%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV323-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:32:07 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SWV323-2 : TPTP v9.0.0. Released v3.2.0.
% 0.05/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 09:46:50 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.40 % SZS status Unsatisfiable
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(c_in_type, type, (
% 0.22/0.40 c_in: ( $i * $i * $i ) > $o)).
% 0.22/0.40 tff(tc_Message_Omsg_type, type, (
% 0.22/0.40 tc_Message_Omsg: $i)).
% 0.22/0.40 tff(c_Message_Osynth_type, type, (
% 0.22/0.40 c_Message_Osynth: $i > $i)).
% 0.22/0.40 tff(c_Message_Oanalz_type, type, (
% 0.22/0.40 c_Message_Oanalz: $i > $i)).
% 0.22/0.40 tff(c_Event_Oknows_type, type, (
% 0.22/0.40 c_Event_Oknows: ( $i * $i ) > $i)).
% 0.22/0.40 tff(v_evs4_type, type, (
% 0.22/0.40 v_evs4: $i)).
% 0.22/0.40 tff(c_Message_Oagent_OSpy_type, type, (
% 0.22/0.40 c_Message_Oagent_OSpy: $i)).
% 0.22/0.40 tff(c_Message_Omsg_OKey_type, type, (
% 0.22/0.40 c_Message_Omsg_OKey: $i > $i)).
% 0.22/0.40 tff(c_Public_OshrK_type, type, (
% 0.22/0.40 c_Public_OshrK: $i > $i)).
% 0.22/0.40 tff(v_A_type, type, (
% 0.22/0.40 v_A: $i)).
% 0.22/0.40 tff(c_union_type, type, (
% 0.22/0.40 c_union: ( $i * $i * $i ) > $i)).
% 0.22/0.40 tff(c_Message_Oparts_type, type, (
% 0.22/0.40 c_Message_Oparts: $i > $i)).
% 0.22/0.40 tff(v_X_type, type, (
% 0.22/0.40 v_X: $i)).
% 0.22/0.40 tff(c_Message_Omsg_OMPair_type, type, (
% 0.22/0.40 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.22/0.40 tff(c_Message_Omsg_OCrypt_type, type, (
% 0.22/0.40 c_Message_Omsg_OCrypt: ( $i * $i ) > $i)).
% 0.22/0.40 tff(v_K_type, type, (
% 0.22/0.40 v_K: $i)).
% 0.22/0.40 tff(c_Message_Omsg_ONonce_type, type, (
% 0.22/0.40 c_Message_Omsg_ONonce: $i > $i)).
% 0.22/0.40 tff(v_NB_type, type, (
% 0.22/0.40 v_NB: $i)).
% 0.22/0.40 tff(v_B_type, type, (
% 0.22/0.40 v_B: $i)).
% 0.22/0.40 tff(v_NA_type, type, (
% 0.22/0.40 v_NA: $i)).
% 0.22/0.40 tff(tc_Event_Oevent_type, type, (
% 0.22/0.40 tc_Event_Oevent: $i)).
% 0.22/0.40 tff(c_List_Oset_type, type, (
% 0.22/0.40 c_List_Oset: ( $i * $i ) > $i)).
% 0.22/0.40 tff(c_Event_Oevent_OSays_type, type, (
% 0.22/0.40 c_Event_Oevent_OSays: ( $i * $i * $i ) > $i)).
% 0.22/0.40 tff(v_sko__usf_type, type, (
% 0.22/0.40 v_sko__usf: ( $i * $i * $i ) > $i)).
% 0.22/0.40 tff(tc_List_Olist_type, type, (
% 0.22/0.40 tc_List_Olist: $i > $i)).
% 0.22/0.40 tff(c_OtwayRees_Ootway_type, type, (
% 0.22/0.40 c_OtwayRees_Ootway: $i)).
% 0.22/0.40 tff(c_Event_Oevent_OGets_type, type, (
% 0.22/0.40 c_Event_Oevent_OGets: ( $i * $i ) > $i)).
% 0.22/0.40 tff(c_insert_type, type, (
% 0.22/0.40 c_insert: ( $i * $i * $i ) > $i)).
