%--------------------------------------------------------------------------
% File     : SWW948+1 : TPTP v9.0.0. Released v7.4.0.
% Domain   : Software Verification
% Problem  : Attack on LAK06 protocol
% Version  : [LT19] axioms : Especial.
% English  : Attack demonstrates violation of aliveness property of tag
%          : guaranteed to reader.

% Refs     : [BO97]  Bull & Otway (1997), The Authentication Protocol
%          : [RS98]  Ryan & Schneider (1998), An Attack on a Recursive Auth
%          : [LT19]  Li & Tiu (2019), Combining ProVerif and Automated Theo
%          : [Li20]  Li (2020), Email to Geoff Sutcliffe
% Source   : [Li20]
% Names    : LAK06-tag-auth.p [LT20]

% Status   : Theorem
% Rating   : 0.55 v9.0.0, 0.58 v7.5.0, 0.66 v7.4.0
% Syntax   : Number of formulae    :  108 (  86 unt;   0 def)
%            Number of atoms       :  135 (  70 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   93 (  66   ~;   0   |;   5   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    8 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   0 prp; 1-2 aty)
%            Number of functors    :   24 (  24 usr;  14 con; 0-2 aty)
%            Number of variables   :   40 (  40   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Generated by a modified version of ProVerif used in the
%            ProVerif-ATP project [LT19].
%--------------------------------------------------------------------------
fof(ax0,axiom,
    constr_CONST_0x30 != constr_CONST_1 ).

fof(ax1,axiom,
    constr_CONST_0x30 != constr_CONST_2 ).

fof(ax2,axiom,
    constr_CONST_0x30 != constr_CONST_3 ).

fof(ax3,axiom,
    constr_CONST_0x30 != constr_CONST_4 ).

fof(ax4,axiom,
    constr_CONST_0x30 != constr_ZERO ).

fof(ax5,axiom,
    constr_CONST_0x30 != name_c ).

fof(ax6,axiom,
    constr_CONST_0x30 != name_k ).

fof(ax7,axiom,
    constr_CONST_0x30 != name_objective_R ).

fof(ax8,axiom,
    constr_CONST_0x30 != name_r0x30 ).

fof(ax9,axiom,
    constr_CONST_0x30 != name_r0x30_from_1st ).

fof(ax10,axiom,
    constr_CONST_0x30 != name_r1_from_1st ).

fof(ax11,axiom,
    constr_CONST_1 != constr_CONST_2 ).

fof(ax12,axiom,
    constr_CONST_1 != constr_CONST_3 ).

fof(ax13,axiom,
    constr_CONST_1 != constr_CONST_4 ).

fof(ax14,axiom,
    constr_CONST_1 != constr_ZERO ).

fof(ax15,axiom,
    constr_CONST_1 != name_c ).

fof(ax16,axiom,
    constr_CONST_1 != name_k ).

fof(ax17,axiom,
    constr_CONST_1 != name_objective_R ).

fof(ax18,axiom,
    constr_CONST_1 != name_r0x30 ).

fof(ax19,axiom,
    constr_CONST_1 != name_r0x30_from_1st ).

fof(ax20,axiom,
    constr_CONST_1 != name_r1_from_1st ).

fof(ax21,axiom,
    constr_CONST_2 != constr_CONST_3 ).

fof(ax22,axiom,
    constr_CONST_2 != constr_CONST_4 ).

fof(ax23,axiom,
    constr_CONST_2 != constr_ZERO ).

fof(ax24,axiom,
    constr_CONST_2 != name_c ).

fof(ax25,axiom,
    constr_CONST_2 != name_k ).

fof(ax26,axiom,
    constr_CONST_2 != name_objective_R ).

fof(ax27,axiom,
    constr_CONST_2 != name_r0x30 ).

fof(ax28,axiom,
    constr_CONST_2 != name_r0x30_from_1st ).

fof(ax29,axiom,
    constr_CONST_2 != name_r1_from_1st ).

fof(ax30,axiom,
    constr_CONST_3 != constr_CONST_4 ).

fof(ax31,axiom,
    constr_CONST_3 != constr_ZERO ).

fof(ax32,axiom,
    constr_CONST_3 != name_c ).

fof(ax33,axiom,
    constr_CONST_3 != name_k ).

fof(ax34,axiom,
    constr_CONST_3 != name_objective_R ).

fof(ax35,axiom,
    constr_CONST_3 != name_r0x30 ).

fof(ax36,axiom,
    constr_CONST_3 != name_r0x30_from_1st ).

fof(ax37,axiom,
    constr_CONST_3 != name_r1_from_1st ).

fof(ax38,axiom,
    constr_CONST_4 != constr_ZERO ).

fof(ax39,axiom,
    constr_CONST_4 != name_c ).

fof(ax40,axiom,
    constr_CONST_4 != name_k ).

fof(ax41,axiom,
    constr_CONST_4 != name_objective_R ).

