TPTP Problem File: SWW949+1.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : SWW949+1 : TPTP v8.2.0. Released v7.4.0.
% Domain : Software Verification
% Problem : Attack on SM08 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 : SM08-tag-auth.p [LT20]
% Status : Theorem
% Rating : 0.61 v8.2.0, 0.67 v8.1.0, 0.58 v7.5.0, 0.69 v7.4.0
% Syntax : Number of formulae : 124 ( 98 unt; 0 def)
% Number of atoms : 156 ( 82 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 110 ( 78 ~; 0 |; 6 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 29 ( 29 usr; 15 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 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_objective ).
fof(ax7,axiom,
constr_CONST_0x30 != name_r1 ).
fof(ax8,axiom,
constr_CONST_0x30 != name_r1_from_1st ).
fof(ax9,axiom,
constr_CONST_0x30 != name_r2_from_1st ).
fof(ax10,axiom,
constr_CONST_0x30 != name_t ).
fof(ax11,axiom,
constr_CONST_0x30 != name_u ).
fof(ax12,axiom,
constr_CONST_1 != constr_CONST_2 ).
fof(ax13,axiom,
constr_CONST_1 != constr_CONST_3 ).
fof(ax14,axiom,
constr_CONST_1 != constr_CONST_4 ).
fof(ax15,axiom,
constr_CONST_1 != constr_ZERO ).
fof(ax16,axiom,
constr_CONST_1 != name_c ).
fof(ax17,axiom,
constr_CONST_1 != name_objective ).
fof(ax18,axiom,
constr_CONST_1 != name_r1 ).
fof(ax19,axiom,
constr_CONST_1 != name_r1_from_1st ).
fof(ax20,axiom,
constr_CONST_1 != name_r2_from_1st ).
fof(ax21,axiom,
constr_CONST_1 != name_t ).
fof(ax22,axiom,
constr_CONST_1 != name_u ).
fof(ax23,axiom,
constr_CONST_2 != constr_CONST_3 ).
fof(ax24,axiom,
constr_CONST_2 != constr_CONST_4 ).
fof(ax25,axiom,
constr_CONST_2 != constr_ZERO ).
fof(ax26,axiom,
constr_CONST_2 != name_c ).
fof(ax27,axiom,
constr_CONST_2 != name_objective ).
fof(ax28,axiom,
constr_CONST_2 != name_r1 ).
fof(ax29,axiom,
constr_CONST_2 != name_r1_from_1st ).
fof(ax30,axiom,
constr_CONST_2 != name_r2_from_1st ).
fof(ax31,axiom,
constr_CONST_2 != name_t ).
fof(ax32,axiom,
constr_CONST_2 != name_u ).
fof(ax33,axiom,
constr_CONST_3 != constr_CONST_4 ).
fof(ax34,axiom,
constr_CONST_3 != constr_ZERO ).
fof(ax35,axiom,
constr_CONST_3 != name_c ).
fof(ax36,axiom,
constr_CONST_3 != name_objective ).
fof(ax37,axiom,
constr_CONST_3 != name_r1 ).
fof(ax38,axiom,
constr_CONST_3 != name_r1_from_1st ).
fof(ax39,axiom,
constr_CONST_3 != name_r2_from_1st ).
fof(ax40,axiom,
constr_CONST_3 != name_t ).
fof(ax41,axiom,
constr_CONST_3 != name_u ).
fof(ax42,axiom,
constr_CONST_4 != constr_ZERO ).
fof(ax43,axiom,
constr_CONST_4 != name_c ).
fof(ax44,axiom,
constr_CONST_4 != name_objective ).
fof(ax45,axiom,
constr_CONST_4 != name_r1 ).
fof(ax46,axiom,
constr_CONST_4 != name_r1_from_1st ).
fof(ax47,axiom,
constr_CONST_4 != name_r2_from_1st ).
fof(ax48,axiom,
constr_CONST_4 != name_t ).
fof(ax49,axiom,
constr_CONST_4 != name_u ).
fof(ax50,axiom,
constr_ZERO != name_c ).
fof(ax51,axiom,
constr_ZERO != name_objective ).
fof(ax52,axiom,
constr_ZERO != name_r1 ).
fof(ax53,axiom,
constr_ZERO != name_r1_from_1st ).
fof(ax54,axiom,
constr_ZERO != name_r2_from_1st ).
fof(ax55,axiom,
constr_ZERO != name_t ).