% 0.22/0.40 tff(tc_Message_Oagent_type, type, (
% 0.22/0.40 tc_Message_Oagent: $i)).
% 0.22/0.40 tff(c_Event_Obad_type, type, (
% 0.22/0.40 c_Event_Obad: $i)).
% 0.22/0.40 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)).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 (^[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)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 (![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))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 (![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))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (^[V_X: $i, V_B: $i, V_evs: $i] : trans(monotonicity(rewrite(((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) <=> ((~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))), ((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (((~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)))), rewrite((((~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))), ((((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(6,plain,
% 0.22/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) <=> ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.22/0.40 tff(7,axiom,(![V_X: $i, V_B: $i, V_evs: $i] : (((~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))) | c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_OtwayRees_OGets__imp__Says__dest_0')).
% 0.22/0.40 tff(8,plain,
% 0.22/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.22/0.40 tff(10,plain,(
% 0.22/0.40 ![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.22/0.40 inference(skolemize,[status(sab)],[9])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 (![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 (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)),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(13,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/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (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)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.22/0.40 tff(15,plain,
% 0.22/0.40 (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))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(16,axiom,(c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.22/0.40 tff(17,plain,
% 0.22/0.40 (c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.22/0.40 tff(18,plain,
% 0.22/0.40 (((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (c_in(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))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(19,plain,
% 0.22/0.40 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | (c_in(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))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(20,plain,
% 0.22/0.40 ((~![V_X: $i, V_B: $i, V_evs: $i] : (c_in(c_Event_Oevent_OSays(v_sko__usf(V_B, V_X, V_evs), V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(V_evs, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent))))) | c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent) | (~c_in(c_Event_Oevent_OGets(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | (~c_in(v_evs4, c_OtwayRees_Ootway, tc_List_Olist(tc_Event_Oevent)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.22/0.41 tff(21,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[20, 17, 14, 11, 1])).
% 0.22/0.41 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,[]))).
% 0.22/0.41 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)).
% 0.22/0.41 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)).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 (^[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)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(26,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.22/0.41 tff(27,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 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/sandbox2/benchmark/theBenchmark.p','cls_Event_OSays__imp__analz__Spy__dest_0')).
% 0.22/0.41 tff(29,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.41 tff(30,plain,(
% 0.22/0.41 ![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))),
% 0.22/0.41 inference(skolemize,[status(sab)],[29])).
% 0.22/0.41 tff(31,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.22/0.41 tff(32,plain,
% 0.22/0.41 (((~![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_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))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(33,plain,
% 0.22/0.41 ((~![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_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))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 ((~![V_X: $i, V_B: $i, V_A: $i, V_evs: $i] : ((~c_in(c_Event_Oevent_OSays(V_A, V_B, V_X), c_List_Oset(V_evs, tc_Event_Oevent), tc_Event_Oevent)) | c_in(V_X, c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, V_evs)), tc_Message_Omsg))) | (~c_in(c_Event_Oevent_OSays(v_sko__usf(v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), v_evs4), v_B, c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))))), c_List_Oset(v_evs4, tc_Event_Oevent), tc_Event_Oevent)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[34, 31, 24, 23])).
% 0.22/0.41 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,[]))).
% 0.22/0.41 tff(37,plain,
% 0.22/0.41 (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)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[36, 22])).
% 0.22/0.41 tff(38,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_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)), introduced(assumption)).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 (^[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)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(40,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(42,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/sandbox2/benchmark/theBenchmark.p','cls_Message_Osynth_OInj_0')).
% 0.22/0.41 tff(43,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.22/0.41 tff(44,plain,(
% 0.22/0.41 ![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))),
% 0.22/0.41 inference(skolemize,[status(sab)],[43])).
% 0.22/0.41 tff(45,plain,
% 0.22/0.41 (![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))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.22/0.41 tff(46,plain,
% 0.22/0.41 (((~![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(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_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(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_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(47,plain,
% 0.22/0.41 ((~![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(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_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(48,plain,
% 0.22/0.41 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA), c_Message_Omsg_OMPair(v_X, c_Message_Omsg_OCrypt(c_Public_OshrK(v_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K))))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.41 tff(49,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[48, 45, 38, 37])).
