TSTP Solution File: SWV308-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV308-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 15:11:02 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV308-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 02:24:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(c_in_type, type, (
% 0.12/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(tc_Message_Omsg_type, type, (
% 0.12/0.39 tc_Message_Omsg: $i)).
% 0.12/0.39 tff(c_Message_Oanalz_type, type, (
% 0.12/0.39 c_Message_Oanalz: $i > $i)).
% 0.12/0.39 tff(c_Event_Oknows_type, type, (
% 0.12/0.39 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.12/0.39 tff(v_evs4_type, type, (
% 0.12/0.39 v_evs4: $i)).
% 0.12/0.39 tff(c_Message_Oagent_OSpy_type, type, (
% 0.12/0.39 c_Message_Oagent_OSpy: $i)).
% 0.12/0.39 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.12/0.39 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.12/0.39 tff(c_Message_Omsg_OMPair_type, type, (
% 0.12/0.39 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.12/0.39 tff(c_Message_Omsg_OAgent_type, type, (
% 0.12/0.39 c_Message_Omsg_OAgent: $i > $i)).
% 0.12/0.39 tff(v_B_type, type, (
% 0.12/0.39 v_B: $i)).
% 0.12/0.39 tff(v_A_type, type, (
% 0.12/0.39 v_A: $i)).
% 0.12/0.39 tff(v_NA_type, type, (
% 0.12/0.39 v_NA: $i)).
% 0.12/0.39 tff(c_Public_OshrK_type, type, (
% 0.12/0.39 c_Public_OshrK: $i > $i)).
% 0.12/0.39 tff(c_Message_Omsg_OKey_type, type, (
% 0.12/0.39 c_Message_Omsg_OKey: $i > $i)).
% 0.12/0.39 tff(c_Message_Oparts_type, type, (
% 0.12/0.39 c_Message_Oparts: $i > $i)).
% 0.12/0.39 tff(tc_List_Olist_type, type, (
% 0.12/0.39 tc_List_Olist: $i > $i)).
% 0.12/0.39 tff(tc_Event_Oevent_type, type, (
% 0.12/0.39 tc_Event_Oevent: $i)).
% 0.12/0.39 tff(c_OtwayRees_Ootway_type, type, (
% 0.12/0.39 c_OtwayRees_Ootway: $i)).
% 0.12/0.39 tff(tc_Message_Oagent_type, type, (
% 0.12/0.39 tc_Message_Oagent: $i)).
% 0.12/0.39 tff(c_Event_Obad_type, type, (
% 0.12/0.39 c_Event_Obad: $i)).
% 0.12/0.39 tff(c_Message_Osynth_type, type, (
% 0.12/0.39 c_Message_Osynth: $i > $i)).
% 0.12/0.39 tff(v_A_H_type, type, (
% 0.12/0.39 v_A_H: $i)).
% 0.12/0.39 tff(v_NA_H_type, type, (
% 0.12/0.39 v_NA_H: $i)).
% 0.12/0.39 tff(c_union_type, type, (
% 0.12/0.39 c_union: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(v_X_type, type, (
% 0.12/0.39 v_X: $i)).
% 0.12/0.39 tff(v_K_type, type, (
% 0.12/0.39 v_K: $i)).
% 0.12/0.39 tff(c_Message_Omsg_ONonce_type, type, (
% 0.12/0.39 c_Message_Omsg_ONonce: $i > $i)).
% 0.12/0.39 tff(v_NB_type, type, (
% 0.12/0.39 v_NB: $i)).
% 0.12/0.39 tff(v_Ba_type, type, (
% 0.12/0.39 v_Ba: $i)).
% 0.12/0.39 tff(v_NAa_type, type, (
% 0.12/0.39 v_NAa: $i)).
% 0.12/0.39 tff(c_List_Oset_type, type, (
% 0.12/0.39 c_List_Oset: ( $i * $i ) > $i)).
