TSTP Solution File: SWV332-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV332-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:11:14 EDT 2022
% Result : Unsatisfiable 0.90s 0.85s
% Output : Proof 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV332-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 02:38:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.90/0.85 % SZS status Unsatisfiable
% 0.90/0.85 % SZS output start Proof
% 0.90/0.85 tff(c_in_type, type, (
% 0.90/0.85 c_in: ( $i * $i * $i ) > $o)).
% 0.90/0.85 tff(tc_Message_Omsg_type, type, (
% 0.90/0.85 tc_Message_Omsg: $i)).
% 0.90/0.85 tff(c_Message_Oanalz_type, type, (
% 0.90/0.85 c_Message_Oanalz: $i > $i)).
% 0.90/0.85 tff(c_Event_Oknows_type, type, (
% 0.90/0.85 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.90/0.85 tff(v_evs4_type, type, (
% 0.90/0.85 v_evs4: $i)).
% 0.90/0.85 tff(c_Message_Oagent_OSpy_type, type, (
% 0.90/0.85 c_Message_Oagent_OSpy: $i)).
% 0.90/0.85 tff(c_Message_Omsg_OMPair_type, type, (
% 0.90/0.85 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.90/0.85 tff(c_Message_Omsg_ONonce_type, type, (
% 0.90/0.85 c_Message_Omsg_ONonce: $i > $i)).
% 0.90/0.85 tff(v_NB_type, type, (
% 0.90/0.85 v_NB: $i)).
% 0.90/0.85 tff(v_NA_type, type, (
% 0.90/0.85 v_NA: $i)).
% 0.90/0.85 tff(c_Message_Omsg_OKey_type, type, (
% 0.90/0.85 c_Message_Omsg_OKey: $i > $i)).
% 0.90/0.85 tff(v_K_type, type, (
% 0.90/0.85 v_K: $i)).
% 0.90/0.85 tff(c_Message_Omsg_OAgent_type, type, (
% 0.90/0.85 c_Message_Omsg_OAgent: $i > $i)).
% 0.90/0.85 tff(v_Ba_type, type, (
% 0.90/0.85 v_Ba: $i)).
% 0.90/0.85 tff(tc_Message_Oagent_type, type, (
% 0.90/0.85 tc_Message_Oagent: $i)).
% 0.90/0.85 tff(c_Event_Obad_type, type, (
% 0.90/0.85 c_Event_Obad: $i)).
% 0.90/0.85 tff(v_Aa_type, type, (
% 0.90/0.85 v_Aa: $i)).
% 0.90/0.85 tff(tc_Event_Oevent_type, type, (
% 0.90/0.85 tc_Event_Oevent: $i)).
% 0.90/0.85 tff(c_List_Oset_type, type, (
% 0.90/0.85 c_List_Oset: ( $i * $i ) > $i)).
% 0.90/0.85 tff(c_Event_Oevent_OSays_type, type, (
% 0.90/0.85 c_Event_Oevent_OSays: ( $i * $i * $i ) > $i)).
% 0.90/0.85 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.90/0.85 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.90/0.85 tff(c_Public_OshrK_type, type, (
% 0.90/0.85 c_Public_OshrK: $i > $i)).
% 0.90/0.85 tff(c_Message_Oagent_OServer_type, type, (
% 0.90/0.85 c_Message_Oagent_OServer: $i)).
% 0.90/0.85 tff(v_B_type, type, (
% 0.90/0.85 v_B: $i)).
% 0.90/0.85 tff(v_A_type, type, (
% 0.90/0.85 v_A: $i)).
% 0.90/0.85 tff(v_sko__2jj_type, type, (
% 0.90/0.85 v_sko__2jj: ( $i * $i * $i * $i ) > $i)).
% 0.90/0.85 tff(v_sko__2ji_type, type, (
% 0.90/0.85 v_sko__2ji: ( $i * $i * $i * $i ) > $i)).
% 0.90/0.85 tff(c_Message_Oparts_type, type, (
% 0.90/0.85 c_Message_Oparts: $i > $i)).
% 0.90/0.85 tff(tc_List_Olist_type, type, (
% 0.90/0.85 tc_List_Olist: $i > $i)).
% 0.90/0.85 tff(c_Yahalom_Oyahalom_type, type, (
% 0.90/0.85 c_Yahalom_Oyahalom: $i)).
