TPTP Problem File: SWV010^7.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV010^7 : TPTP v8.2.0. Released v5.5.0.
% Domain : Software Verification
% Problem : Fact 1 of the Neumann-Stubblebine analysis
% Version : [Ben12] axioms.
% English :
% Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% : [Wei99] Weidenbach (1999), Towards and Automatic Analysis of S
% : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source : [Ben12]
% Names : s4-cumul-GSV010+1 [Ben12]
% Status : Satisfiable
% Rating : 0.33 v8.2.0, 0.67 v6.1.0, 0.50 v5.5.0
% Syntax : Number of formulae : 124 ( 48 unt; 59 typ; 32 def)
% Number of atoms : 236 ( 36 equ; 0 cnn)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 431 ( 5 ~; 5 |; 9 &; 402 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 215 ( 215 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 64 usr; 13 con; 0-4 aty)
% Number of variables : 142 ( 67 ^; 68 !; 7 ?; 142 :)
% SPC : TH0_SAT_EQU_NAR
% Comments : Goedel translation of SWV010+1
%------------------------------------------------------------------------------
%----Include axioms for Modal logic S4 under cumulative domains
include('Axioms/LCL015^0.ax').
include('Axioms/LCL013^5.ax').
include('Axioms/LCL015^1.ax').
%------------------------------------------------------------------------------
thf(a_holds_type,type,
a_holds: mu > $i > $o ).
thf(a_stored_type,type,
a_stored: mu > $i > $o ).
thf(fresh_to_b_type,type,
fresh_to_b: mu > $i > $o ).
thf(b_holds_type,type,
b_holds: mu > $i > $o ).
thf(b_stored_type,type,
b_stored: mu > $i > $o ).
thf(party_of_protocol_type,type,
party_of_protocol: mu > $i > $o ).
thf(t_holds_type,type,
t_holds: mu > $i > $o ).
thf(message_type,type,
message: mu > $i > $o ).
thf(an_a_nonce_type,type,
an_a_nonce: mu ).
thf(existence_of_an_a_nonce_ax,axiom,
! [V: $i] : ( exists_in_world @ an_a_nonce @ V ) ).
thf(generate_b_nonce_type,type,
generate_b_nonce: mu > mu ).
thf(existence_of_generate_b_nonce_ax,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( generate_b_nonce @ V1 ) @ V ) ).
thf(generate_expiration_time_type,type,
generate_expiration_time: mu > mu ).
thf(existence_of_generate_expiration_time_ax,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( generate_expiration_time @ V1 ) @ V ) ).
thf(pair_type,type,
pair: mu > mu > mu ).
thf(existence_of_pair_ax,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( pair @ V2 @ V1 ) @ V ) ).
thf(a_type,type,
a: mu ).
thf(existence_of_a_ax,axiom,
! [V: $i] : ( exists_in_world @ a @ V ) ).
thf(at_type,type,
at: mu ).
thf(existence_of_at_ax,axiom,
! [V: $i] : ( exists_in_world @ at @ V ) ).
thf(b_type,type,
b: mu ).
thf(existence_of_b_ax,axiom,
! [V: $i] : ( exists_in_world @ b @ V ) ).
thf(bt_type,type,
bt: mu ).
thf(existence_of_bt_ax,axiom,
! [V: $i] : ( exists_in_world @ bt @ V ) ).
thf(generate_key_type,type,
generate_key: mu > mu ).
thf(existence_of_generate_key_ax,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( generate_key @ V1 ) @ V ) ).
thf(quadruple_type,type,
quadruple: mu > mu > mu > mu > mu ).
thf(existence_of_quadruple_ax,axiom,
! [V: $i,V4: mu,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( quadruple @ V4 @ V3 @ V2 @ V1 ) @ V ) ).
thf(key_type,type,
key: mu > mu > mu ).
thf(existence_of_key_ax,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( key @ V2 @ V1 ) @ V ) ).
thf(encrypt_type,type,
encrypt: mu > mu > mu ).
thf(existence_of_encrypt_ax,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( encrypt @ V2 @ V1 ) @ V ) ).
thf(triple_type,type,
triple: mu > mu > mu > mu ).
