Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SWV281-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n002.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 05:31:58 AM UTC 2025

% Result   : Unsatisfiable 0.22s 0.50s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SWV281-2 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Jun 20 09:39:01 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 0.22/0.50  % SZS status Unsatisfiable
% 0.22/0.50  % SZS output start Proof
% 0.22/0.50  tff(c_in_type, type, (
% 0.22/0.50     c_in: ( $i * $i * $i ) > $o)).
% 0.22/0.50  tff(tc_Message_Omsg_type, type, (
% 0.22/0.50     tc_Message_Omsg: $i)).
% 0.22/0.50  tff(c_Event_Oused_type, type, (
% 0.22/0.50     c_Event_Oused: $i > $i)).
% 0.22/0.50  tff(v_evs_H_type, type, (
% 0.22/0.50     v_evs_H: $i)).
% 0.22/0.50  tff(c_Message_Omsg_ONonce_type, type, (
% 0.22/0.50     c_Message_Omsg_ONonce: $i > $i)).
% 0.22/0.50  tff(c_plus_type, type, (
% 0.22/0.50     c_plus: ( $i * $i * $i ) > $i)).
% 0.22/0.50  tff(tc_nat_type, type, (
% 0.22/0.50     tc_nat: $i)).
% 0.22/0.50  tff(c_List_Olist_ONil_type, type, (
% 0.22/0.50     c_List_Olist_ONil: $i)).
% 0.22/0.50  tff(elem_1_type, type, (
% 0.22/0.50     elem_1: $i)).
% 0.22/0.50  tff(v_sko__urX_type, type, (
% 0.22/0.50     v_sko__urX: $i > $i)).
% 0.22/0.50  tff(inj_0_type, type, (
% 0.22/0.50     inj_0: ( $i * $i ) > $i)).
% 0.22/0.50  tff(v_evs_type, type, (
% 0.22/0.50     v_evs: $i)).
% 0.22/0.50  tff(c_lessequals_type, type, (
% 0.22/0.50     c_lessequals: ( $i * $i * $i ) > $o)).
% 0.22/0.50  tff(c_0_type, type, (
% 0.22/0.50     c_0: $i)).
% 0.22/0.50  tff(c_List_Olist_OCons_type, type, (
% 0.22/0.50     c_List_Olist_OCons: ( $i * $i * $i ) > $i)).
% 0.22/0.50  tff(1,plain,
% 0.22/0.50      (![V_n: $i, V_m: $i, V_k: $i] : ((~(c_plus(V_m, V_k, tc_nat) = c_plus(V_n, V_k, tc_nat))) | (V_m = V_n)) <=> ![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)),
% 0.22/0.50      inference(rewrite,[status(thm)],[])).
% 0.22/0.50  tff(2,plain,
% 0.22/0.50      (![V_n: $i, V_m: $i, V_k: $i] : ((~(c_plus(V_m, V_k, tc_nat) = c_plus(V_n, V_k, tc_nat))) | (V_m = V_n)) <=> ![V_n: $i, V_m: $i, V_k: $i] : ((~(c_plus(V_m, V_k, tc_nat) = c_plus(V_n, V_k, tc_nat))) | (V_m = V_n))),
% 0.22/0.50      inference(rewrite,[status(thm)],[])).
% 0.22/0.50  tff(3,axiom,(![V_n: $i, V_m: $i, V_k: $i] : ((~(c_plus(V_m, V_k, tc_nat) = c_plus(V_n, V_k, tc_nat))) | (V_m = V_n))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Nat_Onat__add__right__cancel_0')).
% 0.22/0.50  tff(4,plain,
% 0.22/0.50      (![V_n: $i, V_m: $i, V_k: $i] : ((~(c_plus(V_m, V_k, tc_nat) = c_plus(V_n, V_k, tc_nat))) | (V_m = V_n))),
% 0.22/0.50      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.50  tff(5,plain,(
% 0.22/0.50      ![V_n: $i, V_m: $i, V_k: $i] : ((~(c_plus(V_m, V_k, tc_nat) = c_plus(V_n, V_k, tc_nat))) | (V_m = V_n))),
% 0.22/0.50      inference(skolemize,[status(sab)],[4])).
% 0.22/0.50  tff(6,plain,
% 0.22/0.50      (![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)),
% 0.22/0.50      inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.50  tff(7,plain,
% 0.22/0.50      ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)) | (inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) = elem!1)),
% 0.22/0.50      inference(quant_inst,[status(thm)],[])).
% 0.22/0.50  tff(8,plain,
% 0.22/0.50      (inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) = elem!1),
% 0.22/0.50      inference(unit_resolution,[status(thm)],[7, 6])).
