TSTP Solution File: SWW957+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWW957+1 : TPTP v8.1.2. Released v7.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 Apr 30 20:50:56 EDT 2024

% Result   : Theorem 7.41s 1.35s
% Output   : CNFRefutation 7.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   83 (  34 unt;   0 def)
%            Number of atoms       :  138 (  22 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  100 (  45   ~;  44   |;   1   &)
%                                         (   3 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-2 aty)
%            Number of variables   :   85 (  85   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f46,axiom,
    ! [VAR_X_14,VAR_Y_15] : constr_split(constr_concat(VAR_X_14,VAR_Y_15)) = tuple_2(VAR_X_14,VAR_Y_15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f47,axiom,
    ! [VAR_X1_0X30,VAR_X2_0X30,VAR_Y1_0X30,VAR_Y2_0X30] : constr_xor(constr_concat(VAR_X1_0X30,VAR_Y1_0X30),constr_concat(VAR_X2_0X30,VAR_Y2_0X30)) = constr_concat(constr_xor(VAR_X1_0X30,VAR_X2_0X30),constr_xor(VAR_Y1_0X30,VAR_Y2_0X30)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f48,axiom,
    ! [VAR_X_12,VAR_Y_13] : constr_C(constr_xor(VAR_X_12,VAR_Y_13)) = constr_xor(constr_C(VAR_X_12),constr_C(VAR_Y_13)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f49,axiom,
    ! [VAR_X_11] : constr_xor(VAR_X_11,VAR_X_11) = constr_ZERO,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f50,axiom,
    ! [VAR_X_10X30] : constr_xor(VAR_X_10X30,constr_ZERO) = VAR_X_10X30,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f51,axiom,
    ! [VAR_X_8,VAR_Y_9] : constr_xor(VAR_X_8,VAR_Y_9) = constr_xor(VAR_Y_9,VAR_X_8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f52,axiom,
    ! [VAR_X_0X30,VAR_Y_0X30,VAR_Z_0X30] : constr_xor(VAR_X_0X30,constr_xor(VAR_Y_0X30,VAR_Z_0X30)) = constr_xor(constr_xor(VAR_X_0X30,VAR_Y_0X30),VAR_Z_0X30),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f53,axiom,
    ! [VAR_V_31,VAR_V_32] :
      ( ( pred_attacker(VAR_V_31)
        & pred_attacker(VAR_V_32) )
     => pred_attacker(constr_xor(VAR_V_31,VAR_V_32)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f55,axiom,
    ! [VAR_V_34] :
      ( pred_attacker(VAR_V_34)
     => pred_attacker(constr_split(VAR_V_34)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f59,axiom,
    ! [VAR_V_49,VAR_V_50X30] :
      ( pred_attacker(tuple_enc_oracle_out_2(VAR_V_49,VAR_V_50X30))
     => pred_attacker(VAR_V_50X30) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f60,axiom,
    ! [VAR_V_53] :
      ( pred_attacker(VAR_V_53)
     => pred_attacker(tuple_enc_oracle_in_1(VAR_V_53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f63,axiom,
    pred_attacker(constr_ZERO),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f73,axiom,
    ! [VAR_V_81,VAR_V_82] :
      ( pred_attacker(tuple_B_out_1(VAR_V_81,VAR_V_82))
     => pred_attacker(VAR_V_82) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f75,axiom,
    ! [VAR_V_98,VAR_V_99] :
      ( pred_attacker(tuple_2(VAR_V_98,VAR_V_99))
     => pred_attacker(VAR_V_98) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f82,axiom,
    ! [VAR_M_150X30] :
      ( pred_attacker(tuple_enc_oracle_in_1(VAR_M_150X30))
     => pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(VAR_M_150X30,constr_C(VAR_M_150X30)),constr_RC4(name_v,name_Kab)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f83,axiom,
    pred_attacker(tuple_B_out_1(name_v,constr_xor(constr_concat(name_objective,constr_C(name_objective)),constr_RC4(name_v,name_Kab)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f84,conjecture,
    pred_attacker(name_objective),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f85,negated_conjecture,
    ~ pred_attacker(name_objective),
    inference(negated_conjecture,[status(cth)],[f84]) ).

