%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV337-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n014.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 : Wed May 29 18:05:16 EDT 2024

% Result   : Unsatisfiable 0.21s 0.54s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SWV337-2 : TPTP v8.2.0. Released v3.2.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n014.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 May 27 01:16:09 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.21/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.54  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.vlssXdV2Hm/cvc5---1.0.5_14790.smt2
% 0.21/0.54  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.vlssXdV2Hm/cvc5---1.0.5_14790.smt2
% 0.21/0.56  (assume a0 (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent)))
% 0.21/0.56  (assume a1 (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))
% 0.21/0.56  (assume a2 (not (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))
% 0.21/0.56  (assume a3 (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))
% 0.21/0.56  (assume a4 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))
% 0.21/0.56  (assume a5 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))
% 0.21/0.56  (assume a6 (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))))
% 0.21/0.56  (assume a7 (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))
% 0.21/0.56  (assume a8 (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))
% 0.21/0.56  (assume a9 (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))
% 0.21/0.56  (step t1 (cl (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule or_pos)
% 0.21/0.56  (step t2 (cl (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule reordering :premises (t1))
% 0.21/0.56  (step t3 (cl (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule or_pos)
% 0.21/0.56  (step t4 (cl (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule reordering :premises (t3))
% 0.21/0.56  (step t5 (cl (not (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule or_pos)
% 0.21/0.56  (step t6 (cl (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg) (not (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule reordering :premises (t5))
% 0.21/0.56  (step t7 (cl (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule or_pos)
% 0.21/0.56  (step t8 (cl (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule reordering :premises (t7))
% 0.21/0.56  (step t9 (cl (not (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule or_pos)
% 0.21/0.56  (step t10 (cl (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg) (not (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule reordering :premises (t9))
% 0.21/0.56  (step t11 (cl (=> (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) :rule implies_neg1)
% 0.21/0.56  (anchor :step t12)
% 0.21/0.56  (assume t12.a0 (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))
% 0.21/0.56  (step t12.t1 (cl (or (not (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule forall_inst :args ((:= V_evs tptp.v_evs4) (:= V_B tptp.v_A) (:= V_X (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X))))
% 0.21/0.56  (step t12.t2 (cl (not (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule or :premises (t12.t1))
% 0.21/0.56  (step t12.t3 (cl (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t12.t2 t12.a0))
% 0.21/0.56  (step t12 (cl (not (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule subproof :discharge (t12.a0))
% 0.21/0.56  (step t13 (cl (=> (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t11 t12))
% 0.21/0.56  (step t14 (cl (=> (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule implies_neg2)
% 0.21/0.56  (step t15 (cl (=> (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (=> (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule resolution :premises (t13 t14))
% 0.21/0.56  (step t16 (cl (=> (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule contraction :premises (t15))
% 0.21/0.56  (step t17 (cl (not (forall ((V_evs $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule implies :premises (t16))
% 0.21/0.56  (step t18 (cl (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OGets tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X)) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t17 a9))
% 0.21/0.56  (step t19 (cl (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule resolution :premises (t10 a0 a1 t18))
% 0.21/0.56  (step t20 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) :rule implies_neg1)
% 0.21/0.56  (anchor :step t21)
% 0.21/0.56  (assume t21.a0 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))
% 0.21/0.56  (step t21.t1 (cl (or (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule forall_inst :args ((:= V_X (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))))) (:= V_Y tptp.v_X) (:= V_H (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4))))
% 0.21/0.56  (step t21.t2 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule or :premises (t21.t1))
% 0.21/0.56  (step t21.t3 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t21.t2 t21.a0))
% 0.21/0.56  (step t21 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule subproof :discharge (t21.a0))
% 0.21/0.56  (step t22 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t20 t21))
% 0.21/0.56  (step t23 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule implies_neg2)
% 0.21/0.56  (step t24 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule resolution :premises (t22 t23))
% 0.21/0.56  (step t25 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule contraction :premises (t24))
% 0.21/0.56  (step t26 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule implies :premises (t25))
% 0.21/0.56  (step t27 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) tptp.v_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t26 a5))
% 0.21/0.56  (step t28 (cl (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule resolution :premises (t8 t19 t27))
% 0.21/0.56  (step t29 (cl (not (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) :rule or_pos)
% 0.21/0.56  (step t30 (cl (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule reordering :premises (t29))
% 0.21/0.56  (step t31 (cl (=> (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule implies_neg1)
