TSTP Solution File: SWV751-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV751-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %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 : 600s
% DateTime : Wed Jul 20 21:45:01 EDT 2022
% Result : Unsatisfiable 118.12s 118.35s
% Output : Refutation 119.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 34
% Syntax : Number of clauses : 125 ( 58 unt; 10 nHn; 125 RR)
% Number of literals : 206 ( 0 equ; 103 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 30 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
( ~ hBOOL(c_in(u,c_Set_Oinsert(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),w),w))
| equal(u,v) ),
file('SWV751-1.p',unknown),
[] ).
cnf(70,axiom,
( ~ hBOOL(hAPP(u,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(u,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(u,v)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(215,axiom,
( ~ hBOOL(hAPP(u,v))
| ~ c_lessequals(u,w,tc_fun(x,tc_bool))
| hBOOL(hAPP(w,v)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(231,axiom,
( ~ c_lessequals(c_Set_Oinsert(u,v,w),x,tc_fun(w,tc_bool))
| hBOOL(c_in(u,x,w)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(253,axiom,
c_lessequals(c_Set_Oinsert(u,c_Message_Oanalz(v),tc_Message_Omsg),c_Message_Oanalz(c_Set_Oinsert(u,v,tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),
file('SWV751-1.p',unknown),
[] ).
cnf(263,axiom,
hBOOL(c_in(hAPP(c_Public_OshrK,u),c_Message_OsymKeys,tc_nat)),
file('SWV751-1.p',unknown),
[] ).
cnf(266,axiom,
( ~ hBOOL(c_in(hAPP(c_Message_OinvKey,u),c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(u,c_Message_OsymKeys,tc_nat)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(269,axiom,
~ hBOOL(c_in(hAPP(c_Public_OpublicKey(u),v),c_Message_OsymKeys,tc_nat)),
file('SWV751-1.p',unknown),
[] ).
cnf(271,axiom,
c_lessequals(c_Event_OinitState(u),c_Event_Oknows(u,v),tc_fun(tc_Message_Omsg,tc_bool)),
file('SWV751-1.p',unknown),
[] ).
cnf(276,axiom,
~ hBOOL(c_in(hAPP(c_Message_OinvKey,hAPP(c_Public_OpublicKey(u),v)),c_Message_OsymKeys,tc_nat)),
file('SWV751-1.p',unknown),
[] ).
cnf(326,axiom,
equal(c_Message_Oparts(c_Message_Oanalz(u)),c_Message_Oparts(u)),
file('SWV751-1.p',unknown),
[] ).
cnf(342,axiom,
( ~ hBOOL(c_in(u,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v)),tc_Message_Omsg))
| hBOOL(c_in(u,c_Event_Oused(v),tc_Message_Omsg)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(377,axiom,
hBOOL(c_in(hAPP(c_Message_Omsg_OKey,hAPP(c_Public_OshrK,u)),c_Event_OinitState(u),tc_Message_Omsg)),
file('SWV751-1.p',unknown),
[] ).
cnf(382,axiom,
~ hBOOL(c_in(c_Message_Omsg_OCrypt(u,v),c_Message_Oparts(c_Event_OinitState(w)),tc_Message_Omsg)),
file('SWV751-1.p',unknown),
[] ).
cnf(388,axiom,
( ~ hBOOL(c_in(u,v,tc_Message_Omsg))
| hBOOL(c_in(u,c_Message_Oparts(v),tc_Message_Omsg)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(393,axiom,
( ~ hBOOL(c_in(u,v,w))
| equal(c_Set_Oinsert(u,v,w),v) ),
file('SWV751-1.p',unknown),
[] ).
cnf(425,axiom,
equal(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),c_Set_Oinsert(v,c_Set_Oinsert(u,w,x),x)),
file('SWV751-1.p',unknown),
[] ).
cnf(432,axiom,
equal(hAPP(c_Message_OinvKey,hAPP(c_Public_OshrK,u)),hAPP(c_Public_OshrK,u)),
file('SWV751-1.p',unknown),
[] ).
cnf(433,axiom,
( ~ equal(hAPP(c_Message_OinvKey,u),hAPP(c_Message_OinvKey,v))
| equal(u,v) ),
file('SWV751-1.p',unknown),
[] ).