fof(ax42,axiom,
    constr_CONST_4 != name_r0x30 ).

fof(ax43,axiom,
    constr_CONST_4 != name_r0x30_from_1st ).

fof(ax44,axiom,
    constr_CONST_4 != name_r1_from_1st ).

fof(ax45,axiom,
    constr_ZERO != name_c ).

fof(ax46,axiom,
    constr_ZERO != name_k ).

fof(ax47,axiom,
    constr_ZERO != name_objective_R ).

fof(ax48,axiom,
    constr_ZERO != name_r0x30 ).

fof(ax49,axiom,
    constr_ZERO != name_r0x30_from_1st ).

fof(ax50,axiom,
    constr_ZERO != name_r1_from_1st ).

fof(ax51,axiom,
    name_c != name_k ).

fof(ax52,axiom,
    name_c != name_objective_R ).

fof(ax53,axiom,
    name_c != name_r0x30 ).

fof(ax54,axiom,
    name_c != name_r0x30_from_1st ).

fof(ax55,axiom,
    name_c != name_r1_from_1st ).

fof(ax56,axiom,
    name_k != name_objective_R ).

fof(ax57,axiom,
    name_k != name_r0x30 ).

fof(ax58,axiom,
    name_k != name_r0x30_from_1st ).

fof(ax59,axiom,
    name_k != name_r1_from_1st ).

fof(ax60,axiom,
    name_objective_R != name_r0x30 ).

fof(ax61,axiom,
    name_objective_R != name_r0x30_from_1st ).

fof(ax62,axiom,
    name_objective_R != name_r1_from_1st ).

fof(ax63,axiom,
    name_r0x30 != name_r0x30_from_1st ).

fof(ax64,axiom,
    name_r0x30 != name_r1_from_1st ).

fof(ax65,axiom,
    name_r0x30_from_1st != name_r1_from_1st ).

fof(ax66,axiom,
    ! [VAR_X_10X30] : constr_xor(VAR_X_10X30,VAR_X_10X30) = constr_ZERO ).

fof(ax67,axiom,
    ! [VAR_X_9] : constr_xor(VAR_X_9,constr_ZERO) = VAR_X_9 ).

fof(ax68,axiom,
    ! [VAR_X_7,VAR_Y_8] : constr_xor(VAR_X_7,VAR_Y_8) = constr_xor(VAR_Y_8,VAR_X_7) ).

fof(ax69,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) ).

fof(ax70,axiom,
    ! [VAR_V_30X30,VAR_V_31] :
      ( ( pred_attacker(VAR_V_30X30)
        & pred_attacker(VAR_V_31) )
     => pred_attacker(constr_xor(VAR_V_30X30,VAR_V_31)) ) ).

fof(ax71,axiom,
    pred_attacker(tuple_true) ).

fof(ax72,axiom,
    ! [VAR_V_34] :
      ( pred_attacker(VAR_V_34)
     => pred_attacker(tuple_knowledge_from_1st_round_out_3(VAR_V_34)) ) ).

fof(ax73,axiom,
    ! [VAR_V_37] :
      ( pred_attacker(tuple_knowledge_from_1st_round_out_3(VAR_V_37))
     => pred_attacker(VAR_V_37) ) ).

fof(ax74,axiom,
    ! [VAR_V_41,VAR_V_42] :
      ( ( pred_attacker(VAR_V_41)
        & pred_attacker(VAR_V_42) )
     => pred_attacker(tuple_knowledge_from_1st_round_out_2(VAR_V_41,VAR_V_42)) ) ).

fof(ax75,axiom,
    ! [VAR_V_49,VAR_V_50X30] :
      ( pred_attacker(tuple_knowledge_from_1st_round_out_2(VAR_V_49,VAR_V_50X30))
     => pred_attacker(VAR_V_49) ) ).

fof(ax76,axiom,
    ! [VAR_V_52,VAR_V_53] :
      ( pred_attacker(tuple_knowledge_from_1st_round_out_2(VAR_V_52,VAR_V_53))
     => pred_attacker(VAR_V_53) ) ).

fof(ax77,axiom,
    ! [VAR_V_56] :
      ( pred_attacker(VAR_V_56)
     => pred_attacker(tuple_knowledge_from_1st_round_out_1(VAR_V_56)) ) ).

fof(ax78,axiom,
    ! [VAR_V_59] :
      ( pred_attacker(tuple_knowledge_from_1st_round_out_1(VAR_V_59))
     => pred_attacker(VAR_V_59) ) ).

fof(ax79,axiom,
    ! [VAR_V_62] :
      ( pred_attacker(VAR_V_62)
     => pred_attacker(constr_h(VAR_V_62)) ) ).

fof(ax80,axiom,
    pred_attacker(tuple_false) ).

fof(ax81,axiom,
    pred_attacker(constr_ZERO) ).

fof(ax82,axiom,
    ! [VAR_V_64] :
      ( pred_attacker(VAR_V_64)
     => pred_attacker(tuple_R_out_4(VAR_V_64)) ) ).

