TPTP Problem File: SWW956+1.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : SWW956+1 : TPTP v8.2.0. Released v7.4.0.
% Domain : Software Verification
% Problem : Attack on Diffie-Hellman Key Exchange Protocol
% Version : [LT19] axioms : Especial.
% English : Attack demonstrates violation of secrecy property.
% 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 : DH.p [LT20]
% Status : Theorem
% Rating : 0.44 v8.1.0, 0.39 v7.5.0, 0.47 v7.4.0
% Syntax : Number of formulae : 94 ( 70 unt; 0 def)
% Number of atoms : 127 ( 57 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 55 ~; 0 |; 9 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 25 ( 25 usr; 13 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 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 != name_G_8 ).
fof(ax5,axiom,
constr_CONST_0x30 != name_Na ).
fof(ax6,axiom,
constr_CONST_0x30 != name_Nb ).
fof(ax7,axiom,
constr_CONST_0x30 != name_P_7 ).
fof(ax8,axiom,
constr_CONST_0x30 != name_c ).
fof(ax9,axiom,
constr_CONST_0x30 != name_objective ).
fof(ax10,axiom,
constr_CONST_1 != constr_CONST_2 ).
fof(ax11,axiom,
constr_CONST_1 != constr_CONST_3 ).
fof(ax12,axiom,
constr_CONST_1 != constr_CONST_4 ).
fof(ax13,axiom,
constr_CONST_1 != name_G_8 ).
fof(ax14,axiom,
constr_CONST_1 != name_Na ).
fof(ax15,axiom,
constr_CONST_1 != name_Nb ).
fof(ax16,axiom,
constr_CONST_1 != name_P_7 ).
fof(ax17,axiom,
constr_CONST_1 != name_c ).
fof(ax18,axiom,
constr_CONST_1 != name_objective ).
fof(ax19,axiom,
constr_CONST_2 != constr_CONST_3 ).
fof(ax20,axiom,
constr_CONST_2 != constr_CONST_4 ).
fof(ax21,axiom,
constr_CONST_2 != name_G_8 ).
fof(ax22,axiom,
constr_CONST_2 != name_Na ).
fof(ax23,axiom,
constr_CONST_2 != name_Nb ).
fof(ax24,axiom,
constr_CONST_2 != name_P_7 ).
fof(ax25,axiom,
constr_CONST_2 != name_c ).
fof(ax26,axiom,
constr_CONST_2 != name_objective ).
fof(ax27,axiom,
constr_CONST_3 != constr_CONST_4 ).
fof(ax28,axiom,
constr_CONST_3 != name_G_8 ).
fof(ax29,axiom,
constr_CONST_3 != name_Na ).
fof(ax30,axiom,
constr_CONST_3 != name_Nb ).
fof(ax31,axiom,
constr_CONST_3 != name_P_7 ).
fof(ax32,axiom,
constr_CONST_3 != name_c ).
fof(ax33,axiom,
constr_CONST_3 != name_objective ).
fof(ax34,axiom,
constr_CONST_4 != name_G_8 ).
fof(ax35,axiom,
constr_CONST_4 != name_Na ).
fof(ax36,axiom,
constr_CONST_4 != name_Nb ).
fof(ax37,axiom,
constr_CONST_4 != name_P_7 ).
fof(ax38,axiom,
constr_CONST_4 != name_c ).
fof(ax39,axiom,
constr_CONST_4 != name_objective ).
fof(ax40,axiom,
name_G_8 != name_Na ).
fof(ax41,axiom,
name_G_8 != name_Nb ).
fof(ax42,axiom,
name_G_8 != name_P_7 ).
fof(ax43,axiom,
name_G_8 != name_c ).
fof(ax44,axiom,
name_G_8 != name_objective ).
fof(ax45,axiom,
name_Na != name_Nb ).
fof(ax46,axiom,
name_Na != name_P_7 ).
fof(ax47,axiom,
name_Na != name_c ).
fof(ax48,axiom,
name_Na != name_objective ).
