%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV318-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:32:06 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SWV318-2 : TPTP v9.0.0. Released v3.2.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:42:12 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(c_in_type, type, (
% 0.19/0.37 c_in: ( $i * $i * $i ) > $o)).
% 0.19/0.37 tff(tc_Message_Omsg_type, type, (
% 0.19/0.37 tc_Message_Omsg: $i)).
% 0.19/0.37 tff(c_Message_Oparts_type, type, (
% 0.19/0.37 c_Message_Oparts: $i > $i)).
% 0.19/0.37 tff(c_Event_Oknows_type, type, (
% 0.19/0.37 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.19/0.37 tff(v_evs4_type, type, (
% 0.19/0.37 v_evs4: $i)).
% 0.19/0.37 tff(c_Message_Oagent_OSpy_type, type, (
% 0.19/0.37 c_Message_Oagent_OSpy: $i)).
% 0.19/0.37 tff(c_Message_Omsg_OKey_type, type, (
% 0.19/0.37 c_Message_Omsg_OKey: $i > $i)).
% 0.19/0.37 tff(c_Public_OshrK_type, type, (
% 0.19/0.37 c_Public_OshrK: $i > $i)).
% 0.19/0.37 tff(v_A_type, type, (
% 0.19/0.37 v_A: $i)).
% 0.19/0.37 tff(c_insert_type, type, (
% 0.19/0.37 c_insert: ( $i * $i * $i ) > $i)).
% 0.19/0.37 tff(v_X_type, type, (
% 0.19/0.37 v_X: $i)).
% 0.19/0.37 tff(c_Message_Omsg_OMPair_type, type, (
% 0.19/0.37 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.19/0.37 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.19/0.37 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.19/0.37 tff(v_K_type, type, (
% 0.19/0.37 v_K: $i)).
% 0.19/0.37 tff(c_Message_Omsg_ONonce_type, type, (
% 0.19/0.37 c_Message_Omsg_ONonce: $i > $i)).
% 0.19/0.37 tff(v_NB_type, type, (
% 0.19/0.37 v_NB: $i)).
% 0.19/0.37 tff(v_B_type, type, (
% 0.19/0.37 v_B: $i)).
% 0.19/0.37 tff(v_NA_type, type, (
% 0.19/0.37 v_NA: $i)).
% 0.19/0.37 tff(c_Message_Oanalz_type, type, (
% 0.19/0.37 c_Message_Oanalz: $i > $i)).
% 0.19/0.37 tff(tc_Event_Oevent_type, type, (
% 0.19/0.37 tc_Event_Oevent: $i)).
% 0.19/0.37 tff(c_List_Oset_type, type, (
% 0.19/0.37 c_List_Oset: ( $i * $i ) > $i)).
% 0.19/0.37 tff(c_Event_Oevent_OSays_type, type, (
% 0.19/0.37 c_Event_Oevent_OSays: ( $i * $i * $i ) > $i)).
% 0.19/0.37 tff(v_sko__usf_type, type, (
% 0.19/0.37 v_sko__usf: ( $i * $i * $i ) > $i)).
% 0.19/0.37 tff(c_Event_Oevent_OGets_type, type, (
% 0.19/0.37 c_Event_Oevent_OGets: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tc_List_Olist_type, type, (
% 0.19/0.37 tc_List_Olist: $i > $i)).
% 0.19/0.37 tff(c_OtwayRees_Ootway_type, type, (
% 0.19/0.37 c_OtwayRees_Ootway: $i)).
% 0.19/0.37 tff(tc_Message_Oagent_type, type, (
% 0.19/0.37 tc_Message_Oagent: $i)).
% 0.19/0.37 tff(c_Event_Obad_type, type, (
% 0.19/0.37 c_Event_Obad: $i)).
% 0.19/0.37 tff(1,assumption,(~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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)), introduced(assumption)).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(3,axiom,(c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_3')).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (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))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(6,axiom,(c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (^[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)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (^[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))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.37 tff(13,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')).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.37 tff(16,plain,(
% 0.19/0.37 ![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))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[15])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[20, 17, 7, 4, 1])).
% 0.19/0.38 tff(22,plain,(c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(23,assumption,(c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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)), introduced(assumption)).