% 0.22/0.50  tff(9,plain,
% 0.22/0.50      (^[V_n: $i, V_m: $i] : refl(c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat) <=> c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat))),
% 0.22/0.50      inference(bind,[status(th)],[])).
% 0.22/0.50  tff(10,plain,
% 0.22/0.50      (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat) <=> ![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)),
% 0.22/0.50      inference(quant_intro,[status(thm)],[9])).
% 0.22/0.50  tff(11,plain,
% 0.22/0.50      (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat) <=> ![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)),
% 0.22/0.50      inference(rewrite,[status(thm)],[])).
% 0.22/0.50  tff(12,axiom,(![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Nat_Ole__add2_0')).
% 0.22/0.50  tff(13,plain,
% 0.22/0.50      (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)),
% 0.22/0.50      inference(modus_ponens,[status(thm)],[12, 11])).
% 0.22/0.50  tff(14,plain,(
% 0.22/0.50      ![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)),
% 0.22/0.50      inference(skolemize,[status(sab)],[13])).
% 0.22/0.50  tff(15,plain,
% 0.22/0.50      (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)),
% 0.22/0.50      inference(modus_ponens,[status(thm)],[14, 10])).
% 0.22/0.50  tff(16,plain,
% 0.22/0.50      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(v_sko__urX(v_evs), c_plus(elem!1, v_sko__urX(v_evs), tc_nat), tc_nat)),
% 0.22/0.50      inference(quant_inst,[status(thm)],[])).
% 0.22/0.50  tff(17,plain,
% 0.22/0.50      (c_lessequals(v_sko__urX(v_evs), c_plus(elem!1, v_sko__urX(v_evs), tc_nat), tc_nat)),
% 0.22/0.50      inference(unit_resolution,[status(thm)],[16, 15])).
% 0.22/0.51  tff(18,plain,
% 0.22/0.51      (^[V_U: $i, V_evs: $i] : refl(((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat))) <=> ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat))))),
% 0.22/0.51      inference(bind,[status(th)],[])).
% 0.22/0.51  tff(19,plain,
% 0.22/0.51      (![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat))) <=> ![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))),
% 0.22/0.51      inference(quant_intro,[status(thm)],[18])).
% 0.22/0.51  tff(20,plain,
% 0.22/0.51      (![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat))) <=> ![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(21,axiom,(![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Public_ONonce__supply__lemma_0')).
% 0.22/0.51  tff(22,plain,
% 0.22/0.51      (![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[21, 20])).
% 0.22/0.51  tff(23,plain,(
% 0.22/0.51      ![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))),
% 0.22/0.51      inference(skolemize,[status(sab)],[22])).
% 0.22/0.51  tff(24,plain,
% 0.22/0.51      (![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[23, 19])).
% 0.22/0.51  tff(25,plain,
% 0.22/0.51      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(elem!1, v_sko__urX(v_evs), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(elem!1, v_sko__urX(v_evs), tc_nat), tc_nat)))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(26,plain,
% 0.22/0.51      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(elem!1, v_sko__urX(v_evs), tc_nat), tc_nat)))),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(27,plain,
% 0.22/0.51      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(elem!1, v_sko__urX(v_evs), tc_nat), tc_nat))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.22/0.51  tff(28,plain,
% 0.22/0.51      (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[27, 24, 17])).
% 0.22/0.51  tff(29,plain,
% 0.22/0.51      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(30,plain,
% 0.22/0.51      (c_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[29, 15])).
% 0.22/0.51  tff(31,plain,
% 0.22/0.51      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(32,plain,
% 0.22/0.51      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(33,plain,
% 0.22/0.51      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[32, 31])).
% 0.22/0.51  tff(34,plain,
% 0.22/0.51      (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[33, 24, 30])).
% 0.22/0.51  tff(35,plain,
% 0.22/0.51      (^[V_V: $i, V_U: $i] : refl((c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V)) <=> (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V)))),
% 0.22/0.51      inference(bind,[status(th)],[])).
% 0.22/0.51  tff(36,plain,
% 0.22/0.51      (![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V)) <=> ![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))),
% 0.22/0.51      inference(quant_intro,[status(thm)],[35])).
% 0.22/0.51  tff(37,plain,
% 0.22/0.51      (![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V)) <=> ![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(38,plain,
% 0.22/0.51      (^[V_V: $i, V_U: $i] : rewrite((((V_U = V_V) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V)))),
% 0.22/0.51      inference(bind,[status(th)],[])).