fof(ax49,axiom,
name_Nb != name_P_7 ).
fof(ax50,axiom,
name_Nb != name_c ).
fof(ax51,axiom,
name_Nb != name_objective ).
fof(ax52,axiom,
name_P_7 != name_c ).
fof(ax53,axiom,
name_P_7 != name_objective ).
fof(ax54,axiom,
name_c != name_objective ).
fof(ax55,axiom,
! [VAR_K_0X30,VAR_M_0X30] : constr_dec(constr_enc(VAR_M_0X30,VAR_K_0X30),VAR_K_0X30) = VAR_M_0X30 ).
fof(ax56,axiom,
! [VAR_G_0X30,VAR_P_0X30,VAR_X_0X30,VAR_Y_0X30] : constr_mod(constr_exp(constr_exp(VAR_G_0X30,VAR_X_0X30),VAR_Y_0X30),VAR_P_0X30) = constr_mod(constr_exp(constr_exp(VAR_G_0X30,VAR_Y_0X30),VAR_X_0X30),VAR_P_0X30) ).
fof(ax57,axiom,
pred_attacker(tuple_true) ).
fof(ax58,axiom,
! [VAR_V_30X30,VAR_V_31] :
( ( pred_attacker(VAR_V_30X30)
& pred_attacker(VAR_V_31) )
=> pred_attacker(constr_mod(VAR_V_30X30,VAR_V_31)) ) ).
fof(ax59,axiom,
pred_attacker(tuple_false) ).
fof(ax60,axiom,
! [VAR_V_34,VAR_V_35] :
( ( pred_attacker(VAR_V_34)
& pred_attacker(VAR_V_35) )
=> pred_attacker(constr_exp(VAR_V_34,VAR_V_35)) ) ).
fof(ax61,axiom,
! [VAR_V_38,VAR_V_39] :
( ( pred_attacker(VAR_V_38)
& pred_attacker(VAR_V_39) )
=> pred_attacker(constr_enc(VAR_V_38,VAR_V_39)) ) ).
fof(ax62,axiom,
! [VAR_V_42,VAR_V_43] :
( ( pred_attacker(VAR_V_42)
& pred_attacker(VAR_V_43) )
=> pred_attacker(constr_dec(VAR_V_42,VAR_V_43)) ) ).
fof(ax63,axiom,
pred_attacker(constr_CONST_4) ).
fof(ax64,axiom,
pred_attacker(constr_CONST_3) ).
fof(ax65,axiom,
pred_attacker(constr_CONST_2) ).
fof(ax66,axiom,
pred_attacker(constr_CONST_1) ).
fof(ax67,axiom,
pred_attacker(constr_CONST_0x30) ).
fof(ax68,axiom,
! [VAR_V_45] :
( pred_attacker(VAR_V_45)
=> pred_attacker(tuple_B_out_3(VAR_V_45)) ) ).
fof(ax69,axiom,
! [VAR_V_48] :
( pred_attacker(tuple_B_out_3(VAR_V_48))
=> pred_attacker(VAR_V_48) ) ).
fof(ax70,axiom,
! [VAR_V_51] :
( pred_attacker(VAR_V_51)
=> pred_attacker(tuple_B_in_2(VAR_V_51)) ) ).
fof(ax71,axiom,
! [VAR_V_54] :
( pred_attacker(tuple_B_in_2(VAR_V_54))
=> pred_attacker(VAR_V_54) ) ).
fof(ax72,axiom,
! [VAR_V_58,VAR_V_59] :
( ( pred_attacker(VAR_V_58)
& pred_attacker(VAR_V_59) )
=> pred_attacker(tuple_B_in_1(VAR_V_58,VAR_V_59)) ) ).
fof(ax73,axiom,
! [VAR_V_66,VAR_V_67] :
( pred_attacker(tuple_B_in_1(VAR_V_66,VAR_V_67))
=> pred_attacker(VAR_V_66) ) ).
