TSTP Solution File: SWV236+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV236+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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 : Fri May 19 12:14:24 EDT 2023

% Result   : Theorem 3.47s 1.83s
% Output   : Refutation 3.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   72 (  31 unt;  14 typ;   0 def)
%            Number of atoms       :  119 (  10 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  463 (   2   ~;   0   |;  37   &; 400   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;  11 con; 0-2 aty)
%            Number of variables   :   89 (   0   ^;  86   !;   3   ?;  89   :)

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

thf(crypt_type,type,
    crypt: $i > $i > $i ).

thf(xor_type,type,
    xor: $i > $i > $i ).

thf(km_type,type,
    km: $i ).

thf(exp_type,type,
    exp: $i ).

thf(data_type,type,
    data: $i ).

thf(decrypt_type,type,
    decrypt: $i > $i > $i ).

thf(imp_type,type,
    imp: $i ).

thf(kp_type,type,
    kp: $i ).

thf(eurk_type,type,
    eurk: $i ).

thf(id_type,type,
    id: $i ).

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

thf(pin_type,type,
    pin: $i ).

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

thf(22,axiom,
    p @ ( crypt @ ( xor @ km @ data ) @ eurk ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_8) ).

thf(69,plain,
    p @ ( crypt @ ( xor @ km @ data ) @ eurk ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ data ) @ B ) ) )
     => ( p @ ( crypt @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_data) ).

thf(56,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ data ) @ B ) ) )
     => ( p @ ( crypt @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( p @ ( crypt @ ( xor @ A @ data ) @ B ) )
     => ( p @ ( crypt @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_cv_is_known_to_be_zero) ).

thf(42,plain,
    ! [A: $i,B: $i] :
      ( ( p @ ( crypt @ ( xor @ A @ data ) @ B ) )
     => ( p @ ( crypt @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( decrypt @ A @ ( crypt @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',encryption_decryption_cancellation) ).

thf(52,plain,
    ! [A: $i,B: $i] :
      ( ( decrypt @ A @ ( crypt @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(17,axiom,
    p @ ( crypt @ ( xor @ km @ exp ) @ eurk ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_7) ).

thf(60,plain,
    p @ ( crypt @ ( xor @ km @ exp ) @ eurk ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( xor @ A @ ( xor @ B @ C ) )
      = ( xor @ ( xor @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_associative) ).

thf(65,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( xor @ A @ ( xor @ B @ C ) )
      = ( xor @ ( xor @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( xor @ A @ A )
      = id ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_rules_2) ).

thf(77,plain,
    ! [A: $i] :
      ( ( xor @ A @ A )
      = id ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(26,axiom,
    p @ ( crypt @ ( xor @ km @ pin ) @ pp ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_6) ).

thf(73,plain,
    p @ ( crypt @ ( xor @ km @ pin ) @ pp ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(3,axiom,
    p @ exp,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_9) ).

thf(32,plain,
    p @ exp,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( p @ ( crypt @ A @ B ) )
        & ( p @ C )
        & ( p @ ( crypt @ ( xor @ km @ imp ) @ D ) )
        & ( p @ ( crypt @ ( xor @ km @ exp ) @ E ) ) )
     => ( p @ ( crypt @ ( xor @ E @ F ) @ ( decrypt @ ( xor @ C @ D ) @ ( crypt @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_translate) ).

thf(44,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( p @ ( crypt @ A @ B ) )
        & ( p @ C )
        & ( p @ ( crypt @ ( xor @ km @ imp ) @ D ) )
        & ( p @ ( crypt @ ( xor @ km @ exp ) @ E ) ) )
     => ( p @ ( crypt @ ( xor @ E @ F ) @ ( decrypt @ ( xor @ C @ D ) @ ( crypt @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(24,axiom,
    p @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_account_number) ).

thf(71,plain,
    p @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ B )
        & ( p @ A ) )
     => ( p @ ( crypt @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_knowledge) ).

thf(50,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ B )
        & ( p @ A ) )
     => ( p @ ( crypt @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(25,axiom,
    p @ pin,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_5) ).

thf(72,plain,
    p @ pin,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ ( crypt @ ( xor @ km @ A ) @ B ) )
        & ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ exp ) @ C ) ) )
     => ( p @ ( crypt @ ( xor @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_export) ).

thf(58,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ ( crypt @ ( xor @ km @ A ) @ B ) )
        & ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ exp ) @ C ) ) )
     => ( p @ ( crypt @ ( xor @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(1,conjecture,
    ? [A: $i] :
      ( ( p @ ( crypt @ ( xor @ km @ exp ) @ A ) )
      & ( p @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',find_known_exporter) ).

thf(2,negated_conjecture,
    ~ ? [A: $i] :
        ( ( p @ ( crypt @ ( xor @ km @ exp ) @ A ) )
        & ( p @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(30,plain,
    ~ ? [A: $i] :
        ( ( p @ ( crypt @ ( xor @ km @ exp ) @ A ) )
        & ( p @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ A )
        & ( p @ B ) )
     => ( p @ ( xor @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',combine_with_XOR) ).