% 0.22/0.51  tff(39,plain,
% 0.22/0.51      (![V_V: $i, V_U: $i] : (((V_U = V_V) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg)) <=> ![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))),
% 0.22/0.51      inference(quant_intro,[status(thm)],[38])).
% 0.22/0.51  tff(40,axiom,(![V_V: $i, V_U: $i] : (((V_U = V_V) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.22/0.51  tff(41,plain,
% 0.22/0.51      (![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[40, 39])).
% 0.22/0.51  tff(42,plain,
% 0.22/0.51      (![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[41, 37])).
% 0.22/0.51  tff(43,plain,(
% 0.22/0.51      ![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))),
% 0.22/0.51      inference(skolemize,[status(sab)],[42])).
% 0.22/0.51  tff(44,plain,
% 0.22/0.51      (![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[43, 36])).
% 0.22/0.51  tff(45,plain,
% 0.22/0.51      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(46,plain,
% 0.22/0.51      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(47,plain,
% 0.22/0.51      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[46, 45])).
% 0.22/0.51  tff(48,plain,
% 0.22/0.51      (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[47, 44, 34, 28])).
% 0.22/0.51  tff(49,plain,
% 0.22/0.51      (^[V_y: $i] : refl((c_plus(c_0, V_y, tc_nat) = V_y) <=> (c_plus(c_0, V_y, tc_nat) = V_y))),
% 0.22/0.51      inference(bind,[status(th)],[])).
% 0.22/0.51  tff(50,plain,
% 0.22/0.51      (![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y) <=> ![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)),
% 0.22/0.51      inference(quant_intro,[status(thm)],[49])).
% 0.22/0.51  tff(51,plain,
% 0.22/0.51      (![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y) <=> ![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(52,axiom,(![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Nat_Oop_A_L_Oadd__0_0')).
% 0.22/0.51  tff(53,plain,
% 0.22/0.51      (![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.51  tff(54,plain,(
% 0.22/0.51      ![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)),
% 0.22/0.51      inference(skolemize,[status(sab)],[53])).
% 0.22/0.51  tff(55,plain,
% 0.22/0.51      (![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[54, 50])).
% 0.22/0.51  tff(56,plain,
% 0.22/0.51      ((~![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)) | (c_plus(c_0, v_sko__urX(v_evs_H), tc_nat) = v_sko__urX(v_evs_H))),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(57,plain,
% 0.22/0.51      (c_plus(c_0, v_sko__urX(v_evs_H), tc_nat) = v_sko__urX(v_evs_H)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[56, 55])).
% 0.22/0.51  tff(58,plain,
% 0.22/0.51      (v_sko__urX(v_evs_H) = c_plus(c_0, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.51      inference(symmetry,[status(thm)],[57])).
% 0.22/0.51  tff(59,plain,
% 0.22/0.51      (c_lessequals(v_sko__urX(v_evs_H), v_sko__urX(v_evs_H), tc_nat) <=> c_lessequals(v_sko__urX(v_evs_H), c_plus(c_0, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.51      inference(monotonicity,[status(thm)],[58])).
% 0.22/0.51  tff(60,plain,
% 0.22/0.51      (c_lessequals(v_sko__urX(v_evs_H), c_plus(c_0, v_sko__urX(v_evs_H), tc_nat), tc_nat) <=> c_lessequals(v_sko__urX(v_evs_H), v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.51      inference(symmetry,[status(thm)],[59])).
% 0.22/0.51  tff(61,plain,
% 0.22/0.51      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(v_sko__urX(v_evs_H), c_plus(c_0, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(62,plain,
% 0.22/0.51      (c_lessequals(v_sko__urX(v_evs_H), c_plus(c_0, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[61, 15])).
% 0.22/0.51  tff(63,plain,
% 0.22/0.51      (c_lessequals(v_sko__urX(v_evs_H), v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[62, 60])).
% 0.22/0.51  tff(64,plain,
% 0.22/0.51      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(65,plain,
% 0.22/0.51      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(66,plain,
% 0.22/0.51      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[65, 64])).
% 0.22/0.51  tff(67,plain,
% 0.22/0.51      ((~c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[66, 24])).
% 0.22/0.51  tff(68,plain,
% 0.22/0.51      (~c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[67, 63])).
% 0.22/0.51  tff(69,plain,
% 0.22/0.51      (c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)) = c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.51      inference(monotonicity,[status(thm)],[48])).
% 0.22/0.51  tff(70,plain,
% 0.22/0.51      (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.51      inference(monotonicity,[status(thm)],[69])).
% 0.22/0.51  tff(71,plain,
% 0.22/0.51      ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.22/0.51      inference(monotonicity,[status(thm)],[70])).