% 0.90/0.85 tff(v_X_type, type, (
% 0.90/0.85 v_X: $i)).
% 0.90/0.85 tff(c_Event_Oevent_OGets_type, type, (
% 0.90/0.85 c_Event_Oevent_OGets: ( $i * $i ) > $i)).
% 0.90/0.85 tff(1,assumption,(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)), introduced(assumption)).
% 0.90/0.85 tff(2,plain,
% 0.90/0.85 ((~c_in(v_B, c_Event_Obad, tc_Message_Oagent)) <=> (~c_in(v_B, c_Event_Obad, tc_Message_Oagent))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(3,axiom,(~c_in(v_B, c_Event_Obad, tc_Message_Oagent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_9')).
% 0.90/0.85 tff(4,plain,
% 0.90/0.85 (~c_in(v_B, c_Event_Obad, tc_Message_Oagent)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.90/0.85 tff(5,plain,
% 0.90/0.85 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(6,axiom,(c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_8')).
% 0.90/0.85 tff(7,plain,
% 0.90/0.85 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.90/0.85 tff(8,plain,
% 0.90/0.85 (c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)) <=> c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(9,axiom,(c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.90/0.85 tff(10,plain,
% 0.90/0.85 (c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.90/0.85 tff(11,plain,
% 0.90/0.85 (^[V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), 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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(12,plain,
% 0.90/0.85 (![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[11])).
% 0.90/0.85 tff(13,plain,
% 0.90/0.85 (![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(14,plain,
% 0.90/0.85 (^[V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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_Yahalom_Oyahalom, 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(c_Message_Omsg_OAgent(V_A), 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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, 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(c_Message_Omsg_OAgent(V_A), 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(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, 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(c_Message_Omsg_OAgent(V_A), 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(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), 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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(15,plain,
% 0.90/0.85 (![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[14])).
% 0.90/0.85 tff(16,axiom,(![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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_Yahalom_OB__trusts__YM4__shrK_0')).
% 0.90/0.85 tff(17,plain,
% 0.90/0.85 (![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.90/0.85 tff(18,plain,
% 0.90/0.85 (![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.90/0.85 tff(19,plain,(
% 0.90/0.85 ![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.90/0.85 inference(skolemize,[status(sab)],[18])).
% 0.90/0.85 tff(20,plain,
% 0.90/0.85 (![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.90/0.85 tff(21,plain,
% 0.90/0.85 (((~![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), 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_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), 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_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(22,plain,
% 0.90/0.85 (((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, 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(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> (c_in(v_B, c_Event_Obad, tc_Message_Oagent) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(23,plain,
% 0.90/0.85 (((~![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, 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(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), 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_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[22])).
% 0.90/0.85 tff(24,plain,
% 0.90/0.85 (((~![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, 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(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), 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_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.90/0.85 inference(transitivity,[status(thm)],[23, 21])).
% 0.90/0.85 tff(25,plain,
% 0.90/0.85 ((~![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, 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(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(26,plain,
% 0.90/0.86 ((~![V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(V_A, V_B, V_K, V_evs)), c_Message_Omsg_ONonce(v_sko__2jj(V_A, V_B, V_K, V_evs)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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(c_Message_Omsg_OAgent(V_A), 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_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.90/0.86 tff(27,plain,
% 0.90/0.86 (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[26, 20, 10, 7, 4])).
% 0.90/0.86 tff(28,plain,
% 0.90/0.86 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H)))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(29,plain,
% 0.90/0.86 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H)) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[28])).
% 0.90/0.86 tff(30,plain,
% 0.90/0.86 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H)) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(31,plain,
% 0.90/0.86 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_B = V_B_H)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_B = V_B_H)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_B = V_B_H)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_B = V_B_H)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(32,plain,
% 0.90/0.86 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_B = V_B_H)) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[31])).
% 0.90/0.86 tff(33,axiom,(![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_B = V_B_H))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_Ounique__session__keys_1')).
% 0.90/0.86 tff(34,plain,
% 0.90/0.86 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.90/0.86 tff(35,plain,
% 0.90/0.86 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.90/0.86 tff(36,plain,(
% 0.90/0.86 ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))),
% 0.90/0.86 inference(skolemize,[status(sab)],[35])).
