TSTP Solution File: SWV346-2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV346-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n028.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 18:05:19 EDT 2024
% Result : Unsatisfiable 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV346-2 : TPTP v8.2.0. Released v3.2.0.
% 0.03/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n028.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 : Sun May 26 21:59:09 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.fuAdT2jMSG/cvc5---1.0.5_8609.smt2
% 0.20/0.52 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.fuAdT2jMSG/cvc5---1.0.5_8609.smt2
% 0.20/0.53 (assume a0 (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na V_na_H))))
% 0.20/0.53 (assume a1 (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent)))
% 0.20/0.53 (assume a2 (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))
% 0.20/0.53 (assume a3 (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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))
% 0.20/0.53 (assume a4 (not (= tptp.v_na (tptp.c_Message_Omsg_ONonce tptp.v_NA))))
% 0.20/0.53 (step t1 (cl (=> (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na)))) :rule implies_neg1)
% 0.20/0.53 (anchor :step t2)
% 0.20/0.53 (assume t2.a0 (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na))))
% 0.20/0.53 (step t2.t1 (cl (or (not (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na)))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na)))) :rule forall_inst :args ((:= V_evs tptp.v_evso) (:= V_A_H tptp.v_Aa) (:= V_B_H tptp.v_Ba) (:= V_K tptp.v_K) (:= V_na_H (tptp.c_Message_Omsg_ONonce tptp.v_NA)) (:= V_nb_H (tptp.c_Message_Omsg_ONonce tptp.v_NB)) (:= V_X_H tptp.v_X) (:= V_A tptp.v_A) (:= V_B tptp.v_B) (:= V_na tptp.v_na) (:= V_nb tptp.v_nb) (:= V_X (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))))))
% 0.20/0.53 (step t2.t2 (cl (not (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na)))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) :rule or :premises (t2.t1))
% 0.20/0.53 (step t2.t3 (cl (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) :rule resolution :premises (t2.t2 t2.a0))
% 0.20/0.53 (step t2 (cl (not (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na)))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) :rule subproof :discharge (t2.a0))
% 0.20/0.53 (step t3 (cl (=> (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) :rule resolution :premises (t1 t2))
% 0.20/0.53 (step t4 (cl (=> (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) (not (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na)))) :rule implies_neg2)
% 0.20/0.53 (step t5 (cl (=> (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) (=> (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na)))) :rule resolution :premises (t3 t4))
% 0.20/0.53 (step t6 (cl (=> (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na)))) :rule contraction :premises (t5))
% 0.20/0.53 (step t7 (cl (not (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na)))) (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) :rule implies :premises (t6))
% 0.20/0.53 (step t8 (cl (not (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na)) :rule or_pos)
% 0.20/0.53 (step t9 (cl (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na) (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na)))) :rule reordering :premises (t8))
% 0.20/0.53 (step t10 (cl (not (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na))) :rule not_symm :premises (a4))
% 0.20/0.53 (step t11 (cl (not (or (not (tptp.c_in tptp.v_evso tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_Aa (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK tptp.v_Aa) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_Ba) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey 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_evso 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.v_na 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_evso tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= (tptp.c_Message_Omsg_ONonce tptp.v_NA) tptp.v_na)))) :rule resolution :premises (t9 t10 a1 a2 a3))
% 0.20/0.53 (step t12 (cl (not (= (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na V_na_H))) (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na))))) (not (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na V_na_H)))) (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na)))) :rule equiv_pos2)
% 0.20/0.53 (anchor :step t13 :args ((V_evs $$unsorted) (:= V_evs V_evs) (V_A_H $$unsorted) (:= V_A_H V_A_H) (V_B_H $$unsorted) (:= V_B_H V_B_H) (V_K $$unsorted) (:= V_K V_K) (V_na_H $$unsorted) (:= V_na_H V_na_H) (V_nb_H $$unsorted) (:= V_nb_H V_nb_H) (V_X_H $$unsorted) (:= V_X_H V_X_H) (V_A $$unsorted) (:= V_A V_A) (V_B $$unsorted) (:= V_B V_B) (V_na $$unsorted) (:= V_na V_na) (V_nb $$unsorted) (:= V_nb V_nb) (V_X $$unsorted) (:= V_X V_X)))
% 0.20/0.53 (step t13.t1 (cl (= V_evs V_evs)) :rule refl)
% 0.20/0.53 (step t13.t2 (cl (= V_A_H V_A_H)) :rule refl)
% 0.20/0.53 (step t13.t3 (cl (= V_B_H V_B_H)) :rule refl)
% 0.20/0.53 (step t13.t4 (cl (= V_K V_K)) :rule refl)
% 0.20/0.53 (step t13.t5 (cl (= V_na_H V_na_H)) :rule refl)
% 0.20/0.53 (step t13.t6 (cl (= V_nb_H V_nb_H)) :rule refl)
% 0.20/0.53 (step t13.t7 (cl (= V_X_H V_X_H)) :rule refl)
% 0.20/0.53 (step t13.t8 (cl (= V_A V_A)) :rule refl)
% 0.20/0.53 (step t13.t9 (cl (= V_B V_B)) :rule refl)
% 0.20/0.53 (step t13.t10 (cl (= V_na V_na)) :rule refl)
% 0.20/0.53 (step t13.t11 (cl (= V_nb V_nb)) :rule refl)
% 0.20/0.53 (step t13.t12 (cl (= V_X V_X)) :rule refl)
% 0.20/0.53 (step t13.t13 (cl (= (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in V_evs tptp.c_Yahalom_Oyahalom (tptp.tc_List_Olist tptp.tc_Event_Oevent))))) :rule refl)
% 0.20/0.53 (step t13.t14 (cl (= (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule refl)
% 0.20/0.53 (step t13.t15 (cl (= (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))) :rule refl)
% 0.20/0.53 (step t13.t16 (cl (= (= V_na V_na_H) (= V_na_H V_na))) :rule all_simplify)
% 0.20/0.53 (step t13.t17 (cl (= (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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na V_na_H)) (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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na)))) :rule cong :premises (t13.t13 t13.t14 t13.t15 t13.t16))
% 0.20/0.53 (step t13 (cl (= (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na V_na_H))) (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na))))) :rule bind)
% 0.20/0.53 (step t14 (cl (forall ((V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_na_H $$unsorted) (V_nb_H $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_na $$unsorted) (V_nb $$unsorted) (V_X $$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_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OCrypt (tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OMPair V_na_H V_nb_H)))) V_X_H)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (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)))) V_X)) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (= V_na_H V_na)))) :rule resolution :premises (t12 t13 a0))
% 0.20/0.53 (step t15 (cl) :rule resolution :premises (t7 t11 t14))
% 0.20/0.53
% 0.20/0.53 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.fuAdT2jMSG/cvc5---1.0.5_8609.smt2
% 0.20/0.53 % cvc5---1.0.5 exiting
% 0.20/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------