% 0.22/0.51  tff(72,plain,
% 0.22/0.51      (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[28, 71])).
% 0.22/0.51  tff(73,plain,
% 0.22/0.51      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = v_sko__urX(v_evs_H)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = v_sko__urX(v_evs_H)))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(74,plain,
% 0.22/0.51      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = v_sko__urX(v_evs_H)))),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(75,plain,
% 0.22/0.51      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_sko__urX(v_evs_H)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = v_sko__urX(v_evs_H))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[74, 73])).
% 0.22/0.51  tff(76,plain,
% 0.22/0.51      (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = v_sko__urX(v_evs_H)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[75, 44, 72, 68])).
% 0.22/0.51  tff(77,plain,
% 0.22/0.51      (v_sko__urX(v_evs_H) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.51      inference(symmetry,[status(thm)],[76])).
% 0.22/0.51  tff(78,plain,
% 0.22/0.51      (c_plus(c_0, v_sko__urX(v_evs_H), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.51      inference(transitivity,[status(thm)],[57, 77])).
% 0.22/0.51  tff(79,plain,
% 0.22/0.51      (inj_0(v_sko__urX(v_evs_H), c_plus(c_0, v_sko__urX(v_evs_H), tc_nat)) = inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.51      inference(monotonicity,[status(thm)],[78])).
% 0.22/0.51  tff(80,plain,
% 0.22/0.51      ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)) | (inj_0(v_sko__urX(v_evs_H), c_plus(c_0, v_sko__urX(v_evs_H), tc_nat)) = c_0)),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(81,plain,
% 0.22/0.51      (inj_0(v_sko__urX(v_evs_H), c_plus(c_0, v_sko__urX(v_evs_H), tc_nat)) = c_0),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[80, 6])).
% 0.22/0.51  tff(82,plain,
% 0.22/0.51      (c_0 = inj_0(v_sko__urX(v_evs_H), c_plus(c_0, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.51      inference(symmetry,[status(thm)],[81])).
% 0.22/0.51  tff(83,plain,
% 0.22/0.51      (c_0 = elem!1),
% 0.22/0.51      inference(transitivity,[status(thm)],[82, 79, 8])).
% 0.22/0.51  tff(84,plain,
% 0.22/0.51      (c_plus(c_0, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs), tc_nat)),
% 0.22/0.51      inference(monotonicity,[status(thm)],[83])).
% 0.22/0.51  tff(85,plain,
% 0.22/0.51      ((~![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)) | (c_plus(c_0, v_sko__urX(v_evs), tc_nat) = v_sko__urX(v_evs))),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(86,plain,
% 0.22/0.51      (c_plus(c_0, v_sko__urX(v_evs), tc_nat) = v_sko__urX(v_evs)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[85, 55])).
% 0.22/0.51  tff(87,plain,
% 0.22/0.51      (v_sko__urX(v_evs) = c_plus(c_0, v_sko__urX(v_evs), tc_nat)),
% 0.22/0.51      inference(symmetry,[status(thm)],[86])).
% 0.22/0.51  tff(88,plain,
% 0.22/0.51      (v_sko__urX(v_evs) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.51      inference(transitivity,[status(thm)],[87, 84, 48])).
% 0.22/0.51  tff(89,plain,
% 0.22/0.51      (c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.51      inference(monotonicity,[status(thm)],[88])).
% 0.22/0.51  tff(90,plain,
% 0.22/0.51      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.51      inference(symmetry,[status(thm)],[89])).
% 0.22/0.51  tff(91,plain,
% 0.22/0.51      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(92,plain,
% 0.22/0.51      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[91, 15])).
% 0.22/0.51  tff(93,plain,
% 0.22/0.51      (c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[92, 90])).
% 0.22/0.51  tff(94,plain,
% 0.22/0.51      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(95,plain,
% 0.22/0.51      (((~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat))) <=> ((~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(96,plain,
% 0.22/0.51      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))))),
% 0.22/0.52      inference(monotonicity,[status(thm)],[95])).
% 0.22/0.52  tff(97,plain,
% 0.22/0.52      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)))),
% 0.22/0.52      inference(transitivity,[status(thm)],[96, 94])).
% 0.22/0.52  tff(98,plain,
% 0.22/0.52      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))),
% 0.22/0.52      inference(quant_inst,[status(thm)],[])).
% 0.22/0.52  tff(99,plain,
% 0.22/0.52      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.22/0.52      inference(modus_ponens,[status(thm)],[98, 97])).
% 0.22/0.52  tff(100,plain,
% 0.22/0.52      ((~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[99, 24])).