% 0.90/0.86 tff(37,plain,
% 0.90/0.86 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.90/0.86 tff(38,plain,
% 0.90/0.86 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))) | ((v_B = v_Ba) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))) | (v_B = v_Ba) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(39,plain,
% 0.98/0.86 (((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_B = v_Ba)) <=> ((v_B = v_Ba) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(40,plain,
% 0.98/0.86 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_B = v_Ba))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))) | ((v_B = v_Ba) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.98/0.86 inference(monotonicity,[status(thm)],[39])).
% 0.98/0.86 tff(41,plain,
% 0.98/0.86 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_B = v_Ba))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))) | (v_B = v_Ba) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.86 inference(transitivity,[status(thm)],[40, 38])).
% 0.98/0.86 tff(42,plain,
% 0.98/0.86 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (v_B = v_Ba))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(43,plain,
% 0.98/0.86 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (V_B = V_B_H))) | (v_B = v_Ba) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.98/0.86 tff(44,plain,
% 0.98/0.86 (v_B = v_Ba),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[43, 37, 10, 27, 1])).
% 0.98/0.86 tff(45,plain,
% 0.98/0.86 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : refl(((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(46,plain,
% 0.98/0.87 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[45])).
% 0.98/0.87 tff(47,plain,
% 0.98/0.87 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(48,plain,
% 0.98/0.87 (^[V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_A = V_A_H)) <=> (((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_A = V_A_H)))), rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_A = V_A_H)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_A = V_A_H)) <=> ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(49,plain,
% 0.98/0.87 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_A = V_A_H)) <=> ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[48])).
% 0.98/0.87 tff(50,axiom,(![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | (V_A = V_A_H))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Yahalom_Ounique__session__keys_0')).
% 0.98/0.87 tff(51,plain,
% 0.98/0.87 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.98/0.87 tff(52,plain,
% 0.98/0.87 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.98/0.87 tff(53,plain,(
% 0.98/0.87 ![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(skolemize,[status(sab)],[52])).
% 0.98/0.87 tff(54,plain,
% 0.98/0.87 (![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.98/0.87 tff(55,plain,
% 0.98/0.87 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((v_A = v_Aa) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (v_A = v_Aa) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(56,plain,
% 0.98/0.87 (((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_A = v_Aa) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))) <=> ((v_A = v_Aa) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(57,plain,
% 0.98/0.87 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_A = v_Aa) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((v_A = v_Aa) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[56])).
% 0.98/0.87 tff(58,plain,
% 0.98/0.87 (((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_A = v_Aa) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))) <=> ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (v_A = v_Aa) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(transitivity,[status(thm)],[57, 55])).
% 0.98/0.87 tff(59,plain,
% 0.98/0.87 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (v_A = v_Aa) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(60,plain,
% 0.98/0.87 ((~![V_B_H: $i, V_A_H: $i, V_X_H: $i, V_nb_H: $i, V_nb: $i, V_na: $i, V_X: $i, V_B: $i, V_A: $i, V_na_H: $i, V_K: $i, V_evs: $i] : ((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (V_A = V_A_H) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), V_X)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A_H, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na_H, V_nb_H)))), V_X_H)), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))) | (v_A = v_Aa) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_sko__2ji(v_A, v_B, v_K, v_evs4)), c_Message_Omsg_ONonce(v_sko__2jj(v_A, v_B, v_K, v_evs4)))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.98/0.87 tff(61,plain,
% 0.98/0.87 (v_A = v_Aa),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[60, 54, 10, 27, 1])).
% 0.98/0.87 tff(62,plain,
% 0.98/0.87 (![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X))) <=> ![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(63,plain,
% 0.98/0.87 (^[V_U: $i] : trans(monotonicity(rewrite(((~(V_U = v_X)) | (~(v_B = v_Ba))) <=> ((~(v_B = v_Ba)) | (~(V_U = v_X)))), ((((~(V_U = v_X)) | (~(v_B = v_Ba))) | (~(v_A = v_Aa))) <=> (((~(v_B = v_Ba)) | (~(V_U = v_X))) | (~(v_A = v_Aa))))), rewrite((((~(v_B = v_Ba)) | (~(V_U = v_X))) | (~(v_A = v_Aa))) <=> ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))), ((((~(V_U = v_X)) | (~(v_B = v_Ba))) | (~(v_A = v_Aa))) <=> ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(64,plain,
% 0.98/0.87 (![V_U: $i] : (((~(V_U = v_X)) | (~(v_B = v_Ba))) | (~(v_A = v_Aa))) <=> ![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[63])).