cnf(441,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,v,w),x))
| hBOOL(hAPP(v,x))
| equal(u,x) ),
file('SWV751-1.p',unknown),
[] ).
cnf(456,axiom,
hBOOL(hAPP(c_Set_Oinsert(u,v,w),u)),
file('SWV751-1.p',unknown),
[] ).
cnf(457,axiom,
equal(hAPP(c_Message_OinvKey,hAPP(c_Message_OinvKey,u)),u),
file('SWV751-1.p',unknown),
[] ).
cnf(458,axiom,
~ equal(hAPP(c_Public_OshrK,u),hAPP(c_Public_OpublicKey(v),w)),
file('SWV751-1.p',unknown),
[] ).
cnf(471,axiom,
~ equal(hAPP(c_Public_OpublicKey(u),v),hAPP(c_Message_OinvKey,hAPP(c_Public_OpublicKey(w),x))),
file('SWV751-1.p',unknown),
[] ).
cnf(521,axiom,
( ~ hBOOL(c_in(c_Event_Oevent_OSays(u,v,c_Message_Omsg_OCrypt(w,c_Message_Omsg_OMPair(x,c_Message_Omsg_OMPair(y,c_Message_Omsg_OMPair(z,x1))))),c_List_Oset(x2,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(x1,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,x2)),tc_Message_Omsg)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(523,axiom,
( ~ hBOOL(c_in(u,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,hAPP(c_Public_OshrK,v)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,u)),tc_Message_Omsg))
| hBOOL(c_in(v,c_Event_Obad,tc_Message_Oagent)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(525,axiom,
( ~ hBOOL(c_in(u,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v,c_Message_Omsg_OCrypt(w,c_Message_Omsg_OMPair(x,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(y),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,z),x1))))),c_List_Oset(u,tc_Event_Oevent),tc_Event_Oevent))
| equal(w,hAPP(c_Public_OshrK,v)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(530,axiom,
( ~ hBOOL(c_in(u,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v,c_Message_Omsg_OCrypt(w,c_Message_Omsg_OMPair(x,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(y),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,z),x1))))),c_List_Oset(u,tc_Event_Oevent),tc_Event_Oevent))
| equal(x1,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,y),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,z),c_Message_Omsg_OAgent(v)))) ),
file('SWV751-1.p',unknown),
[] ).
cnf(540,axiom,
( ~ hBOOL(c_in(u,v,tc_Message_Omsg))
| hBOOL(c_in(u,c_Message_Oanalz(v),tc_Message_Omsg)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(558,axiom,
( ~ hBOOL(hAPP(u,v))
| hBOOL(c_in(v,u,w)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(559,axiom,
( ~ hBOOL(c_in(u,v,w))
| hBOOL(hAPP(v,u)) ),
file('SWV751-1.p',unknown),
[] ).
cnf(601,axiom,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(v_K_H,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)),
file('SWV751-1.p',unknown),
[] ).
cnf(603,axiom,
~ hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent)),
file('SWV751-1.p',unknown),
[] ).
cnf(605,axiom,
hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
file('SWV751-1.p',unknown),
[] ).
cnf(719,plain,
( ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,hAPP(c_Public_OshrK,v_A)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,u)),tc_Message_Omsg))
| ~ hBOOL(c_in(u,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) ),
inference(res,[status(thm),theory(equality)],[523,603]),
[iquote('0:Res:523.2,603.0')] ).
cnf(783,plain,
( ~ hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| equal(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))),v_X) ),
inference(res,[status(thm),theory(equality)],[601,530]),
[iquote('0:Res:601.0,530.1')] ).
cnf(784,plain,
( ~ hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| equal(hAPP(c_Public_OshrK,v_A),v_K_H) ),
inference(res,[status(thm),theory(equality)],[601,525]),
[iquote('0:Res:601.0,525.1')] ).
cnf(786,plain,
hBOOL(c_in(v_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[601,521]),
[iquote('0:Res:601.0,521.0')] ).
cnf(789,plain,
equal(hAPP(c_Public_OshrK,v_A),v_K_H),
inference(mrr,[status(thm)],[784,605]),
[iquote('0:MRR:784.0,605.0')] ).
cnf(791,plain,
equal(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))),v_X),
inference(mrr,[status(thm)],[783,605]),
[iquote('0:MRR:783.0,605.0')] ).