fof(f131,plain,
    ! [X0,X1] : constr_split(constr_concat(X0,X1)) = tuple_2(X0,X1),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f132,plain,
    ! [X0,X1,X2,X3] : constr_xor(constr_concat(X0,X1),constr_concat(X2,X3)) = constr_concat(constr_xor(X0,X2),constr_xor(X1,X3)),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f133,plain,
    ! [X0,X1] : constr_C(constr_xor(X0,X1)) = constr_xor(constr_C(X0),constr_C(X1)),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f134,plain,
    ! [X0] : constr_xor(X0,X0) = constr_ZERO,
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f135,plain,
    ! [X0] : constr_xor(X0,constr_ZERO) = X0,
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f136,plain,
    ! [X0,X1] : constr_xor(X0,X1) = constr_xor(X1,X0),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f137,plain,
    ! [X0,X1,X2] : constr_xor(X0,constr_xor(X1,X2)) = constr_xor(constr_xor(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f138,plain,
    ! [VAR_V_31,VAR_V_32] :
      ( ~ pred_attacker(VAR_V_31)
      | ~ pred_attacker(VAR_V_32)
      | pred_attacker(constr_xor(VAR_V_31,VAR_V_32)) ),
    inference(pre_NNF_transformation,[status(esa)],[f53]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ~ pred_attacker(X0)
      | ~ pred_attacker(X1)
      | pred_attacker(constr_xor(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f138]) ).

fof(f141,plain,
    ! [VAR_V_34] :
      ( ~ pred_attacker(VAR_V_34)
      | pred_attacker(constr_split(VAR_V_34)) ),
    inference(pre_NNF_transformation,[status(esa)],[f55]) ).

fof(f142,plain,
    ! [X0] :
      ( ~ pred_attacker(X0)
      | pred_attacker(constr_split(X0)) ),
    inference(cnf_transformation,[status(esa)],[f141]) ).

fof(f149,plain,
    ! [VAR_V_49,VAR_V_50X30] :
      ( ~ pred_attacker(tuple_enc_oracle_out_2(VAR_V_49,VAR_V_50X30))
      | pred_attacker(VAR_V_50X30) ),
    inference(pre_NNF_transformation,[status(esa)],[f59]) ).

fof(f150,plain,
    ! [VAR_V_50X30] :
      ( ! [VAR_V_49] : ~ pred_attacker(tuple_enc_oracle_out_2(VAR_V_49,VAR_V_50X30))
      | pred_attacker(VAR_V_50X30) ),
    inference(miniscoping,[status(esa)],[f149]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( ~ pred_attacker(tuple_enc_oracle_out_2(X0,X1))
      | pred_attacker(X1) ),
    inference(cnf_transformation,[status(esa)],[f150]) ).

fof(f152,plain,
    ! [VAR_V_53] :
      ( ~ pred_attacker(VAR_V_53)
      | pred_attacker(tuple_enc_oracle_in_1(VAR_V_53)) ),
    inference(pre_NNF_transformation,[status(esa)],[f60]) ).

fof(f153,plain,
    ! [X0] :
      ( ~ pred_attacker(X0)
      | pred_attacker(tuple_enc_oracle_in_1(X0)) ),
    inference(cnf_transformation,[status(esa)],[f152]) ).

fof(f158,plain,
    pred_attacker(constr_ZERO),
    inference(cnf_transformation,[status(esa)],[f63]) ).

fof(f173,plain,
    ! [VAR_V_81,VAR_V_82] :
      ( ~ pred_attacker(tuple_B_out_1(VAR_V_81,VAR_V_82))
      | pred_attacker(VAR_V_82) ),
    inference(pre_NNF_transformation,[status(esa)],[f73]) ).

fof(f174,plain,
    ! [VAR_V_82] :
      ( ! [VAR_V_81] : ~ pred_attacker(tuple_B_out_1(VAR_V_81,VAR_V_82))
      | pred_attacker(VAR_V_82) ),
    inference(miniscoping,[status(esa)],[f173]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( ~ pred_attacker(tuple_B_out_1(X0,X1))
      | pred_attacker(X1) ),
    inference(cnf_transformation,[status(esa)],[f174]) ).

fof(f178,plain,
    ! [VAR_V_98,VAR_V_99] :
      ( ~ pred_attacker(tuple_2(VAR_V_98,VAR_V_99))
      | pred_attacker(VAR_V_98) ),
    inference(pre_NNF_transformation,[status(esa)],[f75]) ).