% 0.22/0.52  tff(101,plain,
% 0.22/0.52      (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[100, 93])).
% 0.22/0.52  tff(102,plain,
% 0.22/0.52      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.52      inference(rewrite,[status(thm)],[])).
% 0.22/0.52  tff(103,plain,
% 0.22/0.52      ((c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))) <=> (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.52      inference(rewrite,[status(thm)],[])).
% 0.22/0.52  tff(104,plain,
% 0.22/0.52      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))))),
% 0.22/0.52      inference(monotonicity,[status(thm)],[103])).
% 0.22/0.52  tff(105,plain,
% 0.22/0.52      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.52      inference(transitivity,[status(thm)],[104, 102])).
% 0.22/0.52  tff(106,plain,
% 0.22/0.52      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.52      inference(quant_inst,[status(thm)],[])).
% 0.22/0.52  tff(107,plain,
% 0.22/0.52      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.52      inference(modus_ponens,[status(thm)],[106, 105])).
% 0.22/0.52  tff(108,plain,
% 0.22/0.52      (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[107, 44, 34, 101])).
% 0.22/0.52  tff(109,plain,
% 0.22/0.52      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.52      inference(monotonicity,[status(thm)],[76, 108])).
% 0.22/0.52  tff(110,plain,
% 0.22/0.52      ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)) | (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = v_evs_H)),
% 0.22/0.52      inference(quant_inst,[status(thm)],[])).
% 0.22/0.52  tff(111,plain,
% 0.22/0.52      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = v_evs_H),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[110, 6])).
% 0.22/0.52  tff(112,plain,
% 0.22/0.52      (v_evs_H = inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.52      inference(symmetry,[status(thm)],[111])).
% 0.22/0.52  tff(113,plain,
% 0.22/0.52      (v_evs_H = elem!1),
% 0.22/0.52      inference(transitivity,[status(thm)],[112, 109, 8])).
% 0.22/0.52  tff(114,plain,
% 0.22/0.52      (c_Event_Oused(v_evs_H) = c_Event_Oused(elem!1)),
% 0.22/0.52      inference(monotonicity,[status(thm)],[113])).
% 0.22/0.52  tff(115,plain,
% 0.22/0.52      ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)) | (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)))),
% 0.22/0.52      inference(quant_inst,[status(thm)],[])).
% 0.22/0.52  tff(116,plain,
% 0.22/0.52      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat))),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[115, 6])).
% 0.22/0.52  tff(117,plain,
% 0.22/0.52      (c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(monotonicity,[status(thm)],[77])).
% 0.22/0.52  tff(118,plain,
% 0.22/0.52      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(symmetry,[status(thm)],[117])).
% 0.22/0.52  tff(119,plain,
% 0.22/0.52      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(quant_inst,[status(thm)],[])).
% 0.22/0.52  tff(120,plain,
% 0.22/0.52      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[119, 15])).
% 0.22/0.52  tff(121,plain,
% 0.22/0.52      (c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(modus_ponens,[status(thm)],[120, 118])).
% 0.22/0.52  tff(122,plain,
% 0.22/0.52      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))),
% 0.22/0.52      inference(rewrite,[status(thm)],[])).
% 0.22/0.52  tff(123,plain,
% 0.22/0.52      (((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat))) <=> ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))),
% 0.22/0.52      inference(rewrite,[status(thm)],[])).
% 0.22/0.52  tff(124,plain,
% 0.22/0.52      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))))),
% 0.22/0.52      inference(monotonicity,[status(thm)],[123])).
% 0.22/0.52  tff(125,plain,
% 0.22/0.52      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))),
% 0.22/0.52      inference(transitivity,[status(thm)],[124, 122])).
% 0.22/0.52  tff(126,plain,
% 0.22/0.52      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))),
% 0.22/0.52      inference(quant_inst,[status(thm)],[])).
% 0.22/0.52  tff(127,plain,
% 0.22/0.52      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))),
% 0.22/0.52      inference(modus_ponens,[status(thm)],[126, 125])).
% 0.22/0.52  tff(128,plain,
% 0.22/0.52      ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[127, 24])).
% 0.22/0.52  tff(129,plain,
% 0.22/0.52      (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[128, 121])).
% 0.22/0.52  tff(130,plain,
% 0.22/0.52      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))),
% 0.22/0.52      inference(rewrite,[status(thm)],[])).
% 0.22/0.52  tff(131,plain,
% 0.22/0.52      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))),
% 0.22/0.52      inference(quant_inst,[status(thm)],[])).
% 0.22/0.52  tff(132,plain,
% 0.22/0.52      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.52      inference(modus_ponens,[status(thm)],[131, 130])).