cnf(794,plain,
( ~ hBOOL(c_in(u,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K_H),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,u)),tc_Message_Omsg)) ),
inference(rew,[status(thm),theory(equality)],[789,719]),
[iquote('0:Rew:789.0,719.0')] ).
cnf(856,plain,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K_H),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[605,794]),
[iquote('0:Res:605.0,794.1')] ).
cnf(912,plain,
hBOOL(c_in(v_K_H,c_Message_OsymKeys,tc_nat)),
inference(spr,[status(thm),theory(equality)],[789,263]),
[iquote('0:SpR:789.0,263.0')] ).
cnf(935,plain,
equal(hAPP(c_Message_OinvKey,v_K_H),v_K_H),
inference(spr,[status(thm),theory(equality)],[789,432]),
[iquote('0:SpR:789.0,432.0')] ).
cnf(1016,plain,
~ hBOOL(hAPP(c_Message_OsymKeys,hAPP(c_Public_OpublicKey(u),v))),
inference(res,[status(thm),theory(equality)],[558,269]),
[iquote('0:Res:558.1,269.0')] ).
cnf(1021,plain,
~ hBOOL(hAPP(c_Message_Oparts(c_Event_OinitState(u)),c_Message_Omsg_OCrypt(v,w))),
inference(res,[status(thm),theory(equality)],[558,382]),
[iquote('0:Res:558.1,382.0')] ).
cnf(1032,plain,
hBOOL(hAPP(c_Message_OsymKeys,v_K_H)),
inference(res,[status(thm),theory(equality)],[912,559]),
[iquote('0:Res:912.0,559.0')] ).
cnf(1037,plain,
hBOOL(hAPP(c_Event_OinitState(u),hAPP(c_Message_Omsg_OKey,hAPP(c_Public_OshrK,u)))),
inference(res,[status(thm),theory(equality)],[377,559]),
[iquote('0:Res:377.0,559.0')] ).
cnf(1069,plain,
~ hBOOL(hAPP(c_Message_OsymKeys,hAPP(c_Message_OinvKey,hAPP(c_Public_OpublicKey(u),v)))),
inference(res,[status(thm),theory(equality)],[558,276]),
[iquote('0:Res:558.1,276.0')] ).
cnf(1124,plain,
( ~ equal(u,hAPP(c_Message_OinvKey,v))
| equal(hAPP(c_Message_OinvKey,u),v) ),
inference(spl,[status(thm),theory(equality)],[457,433]),
[iquote('0:SpL:457.0,433.0')] ).
cnf(1126,plain,
( ~ equal(hAPP(c_Message_OinvKey,u),v_K_H)
| equal(v_K_H,u) ),
inference(spl,[status(thm),theory(equality)],[935,433]),
[iquote('0:SpL:935.0,433.0')] ).
cnf(1130,plain,
( ~ equal(u,v_K_H)
| equal(hAPP(c_Message_OinvKey,u),v_K_H) ),
inference(spl,[status(thm),theory(equality)],[457,1126]),
[iquote('0:SpL:457.0,1126.0')] ).
cnf(1141,plain,
( ~ equal(hAPP(c_Public_OpublicKey(u),v),v_K_H)
| ~ hBOOL(hAPP(c_Message_OsymKeys,v_K_H)) ),
inference(spl,[status(thm),theory(equality)],[1130,1069]),
[iquote('0:SpL:1130.1,1069.0')] ).
cnf(1146,plain,
~ equal(hAPP(c_Public_OpublicKey(u),v),v_K_H),
inference(mrr,[status(thm)],[1141,1032]),
[iquote('0:MRR:1141.1,1032.0')] ).
cnf(1154,plain,
( ~ equal(u,v)
| equal(hAPP(c_Message_OinvKey,u),hAPP(c_Message_OinvKey,v)) ),
inference(spl,[status(thm),theory(equality)],[457,1124]),
[iquote('0:SpL:457.0,1124.0')] ).
cnf(1155,plain,
( ~ equal(u,hAPP(c_Public_OshrK,v))
| equal(hAPP(c_Message_OinvKey,u),hAPP(c_Public_OshrK,v)) ),
inference(spl,[status(thm),theory(equality)],[432,1124]),
[iquote('0:SpL:432.0,1124.0')] ).