% 0.22/0.41 tff(50,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_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.41 tff(51,plain,
% 0.22/0.41 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(52,plain,
% 0.22/0.41 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(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_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.22/0.41 tff(53,plain,
% 0.22/0.41 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(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_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(54,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__synth__analz__iff1_1')).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.22/0.41 tff(56,plain,(
% 0.22/0.41 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))),
% 0.22/0.41 inference(skolemize,[status(sab)],[55])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.22/0.41 tff(58,plain,
% 0.22/0.41 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(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_Osynth(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_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Osynth(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_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(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_Osynth(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_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(59,plain,
% 0.22/0.41 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(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_Osynth(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_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(c_Message_Oanalz(V_H)), tc_Message_Omsg)) | c_in(V_Y, c_Message_Osynth(c_Message_Oanalz(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_Osynth(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_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 ((~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_Osynth(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_B), c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB), c_Message_Omsg_OKey(v_K)))), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (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_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[61, 50])).
% 0.22/0.42 tff(63,plain,
% 0.22/0.42 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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(c_Message_Omsg_OMPair(V_X, V_Y), 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)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.22/0.42 tff(65,plain,
% 0.22/0.42 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(66,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__synth__analz__iff1_0')).
% 0.22/0.42 tff(67,plain,
% 0.22/0.42 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.22/0.42 tff(68,plain,(
% 0.22/0.42 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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))),
% 0.22/0.42 inference(skolemize,[status(sab)],[67])).
% 0.22/0.42 tff(69,plain,
% 0.22/0.42 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.22/0.42 tff(70,plain,
% 0.22/0.42 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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(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_Osynth(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_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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(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_Osynth(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))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(71,plain,
% 0.22/0.42 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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(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_Osynth(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))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(72,plain,
% 0.22/0.42 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), 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(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_Osynth(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)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.22/0.42 tff(73,plain,
% 0.22/0.42 ((~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_Osynth(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)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.22/0.42 tff(74,plain,
% 0.22/0.42 (c_in(v_X, c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[73, 62])).
% 0.22/0.42 tff(75,plain,
% 0.22/0.42 (^[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))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(76,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[75])).
% 0.22/0.42 tff(77,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(78,plain,
% 0.22/0.42 (^[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)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(79,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[78])).
% 0.22/0.42 tff(80,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/sandbox2/benchmark/theBenchmark.p','cls_Message_OFake__parts__insert__in__Un__dest_0')).
% 0.22/0.42 tff(81,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.22/0.42 tff(82,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.22/0.42 tff(83,plain,(
% 0.22/0.42 ![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)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[82])).
% 0.22/0.42 tff(84,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.22/0.42 tff(85,plain,
% 0.22/0.42 (^[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)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(86,plain,
% 0.22/0.42 (![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))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.22/0.42 tff(87,plain,
% 0.22/0.42 (![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))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(88,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/sandbox2/benchmark/theBenchmark.p','cls_Public_OSpy__spies__bad__shrK_0')).
% 0.22/0.42 tff(89,plain,
% 0.22/0.42 (![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))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.22/0.43 tff(90,plain,(
% 0.22/0.43 ![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))),
% 0.22/0.43 inference(skolemize,[status(sab)],[89])).
% 0.22/0.43 tff(91,plain,
% 0.22/0.43 (![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))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.22/0.43 tff(92,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)).
% 0.22/0.43 tff(93,plain,
% 0.22/0.43 ((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))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(94,plain,
% 0.22/0.43 ((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))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(95,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/sandbox2/benchmark/theBenchmark.p','cls_conjecture_7')).
% 0.22/0.43 tff(96,plain,
% 0.22/0.43 (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)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.22/0.43 tff(97,plain,
% 0.22/0.43 (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)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[96, 93])).
% 0.22/0.43 tff(98,plain,
% 0.22/0.43 (c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[97, 92])).