fof(ax56,axiom,
constr_ZERO != name_u ).
fof(ax57,axiom,
name_c != name_objective ).
fof(ax58,axiom,
name_c != name_r1 ).
fof(ax59,axiom,
name_c != name_r1_from_1st ).
fof(ax60,axiom,
name_c != name_r2_from_1st ).
fof(ax61,axiom,
name_c != name_t ).
fof(ax62,axiom,
name_c != name_u ).
fof(ax63,axiom,
name_objective != name_r1 ).
fof(ax64,axiom,
name_objective != name_r1_from_1st ).
fof(ax65,axiom,
name_objective != name_r2_from_1st ).
fof(ax66,axiom,
name_objective != name_t ).
fof(ax67,axiom,
name_objective != name_u ).
fof(ax68,axiom,
name_r1 != name_r1_from_1st ).
fof(ax69,axiom,
name_r1 != name_r2_from_1st ).
fof(ax70,axiom,
name_r1 != name_t ).
fof(ax71,axiom,
name_r1 != name_u ).
fof(ax72,axiom,
name_r1_from_1st != name_r2_from_1st ).
fof(ax73,axiom,
name_r1_from_1st != name_t ).
fof(ax74,axiom,
name_r1_from_1st != name_u ).
fof(ax75,axiom,
name_r2_from_1st != name_t ).
fof(ax76,axiom,
name_r2_from_1st != name_u ).
fof(ax77,axiom,
name_t != name_u ).
fof(ax78,axiom,
! [VAR_X_10X30] : constr_xor(VAR_X_10X30,VAR_X_10X30) = constr_ZERO ).
fof(ax79,axiom,
! [VAR_X_9] : constr_xor(VAR_X_9,constr_ZERO) = VAR_X_9 ).
fof(ax80,axiom,
! [VAR_X_7,VAR_Y_8] : constr_xor(VAR_X_7,VAR_Y_8) = constr_xor(VAR_Y_8,VAR_X_7) ).
fof(ax81,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(ax82,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(ax83,axiom,
pred_attacker(tuple_true) ).
fof(ax84,axiom,
! [VAR_V_34] :
( pred_attacker(VAR_V_34)
=> pred_attacker(tuple_knowledge_from_1st_round_out_3(VAR_V_34)) ) ).
fof(ax85,axiom,
! [VAR_V_37] :
( pred_attacker(tuple_knowledge_from_1st_round_out_3(VAR_V_37))
=> pred_attacker(VAR_V_37) ) ).
fof(ax86,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(ax87,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(ax88,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(ax89,axiom,
! [VAR_V_56] :
( pred_attacker(VAR_V_56)
=> pred_attacker(tuple_knowledge_from_1st_round_out_1(VAR_V_56)) ) ).
fof(ax90,axiom,
! [VAR_V_59] :
( pred_attacker(tuple_knowledge_from_1st_round_out_1(VAR_V_59))
=> pred_attacker(VAR_V_59) ) ).
fof(ax91,axiom,
pred_attacker(tuple_false) ).
fof(ax92,axiom,
! [VAR_V_63,VAR_V_64] :
( ( pred_attacker(VAR_V_63)
& pred_attacker(VAR_V_64) )
=> pred_attacker(constr_f(VAR_V_63,VAR_V_64)) ) ).
fof(ax93,axiom,
! [VAR_V_66] :
( pred_attacker(VAR_V_66)
=> pred_attacker(constr_cyc_shr_quart_len(VAR_V_66)) ) ).
fof(ax94,axiom,
! [VAR_V_68] :
( pred_attacker(VAR_V_68)
=> pred_attacker(constr_cyc_shr_half_len(VAR_V_68)) ) ).
fof(ax95,axiom,
! [VAR_V_70X30] :
( pred_attacker(VAR_V_70X30)
=> pred_attacker(constr_cyc_shl_quart_len(VAR_V_70X30)) ) ).
fof(ax96,axiom,
! [VAR_V_72] :
( pred_attacker(VAR_V_72)
=> pred_attacker(constr_cyc_shl_half_len(VAR_V_72)) ) ).
fof(ax97,axiom,
pred_attacker(constr_ZERO) ).
fof(ax98,axiom,
! [VAR_V_74] :
( pred_attacker(VAR_V_74)
=> pred_attacker(tuple_R_out_4(VAR_V_74)) ) ).