cnf(1277,plain,
~ hBOOL(c_in(v_X,c_Message_Oparts(c_Event_OinitState(u)),tc_Message_Omsg)),
inference(spl,[status(thm),theory(equality)],[791,382]),
[iquote('0:SpL:791.0,382.0')] ).
cnf(1283,plain,
~ hBOOL(hAPP(c_Message_Oparts(c_Event_OinitState(u)),v_X)),
inference(spl,[status(thm),theory(equality)],[791,1021]),
[iquote('0:SpL:791.0,1021.0')] ).
cnf(1460,plain,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K_H),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[540,856]),
[iquote('0:Res:540.1,856.0')] ).
cnf(1462,plain,
~ hBOOL(hAPP(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),hAPP(c_Message_Omsg_OKey,v_K_H))),
inference(res,[status(thm),theory(equality)],[558,1460]),
[iquote('0:Res:558.1,1460.0')] ).
cnf(1477,plain,
~ hBOOL(c_in(v_X,c_Event_OinitState(u),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[388,1277]),
[iquote('0:Res:388.1,1277.0')] ).
cnf(1481,plain,
( ~ hBOOL(c_in(u,v,tc_Message_Omsg))
| hBOOL(hAPP(c_Message_Oparts(v),u)) ),
inference(res,[status(thm),theory(equality)],[388,559]),
[iquote('0:Res:388.1,559.0')] ).
cnf(1482,plain,
~ hBOOL(hAPP(c_Event_OinitState(u),v_X)),
inference(res,[status(thm),theory(equality)],[558,1477]),
[iquote('0:Res:558.1,1477.0')] ).
cnf(1490,plain,
( ~ hBOOL(c_in(u,c_Message_Oanalz(v),tc_Message_Omsg))
| hBOOL(hAPP(c_Message_Oparts(v),u)) ),
inference(spr,[status(thm),theory(equality)],[326,1481]),
[iquote('0:SpR:326.0,1481.1')] ).
cnf(1523,plain,
( ~ equal(hAPP(c_Public_OpublicKey(u),v),w)
| ~ equal(hAPP(c_Public_OpublicKey(x),y),hAPP(c_Message_OinvKey,w)) ),
inference(spl,[status(thm),theory(equality)],[1154,471]),
[iquote('0:SpL:1154.1,471.0')] ).
cnf(1797,plain,
( ~ equal(u,v_K_H)
| ~ hBOOL(c_in(v_K_H,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(u,c_Message_OsymKeys,tc_nat)) ),
inference(spl,[status(thm),theory(equality)],[1130,266]),
[iquote('0:SpL:1130.1,266.0')] ).
cnf(1805,plain,
( ~ equal(u,v_K_H)
| hBOOL(c_in(u,c_Message_OsymKeys,tc_nat)) ),
inference(mrr,[status(thm)],[1797,912]),
[iquote('0:MRR:1797.1,912.0')] ).
cnf(1809,plain,
( ~ equal(hAPP(c_Message_OinvKey,u),v_K_H)
| hBOOL(c_in(u,c_Message_OsymKeys,tc_nat)) ),
inference(res,[status(thm),theory(equality)],[1805,266]),
[iquote('0:Res:1805.1,266.0')] ).
cnf(1811,plain,
( ~ equal(u,v_K_H)
| hBOOL(hAPP(c_Message_OsymKeys,u)) ),
inference(res,[status(thm),theory(equality)],[1805,559]),
[iquote('0:Res:1805.1,559.0')] ).
cnf(1881,plain,
( ~ equal(hAPP(c_Message_OinvKey,u),v_K_H)
| hBOOL(hAPP(c_Message_OsymKeys,u)) ),
inference(res,[status(thm),theory(equality)],[1809,559]),
[iquote('0:Res:1809.1,559.0')] ).
cnf(3087,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),w)) ),
inference(res,[status(thm),theory(equality)],[456,70]),
[iquote('0:Res:456.0,70.0')] ).
cnf(3089,plain,
( ~ equal(v_K_H,c_Public_Okeymode_OSignature)
| ~ hBOOL(hAPP(c_Message_OsymKeys,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(c_Message_OsymKeys,u)) ),
inference(res,[status(thm),theory(equality)],[1811,70]),
[iquote('0:Res:1811.1,70.0')] ).