% 0.12/0.39 tff(c_Event_Oevent_OSays_type, type, (
% 0.12/0.39 c_Event_Oevent_OSays: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(v_sko__usf_type, type, (
% 0.12/0.39 v_sko__usf: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(c_Event_Oevent_OGets_type, type, (
% 0.12/0.39 c_Event_Oevent_OGets: ( $i * $i ) > $i)).
% 0.12/0.39 tff(c_insert_type, type, (
% 0.12/0.39 c_insert: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(1,assumption,(c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)) <=> c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,axiom,(c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 ((~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) <=> (~c_in(v_A, c_Event_Obad, tc_Message_Oagent))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,axiom,(~c_in(v_A, c_Event_Obad, tc_Message_Oagent)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (^[V_A: $i, V_evs: $i] : refl(((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) <=> ![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (^[V_A: $i, V_evs: $i] : rewrite((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), 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_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (![V_A: $i, V_evs: $i] : (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), 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)) <=> ![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.40 tff(13,axiom,(![V_A: $i, V_evs: $i] : (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), 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))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_OtwayRees_OSpy__see__shrK__D__dest_0')).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.12/0.40 tff(16,plain,(
% 0.12/0.40 ![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[15])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (((~![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), 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_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), 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_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (((~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> (c_in(v_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (((~![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), 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_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[19])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (((~![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))) <=> ((~![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), 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_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[20, 18])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 ((~![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | ((~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((~![V_A: $i, V_evs: $i] : ((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | c_in(V_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))) | c_in(v_A, c_Event_Obad, tc_Message_Oagent) | (~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[23, 17, 7, 4, 1])).
% 0.20/0.40 tff(25,plain,(~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (^[V_c: $i, V_H: $i] : refl(((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(29,axiom,(![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Oanalz__into__parts__dest_0')).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,(
% 0.20/0.40 ![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.20/0.40 inference(skolemize,[status(sab)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[35, 32, 25])).
% 0.20/0.40 tff(37,assumption,(~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), introduced(assumption)).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (c_in(c_Event_Oevent_OGets(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) <=> c_in(c_Event_Oevent_OGets(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(39,axiom,(c_in(c_Event_Oevent_OGets(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (c_in(c_Event_Oevent_OGets(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (^[V_X: $i, V_B: $i, V_evs: $i] : refl((c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) <=> (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (^[V_X: $i, V_B: $i, V_evs: $i] : trans(monotonicity(rewrite(((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))), ((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (((~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), rewrite((((~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))), ((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.41 tff(46,axiom,(![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_OtwayRees_OGets__imp__Says__dest_0')).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.41 tff(49,plain,(
% 0.20/0.41 ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(v_sko__usf(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) <=> ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(v_sko__usf(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (c_in(c_Event_Oevent_OSays(v_sko__usf(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[53, 50, 4, 40])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (^[V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : refl(((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg)) <=> ![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(58,axiom,(![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Event_OSays__imp__analz__Spy__dest_0')).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.41 tff(60,plain,(
% 0.20/0.41 ![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.20/0.41 inference(skolemize,[status(sab)],[59])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | ((~c_in(c_Event_Oevent_OSays(v_sko__usf(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(c_Event_Oevent_OSays(v_sko__usf(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | ((~c_in(c_Event_Oevent_OSays(v_sko__usf(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(c_Event_Oevent_OSays(v_sko__usf(v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_Ba, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[64, 61, 54])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(69,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/sandbox/benchmark/theBenchmark.p','cls_Message_OMPair__analz_0')).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.42 tff(71,plain,(
% 0.20/0.42 ![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))),
% 0.20/0.42 inference(skolemize,[status(sab)],[70])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (((~![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_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), 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_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), 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_Y, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), 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_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 ((~![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_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), 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_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~![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_ONonce(v_NAa), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), 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_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 72, 65])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(80,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/sandbox/benchmark/theBenchmark.p','cls_Message_OMPair__analz_1')).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.42 tff(82,plain,(
% 0.20/0.42 ![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))),
% 0.20/0.42 inference(skolemize,[status(sab)],[81])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (((~![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(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, 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(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~![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(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((~![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(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (c_in(v_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[86, 83, 76])).