% 0.22/0.52  tff(133,plain,
% 0.22/0.52      (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[132, 44, 101, 129])).
% 0.22/0.52  tff(134,plain,
% 0.22/0.52      (c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.52      inference(symmetry,[status(thm)],[133])).
% 0.22/0.52  tff(135,plain,
% 0.22/0.52      (c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.52      inference(transitivity,[status(thm)],[134, 108])).
% 0.22/0.52  tff(136,plain,
% 0.22/0.52      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.52      inference(monotonicity,[status(thm)],[76, 135])).
% 0.22/0.52  tff(137,plain,
% 0.22/0.52      (inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) = inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.52      inference(symmetry,[status(thm)],[136])).
% 0.22/0.52  tff(138,plain,
% 0.22/0.52      (c_lessequals(v_sko__urX(v_evs), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(monotonicity,[status(thm)],[88])).
% 0.22/0.52  tff(139,plain,
% 0.22/0.52      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(v_sko__urX(v_evs), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(symmetry,[status(thm)],[138])).
% 0.22/0.52  tff(140,plain,
% 0.22/0.52      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(quant_inst,[status(thm)],[])).
% 0.22/0.52  tff(141,plain,
% 0.22/0.52      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(unit_resolution,[status(thm)],[140, 15])).
% 0.22/0.52  tff(142,plain,
% 0.22/0.52      (c_lessequals(v_sko__urX(v_evs), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.52      inference(modus_ponens,[status(thm)],[141, 139])).
% 0.22/0.53  tff(143,plain,
% 0.22/0.53      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))),
% 0.22/0.53      inference(rewrite,[status(thm)],[])).
% 0.22/0.53  tff(144,plain,
% 0.22/0.53      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))),
% 0.22/0.53      inference(quant_inst,[status(thm)],[])).
% 0.22/0.53  tff(145,plain,
% 0.22/0.53      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat))),
% 0.22/0.53      inference(modus_ponens,[status(thm)],[144, 143])).
% 0.22/0.53  tff(146,plain,
% 0.22/0.53      ((~c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat))),
% 0.22/0.53      inference(unit_resolution,[status(thm)],[145, 24])).
% 0.22/0.53  tff(147,plain,
% 0.22/0.53      (~c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.53      inference(unit_resolution,[status(thm)],[146, 142])).
% 0.22/0.53  tff(148,plain,
% 0.22/0.53      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.53      inference(rewrite,[status(thm)],[])).
% 0.22/0.53  tff(149,plain,
% 0.22/0.53      ((c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))) <=> (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.53      inference(rewrite,[status(thm)],[])).
% 0.22/0.53  tff(150,plain,
% 0.22/0.53      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))))),
% 0.22/0.53      inference(monotonicity,[status(thm)],[149])).
% 0.22/0.53  tff(151,plain,
% 0.22/0.53      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.53      inference(transitivity,[status(thm)],[150, 148])).
% 0.22/0.53  tff(152,plain,
% 0.22/0.53      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.53      inference(quant_inst,[status(thm)],[])).
% 0.22/0.53  tff(153,plain,
% 0.22/0.53      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.53      inference(modus_ponens,[status(thm)],[152, 151])).
% 0.22/0.53  tff(154,plain,
% 0.22/0.53      (c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.53      inference(unit_resolution,[status(thm)],[153, 44, 34, 147])).
% 0.22/0.53  tff(155,plain,
% 0.22/0.53      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.53      inference(monotonicity,[status(thm)],[76, 154])).
% 0.22/0.53  tff(156,plain,
% 0.22/0.53      ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)) | (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = v_evs)),
% 0.22/0.53      inference(quant_inst,[status(thm)],[])).
% 0.22/0.53  tff(157,plain,
% 0.22/0.53      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = v_evs),
% 0.22/0.53      inference(unit_resolution,[status(thm)],[156, 6])).
% 0.22/0.53  tff(158,plain,
% 0.22/0.53      (v_evs = inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.53      inference(symmetry,[status(thm)],[157])).
% 0.22/0.53  tff(159,plain,
% 0.22/0.53      (v_evs = elem!1),
% 0.22/0.53      inference(transitivity,[status(thm)],[158, 155, 8])).
% 0.22/0.53  tff(160,plain,
% 0.22/0.53      (c_Event_Oused(v_evs) = c_Event_Oused(elem!1)),
% 0.22/0.53      inference(monotonicity,[status(thm)],[159])).
% 0.22/0.53  tff(161,plain,
% 0.22/0.53      (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)),
% 0.22/0.53      inference(monotonicity,[status(thm)],[160])).