cnf(3094,plain,
( ~ equal(hAPP(c_Message_OinvKey,c_Public_Okeymode_OEncryption),v_K_H)
| ~ equal(v_K_H,c_Public_Okeymode_OSignature)
| hBOOL(hAPP(c_Message_OsymKeys,u)) ),
inference(res,[status(thm),theory(equality)],[1881,3089]),
[iquote('0:Res:1881.1,3089.1')] ).
cnf(3136,plain,
( ~ equal(u,hAPP(c_Public_OshrK,v))
| equal(hAPP(c_Message_OinvKey,hAPP(c_Message_OinvKey,u)),hAPP(c_Message_OinvKey,u)) ),
inference(spr,[status(thm),theory(equality)],[1155,432]),
[iquote('0:SpR:1155.1,432.0')] ).
cnf(3139,plain,
( ~ equal(u,hAPP(c_Public_OshrK,v))
| hBOOL(hAPP(c_Event_OinitState(v),hAPP(c_Message_Omsg_OKey,hAPP(c_Message_OinvKey,u)))) ),
inference(spr,[status(thm),theory(equality)],[1155,1037]),
[iquote('0:SpR:1155.1,1037.0')] ).
cnf(3182,plain,
( ~ equal(u,hAPP(c_Public_OshrK,v))
| equal(hAPP(c_Message_OinvKey,u),u) ),
inference(rew,[status(thm),theory(equality)],[457,3136]),
[iquote('0:Rew:457.0,3136.1')] ).
cnf(3187,plain,
( ~ equal(u,hAPP(c_Public_OshrK,v))
| hBOOL(hAPP(c_Event_OinitState(v),hAPP(c_Message_Omsg_OKey,u))) ),
inference(rew,[status(thm),theory(equality)],[3182,3139]),
[iquote('0:Rew:3182.1,3139.1')] ).
cnf(3974,plain,
hBOOL(c_in(v_X,c_Event_Oused(v_evs),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[786,342]),
[iquote('0:Res:786.0,342.0')] ).
cnf(3984,plain,
equal(c_Set_Oinsert(v_X,c_Event_Oused(v_evs),tc_Message_Omsg),c_Event_Oused(v_evs)),
inference(res,[status(thm),theory(equality)],[3974,393]),
[iquote('0:Res:3974.0,393.0')] ).
cnf(3985,plain,
hBOOL(hAPP(c_Event_Oused(v_evs),v_X)),
inference(res,[status(thm),theory(equality)],[3974,559]),
[iquote('0:Res:3974.0,559.0')] ).
cnf(4029,plain,
c_lessequals(c_Set_Oinsert(v_X,c_Message_Oanalz(c_Event_Oused(v_evs)),tc_Message_Omsg),c_Message_Oanalz(c_Event_Oused(v_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(spr,[status(thm),theory(equality)],[3984,253]),
[iquote('0:SpR:3984.0,253.0')] ).
cnf(4433,plain,
( ~ equal(hAPP(c_Message_OinvKey,c_Public_Okeymode_OEncryption),v_K_H)
| ~ equal(v_K_H,c_Public_Okeymode_OSignature) ),
inference(res,[status(thm),theory(equality)],[3094,1016]),
[iquote('0:Res:3094.2,1016.0')] ).
cnf(4440,plain,
( ~ equal(c_Public_Okeymode_OEncryption,u)
| ~ equal(hAPP(c_Message_OinvKey,u),v_K_H)
| ~ equal(v_K_H,c_Public_Okeymode_OSignature) ),
inference(spl,[status(thm),theory(equality)],[1154,4433]),
[iquote('0:SpL:1154.1,4433.0')] ).
cnf(4855,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v),w))
| equal(w,u) ),
inference(res,[status(thm),theory(equality)],[558,16]),
[iquote('0:Res:558.1,16.0')] ).
cnf(5358,plain,
hBOOL(c_in(v_X,c_Message_Oanalz(c_Event_Oused(v_evs)),tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[4029,231]),
[iquote('0:Res:4029.0,231.0')] ).
