )).

cnf(cls_Message_Oagent_Osize__3_0,axiom,
    ( c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) = c_0 )).

cnf(cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0,axiom,
    ( c_Message_OinvKey(c_Message_OinvKey(V_y)) = V_y )).

cnf(cls_Message_OinvKey__eq_0,axiom,
    ( c_Message_OinvKey(V_K) != c_Message_OinvKey(V_K_H)
    | V_K = V_K_H )).

cnf(cls_Message_OkeysFor__Un_0,axiom,
    ( c_Message_OkeysFor(c_union(V_H,V_H_H,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(V_H),c_Message_OkeysFor(V_H_H),tc_nat) )).

cnf(cls_Message_OkeysFor__empty_0,axiom,
    ( c_Message_OkeysFor(c_emptyset) = c_emptyset )).

cnf(cls_Message_OkeysFor__insert__Agent_0,axiom,
    ( c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(V_A),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H) )).

cnf(cls_Message_OkeysFor__insert__Crypt_0,axiom,
    ( c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(V_K),c_Message_OkeysFor(V_H),tc_nat) )).

cnf(cls_Message_OkeysFor__insert__Hash_0,axiom,
    ( c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(V_X),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H) )).

cnf(cls_Message_OkeysFor__insert__Key_0,axiom,
    ( c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(V_K),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H) )).

cnf(cls_Message_OkeysFor__insert__MPair_0,axiom,
    ( c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H) )).

cnf(cls_Message_OkeysFor__insert__Nonce_0,axiom,
    ( c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(V_N),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H) )).

cnf(cls_Message_OkeysFor__insert__Number_0,axiom,
    ( c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(V_N),V_H,tc_Message_Omsg)) = c_Message_OkeysFor(V_H) )).

cnf(cls_Message_Omsg_Oinject__1_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_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_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_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_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_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_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_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_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_Omsg_Osize__1_0,axiom,
    ( c_Nat_Osize(c_Message_Omsg_OAgent(V_agent),tc_Message_Omsg) = c_0 )).

cnf(cls_Message_Omsg_Osize__2_0,axiom,
    ( c_Nat_Osize(c_Message_Omsg_ONumber(V_nat),tc_Message_Omsg) = c_0 )).

cnf(cls_Message_Omsg_Osize__3_0,axiom,
    ( c_Nat_Osize(c_Message_Omsg_ONonce(V_nat),tc_Message_Omsg) = c_0 )).

cnf(cls_Message_Omsg_Osize__4_0,axiom,
    ( c_Nat_Osize(c_Message_Omsg_OKey(V_nat),tc_Message_Omsg) = c_0 )).

cnf(cls_Message_Omsg_Osize__5_0,axiom,
    ( c_Nat_Osize(c_Message_Omsg_OHash(V_msg),tc_Message_Omsg) = c_plus(c_Nat_Osize(V_msg,tc_Message_Omsg),c_Suc(c_0),tc_nat) )).

cnf(cls_Message_Omsg_Osize__6_0,axiom,
    ( c_Nat_Osize(c_Message_Omsg_OMPair(V_msg1,V_msg2),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(V_msg1,tc_Message_Omsg),c_Nat_Osize(V_msg2,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat) )).

cnf(cls_Message_Omsg_Osize__7_0,axiom,
    ( c_Nat_Osize(c_Message_Omsg_OCrypt(V_nat,V_msg),tc_Message_Omsg) = c_plus(c_Nat_Osize(V_msg,tc_Message_Omsg),c_Suc(c_0),tc_nat) )).

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__Un_0,axiom,
    ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),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__empty_0,axiom,
    ( c_Message_Oparts(c_emptyset) = c_emptyset )).

cnf(cls_Message_Ostrange__Un__eq_0,axiom,
    ( c_union(V_A,c_union(V_B,V_A,T_a),T_a) = c_union(V_B,V_A,T_a) )).

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