% 0.98/0.88 tff(65,axiom,(![V_U: $i] : (((~(V_U = v_X)) | (~(v_B = v_Ba))) | (~(v_A = v_Aa)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_11')).
% 0.98/0.88 tff(66,plain,
% 0.98/0.88 (![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.98/0.88 tff(67,plain,
% 0.98/0.88 (![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.98/0.88 tff(68,plain,(
% 0.98/0.88 ![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))),
% 0.98/0.88 inference(skolemize,[status(sab)],[67])).
% 0.98/0.88 tff(69,plain,
% 0.98/0.88 (((~![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))) | ((~(v_B = v_Ba)) | (~(v_A = v_Aa)))) <=> ((~![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))) | (~(v_B = v_Ba)) | (~(v_A = v_Aa)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(70,plain,
% 0.98/0.88 (((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | $false) <=> ((~(v_B = v_Ba)) | (~(v_A = v_Aa)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(71,plain,
% 0.98/0.88 ((~$true) <=> $false),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(72,plain,
% 0.98/0.88 ((v_X = v_X) <=> $true),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(73,plain,
% 0.98/0.88 ((~(v_X = v_X)) <=> (~$true)),
% 0.98/0.88 inference(monotonicity,[status(thm)],[72])).
% 0.98/0.88 tff(74,plain,
% 0.98/0.88 ((~(v_X = v_X)) <=> $false),
% 0.98/0.88 inference(transitivity,[status(thm)],[73, 71])).
% 0.98/0.88 tff(75,plain,
% 0.98/0.88 (((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(v_X = v_X))) <=> ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | $false)),
% 0.98/0.88 inference(monotonicity,[status(thm)],[74])).
% 0.98/0.88 tff(76,plain,
% 0.98/0.88 (((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(v_X = v_X))) <=> ((~(v_B = v_Ba)) | (~(v_A = v_Aa)))),
% 0.98/0.88 inference(transitivity,[status(thm)],[75, 70])).
% 0.98/0.88 tff(77,plain,
% 0.98/0.88 (((~![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))) | ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(v_X = v_X)))) <=> ((~![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))) | ((~(v_B = v_Ba)) | (~(v_A = v_Aa))))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[76])).
% 0.98/0.88 tff(78,plain,
% 0.98/0.88 (((~![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))) | ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(v_X = v_X)))) <=> ((~![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))) | (~(v_B = v_Ba)) | (~(v_A = v_Aa)))),
% 0.98/0.88 inference(transitivity,[status(thm)],[77, 69])).
% 0.98/0.88 tff(79,plain,
% 0.98/0.88 ((~![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))) | ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(v_X = v_X)))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(80,plain,
% 0.98/0.88 ((~![V_U: $i] : ((~(v_B = v_Ba)) | (~(v_A = v_Aa)) | (~(V_U = v_X)))) | (~(v_B = v_Ba)) | (~(v_A = v_Aa))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.98/0.88 tff(81,plain,
% 0.98/0.88 ((~(v_B = v_Ba)) | (~(v_A = v_Aa))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[80, 68])).
% 0.98/0.88 tff(82,plain,
% 0.98/0.88 ($false),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[81, 61, 44])).
% 0.98/0.88 tff(83,plain,(~c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.88 tff(84,plain,
% 0.98/0.88 (c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) <=> c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(85,axiom,(c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.98/0.88 tff(86,plain,
% 0.98/0.88 (c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.98/0.88 tff(87,plain,
% 0.98/0.88 (^[V_X: $i, V_B: $i, V_evs: $i] : refl((c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(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_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(88,plain,
% 0.98/0.88 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[87])).
% 0.98/0.88 tff(89,plain,
% 0.98/0.88 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(90,plain,
% 0.98/0.88 (^[V_X: $i, V_B: $i, V_evs: $i] : trans(monotonicity(rewrite(((~c_in(V_evs, c_Yahalom_Oyahalom, 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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))), ((((~c_in(V_evs, c_Yahalom_Oyahalom, 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(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> (((~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))), 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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))), ((((~c_in(V_evs, c_Yahalom_Oyahalom, 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(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(91,plain,
% 0.98/0.88 (![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_Yahalom_Oyahalom, 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(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[90])).