% 0.22/0.53  tff(162,plain,
% 0.22/0.53      (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.53      inference(symmetry,[status(thm)],[161])).
% 0.22/0.53  tff(163,plain,
% 0.22/0.53      ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.22/0.53      inference(monotonicity,[status(thm)],[162])).
% 0.22/0.53  tff(164,plain,
% 0.22/0.53      (inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) = inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.53      inference(symmetry,[status(thm)],[109])).
% 0.22/0.53  tff(165,plain,
% 0.22/0.53      (elem!1 = inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.53      inference(symmetry,[status(thm)],[8])).
% 0.22/0.53  tff(166,plain,
% 0.22/0.53      (elem!1 = v_evs_H),
% 0.22/0.53      inference(transitivity,[status(thm)],[165, 164, 111])).
% 0.22/0.53  tff(167,plain,
% 0.22/0.53      (v_sko__urX(elem!1) = v_sko__urX(v_evs_H)),
% 0.22/0.53      inference(monotonicity,[status(thm)],[166])).
% 0.22/0.53  tff(168,plain,
% 0.22/0.53      (v_sko__urX(elem!1) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.53      inference(transitivity,[status(thm)],[167, 77])).
% 0.22/0.53  tff(169,plain,
% 0.22/0.53      (c_lessequals(v_sko__urX(elem!1), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.53      inference(monotonicity,[status(thm)],[168])).
% 0.22/0.53  tff(170,plain,
% 0.22/0.53      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(v_sko__urX(elem!1), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.53      inference(symmetry,[status(thm)],[169])).
% 0.22/0.53  tff(171,plain,
% 0.22/0.53      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.53      inference(quant_inst,[status(thm)],[])).
% 0.22/0.53  tff(172,plain,
% 0.22/0.53      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.53      inference(unit_resolution,[status(thm)],[171, 15])).
% 0.22/0.53  tff(173,plain,
% 0.22/0.53      (c_lessequals(v_sko__urX(elem!1), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.53      inference(modus_ponens,[status(thm)],[172, 170])).
% 0.22/0.53  tff(174,plain,
% 0.22/0.53      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))),
% 0.22/0.53      inference(rewrite,[status(thm)],[])).
% 0.22/0.53  tff(175,plain,
% 0.22/0.53      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))),
% 0.22/0.53      inference(quant_inst,[status(thm)],[])).
% 0.22/0.53  tff(176,plain,
% 0.22/0.53      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat))),
% 0.22/0.53      inference(modus_ponens,[status(thm)],[175, 174])).
% 0.22/0.53  tff(177,plain,
% 0.22/0.53      ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat))),
% 0.22/0.53      inference(unit_resolution,[status(thm)],[176, 24])).
% 0.22/0.53  tff(178,plain,
% 0.22/0.53      (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)),
% 0.22/0.53      inference(unit_resolution,[status(thm)],[177, 173])).
% 0.22/0.53  tff(179,plain,
% 0.22/0.53      (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.53      inference(modus_ponens,[status(thm)],[178, 163])).
% 0.22/0.53  tff(180,plain,
% 0.22/0.53      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.53      inference(rewrite,[status(thm)],[])).
% 0.22/0.53  tff(181,plain,
% 0.22/0.53      ((c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))) <=> (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.53      inference(rewrite,[status(thm)],[])).
% 0.22/0.53  tff(182,plain,
% 0.22/0.53      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))))),
% 0.22/0.54      inference(monotonicity,[status(thm)],[181])).
% 0.22/0.54  tff(183,plain,
% 0.22/0.54      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.54      inference(transitivity,[status(thm)],[182, 180])).
% 0.22/0.54  tff(184,plain,
% 0.22/0.54      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.54      inference(quant_inst,[status(thm)],[])).
% 0.22/0.54  tff(185,plain,
% 0.22/0.54      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.54      inference(modus_ponens,[status(thm)],[184, 183])).
% 0.22/0.54  tff(186,plain,
% 0.22/0.54      (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.54      inference(unit_resolution,[status(thm)],[185, 44, 34])).
% 0.22/0.54  tff(187,plain,
% 0.22/0.54      (c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.54      inference(unit_resolution,[status(thm)],[186, 179])).
% 0.22/0.54  tff(188,plain,
% 0.22/0.54      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.54      inference(monotonicity,[status(thm)],[76, 187])).
% 0.22/0.54  tff(189,plain,
% 0.22/0.54      ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)) | (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)))),
% 0.22/0.54      inference(quant_inst,[status(thm)],[])).
% 0.22/0.54  tff(190,plain,
% 0.22/0.54      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat))),
% 0.22/0.54      inference(unit_resolution,[status(thm)],[189, 6])).