fof(f179,plain,
    ! [VAR_V_98] :
      ( ! [VAR_V_99] : ~ pred_attacker(tuple_2(VAR_V_98,VAR_V_99))
      | pred_attacker(VAR_V_98) ),
    inference(miniscoping,[status(esa)],[f178]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( ~ pred_attacker(tuple_2(X0,X1))
      | pred_attacker(X0) ),
    inference(cnf_transformation,[status(esa)],[f179]) ).

fof(f192,plain,
    ! [VAR_M_150X30] :
      ( ~ pred_attacker(tuple_enc_oracle_in_1(VAR_M_150X30))
      | pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(VAR_M_150X30,constr_C(VAR_M_150X30)),constr_RC4(name_v,name_Kab)))) ),
    inference(pre_NNF_transformation,[status(esa)],[f82]) ).

fof(f193,plain,
    ! [X0] :
      ( ~ pred_attacker(tuple_enc_oracle_in_1(X0))
      | pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X0,constr_C(X0)),constr_RC4(name_v,name_Kab)))) ),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f194,plain,
    pred_attacker(tuple_B_out_1(name_v,constr_xor(constr_concat(name_objective,constr_C(name_objective)),constr_RC4(name_v,name_Kab)))),
    inference(cnf_transformation,[status(esa)],[f83]) ).

fof(f195,plain,
    ~ pred_attacker(name_objective),
    inference(cnf_transformation,[status(esa)],[f85]) ).

fof(f196,plain,
    ! [X0,X1] : constr_concat(constr_xor(X0,X0),constr_xor(X1,X1)) = constr_ZERO,
    inference(paramodulation,[status(thm)],[f132,f134]) ).

fof(f197,plain,
    ! [X0] : constr_concat(constr_ZERO,constr_xor(X0,X0)) = constr_ZERO,
    inference(forward_demodulation,[status(thm)],[f134,f196]) ).

fof(f198,plain,
    constr_concat(constr_ZERO,constr_ZERO) = constr_ZERO,
    inference(forward_demodulation,[status(thm)],[f134,f197]) ).

fof(f204,plain,
    ! [X0] : X0 = constr_xor(constr_ZERO,X0),
    inference(paramodulation,[status(thm)],[f135,f136]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( ~ pred_attacker(constr_concat(X0,X1))
      | pred_attacker(tuple_2(X0,X1)) ),
    inference(paramodulation,[status(thm)],[f131,f142]) ).

fof(f223,plain,
    ! [X0] : constr_C(constr_xor(X0,X0)) = constr_ZERO,
    inference(paramodulation,[status(thm)],[f134,f133]) ).

fof(f224,plain,
    constr_C(constr_ZERO) = constr_ZERO,
    inference(forward_demodulation,[status(thm)],[f134,f223]) ).

fof(f246,plain,
    ! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = constr_xor(constr_ZERO,X1),
    inference(paramodulation,[status(thm)],[f134,f137]) ).

fof(f247,plain,
    ! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = X1,
    inference(forward_demodulation,[status(thm)],[f204,f246]) ).

fof(f254,plain,
    ( spl0_0
  <=> pred_attacker(constr_ZERO) ),
    introduced(split_symbol_definition) ).

fof(f256,plain,
    ( ~ pred_attacker(constr_ZERO)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f254]) ).

fof(f304,plain,
    ! [X0,X1] :
      ( ~ pred_attacker(X0)
      | ~ pred_attacker(constr_xor(X0,X1))
      | pred_attacker(X1) ),
    inference(paramodulation,[status(thm)],[f247,f139]) ).

fof(f359,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f256,f158]) ).

fof(f360,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f359]) ).

fof(f431,plain,
    ! [X0] :
      ( ~ pred_attacker(tuple_enc_oracle_in_1(X0))
      | pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(X0,constr_C(X0))))) ),
    inference(forward_demodulation,[status(thm)],[f136,f193]) ).

fof(f432,plain,
    ! [X0] :
      ( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(X0,constr_C(X0)))))
      | ~ pred_attacker(X0) ),
    inference(resolution,[status(thm)],[f431,f153]) ).

fof(f434,plain,
    pred_attacker(tuple_B_out_1(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(name_objective,constr_C(name_objective))))),
    inference(forward_demodulation,[status(thm)],[f136,f194]) ).