cnf(5387,plain,
hBOOL(hAPP(c_Message_Oparts(c_Event_Oused(v_evs)),v_X)),
inference(res,[status(thm),theory(equality)],[5358,1490]),
[iquote('0:Res:5358.0,1490.0')] ).
cnf(6114,plain,
hBOOL(hAPP(c_Set_Oinsert(u,c_Set_Oinsert(v,w,x),x),v)),
inference(spr,[status(thm),theory(equality)],[425,456]),
[iquote('0:SpR:425.0,456.0')] ).
cnf(7562,plain,
( ~ hBOOL(hAPP(c_Event_OinitState(u),v))
| hBOOL(hAPP(c_Event_Oknows(u,w),v)) ),
inference(res,[status(thm),theory(equality)],[271,215]),
[iquote('0:Res:271.0,215.1')] ).
cnf(31508,plain,
~ hBOOL(hAPP(c_Event_OinitState(c_Message_Oagent_OSpy),hAPP(c_Message_Omsg_OKey,v_K_H))),
inference(res,[status(thm),theory(equality)],[7562,1462]),
[iquote('0:Res:7562.1,1462.0')] ).
cnf(31513,plain,
~ equal(hAPP(c_Public_OshrK,c_Message_Oagent_OSpy),v_K_H),
inference(res,[status(thm),theory(equality)],[3187,31508]),
[iquote('0:Res:3187.1,31508.0')] ).
cnf(52021,plain,
hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,u,v),v),w)),
inference(res,[status(thm),theory(equality)],[6114,3087]),
[iquote('0:Res:6114.0,3087.0')] ).
cnf(52022,plain,
hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),v),w)),
inference(rew,[status(thm),theory(equality)],[425,52021]),
[iquote('0:Rew:425.0,52021.0')] ).
cnf(52038,plain,
( hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,u,v),w))
| equal(c_Public_Okeymode_OEncryption,w) ),
inference(res,[status(thm),theory(equality)],[52022,441]),
[iquote('0:Res:52022.0,441.0')] ).
cnf(52061,plain,
( equal(c_Public_Okeymode_OEncryption,u)
| equal(u,c_Public_Okeymode_OSignature) ),
inference(res,[status(thm),theory(equality)],[52038,4855]),
[iquote('0:Res:52038.0,4855.0')] ).
cnf(52618,plain,
( equal(hAPP(c_Public_OshrK,v_A),c_Public_Okeymode_OEncryption)
| equal(v_K_H,c_Public_Okeymode_OSignature) ),
inference(spr,[status(thm),theory(equality)],[52061,789]),
[iquote('0:SpR:52061.1,789.0')] ).
cnf(52729,plain,
( equal(hAPP(c_Message_OinvKey,hAPP(c_Public_OshrK,u)),c_Public_Okeymode_OEncryption)
| equal(hAPP(c_Public_OshrK,u),c_Public_Okeymode_OSignature) ),
inference(spr,[status(thm),theory(equality)],[52061,432]),
[iquote('0:SpR:52061.1,432.0')] ).
cnf(55623,plain,
( equal(c_Message_Oparts(c_Event_Oused(v_evs)),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OSignature,v_X)) ),
inference(spr,[status(thm),theory(equality)],[52061,5387]),
[iquote('0:SpR:52061.1,5387.0')] ).
cnf(59675,plain,
( equal(c_Event_Oused(v_evs),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OSignature,v_X)) ),
inference(spr,[status(thm),theory(equality)],[52061,3985]),
[iquote('0:SpR:52061.1,3985.0')] ).
cnf(60423,plain,
( ~ equal(c_Public_Okeymode_OEncryption,u)
| ~ equal(v_K_H,c_Public_Okeymode_OSignature)
| ~ equal(v_K_H,c_Public_Okeymode_OSignature)
| equal(hAPP(c_Message_OinvKey,u),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[52061,4440]),
[iquote('0:SpL:52061.1,4440.1')] ).
cnf(60484,plain,
( ~ equal(v_K_H,c_Public_Okeymode_OSignature)
| equal(hAPP(c_Public_OpublicKey(u),v),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[52061,1146]),
[iquote('0:SpL:52061.1,1146.0')] ).