% 0.98/0.88 tff(92,axiom,(![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_Yahalom_Oyahalom, 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(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_Yahalom_OGets__imp__analz__Spy__dest_0')).
% 0.98/0.88 tff(93,plain,
% 0.98/0.88 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.98/0.88 tff(94,plain,
% 0.98/0.88 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.98/0.88 tff(95,plain,(
% 0.98/0.88 ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(skolemize,[status(sab)],[94])).
% 0.98/0.88 tff(96,plain,
% 0.98/0.88 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.98/0.88 tff(97,plain,
% 0.98/0.88 (((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) <=> ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(98,plain,
% 0.98/0.88 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(99,plain,
% 0.98/0.88 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg) | (~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_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Event_Oevent_OGets(v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X)), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.98/0.88 tff(100,plain,
% 0.98/0.88 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[99, 96, 10, 86])).
% 0.98/0.88 tff(101,plain,
% 0.98/0.88 (^[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_X, 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_X, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(102,plain,
% 0.98/0.88 (![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_X, 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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[101])).
% 0.98/0.88 tff(103,plain,
% 0.98/0.88 (![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_X, 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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(104,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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__analz_1')).
% 0.98/0.88 tff(105,plain,
% 0.98/0.88 (![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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.98/0.88 tff(106,plain,(
% 0.98/0.88 ![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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(skolemize,[status(sab)],[105])).
% 0.98/0.88 tff(107,plain,
% 0.98/0.88 (![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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.98/0.88 tff(108,plain,
% 0.98/0.88 (((~![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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), 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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(109,plain,
% 0.98/0.88 ((~![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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(110,plain,
% 0.98/0.88 ((~![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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), v_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.98/0.88 tff(111,plain,
% 0.98/0.88 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[110, 107, 100])).
% 0.98/0.88 tff(112,plain,
% 0.98/0.88 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(113,plain,
% 0.98/0.88 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[112])).
% 0.98/0.88 tff(114,plain,
% 0.98/0.88 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(115,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz__conj__parts_0')).
% 0.98/0.88 tff(116,plain,
% 0.98/0.88 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.98/0.88 tff(117,plain,(
% 0.98/0.88 ![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(skolemize,[status(sab)],[116])).
% 0.98/0.88 tff(118,plain,
% 0.98/0.88 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.98/0.88 tff(119,plain,
% 0.98/0.88 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(120,plain,
% 0.98/0.88 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(121,plain,
% 0.98/0.88 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.98/0.88 tff(122,plain,
% 0.98/0.88 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[121, 118, 111])).
% 0.98/0.88 tff(123,plain,
% 0.98/0.88 (^[V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : refl((c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) <=> (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(124,plain,
% 0.98/0.88 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) <=> ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[123])).
% 0.98/0.88 tff(125,plain,
% 0.98/0.88 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) <=> ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(126,plain,
% 0.98/0.88 (^[V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : trans(monotonicity(rewrite((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) <=> (c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ((c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), rewrite(((c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))), (((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(127,plain,
% 0.98/0.88 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[126])).
% 0.98/0.89 tff(128,axiom,(![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : ((((~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), 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_Yahalom_OA__trusts__YM3_0')).
% 0.98/0.89 tff(129,plain,
% 0.98/0.89 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.98/0.89 tff(130,plain,
% 0.98/0.89 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.98/0.89 tff(131,plain,(
% 0.98/0.89 ![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.89 inference(skolemize,[status(sab)],[130])).
% 0.98/0.89 tff(132,plain,
% 0.98/0.89 (![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.98/0.89 tff(133,plain,
% 0.98/0.89 (((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(134,plain,
% 0.98/0.89 ((c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent)))) <=> ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(135,plain,
% 0.98/0.89 (((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) <=> ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | ((~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[134])).
% 0.98/0.89 tff(136,plain,
% 0.98/0.89 (((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) <=> ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[135, 133])).