fof(ax83,axiom,
    ! [VAR_V_67] :
      ( pred_attacker(tuple_R_out_4(VAR_V_67))
     => pred_attacker(VAR_V_67) ) ).

fof(ax84,axiom,
    ! [VAR_V_70X30] :
      ( pred_attacker(VAR_V_70X30)
     => pred_attacker(tuple_R_out_3(VAR_V_70X30)) ) ).

fof(ax85,axiom,
    ! [VAR_V_73] :
      ( pred_attacker(tuple_R_out_3(VAR_V_73))
     => pred_attacker(VAR_V_73) ) ).

fof(ax86,axiom,
    ! [VAR_V_76] :
      ( pred_attacker(VAR_V_76)
     => pred_attacker(tuple_R_out_1(VAR_V_76)) ) ).

fof(ax87,axiom,
    ! [VAR_V_79] :
      ( pred_attacker(tuple_R_out_1(VAR_V_79))
     => pred_attacker(VAR_V_79) ) ).

fof(ax88,axiom,
    ! [VAR_V_83,VAR_V_84] :
      ( ( pred_attacker(VAR_V_83)
        & pred_attacker(VAR_V_84) )
     => pred_attacker(tuple_R_in_2(VAR_V_83,VAR_V_84)) ) ).

fof(ax89,axiom,
    ! [VAR_V_91,VAR_V_92] :
      ( pred_attacker(tuple_R_in_2(VAR_V_91,VAR_V_92))
     => pred_attacker(VAR_V_91) ) ).

fof(ax90,axiom,
    ! [VAR_V_94,VAR_V_95] :
      ( pred_attacker(tuple_R_in_2(VAR_V_94,VAR_V_95))
     => pred_attacker(VAR_V_95) ) ).

fof(ax91,axiom,
    pred_attacker(constr_CONST_4) ).

fof(ax92,axiom,
    pred_attacker(constr_CONST_3) ).

fof(ax93,axiom,
    pred_attacker(constr_CONST_2) ).

fof(ax94,axiom,
    pred_attacker(constr_CONST_1) ).

fof(ax95,axiom,
    pred_attacker(constr_CONST_0x30) ).

fof(ax96,axiom,
    ! [VAR_V_10X301,VAR_V_10X302] :
      ( ( pred_mess(VAR_V_10X302,VAR_V_10X301)
        & pred_attacker(VAR_V_10X302) )
     => pred_attacker(VAR_V_10X301) ) ).

fof(ax97,axiom,
    ! [VAR_V_10X303,VAR_V_10X304] :
      ( ( pred_attacker(VAR_V_10X304)
        & pred_attacker(VAR_V_10X303) )
     => pred_mess(VAR_V_10X304,VAR_V_10X303) ) ).

fof(ax98,axiom,
    pred_attacker(name_c) ).

fof(ax99,axiom,
    ! [VAR_V_10X306] : pred_equal(VAR_V_10X306,VAR_V_10X306) ).

fof(ax100,axiom,
    ! [VAR_V_10X307] : pred_attacker(name_new0x2Dname(VAR_V_10X307)) ).

fof(ax101,axiom,
    pred_attacker(tuple_knowledge_from_1st_round_out_1(name_r0x30_from_1st)) ).

fof(ax102,axiom,
    pred_attacker(tuple_knowledge_from_1st_round_out_2(name_r1_from_1st,constr_h(constr_xor(constr_xor(name_r0x30_from_1st,name_r1_from_1st),name_k)))) ).

fof(ax103,axiom,
    pred_attacker(tuple_knowledge_from_1st_round_out_3(constr_h(constr_xor(constr_xor(constr_h(constr_xor(constr_xor(name_r0x30_from_1st,name_r1_from_1st),name_k)),name_k),name_r0x30_from_1st)))) ).

fof(ax104,axiom,
    pred_attacker(tuple_R_out_1(name_r0x30)) ).

fof(ax105,axiom,
    ! [VAR_R1_IN_234] :
      ( pred_attacker(tuple_R_in_2(VAR_R1_IN_234,constr_h(constr_xor(constr_xor(name_r0x30,VAR_R1_IN_234),name_k))))
     => pred_attacker(tuple_R_out_3(constr_h(constr_xor(constr_xor(constr_h(constr_xor(constr_xor(name_r0x30,VAR_R1_IN_234),name_k)),name_k),name_r0x30)))) ) ).

fof(ax106,axiom,
    ! [VAR_R1_IN_244] :
      ( pred_attacker(tuple_R_in_2(VAR_R1_IN_244,constr_h(constr_xor(constr_xor(name_r0x30,VAR_R1_IN_244),name_k))))
     => pred_attacker(tuple_R_out_4(name_objective_R)) ) ).

fof(co0,conjecture,
    pred_attacker(name_objective_R) ).

%--------------------------------------------------------------------------