cnf(60548,plain,
( ~ equal(hAPP(c_Public_OshrK,u),c_Public_Okeymode_OSignature)
| equal(hAPP(c_Public_OpublicKey(v),w),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[52061,458]),
[iquote('0:SpL:52061.1,458.0')] ).
cnf(61051,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,v_X))
| equal(c_Message_Oparts(c_Event_OinitState(u)),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[52061,1283]),
[iquote('0:SpL:52061.1,1283.0')] ).
cnf(61403,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,v_X))
| equal(c_Event_OinitState(u),c_Public_Okeymode_OEncryption) ),
inference(spl,[status(thm),theory(equality)],[52061,1482]),
[iquote('0:SpL:52061.1,1482.0')] ).
cnf(61998,plain,
( equal(v_K_H,c_Public_Okeymode_OEncryption)
| equal(v_K_H,c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[789,52618]),
[iquote('0:Rew:789.0,52618.0')] ).
cnf(62004,plain,
( equal(c_Message_Oparts(c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption)
| hBOOL(hAPP(c_Public_Okeymode_OSignature,v_X)) ),
inference(rew,[status(thm),theory(equality)],[59675,55623]),
[iquote('0:Rew:59675.0,55623.0')] ).
cnf(62041,plain,
( ~ hBOOL(hAPP(c_Public_Okeymode_OSignature,v_X))
| equal(c_Message_Oparts(c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[61403,61051]),
[iquote('0:Rew:61403.1,61051.1')] ).
cnf(62042,plain,
equal(c_Message_Oparts(c_Public_Okeymode_OEncryption),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[62041,62004]),
[iquote('0:MRR:62041.0,62004.1')] ).
cnf(62127,plain,
( equal(hAPP(c_Public_OshrK,u),c_Public_Okeymode_OEncryption)
| equal(hAPP(c_Public_OshrK,u),c_Public_Okeymode_OSignature) ),
inference(rew,[status(thm),theory(equality)],[432,52729]),
[iquote('0:Rew:432.0,52729.0')] ).
cnf(64315,plain,
( ~ equal(c_Public_Okeymode_OEncryption,u)
| ~ equal(v_K_H,c_Public_Okeymode_OSignature)
| equal(hAPP(c_Message_OinvKey,u),c_Public_Okeymode_OEncryption) ),
inference(obv,[status(thm),theory(equality)],[60423]),
[iquote('0:Obv:60423.1')] ).
cnf(67280,plain,
equal(v_K_H,c_Public_Okeymode_OEncryption),
inference(spt,[spt(split,[position(s1)])],[61998]),
[iquote('1:Spt:61998.0')] ).
cnf(67471,plain,
~ equal(hAPP(c_Public_OpublicKey(u),v),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[67280,1146]),
[iquote('1:Rew:67280.0,1146.0')] ).
cnf(67568,plain,
~ equal(hAPP(c_Public_OshrK,c_Message_Oagent_OSpy),c_Public_Okeymode_OEncryption),
inference(rew,[status(thm),theory(equality)],[67280,31513]),
[iquote('1:Rew:67280.0,31513.0')] ).
cnf(70207,plain,
~ equal(hAPP(c_Public_OshrK,u),c_Public_Okeymode_OSignature),
inference(mrr,[status(thm)],[60548,67471]),
[iquote('1:MRR:60548.1,67471.0')] ).
cnf(70235,plain,
equal(hAPP(c_Public_OshrK,u),c_Public_Okeymode_OEncryption),
inference(mrr,[status(thm)],[62127,70207]),
[iquote('1:MRR:62127.1,70207.0')] ).
cnf(70236,plain,
$false,
inference(unc,[status(thm)],[70235,67568]),
[iquote('1:UnC:70235.0,67568.0')] ).
cnf(71852,plain,
~ equal(v_K_H,c_Public_Okeymode_OEncryption),
inference(spt,[spt(split,[position(sa)])],[70236,67280]),
[iquote('1:Spt:70236.0,61998.0,67280.0')] ).
cnf(71853,plain,
equal(v_K_H,c_Public_Okeymode_OSignature),
inference(spt,[spt(split,[position(s2)])],[61998]),
[iquote('1:Spt:70236.0,61998.1')] ).
cnf(72067,plain,
( ~ equal(c_Public_Okeymode_OSignature,c_Public_Okeymode_OSignature)
| equal(hAPP(c_Public_OpublicKey(u),v),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[71853,60484]),
[iquote('1:Rew:71853.0,60484.0')] ).