% 0.22/0.43 tff(99,plain,
% 0.22/0.43 (((~![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))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(100,plain,
% 0.22/0.43 ((~![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))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(101,plain,
% 0.22/0.43 ((~![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)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.22/0.43 tff(102,plain,
% 0.22/0.43 (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[101, 98, 91])).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 (^[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)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(104,plain,
% 0.22/0.43 (![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))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[103])).
% 0.22/0.43 tff(105,plain,
% 0.22/0.43 (![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))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(106,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/sandbox2/benchmark/theBenchmark.p','cls_Message_Oparts_OInj_0')).
% 0.22/0.43 tff(107,plain,
% 0.22/0.43 (![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))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.22/0.43 tff(108,plain,(
% 0.22/0.43 ![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))),
% 0.22/0.43 inference(skolemize,[status(sab)],[107])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 (![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))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 (((~![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))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 ((~![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))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(112,plain,
% 0.22/0.43 ((~![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)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.43 tff(113,plain,
% 0.22/0.43 (~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)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[112, 92, 109])).
% 0.22/0.43 tff(114,plain,
% 0.22/0.43 (^[V_b: $i, V_a: $i, T_a: $i, V_B: $i] : refl(((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)) <=> ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(115,plain,
% 0.22/0.43 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[114])).
% 0.22/0.43 tff(116,plain,
% 0.22/0.43 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(117,axiom,(![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OinsertCI_0')).
% 0.22/0.43 tff(118,plain,
% 0.22/0.43 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.22/0.43 tff(119,plain,(
% 0.22/0.43 ![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.22/0.43 inference(skolemize,[status(sab)],[118])).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.22/0.43 tff(121,plain,
% 0.22/0.43 (((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, 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_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, 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))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(122,plain,
% 0.22/0.43 ((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, 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))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 ((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_insert(v_X, c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4), tc_Message_Omsg), tc_Message_Omsg)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[123, 120, 113, 102])).
% 0.22/0.43 tff(125,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,[]))).
% 0.22/0.43 tff(126,plain,
% 0.22/0.43 (((~![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_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_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)))) <=> ((~![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_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_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)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 ((c_in(c_Message_Omsg_OKey(c_Public_OshrK(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_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_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_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)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(128,plain,
% 0.22/0.43 (((~![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_OKey(c_Public_OshrK(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_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_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_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_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))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[127])).
% 0.22/0.44 tff(129,plain,
% 0.22/0.44 (((~![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_OKey(c_Public_OshrK(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_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_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_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_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)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[128, 126])).
% 0.22/0.44 tff(130,plain,
% 0.22/0.44 ((~![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_OKey(c_Public_OshrK(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_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)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(131,plain,
% 0.22/0.44 ((~![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_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_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))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.22/0.44 tff(132,plain,
% 0.22/0.44 (c_in(c_Message_Omsg_OKey(c_Public_OshrK(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))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[131, 125, 84])).
% 0.22/0.44 tff(133,plain,
% 0.22/0.44 (c_in(c_Message_Omsg_OKey(c_Public_OshrK(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)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[132, 74])).
% 0.22/0.44 tff(134,plain,
% 0.22/0.44 (^[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))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(135,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[134])).
% 0.22/0.44 tff(136,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(137,plain,
% 0.22/0.44 (^[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))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(138,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[137])).
% 0.22/0.44 tff(139,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/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnE_0')).
% 0.22/0.44 tff(140,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.22/0.44 tff(141,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.22/0.44 tff(142,plain,(
% 0.22/0.44 ![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)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[141])).
% 0.22/0.44 tff(143,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.22/0.44 tff(144,plain,
% 0.22/0.44 (((~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)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(145,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/sandbox2/benchmark/theBenchmark.p','cls_conjecture_6')).
% 0.22/0.44 tff(146,plain,
% 0.22/0.44 ((~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))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.22/0.44 tff(147,plain,
% 0.22/0.44 (~c_in(v_A, c_Event_Obad, tc_Message_Oagent)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[146, 125])).
% 0.22/0.44 tff(148,plain,
% 0.22/0.44 ((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)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(149,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/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.22/0.44 tff(150,plain,
% 0.22/0.44 (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))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.22/0.44 tff(151,plain,
% 0.22/0.44 (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))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[150, 148])).