fof(f435,plain,
    pred_attacker(constr_xor(constr_RC4(name_v,name_Kab),constr_concat(name_objective,constr_C(name_objective)))),
    inference(resolution,[status(thm)],[f434,f175]) ).

fof(f6861,plain,
    ( spl0_94
  <=> pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(constr_ZERO,constr_ZERO)))) ),
    introduced(split_symbol_definition) ).

fof(f6862,plain,
    ( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(constr_ZERO,constr_ZERO))))
    | ~ spl0_94 ),
    inference(component_clause,[status(thm)],[f6861]) ).

fof(f6864,plain,
    ( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(constr_ZERO,constr_ZERO))))
    | ~ pred_attacker(constr_ZERO) ),
    inference(paramodulation,[status(thm)],[f224,f432]) ).

fof(f6865,plain,
    ( spl0_94
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f6864,f6861,f254]) ).

fof(f6866,plain,
    ( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(constr_ZERO,constr_ZERO),constr_RC4(name_v,name_Kab))))
    | ~ spl0_94 ),
    inference(forward_demodulation,[status(thm)],[f136,f6862]) ).

fof(f6867,plain,
    ( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_ZERO,constr_RC4(name_v,name_Kab))))
    | ~ spl0_94 ),
    inference(forward_demodulation,[status(thm)],[f198,f6866]) ).

fof(f6868,plain,
    ( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_RC4(name_v,name_Kab)))
    | ~ spl0_94 ),
    inference(forward_demodulation,[status(thm)],[f204,f6867]) ).

fof(f7285,plain,
    ( pred_attacker(constr_RC4(name_v,name_Kab))
    | ~ spl0_94 ),
    inference(resolution,[status(thm)],[f6868,f151]) ).

fof(f8166,plain,
    ( spl0_103
  <=> pred_attacker(constr_concat(name_objective,constr_C(name_objective))) ),
    introduced(split_symbol_definition) ).

fof(f8167,plain,
    ( pred_attacker(constr_concat(name_objective,constr_C(name_objective)))
    | ~ spl0_103 ),
    inference(component_clause,[status(thm)],[f8166]) ).

fof(f8168,plain,
    ( ~ pred_attacker(constr_concat(name_objective,constr_C(name_objective)))
    | spl0_103 ),
    inference(component_clause,[status(thm)],[f8166]) ).

fof(f8972,plain,
    ! [X0] :
      ( ~ pred_attacker(X0)
      | ~ pred_attacker(constr_xor(X0,constr_concat(name_objective,constr_C(name_objective))))
      | spl0_103 ),
    inference(resolution,[status(thm)],[f8168,f304]) ).

fof(f9057,plain,
    ( ~ pred_attacker(constr_RC4(name_v,name_Kab))
    | spl0_103 ),
    inference(resolution,[status(thm)],[f8972,f435]) ).

fof(f9058,plain,
    ( $false
    | ~ spl0_94
    | spl0_103 ),
    inference(forward_subsumption_resolution,[status(thm)],[f9057,f7285]) ).

fof(f9059,plain,
    ( ~ spl0_94
    | spl0_103 ),
    inference(contradiction_clause,[status(thm)],[f9058]) ).

fof(f9061,plain,
    ( pred_attacker(tuple_2(name_objective,constr_C(name_objective)))
    | ~ spl0_103 ),
    inference(resolution,[status(thm)],[f8167,f218]) ).

fof(f9935,plain,
    ( pred_attacker(name_objective)
    | ~ spl0_103 ),
    inference(resolution,[status(thm)],[f9061,f180]) ).

fof(f9936,plain,
    ( $false
    | ~ spl0_103 ),
    inference(forward_subsumption_resolution,[status(thm)],[f9935,f195]) ).

fof(f9937,plain,
    ~ spl0_103,
    inference(contradiction_clause,[status(thm)],[f9936]) ).

fof(f9938,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f360,f6865,f9059,f9937]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWW957+1 : TPTP v8.1.2. Released v7.4.0.
% 0.12/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n002.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 : Mon Apr 29 23:30:54 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 7.41/1.35  % Refutation found
% 7.41/1.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 7.41/1.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.90/1.39  % Elapsed time: 1.019902 seconds
% 7.90/1.39  % CPU time: 7.969564 seconds
% 7.90/1.39  % Total memory used: 168.381 MB
% 7.90/1.39  % Net memory used: 152.720 MB
%------------------------------------------------------------------------------