fof(ax74,axiom,
! [VAR_V_69,VAR_V_70X30] :
( pred_attacker(tuple_B_in_1(VAR_V_69,VAR_V_70X30))
=> pred_attacker(VAR_V_70X30) ) ).
fof(ax75,axiom,
! [VAR_V_73] :
( pred_attacker(VAR_V_73)
=> pred_attacker(tuple_A_out_4(VAR_V_73)) ) ).
fof(ax76,axiom,
! [VAR_V_76] :
( pred_attacker(tuple_A_out_4(VAR_V_76))
=> pred_attacker(VAR_V_76) ) ).
fof(ax77,axiom,
! [VAR_V_79] :
( pred_attacker(VAR_V_79)
=> pred_attacker(tuple_A_out_2(VAR_V_79)) ) ).
fof(ax78,axiom,
! [VAR_V_82] :
( pred_attacker(tuple_A_out_2(VAR_V_82))
=> pred_attacker(VAR_V_82) ) ).
fof(ax79,axiom,
! [VAR_V_86,VAR_V_87] :
( ( pred_attacker(VAR_V_86)
& pred_attacker(VAR_V_87) )
=> pred_attacker(tuple_A_out_1(VAR_V_86,VAR_V_87)) ) ).
fof(ax80,axiom,
! [VAR_V_94,VAR_V_95] :
( pred_attacker(tuple_A_out_1(VAR_V_94,VAR_V_95))
=> pred_attacker(VAR_V_94) ) ).
fof(ax81,axiom,
! [VAR_V_97,VAR_V_98] :
( pred_attacker(tuple_A_out_1(VAR_V_97,VAR_V_98))
=> pred_attacker(VAR_V_98) ) ).
fof(ax82,axiom,
! [VAR_V_10X301] :
( pred_attacker(VAR_V_10X301)
=> pred_attacker(tuple_A_in_3(VAR_V_10X301)) ) ).
fof(ax83,axiom,
! [VAR_V_10X304] :
( pred_attacker(tuple_A_in_3(VAR_V_10X304))
=> pred_attacker(VAR_V_10X304) ) ).
fof(ax84,axiom,
! [VAR_V_110X30,VAR_V_111] :
( ( pred_mess(VAR_V_111,VAR_V_110X30)
& pred_attacker(VAR_V_111) )
=> pred_attacker(VAR_V_110X30) ) ).
fof(ax85,axiom,
! [VAR_V_112,VAR_V_113] :
( ( pred_attacker(VAR_V_113)
& pred_attacker(VAR_V_112) )
=> pred_mess(VAR_V_113,VAR_V_112) ) ).
fof(ax86,axiom,
pred_attacker(name_c) ).
fof(ax87,axiom,
! [VAR_V_115] : pred_equal(VAR_V_115,VAR_V_115) ).
fof(ax88,axiom,
! [VAR_V_116] : pred_attacker(name_new0x2Dname(VAR_V_116)) ).
fof(ax89,axiom,
pred_attacker(tuple_A_out_1(name_P_7,name_G_8)) ).
fof(ax90,axiom,
pred_attacker(tuple_A_out_2(constr_mod(constr_exp(name_G_8,name_Na),name_P_7))) ).
fof(ax91,axiom,
! [VAR_B_186] :
( pred_attacker(tuple_A_in_3(VAR_B_186))
=> pred_attacker(tuple_A_out_4(constr_enc(name_objective,constr_mod(constr_exp(VAR_B_186,name_Na),name_P_7)))) ) ).
fof(ax92,axiom,
! [VAR_A_219,VAR_G_221,VAR_P_220X30] :
( ( pred_attacker(tuple_B_in_2(VAR_A_219))
& pred_attacker(tuple_B_in_1(VAR_P_220X30,VAR_G_221)) )
=> pred_attacker(tuple_B_out_3(constr_mod(constr_exp(VAR_G_221,name_Nb),VAR_P_220X30))) ) ).
fof(co0,conjecture,
pred_attacker(name_objective) ).
%--------------------------------------------------------------------------