fof(ax99,axiom,
! [VAR_V_77] :
( pred_attacker(tuple_R_out_4(VAR_V_77))
=> pred_attacker(VAR_V_77) ) ).
fof(ax100,axiom,
! [VAR_V_80X30] :
( pred_attacker(VAR_V_80X30)
=> pred_attacker(tuple_R_out_3(VAR_V_80X30)) ) ).
fof(ax101,axiom,
! [VAR_V_83] :
( pred_attacker(tuple_R_out_3(VAR_V_83))
=> pred_attacker(VAR_V_83) ) ).
fof(ax102,axiom,
! [VAR_V_86] :
( pred_attacker(VAR_V_86)
=> pred_attacker(tuple_R_out_1(VAR_V_86)) ) ).
fof(ax103,axiom,
! [VAR_V_89] :
( pred_attacker(tuple_R_out_1(VAR_V_89))
=> pred_attacker(VAR_V_89) ) ).
fof(ax104,axiom,
! [VAR_V_93,VAR_V_94] :
( ( pred_attacker(VAR_V_93)
& pred_attacker(VAR_V_94) )
=> pred_attacker(tuple_R_in_2(VAR_V_93,VAR_V_94)) ) ).
fof(ax105,axiom,
! [VAR_V_10X301,VAR_V_10X302] :
( pred_attacker(tuple_R_in_2(VAR_V_10X301,VAR_V_10X302))
=> pred_attacker(VAR_V_10X301) ) ).
fof(ax106,axiom,
! [VAR_V_10X304,VAR_V_10X305] :
( pred_attacker(tuple_R_in_2(VAR_V_10X304,VAR_V_10X305))
=> pred_attacker(VAR_V_10X305) ) ).
fof(ax107,axiom,
pred_attacker(constr_CONST_4) ).
fof(ax108,axiom,
pred_attacker(constr_CONST_3) ).
fof(ax109,axiom,
pred_attacker(constr_CONST_2) ).
fof(ax110,axiom,
pred_attacker(constr_CONST_1) ).
fof(ax111,axiom,
pred_attacker(constr_CONST_0x30) ).
fof(ax112,axiom,
! [VAR_V_111,VAR_V_112] :
( ( pred_mess(VAR_V_112,VAR_V_111)
& pred_attacker(VAR_V_112) )
=> pred_attacker(VAR_V_111) ) ).
fof(ax113,axiom,
! [VAR_V_113,VAR_V_114] :
( ( pred_attacker(VAR_V_114)
& pred_attacker(VAR_V_113) )
=> pred_mess(VAR_V_114,VAR_V_113) ) ).
fof(ax114,axiom,
pred_attacker(name_c) ).
fof(ax115,axiom,
! [VAR_V_116] : pred_equal(VAR_V_116,VAR_V_116) ).
fof(ax116,axiom,
! [VAR_V_117] : pred_attacker(name_new0x2Dname(VAR_V_117)) ).
fof(ax117,axiom,
pred_attacker(tuple_knowledge_from_1st_round_out_1(name_r1_from_1st)) ).
fof(ax118,axiom,
pred_attacker(tuple_knowledge_from_1st_round_out_2(constr_xor(name_t,name_r2_from_1st),constr_f(constr_xor(name_r1_from_1st,name_r2_from_1st),name_t))) ).
fof(ax119,axiom,
pred_attacker(tuple_knowledge_from_1st_round_out_3(constr_xor(name_u,constr_cyc_shr_half_len(name_r2_from_1st)))) ).
fof(ax120,axiom,
pred_attacker(tuple_R_out_1(name_r1)) ).
fof(ax121,axiom,
! [VAR_M1_IN_244] :
( pred_attacker(tuple_R_in_2(VAR_M1_IN_244,constr_f(constr_xor(name_r1,constr_xor(VAR_M1_IN_244,name_t)),name_t)))
=> pred_attacker(tuple_R_out_3(constr_xor(name_u,constr_cyc_shr_half_len(constr_xor(VAR_M1_IN_244,name_t))))) ) ).
fof(ax122,axiom,
! [VAR_M1_IN_250X30] :
( pred_attacker(tuple_R_in_2(VAR_M1_IN_250X30,constr_f(constr_xor(name_r1,constr_xor(VAR_M1_IN_250X30,name_t)),name_t)))
=> pred_attacker(tuple_R_out_4(name_objective)) ) ).
fof(co0,conjecture,
pred_attacker(name_objective) ).
%--------------------------------------------------------------------------