TSTP Solution File: SWV237+1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : SWV237+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  7 08:16:45 EDT 2024

% Result   : Theorem 3.65s 1.86s
% Output   : Refutation 3.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   67 (  26 unt;  15 typ;   0 def)
%            Number of atoms       :  126 (   6 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  415 (   2   ~;   0   |;  48   &; 339   @)
%                                         (   0 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;  13 con; 0-2 aty)
%            Number of variables   :   84 (   0   ^  84   !;   0   ?;  84   :)

% Comments : 
%------------------------------------------------------------------------------
thf(p_type,type,
    p: $i > $o ).

thf(enc_type,type,
    enc: $i > $i > $i ).

thf(pp_type,type,
    pp: $i ).

thf(a_type,type,
    a: $i ).

thf(i_type,type,
    i: $i > $i ).

thf(tc_type,type,
    tc: $i ).

thf(wk_type,type,
    wk: $i ).

thf(tmk_type,type,
    tmk: $i ).

thf(zcmk_type,type,
    zcmk: $i ).

thf(k_type,type,
    k: $i ).

thf(kk_type,type,
    kk: $i ).

thf(lp_type,type,
    lp: $i ).

thf(w_type,type,
    w: $i ).

thf(t1_type,type,
    t1: $i ).

thf(t2_type,type,
    t2: $i ).

thf(21,axiom,
    p @ ( enc @ w @ t1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_knows_3) ).

thf(69,plain,
    p @ ( enc @ w @ t1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',receive_working_key_from_switch) ).

thf(52,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(19,axiom,
    p @ ( enc @ tmk @ pp ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_knows_1) ).

thf(65,plain,
    p @ ( enc @ tmk @ pp ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',data_decrypt) ).

thf(73,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(24,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ B ) ) @ ( enc @ ( i @ tmk ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_translate_from_TMK_to_ZCMK) ).

thf(76,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ B ) ) @ ( enc @ ( i @ tmk ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ tc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_clear_key_as_Tcomms_key) ).

thf(66,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ tc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ B ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_translate_from_ZCMK_to_TMK) ).

thf(48,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(4,axiom,
    p @ a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_knows_8) ).

thf(31,plain,
    p @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( p @ A )
     => ( p @ ( i @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',keys_are_symmetric) ).

thf(43,plain,
    ! [A: $i] :
      ( ( p @ A )
     => ( p @ ( i @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(15,axiom,
    p @ kk,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_knows_6) ).

thf(58,plain,
    p @ kk,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(12,axiom,
    p @ ( enc @ tc @ k ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_knows_5) ).

thf(51,plain,
    p @ ( enc @ tc @ k ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(25,axiom,
    p @ ( enc @ wk @ w ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_knows_2) ).

thf(79,plain,
    p @ ( enc @ wk @ w ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ wk ) @ C ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ B ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',data_translate_between_interchange_keys) ).

thf(62,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ wk ) @ C ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( enc @ A @ ( enc @ ( i @ A ) @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dec_enc_cancel) ).

thf(70,plain,
    ! [A: $i,B: $i] :
      ( ( enc @ A @ ( enc @ ( i @ A ) @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( i @ ( i @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',double_inverse_cancel) ).

thf(28,plain,
    ! [A: $i] :
      ( ( i @ ( i @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ wk ) @ C ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ B ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',data_translate_PIN_from_local_to_interchange_key) ).

thf(38,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ wk ) @ C ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ tc ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',data_encrypt) ).

thf(32,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ tc ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ tmk ) @ B ) @ ( enc @ ( i @ tc ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_a_stored_comms_key) ).

thf(45,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ tmk ) @ B ) @ ( enc @ ( i @ tc ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(18,axiom,
    p @ ( i @ kk ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_knows_7) ).

thf(64,plain,
    p @ ( i @ kk ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ wk ) @ B ) @ ( enc @ ( i @ lp ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',data_translate_PIN_from_local_storage_to_interchange_key) ).

thf(59,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ wk ) @ B ) @ ( enc @ ( i @ lp ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(1,conjecture,
    p @ ( enc @ pp @ a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

thf(2,negated_conjecture,
    ~ ( p @ ( enc @ pp @ a ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(27,plain,
    ~ ( p @ ( enc @ pp @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(26,axiom,
    p @ ( enc @ lp @ t2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_knows_4) ).

thf(80,plain,
    p @ ( enc @ lp @ t2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( enc @ ( i @ A ) @ ( enc @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',enc_dec_cancel) ).

thf(35,plain,
    ! [A: $i,B: $i] :
      ( ( enc @ ( i @ A ) @ ( enc @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',attacker_can_encrypt) ).

thf(40,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ tmk ) @ B ) @ ( enc @ ( i @ tmk ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_a_PIN_derivation_key_under_a_TMK) ).

thf(55,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ B )
        & ( p @ C ) )
     => ( p @ ( enc @ ( enc @ ( i @ tmk ) @ B ) @ ( enc @ ( i @ tmk ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(87,plain,
    $false,
    inference(e,[status(thm)],[69,52,65,73,76,66,48,31,43,58,51,79,62,70,28,38,32,45,64,59,27,80,35,40,55]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWV237+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n027.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 16:37:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.93/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.34/0.98  % [INFO] 	 Parsing done (119ms). 
% 1.34/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.73/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.73/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.73/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.26  % [INFO] 	 Found a conjecture and 24 axioms. Running axiom selection ... 
% 2.06/1.30  % [INFO] 	 Axiom selection finished. Selected 24 axioms (removed 0 axioms). 
% 2.22/1.34  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.22/1.35  % [INFO] 	 Type checking passed. 
% 2.22/1.35  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 3.65/1.86  % External prover 'e' found a proof!
% 3.65/1.86  % [INFO] 	 Killing All external provers ... 
% 3.65/1.86  % Time passed: 1325ms (effective reasoning time: 864ms)
% 3.65/1.86  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.65/1.86  % Axioms used in derivation (24): intruder_knows_3, receive_working_key_from_switch, data_translate_between_interchange_keys, key_translate_from_ZCMK_to_TMK, data_translate_PIN_from_local_storage_to_interchange_key, data_decrypt, intruder_knows_1, data_encrypt, key_translate_from_TMK_to_ZCMK, intruder_knows_7, intruder_knows_4, data_translate_PIN_from_local_to_interchange_key, keys_are_symmetric, dec_enc_cancel, intruder_knows_6, intruder_knows_8, encrypt_clear_key_as_Tcomms_key, intruder_knows_2, attacker_can_encrypt, double_inverse_cancel, encrypt_a_stored_comms_key, intruder_knows_5, enc_dec_cancel, encrypt_a_PIN_derivation_key_under_a_TMK
% 3.65/1.86  % No. of inferences in proof: 52
% 3.65/1.86  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1325 ms resp. 864 ms w/o parsing
% 3.81/1.90  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.81/1.90  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------