thf(61,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ A )
        & ( p @ B ) )
     => ( p @ ( xor @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( xor @ A @ id )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_rules_1) ).

thf(74,plain,
    ! [A: $i] :
      ( ( xor @ A @ id )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ data ) @ B ) ) )
     => ( p @ ( decrypt @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_data) ).

thf(38,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ data ) @ B ) ) )
     => ( p @ ( decrypt @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(23,axiom,
    p @ imp,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_2) ).

thf(70,plain,
    p @ imp,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( crypt @ A @ B ) )
        & ( p @ A ) )
     => ( p @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_knowledge) ).

thf(33,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ ( crypt @ A @ B ) )
        & ( p @ A ) )
     => ( p @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ( ( p @ A )
        & ( p @ B ) )
     => ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_1) ).

thf(80,plain,
    ! [A: $i,B: $i] :
      ( ( ( p @ A )
        & ( p @ B ) )
     => ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( xor @ A @ B )
      = ( xor @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutative) ).

thf(35,plain,
    ! [A: $i,B: $i] :
      ( ( xor @ A @ B )
      = ( xor @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ ( xor @ B @ kp ) ) @ C ) )
        & ( p @ B ) )
     => ( p @ ( crypt @ ( xor @ km @ B ) @ ( xor @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_3) ).

thf(48,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ ( xor @ B @ kp ) ) @ C ) )
        & ( p @ B ) )
     => ( p @ ( crypt @ ( xor @ km @ B ) @ ( xor @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ B ) ) @ C ) )
        & ( p @ B ) )
     => ( p @ ( crypt @ ( xor @ km @ ( xor @ B @ kp ) ) @ ( xor @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_2) ).

thf(63,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( p @ A )
        & ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ B ) ) @ C ) )
        & ( p @ B ) )
     => ( p @ ( crypt @ ( xor @ km @ ( xor @ B @ kp ) ) @ ( xor @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( p @ ( crypt @ ( xor @ A @ B ) @ C ) )
        & ( p @ D )
        & ( p @ ( crypt @ ( xor @ km @ imp ) @ E ) ) )
     => ( p @ ( crypt @ ( xor @ km @ D ) @ ( decrypt @ ( xor @ E @ D ) @ ( crypt @ ( xor @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_import) ).

thf(40,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( p @ ( crypt @ ( xor @ A @ B ) @ C ) )
        & ( p @ D )
        & ( p @ ( crypt @ ( xor @ km @ imp ) @ E ) ) )
     => ( p @ ( crypt @ ( xor @ km @ D ) @ ( decrypt @ ( xor @ E @ D ) @ ( crypt @ ( xor @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(14,axiom,
    p @ data,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_3) ).

thf(55,plain,
    p @ data,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(10,axiom,
    p @ kp,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_1) ).

thf(47,plain,
    p @ kp,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(21,axiom,
    p @ id,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_4) ).

thf(68,plain,
    p @ id,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(82,plain,
    $false,
    inference(e,[status(thm)],[69,56,42,52,60,65,77,73,32,44,71,50,72,58,30,61,74,38,70,33,80,35,48,63,40,55,47,68]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SWV236+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri May 19 02:34:23 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.93/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/1.01  % [INFO] 	 Parsing done (138ms). 
% 1.29/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.65/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.65/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.94/1.28  % [INFO] 	 Found a conjecture and 27 axioms. Running axiom selection ... 
% 1.94/1.32  % [INFO] 	 Axiom selection finished. Selected 27 axioms (removed 0 axioms). 
% 2.19/1.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.19/1.36  % [INFO] 	 Type checking passed. 
% 2.19/1.37  % [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 ... 
% 3.47/1.83  % External prover 'e' found a proof!
% 3.47/1.83  % [INFO] 	 Killing All external provers ... 
% 3.47/1.83  % Time passed: 1319ms (effective reasoning time: 813ms)
% 3.47/1.83  % 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)>
% 3.47/1.83  % Axioms used in derivation (27): initial_knowledge_of_intruder_1, key_import, encrypt_data, xor_associative, initial_knowledge_of_intruder_7, key_part_import___part_2, data_cv_is_known_to_be_zero, initial_knowledge_of_intruder_6, key_export, decrypt_knowledge, encryption_decryption_cancellation, initial_knowledge_of_intruder_9, initial_knowledge_of_intruder_4, key_translate, encrypt_knowledge, initial_knowledge_of_intruder_8, key_part_import___part_3, xor_rules_2, an_account_number, combine_with_XOR, xor_rules_1, initial_knowledge_of_intruder_2, xor_commutative, initial_knowledge_of_intruder_3, key_part_import___part_1, decrypt_data, initial_knowledge_of_intruder_5
% 3.47/1.83  % No. of inferences in proof: 58
% 3.47/1.83  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1319 ms resp. 813 ms w/o parsing
% 3.92/1.95  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.92/1.95  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------