thf(existence_of_triple_ax,axiom,
! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( triple @ V3 @ V2 @ V1 ) @ V ) ).
thf(t_type,type,
t: mu ).
thf(existence_of_t_ax,axiom,
! [V: $i] : ( exists_in_world @ t @ V ) ).
thf(sent_type,type,
sent: mu > mu > mu > mu ).
thf(existence_of_sent_ax,axiom,
! [V: $i,V3: mu,V2: mu,V1: mu] : ( exists_in_world @ ( sent @ V3 @ V2 @ V1 ) @ V ) ).
thf(a_holds_key_at_for_t,axiom,
mvalid @ ( mbox_s4 @ ( a_holds @ ( key @ at @ t ) ) ) ).
thf(a_is_party_of_protocol,axiom,
mvalid @ ( mbox_s4 @ ( party_of_protocol @ a ) ) ).
thf(a_sent_message_i_to_b,axiom,
mvalid @ ( mbox_s4 @ ( message @ ( sent @ a @ b @ ( pair @ a @ an_a_nonce ) ) ) ) ).
thf(a_stored_message_i,axiom,
mvalid @ ( mbox_s4 @ ( a_stored @ ( pair @ b @ an_a_nonce ) ) ) ).
thf(a_forwards_secure,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [U: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [V: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ Y @ Z @ W @ V ) @ at ) @ X @ U ) ) ) ) @ ( mbox_s4 @ ( a_stored @ ( pair @ Y @ Z ) ) ) ) @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ a @ Y @ ( pair @ X @ ( encrypt @ U @ W ) ) ) ) ) @ ( mbox_s4 @ ( a_holds @ ( key @ W @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(b_hold_key_bt_for_t,axiom,
mvalid @ ( mbox_s4 @ ( b_holds @ ( key @ bt @ t ) ) ) ).
thf(b_is_party_of_protocol,axiom,
mvalid @ ( mbox_s4 @ ( party_of_protocol @ b ) ) ).
thf(nonce_a_is_fresh_to_b,axiom,
mvalid @ ( mbox_s4 @ ( fresh_to_b @ an_a_nonce ) ) ).
thf(b_creates_freash_nonces_in_time,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [U: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [V: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ U @ b @ ( pair @ U @ V ) ) ) ) @ ( mbox_s4 @ ( fresh_to_b @ V ) ) ) @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ V ) @ ( encrypt @ ( triple @ U @ V @ ( generate_expiration_time @ V ) ) @ bt ) ) ) ) ) @ ( mbox_s4 @ ( b_stored @ ( pair @ U @ V ) ) ) ) ) ) ) ) ) ) ) ).
thf(b_accepts_secure_session_key,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [V: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ X @ b @ ( pair @ ( encrypt @ ( triple @ X @ V @ ( generate_expiration_time @ Y ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ Y ) @ V ) ) ) ) ) @ ( mbox_s4 @ ( b_stored @ ( pair @ X @ Y ) ) ) ) @ ( mbox_s4 @ ( b_holds @ ( key @ V @ X ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(t_holds_key_at_for_a,axiom,
mvalid @ ( mbox_s4 @ ( t_holds @ ( key @ at @ a ) ) ) ).
thf(t_holds_key_bt_for_b,axiom,
mvalid @ ( mbox_s4 @ ( t_holds @ ( key @ bt @ b ) ) ) ).
thf(t_is_party_of_protocol,axiom,
mvalid @ ( mbox_s4 @ ( party_of_protocol @ t ) ) ).
thf(server_t_generates_key,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [U: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [V: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [W: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Z: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( message @ ( sent @ U @ t @ ( triple @ U @ V @ ( encrypt @ ( triple @ W @ X @ Y ) @ Z ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( t_holds @ ( key @ Z @ U ) ) ) @ ( mbox_s4 @ ( t_holds @ ( key @ X1 @ W ) ) ) ) ) @ ( mbox_s4 @ ( message @ ( sent @ t @ W @ ( triple @ ( encrypt @ ( quadruple @ U @ X @ ( generate_key @ X ) @ Y ) @ X1 ) @ ( encrypt @ ( triple @ W @ ( generate_key @ X ) @ Y ) @ Z ) @ V ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------