## TPTP Problem File: SWV017+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SWV017+1 : TPTP v7.2.0. Released v2.4.0.
% Domain   : Software Verification
% Problem  : Fact 8 of the Neumann-Stubblebine analysis
% Version  : [Wei99] axioms.
% English  :

% Refs     : [Wei99] Weidenbach (1999), Towards and Automatic Analysis of S
%            [Bau99] Baumgartner (1999), FTP'2000 - Problem Sets
% Source   : [Bau99]
% Names    : Fact 8 [Wei99]

% Status   : Satisfiable
% Rating   : 0.00 v5.4.0, 0.14 v5.2.0, 0.25 v5.0.0, 0.00 v4.1.0, 0.25 v4.0.1, 0.00 v3.1.0, 0.83 v2.7.0, 0.33 v2.6.0, 0.50 v2.5.0, 0.33 v2.4.0
% Syntax   : Number of formulae    :   33 (  14 unit)
%            Number of atoms       :   81 (   0 equality)
%            Maximal formula depth :   12 (   4 average)
%            Number of connectives :   50 (   2 ~  ;   0  |;  31  &)
%                                         (   0 <=>;  17 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   13 (   0 propositional; 1-1 arity)
%            Number of functors    :   17 (   7 constant; 0-4 arity)
%            Number of variables   :   56 (   0 singleton;  56 !;   0 ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : FOF_SAT_RFO_NEQ

%--------------------------------------------------------------------------
fof(a_holds_key_at_for_t,axiom,
( a_holds(key(at,t)) )).

fof(a_is_party_of_protocol,axiom,
( party_of_protocol(a) )).

fof(a_sent_message_i_to_b,axiom,
( message(sent(a,b,pair(a,an_a_nonce))) )).

fof(a_stored_message_i,axiom,
( a_stored(pair(b,an_a_nonce)) )).

fof(a_forwards_secure,axiom,
( ! [U,V,W,X,Y,Z] :
& a_stored(pair(Y,Z)) )
=> ( message(sent(a,Y,pair(X,encrypt(U,W))))
& a_holds(key(W,Y)) ) ) )).

fof(b_hold_key_bt_for_t,axiom,
( b_holds(key(bt,t)) )).

fof(b_is_party_of_protocol,axiom,
( party_of_protocol(b) )).

fof(nonce_a_is_fresh_to_b,axiom,
( fresh_to_b(an_a_nonce) )).

fof(b_creates_freash_nonces_in_time,axiom,
( ! [U,V] :
( ( message(sent(U,b,pair(U,V)))
& fresh_to_b(V) )
=> ( message(sent(b,t,triple(b,generate_b_nonce(V),encrypt(triple(U,V,generate_expiration_time(V)),bt))))
& b_stored(pair(U,V)) ) ) )).

fof(b_accepts_secure_session_key,axiom,
( ! [V,X,Y] :
( ( message(sent(X,b,pair(encrypt(triple(X,V,generate_expiration_time(Y)),bt),encrypt(generate_b_nonce(Y),V))))
& a_key(V)
& b_stored(pair(X,Y)) )
=> b_holds(key(V,X)) ) )).

fof(t_holds_key_at_for_a,axiom,
( t_holds(key(at,a)) )).

fof(t_holds_key_bt_for_b,axiom,
( t_holds(key(bt,b)) )).

fof(t_is_party_of_protocol,axiom,
( party_of_protocol(t) )).

fof(server_t_generates_key,axiom,
( ! [U,V,W,X,Y,Z,X1] :
( ( message(sent(U,t,triple(U,V,encrypt(triple(W,X,Y),Z))))
& t_holds(key(Z,U))
& t_holds(key(X1,W))
& a_nonce(X) )
=> message(sent(t,W,triple(encrypt(quadruple(U,X,generate_key(X),Y),X1),encrypt(triple(W,generate_key(X),Y),Z),V))) ) )).

fof(intruder_can_record,axiom,
( ! [U,V,W] :
( message(sent(U,V,W))
=> intruder_message(W) ) )).

fof(intruder_decomposes_pairs,axiom,
( ! [U,V] :
( intruder_message(pair(U,V))
=> ( intruder_message(U)
& intruder_message(V) ) ) )).

fof(intruder_decomposes_triples,axiom,
( ! [U,V,W] :
( intruder_message(triple(U,V,W))
=> ( intruder_message(U)
& intruder_message(V)
& intruder_message(W) ) ) )).

( ! [U,V,W,X] :
=> ( intruder_message(U)
& intruder_message(V)
& intruder_message(W)
& intruder_message(X) ) ) )).

fof(intruder_composes_pairs,axiom,
( ! [U,V] :
( ( intruder_message(U)
& intruder_message(V) )
=> intruder_message(pair(U,V)) ) )).

fof(intruder_composes_triples,axiom,
( ! [U,V,W] :
( ( intruder_message(U)
& intruder_message(V)
& intruder_message(W) )
=> intruder_message(triple(U,V,W)) ) )).

( ! [U,V,W,X] :
( ( intruder_message(U)
& intruder_message(V)
& intruder_message(W)
& intruder_message(X) )
=> intruder_message(quadruple(U,V,W,X)) ) )).

fof(intruder_interception,axiom,
( ! [U,V,W] :
( ( intruder_message(encrypt(U,V))
& intruder_holds(key(V,W))
& party_of_protocol(W) )
=> intruder_message(V) ) )).

fof(intruder_message_sent,axiom,
( ! [U,V,W] :
( ( intruder_message(U)
& party_of_protocol(V)
& party_of_protocol(W) )
=> message(sent(V,W,U)) ) )).

fof(intruder_holds_key,axiom,
( ! [V,W] :
( ( intruder_message(V)
& party_of_protocol(W) )
=> intruder_holds(key(V,W)) ) )).

fof(intruder_key_encrypts,axiom,
( ! [U,V,W] :
( ( intruder_message(U)
& intruder_holds(key(V,W))
& party_of_protocol(W) )
=> intruder_message(encrypt(U,V)) ) )).

fof(an_a_nonce_is_a_nonce,axiom,
( a_nonce(an_a_nonce) )).

fof(generated_keys_are_not_nonces,axiom,
( ! [U] : ~ a_nonce(generate_key(U)) )).

fof(generated_times_and_nonces_are_nonces,axiom,
( ! [U] :
( a_nonce(generate_expiration_time(U))
& a_nonce(generate_b_nonce(U)) ) )).

fof(nothing_is_a_nonce_and_a_key,axiom,
( ! [U] : ~ ( a_key(U)
& a_nonce(U) ) )).

fof(generated_keys_are_keys,axiom,
( ! [U] : a_key(generate_key(U)) )).

fof(an_intruder_nonce_is_a_fresh_intruder_nonce,axiom,
( fresh_intruder_nonce(an_intruder_nonce) )).

fof(can_generate_more_fresh_intruder_nonces,axiom,
( ! [U] :
( fresh_intruder_nonce(U)
=> fresh_intruder_nonce(generate_intruder_nonce(U)) ) )).

fof(fresh_intruder_nonces_are_fresh_to_b,axiom,
( ! [U] :
( fresh_intruder_nonce(U)
=> ( fresh_to_b(U)
& intruder_message(U) ) ) )).

%--------------------------------------------------------------------------
```