% 0.20/0.42 tff(88,assumption,(~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)), introduced(assumption)).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(92,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Osynth_OInj_0')).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.42 tff(94,plain,(
% 0.20/0.42 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.42 inference(skolemize,[status(sab)],[93])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | ((~c_in(v_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | (~c_in(v_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | ((~c_in(v_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | (~c_in(v_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[98, 95, 88, 87])).
% 0.20/0.42 tff(100,plain,(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(102,axiom,(c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_6')).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (^[V_Z: $i, V_H: $i, V_X: $i] : refl((c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg))) <=> (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg))) <=> ![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg))) <=> ![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (^[V_Z: $i, V_H: $i, V_X: $i] : trans(monotonicity(rewrite(((~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))) <=> ((~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))), ((((~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))) | c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg)) <=> (((~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg))) | c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg)))), rewrite((((~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg))) | c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg)) <=> (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))), ((((~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))) | c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg)) <=> (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (![V_Z: $i, V_H: $i, V_X: $i] : (((~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))) | c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg)) <=> ![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.43 tff(109,axiom,(![V_Z: $i, V_H: $i, V_X: $i] : (((~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))) | c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_OFake__parts__insert__in__Un__dest_0')).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.43 tff(112,plain,(
% 0.20/0.43 ![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[111])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | ((~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))) <=> ((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))) <=> ((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | ((~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))) <=> ((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 ((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 ((~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[119, 113, 103])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[120, 100])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a)) <=> (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.44 tff(127,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OUnE_0')).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.20/0.44 tff(130,plain,(
% 0.20/0.44 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[129])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 ((c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg))) <=> (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[134, 132])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[137, 131, 121])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[138, 37])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (^[V_H: $i, V_X: $i, V_K: $i] : refl((c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> ![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (^[V_H: $i, V_X: $i, V_K: $i] : rewrite((((~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (![V_H: $i, V_X: $i, V_K: $i] : (((~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.45 tff(145,axiom,(![V_H: $i, V_X: $i, V_K: $i] : (((~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_OCrypt__synth_0')).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.20/0.45 tff(148,plain,(
% 0.20/0.45 ![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[147])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))) <=> ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[152, 149, 139, 36])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[156, 32, 37, 153])).
% 0.20/0.45 tff(158,plain,(c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 (((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(160,axiom,((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_7')).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[161, 159])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[162, 159])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[164, 159])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[165, 159])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA_H, c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A_H), c_Message_Omsg_OAgent(v_A))))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[167, 159])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[168, 158])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(171,axiom,(c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_5')).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))) <=> ((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 ((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 ((~![V_Z: $i, V_H: $i, V_X: $i] : (c_in(V_Z, c_union(c_Message_Osynth(c_Message_Oanalz(V_H)), c_Message_Oparts(V_H), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(V_X, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | (~c_in(V_Z, c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(v_X, c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[175, 113, 172])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[176, 100])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 ((c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg))) <=> (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_A, T_a) | c_in(V_c, V_B, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_union(c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg), tc_Message_Omsg))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[183, 131, 177])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[184, 169])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 (((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))) <=> ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 ((c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(188,plain,
% 0.20/0.47 (((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))) <=> ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[187])).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 (((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))) <=> ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[188, 186])).
% 0.20/0.47 tff(190,plain,
% 0.20/0.47 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 ((~![V_H: $i, V_X: $i, V_K: $i] : (c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg) | c_in(c_Message_Omsg_OCrypt(V_K, V_X), V_H, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OCrypt(V_K, V_X), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 (c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[191, 149, 185, 36])).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 (((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), 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_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(195,plain,
% 0.20/0.47 ((~![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A), c_Message_Omsg_OMPair(v_NA, c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A), c_Message_Omsg_OAgent(v_B)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.47 tff(196,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[195, 32, 169, 192])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------