cnf(72068,plain,
equal(hAPP(c_Public_OpublicKey(u),v),c_Public_Okeymode_OEncryption),
inference(obv,[status(thm),theory(equality)],[72067]),
[iquote('1:Obv:72067.0')] ).
cnf(72238,plain,
( ~ equal(hAPP(c_Public_OpublicKey(u),v),w)
| ~ equal(hAPP(c_Message_OinvKey,w),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[72068,1523]),
[iquote('1:Rew:72068.0,1523.1')] ).
cnf(74255,plain,
( ~ equal(c_Public_Okeymode_OEncryption,u)
| ~ equal(c_Public_Okeymode_OSignature,c_Public_Okeymode_OSignature)
| equal(hAPP(c_Message_OinvKey,u),c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[71853,64315]),
[iquote('1:Rew:71853.0,64315.1')] ).
cnf(74256,plain,
( ~ equal(c_Public_Okeymode_OEncryption,u)
| equal(hAPP(c_Message_OinvKey,u),c_Public_Okeymode_OEncryption) ),
inference(obv,[status(thm),theory(equality)],[74255]),
[iquote('1:Obv:74255.1')] ).
cnf(74441,plain,
( ~ equal(c_Public_Okeymode_OEncryption,u)
| ~ equal(c_Public_Okeymode_OEncryption,c_Public_Okeymode_OEncryption) ),
inference(rew,[status(thm),theory(equality)],[74256,72238,72068]),
[iquote('1:Rew:74256.1,72238.1,72068.0,72238.0')] ).
cnf(74442,plain,
~ equal(c_Public_Okeymode_OEncryption,u),
inference(obv,[status(thm),theory(equality)],[74441]),
[iquote('1:Obv:74441.1')] ).
cnf(74443,plain,
$false,
inference(unc,[status(thm)],[74442,62042]),
[iquote('1:UnC:74442.0,62042.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV751-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 15:37:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 118.12/118.35
% 118.12/118.35 SPASS V 3.9
% 118.12/118.35 SPASS beiseite: Proof found.
% 118.12/118.35 % SZS status Theorem
% 118.12/118.35 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 118.12/118.35 SPASS derived 58496 clauses, backtracked 3809 clauses, performed 3 splits and kept 29660 clauses.
% 118.12/118.35 SPASS allocated 151578 KBytes.
% 118.12/118.35 SPASS spent 0:1:57.89 on the problem.
% 118.12/118.35 0:00:00.05 for the input.
% 118.12/118.35 0:00:00.00 for the FLOTTER CNF translation.
% 118.12/118.35 0:00:01.16 for inferences.
% 118.12/118.35 0:00:05.09 for the backtracking.
% 118.12/118.35 0:1:50.74 for the reduction.
% 118.12/118.35
% 118.12/118.35
% 118.12/118.35 Here is a proof with depth 11, length 125 :
% 118.12/118.35 % SZS output start Refutation
% See solution above
% 119.01/119.23 Formulae used in the proof : cls_singletonE_0 cls_keymode_Oinduct_0 cls_rev__predicate1D_0 cls_insert__subset_0 cls_analz__insert_0 cls_sym__shrK_0 cls_symKeys__invKey__iff_0 cls_not__symKeys__pubK_0 cls_initState__subset__knows_0 cls_not__symKeys__priK_0 cls_parts__analz_0 cls_usedI_0 cls_shrK__in__initState_0 cls_Crypt__notin__initState_0 cls_parts_OInj_0 cls_insert__absorb_0 cls_insert__commute_0 cls_invKey__shrK_0 cls_invKey__eq_0 cls_insert__code_0 cls_insert__code_1 cls_invKey_0 cls_pubK__neq__shrK_0 cls_publicKey__neq__privateKey_0 cls_NS3__msg__in__parts__spies_0 cls_Spy__analz__shrK_0 cls_Says__Server__message__form_2 cls_Says__Server__message__form_1 cls_analz_OInj_0 cls_mem__def_1 cls_mem__def_0 cls_conjecture_0 cls_conjecture_2 cls_conjecture_4
% 119.01/119.23
%------------------------------------------------------------------------------