%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV237+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 : Thu Aug 31 21:37:09 EDT 2023

% Result   : Theorem 0.19s 0.61s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   42 (  14 unt;  15 typ;   0 def)
%            Number of atoms       :   57 (   6 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   56 (  26   ~;  24   |;   4   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  12 con; 0-2 aty)
%            Number of variables   :   39 (   4 sgn;  18   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    i: $i > $i ).

tff(decl_23,type,
    enc: ( $i * $i ) > $i ).

tff(decl_24,type,
    p: $i > $o ).

tff(decl_25,type,
    tmk: $i ).

tff(decl_26,type,
    zcmk: $i ).

tff(decl_27,type,
    wk: $i ).

tff(decl_28,type,
    tc: $i ).

tff(decl_29,type,
    lp: $i ).

tff(decl_30,type,
    pp: $i ).

tff(decl_31,type,
    w: $i ).

tff(decl_32,type,
    t1: $i ).

tff(decl_33,type,
    t2: $i ).

tff(decl_34,type,
    k: $i ).

tff(decl_35,type,
    kk: $i ).

tff(decl_36,type,
    a: $i ).

fof(encrypt_a_stored_comms_key,axiom,
    ! [X1,X2,X3] :
      ( ( p(X1)
        & p(X2)
        & p(X3) )
     => p(enc(enc(i(tmk),X2),enc(i(tc),X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_a_stored_comms_key) ).

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

fof(dec_enc_cancel,axiom,
    ! [X1,X2] : enc(X1,enc(i(X1),X2)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dec_enc_cancel) ).

fof(double_inverse_cancel,axiom,
    ! [X1] : i(i(X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',double_inverse_cancel) ).

fof(encrypt_clear_key_as_Tcomms_key,axiom,
    ! [X1,X2,X3] :
      ( ( p(X1)
        & p(X2)
        & p(X3) )
     => p(enc(tc,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_clear_key_as_Tcomms_key) ).

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

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

fof(c_0_7,plain,
    ! [X22,X23,X24] :
      ( ~ p(X22)
      | ~ p(X23)
      | ~ p(X24)
      | p(enc(enc(i(tmk),X23),enc(i(tc),X22))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[encrypt_a_stored_comms_key])]) ).

cnf(c_0_8,plain,
    ( p(enc(enc(i(tmk),X2),enc(i(tc),X1)))
    | ~ p(X1)
    | ~ p(X2)
    | ~ p(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_9,plain,
    p(a),
    inference(split_conjunct,[status(thm)],[intruder_knows_8]) ).

fof(c_0_10,plain,
    ! [X6,X7] : enc(X6,enc(i(X6),X7)) = X7,
    inference(variable_rename,[status(thm)],[dec_enc_cancel]) ).

fof(c_0_11,plain,
    ! [X8] : i(i(X8)) = X8,
    inference(variable_rename,[status(thm)],[double_inverse_cancel]) ).

fof(c_0_12,plain,
    ! [X25,X26,X27] :
      ( ~ p(X25)
      | ~ p(X26)
      | ~ p(X27)
      | p(enc(tc,X25)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[encrypt_clear_key_as_Tcomms_key])]) ).

cnf(c_0_13,plain,
    ( p(enc(enc(i(tmk),X1),enc(i(tc),X2)))
    | ~ p(X1)
    | ~ p(X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_14,plain,
    enc(X1,enc(i(X1),X2)) = X2,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    i(i(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    ( p(enc(tc,X1))
    | ~ p(X1)
    | ~ p(X2)
    | ~ p(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( p(enc(enc(i(tmk),X1),X2))
    | ~ p(enc(tc,X2))
    | ~ p(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

cnf(c_0_18,plain,
    ( p(enc(tc,X1))
    | ~ p(X2)
    | ~ p(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_9]) ).

cnf(c_0_19,plain,
    ( p(enc(X1,X2))
    | ~ p(enc(tc,X2))
    | ~ p(enc(tmk,X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]) ).

cnf(c_0_20,plain,
    ( p(enc(tc,X1))
    | ~ p(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_9]) ).

fof(c_0_21,negated_conjecture,
    ~ p(enc(pp,a)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

cnf(c_0_22,plain,
    ( p(enc(X1,X2))
    | ~ p(enc(tmk,X1))
    | ~ p(X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,plain,
    p(enc(tmk,pp)),
    inference(split_conjunct,[status(thm)],[intruder_knows_1]) ).

cnf(c_0_24,negated_conjecture,
    ~ p(enc(pp,a)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_25,plain,
    ( p(enc(pp,X1))
    | ~ p(X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_9])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV237+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 29 09:56:25 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.61  % Version  : CSE_E---1.5
% 0.19/0.61  % Problem  : theBenchmark.p
% 0.19/0.61  % Proof found
% 0.19/0.61  % SZS status Theorem for theBenchmark.p
% 0.19/0.61  % SZS output start Proof
% See solution above
% 0.19/0.62  % Total time : 0.044000 s
% 0.19/0.62  % SZS output end Proof
% 0.19/0.62  % Total time : 0.046000 s
%------------------------------------------------------------------------------