%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV290-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:32:00 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SWV290-2 : TPTP v9.0.0. Released v3.2.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:38:24 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.36 % SZS status Unsatisfiable
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(c_in_type, type, (
% 0.18/0.36 c_in: ( $i * $i * $i ) > $o)).
% 0.18/0.36 tff(tc_Event_Oevent_type, type, (
% 0.18/0.36 tc_Event_Oevent: $i)).
% 0.18/0.36 tff(c_List_Oset_type, type, (
% 0.18/0.36 c_List_Oset: ( $i * $i ) > $i)).
% 0.18/0.36 tff(v_evs_type, type, (
% 0.18/0.36 v_evs: $i)).
% 0.18/0.36 tff(c_Event_Oevent_OSays_type, type, (
% 0.18/0.36 c_Event_Oevent_OSays: ( $i * $i * $i ) > $i)).
% 0.18/0.36 tff(c_Message_Omsg_OMPair_type, type, (
% 0.18/0.36 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.18/0.36 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.18/0.36 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.18/0.36 tff(c_Message_Omsg_OKey_type, type, (
% 0.18/0.36 c_Message_Omsg_OKey: $i > $i)).
% 0.18/0.36 tff(v_K_type, type, (
% 0.18/0.36 v_K: $i)).
% 0.18/0.36 tff(v_NB_type, type, (
% 0.18/0.36 v_NB: $i)).
% 0.18/0.36 tff(c_Public_OshrK_type, type, (
% 0.18/0.36 c_Public_OshrK: $i > $i)).
% 0.18/0.36 tff(v_B_type, type, (
% 0.18/0.36 v_B: $i)).
% 0.18/0.36 tff(v_X_type, type, (
% 0.18/0.36 v_X: $i)).
% 0.18/0.36 tff(v_NA_type, type, (
% 0.18/0.36 v_NA: $i)).
% 0.18/0.36 tff(v_sko__usf_type, type, (
% 0.18/0.36 v_sko__usf: ( $i * $i * $i ) > $i)).
% 0.18/0.36 tff(tc_Message_Omsg_type, type, (
% 0.18/0.36 tc_Message_Omsg: $i)).
% 0.18/0.36 tff(c_Message_Oanalz_type, type, (
% 0.18/0.36 c_Message_Oanalz: $i > $i)).
% 0.18/0.36 tff(c_Event_Oknows_type, type, (
% 0.18/0.36 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.18/0.36 tff(c_Message_Oagent_OSpy_type, type, (
% 0.18/0.36 c_Message_Oagent_OSpy: $i)).
% 0.18/0.36 tff(c_Message_Oparts_type, type, (
% 0.18/0.36 c_Message_Oparts: $i > $i)).
% 0.18/0.36 tff(c_Message_Omsg_OAgent_type, type, (
% 0.18/0.36 c_Message_Omsg_OAgent: $i > $i)).
% 0.18/0.36 tff(c_Message_Oagent_OServer_type, type, (
% 0.18/0.36 c_Message_Oagent_OServer: $i)).
% 0.18/0.36 tff(tc_Message_Oagent_type, type, (
% 0.18/0.36 tc_Message_Oagent: $i)).
% 0.18/0.36 tff(c_Event_Obad_type, type, (
% 0.18/0.36 c_Event_Obad: $i)).
% 0.18/0.36 tff(tc_List_Olist_type, type, (
% 0.18/0.36 tc_List_Olist: $i > $i)).
% 0.18/0.36 tff(c_OtwayRees_Ootway_type, type, (
% 0.18/0.36 c_OtwayRees_Ootway: $i)).
% 0.18/0.36 tff(v_A_type, type, (
% 0.18/0.36 v_A: $i)).
% 0.18/0.36 tff(v_X_H_type, type, (
% 0.18/0.36 v_X_H: $i)).
% 0.18/0.36 tff(c_Event_Oevent_OGets_type, type, (
% 0.18/0.36 c_Event_Oevent_OGets: ( $i * $i ) > $i)).
% 0.18/0.36 tff(1,assumption,(c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)), introduced(assumption)).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 (^[V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : refl(((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(3,plain,
% 0.18/0.36 (![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.36 tff(4,plain,
% 0.18/0.36 (![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (^[V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) <=> (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)))), rewrite((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) <=> ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) <=> ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))), ((((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), rewrite((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), ((((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.18/0.37 tff(7,axiom,(![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_B, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OtwayRees_ONB__Crypt__imp__Server__msg_0')).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.37 tff(10,plain,(
% 0.18/0.37 ![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[9])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 ((~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(13,axiom,(~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)) <=> c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(16,axiom,(c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 ((~c_in(v_B, c_Event_Obad, tc_Message_Oagent)) <=> (~c_in(v_B, c_Event_Obad, tc_Message_Oagent))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(19,axiom,(~c_in(v_B, c_Event_Obad, tc_Message_Oagent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (~c_in(v_B, c_Event_Obad, tc_Message_Oagent)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) <=> c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(22,axiom,(c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (((~![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (c_in(v_B, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)))) <=> ((~![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | c_in(v_B, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (((~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> (c_in(v_B, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (((~![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (c_in(v_B, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[25])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (((~![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | c_in(v_B, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[26, 24])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 ((~![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 ((~![V_X_H: $i, V_NA: $i, V_NB: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_B, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OKey(V_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K)))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(c_Event_Oevent_OSays(V_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(V_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(V_NA, c_Message_Omsg_OMPair(V_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OAgent(V_B)))))))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | c_in(v_B, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OKey(v_K))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OSays(v_B, c_Message_Oagent_OServer, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(v_X_H, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))))))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[29, 23, 20, 17, 14, 11])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (^[V_c: $i, V_H: $i] : refl(((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(34,axiom,(![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz__into__parts__dest_0')).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 (![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.39 tff(36,plain,(
% 0.18/0.39 ![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(skolemize,[status(sab)],[35])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))) <=> ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[40, 37, 30])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(45,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__analz_0')).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.39 tff(47,plain,(
% 0.18/0.39 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(skolemize,[status(sab)],[46])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[51, 48, 41])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 (~c_in(c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[55, 48, 52])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 (^[V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : refl(((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(60,axiom,(![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Event_OSays__imp__analz__Spy__dest_0')).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.40 tff(62,plain,(
% 0.18/0.40 ![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.18/0.40 inference(skolemize,[status(sab)],[61])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | ((~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))) <=> ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | ((~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[66, 63, 56, 1])).
% 0.18/0.40 tff(68,plain,(~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (^[V_X: $i, V_B: $i, V_evs: $i] : refl((c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) <=> (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[69])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (^[V_X: $i, V_B: $i, V_evs: $i] : trans(monotonicity(rewrite(((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))), ((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (((~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), rewrite((((~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))), ((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.40 tff(74,axiom,(![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OtwayRees_OGets__imp__Says__dest_0')).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.18/0.40 tff(77,plain,(
% 0.18/0.40 ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[76])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) <=> c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(80,axiom,(c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | ((~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 ((c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) <=> ((~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 (((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) <=> ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | ((~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[83])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) <=> ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[84, 82])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (~c_in(v_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K))))), v_evs), v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(v_NB, c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs, tc_Event_Oevent), tc_Event_Oevent))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[87, 81, 17, 78, 68])).
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------