% 0.21/0.56  (anchor :step t32)
% 0.21/0.56  (assume t32.a0 (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))
% 0.21/0.56  (step t32.t1 (cl (or (not (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule forall_inst :args ((:= V_U tptp.v_A) (:= V_V tptp.v_B) (:= V_W tptp.v_NA)))
% 0.21/0.56  (step t32.t2 (cl (not (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule or :premises (t32.t1))
% 0.21/0.56  (step t32.t3 (cl (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule resolution :premises (t32.t2 t32.a0))
% 0.21/0.56  (step t32 (cl (not (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule subproof :discharge (t32.a0))
% 0.21/0.56  (step t33 (cl (=> (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule resolution :premises (t31 t32))
% 0.21/0.56  (step t34 (cl (=> (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule implies_neg2)
% 0.21/0.56  (step t35 (cl (=> (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (=> (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule resolution :premises (t33 t34))
% 0.21/0.56  (step t36 (cl (=> (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule contraction :premises (t35))
% 0.21/0.56  (step t37 (cl (not (forall ((V_U $$unsorted) (V_V $$unsorted) (V_W $$unsorted)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_U (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_U) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_W) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_V) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_U) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule implies :premises (t36))
% 0.21/0.56  (step t38 (cl (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule resolution :premises (t37 a3))
% 0.21/0.56  (step t39 (cl (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule or_pos)
% 0.21/0.56  (step t40 (cl (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule reordering :premises (t39))
% 0.21/0.56  (step t41 (cl (=> (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) :rule implies_neg1)
% 0.21/0.56  (anchor :step t42)
% 0.21/0.56  (assume t42.a0 (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))))
% 0.21/0.56  (step t42.t1 (cl (or (not (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule forall_inst :args ((:= V_c (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))))) (:= V_H (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4))))
% 0.21/0.56  (step t42.t2 (cl (not (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule or :premises (t42.t1))
% 0.21/0.56  (step t42.t3 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t42.t2 t42.a0))
% 0.21/0.56  (step t42 (cl (not (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule subproof :discharge (t42.a0))
% 0.21/0.56  (step t43 (cl (=> (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t41 t42))
% 0.21/0.56  (step t44 (cl (=> (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule implies_neg2)
% 0.21/0.56  (step t45 (cl (=> (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (=> (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule resolution :premises (t43 t44))
% 0.21/0.56  (step t46 (cl (=> (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule contraction :premises (t45))
% 0.21/0.56  (step t47 (cl (not (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule implies :premises (t46))
% 0.21/0.56  (step t48 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t47 a6))
% 0.21/0.56  (step t49 (cl (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule resolution :premises (t40 t28 t48))
% 0.21/0.56  (step t50 (cl (=> (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule implies_neg1)
% 0.21/0.56  (anchor :step t51)
% 0.21/0.56  (assume t51.a0 (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))
% 0.21/0.56  (step t51.t1 (cl (or (not (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule forall_inst :args ((:= V_evs tptp.v_evs4) (:= V_A tptp.v_A) (:= V_B tptp.v_B) (:= V_K tptp.v_K) (:= V_na (tptp.c_Message_Omsg_ONonce tptp.v_NA)) (:= V_nb (tptp.c_Message_Omsg_ONonce tptp.v_NB))))
% 0.21/0.56  (step t51.t2 (cl (not (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule or :premises (t51.t1))
% 0.21/0.56  (step t51.t3 (cl (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule resolution :premises (t51.t2 t51.a0))
% 0.21/0.56  (step t51 (cl (not (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule subproof :discharge (t51.a0))
% 0.21/0.56  (step t52 (cl (=> (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule resolution :premises (t50 t51))
% 0.21/0.56  (step t53 (cl (=> (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule implies_neg2)
% 0.21/0.56  (step t54 (cl (=> (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (=> (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule resolution :premises (t52 t53))
% 0.21/0.56  (step t55 (cl (=> (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule contraction :premises (t54))
% 0.21/0.56  (step t56 (cl (not (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_na $$unsorted) (V_nb $$unsorted)) (or (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na V_nb)))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OKey V_K))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule implies :premises (t55))
% 0.21/0.56  (step t57 (cl (or (not (tptp.c_in tptp.v_evs4 tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_A) (tptp.c_Message_Omsg_OKey tptp.v_K))))) (tptp.c_List_Oset tptp.v_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) :rule resolution :premises (t56 a8))
% 0.21/0.56  (step t58 (cl (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) :rule resolution :premises (t30 a0 t38 t49 t57))
% 0.21/0.56  (step t59 (cl (=> (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) :rule implies_neg1)
% 0.21/0.56  (anchor :step t60)
% 0.21/0.56  (assume t60.a0 (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))
% 0.21/0.56  (step t60.t1 (cl (or (not (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule forall_inst :args ((:= V_A tptp.v_A) (:= V_X (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (:= V_evs tptp.v_evs4)))
% 0.21/0.56  (step t60.t2 (cl (not (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule or :premises (t60.t1))
% 0.21/0.56  (step t60.t3 (cl (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t60.t2 t60.a0))