% 0.19/0.38 tff(24,assumption,(~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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)), introduced(assumption)).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (^[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)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(28,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')).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.38 tff(30,plain,(
% 0.19/0.38 ![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))),
% 0.19/0.38 inference(skolemize,[status(sab)],[29])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | ((~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | ((~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[34, 31, 24, 23])).
% 0.19/0.38 tff(36,plain,((~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[36, 22])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (^[V_H: $i] : refl((c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H)) <=> (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H)) <=> ![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H)) <=> ![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(41,axiom,(![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Oparts__analz_0')).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.38 tff(43,plain,(
% 0.19/0.38 ![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.19/0.38 inference(skolemize,[status(sab)],[42])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((~![V_H: $i] : (c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H))) | (c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.19/0.38 inference(symmetry,[status(thm)],[47])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.38 tff(50,assumption,(~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), introduced(assumption)).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.38 tff(52,assumption,(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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)), introduced(assumption)).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(56,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Oparts_OInj_0')).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.38 tff(58,plain,(
% 0.19/0.38 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.38 inference(skolemize,[status(sab)],[57])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(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_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[62, 59, 52])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[63, 51])).
% 0.19/0.39 tff(65,plain,((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), 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(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[65, 37])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(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_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(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_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(70,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_OMPair__parts_0')).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.39 tff(72,plain,(
% 0.19/0.39 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(skolemize,[status(sab)],[71])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(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_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 ((~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[77, 66])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(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_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(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_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(82,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_OMPair__parts_1')).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.39 tff(84,plain,(
% 0.19/0.39 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(skolemize,[status(sab)],[83])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(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_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 ((~c_in(c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[88, 85])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[89, 78])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H))) <=> ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H))) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H))) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(94,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Oparts__cut__eq_0')).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.40 tff(96,plain,(
% 0.19/0.40 ![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[95])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))) | ((~c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))) | (~c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))) | ((~c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(V_X, V_H, tc_Message_Omsg)) = c_Message_Oparts(V_H)))) | (~c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 ((~c_in(v_X, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | (c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[101, 90])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)) = c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg))),
% 0.19/0.40 inference(symmetry,[status(thm)],[102])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (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(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (c_in(c_Message_Omsg_OKey(c_Public_OshrK(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_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.19/0.40 inference(symmetry,[status(thm)],[104])).
% 0.19/0.40 tff(106,assumption,(~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)), introduced(assumption)).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 ((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_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)) <=> (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_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((c_in(c_Message_Omsg_OKey(c_Public_OshrK(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_A, c_Event_Obad, tc_Message_Oagent)) <=> (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_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(109,axiom,(c_in(c_Message_Omsg_OKey(c_Public_OshrK(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_A, c_Event_Obad, tc_Message_Oagent)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_7')).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (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_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (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_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[110, 107])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 106])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (^[V_A: $i, V_evs: $i] : refl(((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)) <=> ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)) <=> ![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg)) <=> ![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(116,axiom,(![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Public_OSpy__spies__bad__shrK_0')).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.40 tff(118,plain,(
% 0.19/0.40 ![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.19/0.40 inference(skolemize,[status(sab)],[117])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (((~![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))) | ((~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg))) <=> ((~![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 ((~![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))) | ((~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 ((~![V_A: $i, V_evs: $i] : ((~c_in(V_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)), c_Event_Oknows(c_Message_Oagent_OSpy, V_evs), tc_Message_Omsg))) | (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[122, 119, 112])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(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_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[126, 59, 106])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (^[V_b: $i, V_a: $i, T_a: $i, V_A: $i] : refl(((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) <=> ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(131,axiom,(![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_Oinsert__iff_2')).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.40 tff(133,plain,(
% 0.19/0.40 ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))),
% 0.19/0.40 inference(skolemize,[status(sab)],[132])).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 (((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) | ((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) | ((~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((~c_in(V_a, V_A, T_a)) | c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[137, 134, 127, 123])).
% 0.19/0.40 tff(139,plain,(c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 (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)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[139, 105])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 (((~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_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~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_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(142,axiom,((~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_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')).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 ((~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_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)), tc_Message_Omsg))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[143, 139])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 ((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(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(146,axiom,(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))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 (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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[147, 145])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 (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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[148, 145])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 (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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[150, 145])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (~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)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[151, 144])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[152, 140])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------