% 0.22/0.44 tff(152,plain,
% 0.22/0.44 (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))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[151, 148])).
% 0.22/0.44 tff(153,plain,
% 0.22/0.44 (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))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.22/0.44 tff(154,plain,
% 0.22/0.44 (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))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[153, 148])).
% 0.22/0.44 tff(155,plain,
% 0.22/0.44 (~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)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[154, 147])).
% 0.22/0.44 tff(156,plain,
% 0.22/0.44 (((~![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_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_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_OKey(c_Public_OshrK(v_A)), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), 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_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_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_OKey(c_Public_OshrK(v_A)), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(157,plain,
% 0.22/0.44 ((c_in(c_Message_Omsg_OKey(c_Public_OshrK(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_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_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_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_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_OKey(c_Public_OshrK(v_A)), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(158,plain,
% 0.22/0.44 (((~![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_OKey(c_Public_OshrK(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_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_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_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_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_OKey(c_Public_OshrK(v_A)), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[157])).
% 0.22/0.44 tff(159,plain,
% 0.22/0.44 (((~![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_OKey(c_Public_OshrK(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_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_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_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_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_OKey(c_Public_OshrK(v_A)), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg))),
% 0.22/0.44 inference(transitivity,[status(thm)],[158, 156])).
% 0.22/0.44 tff(160,plain,
% 0.22/0.44 ((~![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_OKey(c_Public_OshrK(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_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_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)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(161,plain,
% 0.22/0.44 ((~![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_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_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_OKey(c_Public_OshrK(v_A)), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.22/0.44 tff(162,plain,
% 0.22/0.44 (c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[161, 155, 143, 133])).
% 0.22/0.44 tff(163,plain,
% 0.22/0.44 (^[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)))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(164,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[163])).
% 0.22/0.44 tff(165,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(166,axiom,(![V_c: $i, V_H: $i] : ((~c_in(V_c, c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_c, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz__into__parts__dest_0')).
% 0.22/0.44 tff(167,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.22/0.44 tff(168,plain,(
% 0.22/0.44 ![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))),
% 0.22/0.44 inference(skolemize,[status(sab)],[167])).
% 0.22/0.44 tff(169,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.22/0.44 tff(170,plain,
% 0.22/0.44 (((~![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))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(171,plain,
% 0.22/0.45 ((~![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_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))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(172,plain,
% 0.22/0.45 ((~![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_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)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.22/0.45 tff(173,plain,
% 0.22/0.45 (~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)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[172, 155, 169])).
% 0.22/0.45 tff(174,plain,
% 0.22/0.45 (^[V_H: $i, V_K: $i] : refl(((~c_in(c_Message_Omsg_OKey(V_K), 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_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg)))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(175,plain,
% 0.22/0.45 (![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg)) <=> ![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[174])).
% 0.22/0.45 tff(176,plain,
% 0.22/0.45 (![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg)) <=> ![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(177,axiom,(![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OKey__synth_0')).
% 0.22/0.45 tff(178,plain,
% 0.22/0.45 (![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.22/0.45 tff(179,plain,(
% 0.22/0.45 ![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.22/0.45 inference(skolemize,[status(sab)],[178])).
% 0.22/0.45 tff(180,plain,
% 0.22/0.45 (![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.22/0.45 tff(181,plain,
% 0.22/0.45 (((~![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), 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_OKey(c_Public_OshrK(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_OKey(c_Public_OshrK(v_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))) <=> ((~![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), 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_OKey(c_Public_OshrK(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_OKey(c_Public_OshrK(v_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(182,plain,
% 0.22/0.45 ((~![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), 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_OKey(c_Public_OshrK(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_OKey(c_Public_OshrK(v_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(183,plain,
% 0.22/0.45 ((~![V_H: $i, V_K: $i] : ((~c_in(c_Message_Omsg_OKey(V_K), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(V_K), V_H, tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4))), tc_Message_Omsg)) | c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_A)), c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs4)), tc_Message_Omsg)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.22/0.45 tff(184,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[183, 180, 173, 162])).
% 0.22/0.45 % SZS output end Proof
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------