% 0.21/0.56  (step t60 (cl (not (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule subproof :discharge (t60.a0))
% 0.21/0.56  (step t61 (cl (=> (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t59 t60))
% 0.21/0.56  (step t62 (cl (=> (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule implies_neg2)
% 0.21/0.56  (step t63 (cl (=> (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (=> (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule resolution :premises (t61 t62))
% 0.21/0.56  (step t64 (cl (=> (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule contraction :premises (t63))
% 0.21/0.56  (step t65 (cl (not (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A) V_X) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule implies :premises (t64))
% 0.21/0.56  (step t66 (cl (or (not (tptp.c_in tptp.v_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t65 a7))
% 0.21/0.56  (step t67 (cl (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule resolution :premises (t6 t28 t58 t66))
% 0.21/0.56  (step t68 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) :rule implies_neg1)
% 0.21/0.56  (anchor :step t69)
% 0.21/0.56  (assume t69.a0 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))
% 0.21/0.56  (step t69.t1 (cl (or (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule forall_inst :args ((:= V_X (tptp.c_Message_Omsg_OAgent tptp.v_B)) (:= V_Y (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (:= V_H (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4))))
% 0.21/0.56  (step t69.t2 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule or :premises (t69.t1))
% 0.21/0.56  (step t69.t3 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t69.t2 t69.a0))
% 0.21/0.56  (step t69 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule subproof :discharge (t69.a0))
% 0.21/0.56  (step t70 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t68 t69))
% 0.21/0.56  (step t71 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule implies_neg2)
% 0.21/0.56  (step t72 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule resolution :premises (t70 t71))
% 0.21/0.56  (step t73 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule contraction :premises (t72))
% 0.21/0.56  (step t74 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule implies :premises (t73))
% 0.21/0.56  (step t75 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t74 a4))
% 0.21/0.56  (step t76 (cl (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule resolution :premises (t4 t67 t75))
% 0.21/0.56  (step t77 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) :rule implies_neg1)
% 0.21/0.56  (anchor :step t78)
% 0.21/0.56  (assume t78.a0 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))
% 0.21/0.56  (step t78.t1 (cl (or (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule forall_inst :args ((:= V_X (tptp.c_Message_Omsg_OKey tptp.v_K)) (:= V_Y (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (:= V_H (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4))))
% 0.21/0.56  (step t78.t2 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule or :premises (t78.t1))
% 0.21/0.56  (step t78.t3 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t78.t2 t78.a0))
% 0.21/0.56  (step t78 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule subproof :discharge (t78.a0))
% 0.21/0.56  (step t79 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t77 t78))
% 0.21/0.56  (step t80 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule implies_neg2)
% 0.21/0.56  (step t81 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule resolution :premises (t79 t80))
% 0.21/0.56  (step t82 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule contraction :premises (t81))
% 0.21/0.56  (step t83 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule implies :premises (t82))
% 0.21/0.56  (step t84 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey tptp.v_K) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t83 a4))
% 0.21/0.56  (step t85 (cl (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) :rule or_pos)
% 0.21/0.56  (step t86 (cl (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule reordering :premises (t85))
% 0.21/0.56  (step t87 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) :rule implies_neg1)
% 0.21/0.56  (anchor :step t88)
% 0.21/0.56  (assume t88.a0 (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))
% 0.21/0.56  (step t88.t1 (cl (or (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule forall_inst :args ((:= V_X (tptp.c_Message_Omsg_ONonce tptp.v_NA)) (:= V_Y (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (:= V_H (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4))))
% 0.21/0.56  (step t88.t2 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule or :premises (t88.t1))
% 0.21/0.56  (step t88.t3 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t88.t2 t88.a0))
% 0.21/0.56  (step t88 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule subproof :discharge (t88.a0))
% 0.21/0.56  (step t89 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t87 t88))
% 0.21/0.56  (step t90 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule implies_neg2)
% 0.21/0.56  (step t91 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule resolution :premises (t89 t90))
% 0.21/0.56  (step t92 (cl (=> (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)))) :rule contraction :premises (t91))
% 0.21/0.56  (step t93 (cl (not (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_Y (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule implies :premises (t92))
% 0.21/0.56  (step t94 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.c_Message_Omsg_ONonce tptp.v_NB) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t93 a4))
% 0.21/0.56  (step t95 (cl (not (tptp.c_in (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce tptp.v_NA) (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evs4)) tptp.tc_Message_Omsg))) :rule resolution :premises (t86 a2 t94))
% 0.21/0.56  (step t96 (cl) :rule resolution :premises (t2 t76 t84 t95))
% 0.21/0.56  
% 0.21/0.56  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.vlssXdV2Hm/cvc5---1.0.5_14790.smt2
% 0.21/0.56  % cvc5---1.0.5 exiting
% 0.42/0.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------