% 0.98/0.89 tff(137,plain,
% 0.98/0.89 ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(138,plain,
% 0.98/0.89 ((~![V_nb: $i, V_na: $i, V_B: $i, V_A: $i, V_K: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, V_A, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Omsg_OCrypt(c_Public_OshrK(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A), c_Message_Omsg_OKey(V_K))))), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K), c_Message_Omsg_OMPair(V_na, V_nb)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_evs, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))))) | (~c_in(v_evs4, c_Yahalom_Oyahalom, tc_List_Olist(tc_Event_Oevent))) | c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.98/0.89 tff(139,plain,
% 0.98/0.89 (c_in(v_Aa, c_Event_Obad, tc_Message_Oagent) | c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer, v_Aa, c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa), c_Message_Omsg_OKey(v_K))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[138, 132, 10, 122])).
% 0.98/0.89 tff(140,plain,
% 0.98/0.89 (c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[139, 83])).
% 0.98/0.89 tff(141,plain,
% 0.98/0.89 (^[V_X: $i, V_A: $i, V_evs: $i] : refl((c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))) <=> (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(142,plain,
% 0.98/0.89 (![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))) <=> ![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[141])).
% 0.98/0.89 tff(143,plain,
% 0.98/0.89 (![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))) <=> ![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(144,plain,
% 0.98/0.89 (^[V_X: $i, V_A: $i, V_evs: $i] : rewrite((((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(145,plain,
% 0.98/0.89 (![V_X: $i, V_A: $i, V_evs: $i] : (((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[144])).
% 0.98/0.89 tff(146,axiom,(![V_X: $i, V_A: $i, V_evs: $i] : (((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | 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_Public_OCrypt__Spy__analz__bad_0')).
% 0.98/0.89 tff(147,plain,
% 0.98/0.89 (![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.98/0.89 tff(148,plain,
% 0.98/0.89 (![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.98/0.89 tff(149,plain,(
% 0.98/0.89 ![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(skolemize,[status(sab)],[148])).
% 0.98/0.89 tff(150,plain,
% 0.98/0.89 (![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.98/0.89 tff(151,plain,
% 0.98/0.89 (((~![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))) <=> ((~![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(152,plain,
% 0.98/0.89 ((c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent))) <=> ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(153,plain,
% 0.98/0.89 (((~![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))) <=> ((~![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[152])).
% 0.98/0.89 tff(154,plain,
% 0.98/0.89 (((~![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))) <=> ((~![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[153, 151])).
% 0.98/0.89 tff(155,plain,
% 0.98/0.89 ((~![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(156,plain,
% 0.98/0.89 ((~![V_X: $i, V_A: $i, V_evs: $i] : (c_in(V_X, 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_A), V_X), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) | (~c_in(V_A, c_Event_Obad, tc_Message_Oagent)))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa), c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.98/0.89 tff(157,plain,
% 0.98/0.89 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | (~c_in(v_Aa, c_Event_Obad, tc_Message_Oagent))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[156, 150, 111])).
% 0.98/0.89 tff(158,plain,
% 0.98/0.89 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[157, 140])).
% 0.98/0.89 tff(159,plain,
% 0.98/0.89 (^[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)))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(160,plain,
% 0.98/0.89 (![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))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[159])).
% 0.98/0.89 tff(161,plain,
% 0.98/0.89 (![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))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(162,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')).
% 0.98/0.89 tff(163,plain,
% 0.98/0.89 (![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))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.98/0.89 tff(164,plain,(
% 0.98/0.89 ![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))),
% 0.98/0.89 inference(skolemize,[status(sab)],[163])).
% 0.98/0.89 tff(165,plain,
% 0.98/0.89 (![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))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.98/0.89 tff(166,plain,
% 0.98/0.89 (((~![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(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), 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(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(167,plain,
% 0.98/0.90 ((~![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(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(168,plain,
% 0.98/0.90 ((~![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(c_Message_Omsg_OAgent(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.98/0.90 tff(169,plain,
% 0.98/0.90 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[168, 165, 158])).
% 0.98/0.90 tff(170,plain,
% 0.98/0.90 ((~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(171,axiom,(~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_6')).
% 0.98/0.90 tff(172,plain,
% 0.98/0.90 (~c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.98/0.90 tff(173,plain,
% 0.98/0.90 (((~![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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), 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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(174,plain,
% 0.98/0.90 ((~![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_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(175,plain,
% 0.98/0.90 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_ONonce(v_NB))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(v_K), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.98/0.90 tff(176,plain,
% 0.98/0.90 ($false),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[175, 107, 172, 169])).
% 0.98/0.90 % SZS output end Proof
%------------------------------------------------------------------------------