% 0.22/0.54  tff(191,plain,
% 0.22/0.54      (c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)) = inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.54      inference(symmetry,[status(thm)],[190])).
% 0.22/0.54  tff(192,plain,
% 0.22/0.54      (c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)) = c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat))),
% 0.22/0.54      inference(transitivity,[status(thm)],[191, 188, 137, 116])).
% 0.22/0.54  tff(193,plain,
% 0.22/0.54      (c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)),
% 0.22/0.54      inference(monotonicity,[status(thm)],[192, 114])).
% 0.22/0.54  tff(194,plain,
% 0.22/0.54      (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.54      inference(symmetry,[status(thm)],[193])).
% 0.22/0.54  tff(195,plain,
% 0.22/0.54      ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))),
% 0.22/0.54      inference(monotonicity,[status(thm)],[194])).
% 0.22/0.54  tff(196,plain,
% 0.22/0.54      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(v_sko__urX(elem!1), c_plus(elem!1, v_sko__urX(elem!1), tc_nat), tc_nat)),
% 0.22/0.54      inference(quant_inst,[status(thm)],[])).
% 0.22/0.54  tff(197,plain,
% 0.22/0.54      (c_lessequals(v_sko__urX(elem!1), c_plus(elem!1, v_sko__urX(elem!1), tc_nat), tc_nat)),
% 0.22/0.54      inference(unit_resolution,[status(thm)],[196, 15])).
% 0.22/0.54  tff(198,plain,
% 0.22/0.54      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(elem!1, v_sko__urX(elem!1), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(elem!1, v_sko__urX(elem!1), tc_nat), tc_nat)))),
% 0.22/0.54      inference(rewrite,[status(thm)],[])).
% 0.22/0.54  tff(199,plain,
% 0.22/0.54      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(elem!1, v_sko__urX(elem!1), tc_nat), tc_nat)))),
% 0.22/0.54      inference(quant_inst,[status(thm)],[])).
% 0.22/0.54  tff(200,plain,
% 0.22/0.54      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(elem!1, v_sko__urX(elem!1), tc_nat), tc_nat))),
% 0.22/0.54      inference(modus_ponens,[status(thm)],[199, 198])).
% 0.22/0.54  tff(201,plain,
% 0.22/0.54      (~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)),
% 0.22/0.54      inference(unit_resolution,[status(thm)],[200, 24, 197])).
% 0.22/0.54  tff(202,plain,
% 0.22/0.54      (~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.54      inference(modus_ponens,[status(thm)],[201, 195])).
% 0.22/0.54  tff(203,plain,
% 0.22/0.54      (c_Event_Oused(elem!1) = c_Event_Oused(v_evs_H)),
% 0.22/0.54      inference(symmetry,[status(thm)],[114])).
% 0.22/0.54  tff(204,plain,
% 0.22/0.54      ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)) | (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = c_plus(tc_nat, c_List_Olist_ONil, tc_nat))),
% 0.22/0.54      inference(quant_inst,[status(thm)],[])).
% 0.22/0.54  tff(205,plain,
% 0.22/0.54      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = c_plus(tc_nat, c_List_Olist_ONil, tc_nat)),
% 0.22/0.54      inference(unit_resolution,[status(thm)],[204, 6])).
% 0.22/0.54  tff(206,plain,
% 0.22/0.54      (c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)),
% 0.22/0.54      inference(monotonicity,[status(thm)],[160])).
% 0.22/0.54  tff(207,plain,
% 0.22/0.54      (c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.54      inference(symmetry,[status(thm)],[206])).
% 0.22/0.54  tff(208,plain,
% 0.22/0.54      ((~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.22/0.54      inference(monotonicity,[status(thm)],[207])).
% 0.22/0.54  tff(209,plain,
% 0.22/0.54      (c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.54      inference(monotonicity,[status(thm)],[168])).
% 0.22/0.54  tff(210,plain,
% 0.22/0.54      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.54      inference(symmetry,[status(thm)],[209])).
% 0.22/0.54  tff(211,plain,
% 0.22/0.54      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.54      inference(quant_inst,[status(thm)],[])).
% 0.22/0.54  tff(212,plain,
% 0.22/0.54      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.54      inference(unit_resolution,[status(thm)],[211, 15])).
% 0.22/0.54  tff(213,plain,
% 0.22/0.54      (c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.54      inference(modus_ponens,[status(thm)],[212, 210])).
% 0.22/0.54  tff(214,plain,
% 0.22/0.54      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)))),
% 0.22/0.54      inference(rewrite,[status(thm)],[])).
% 0.22/0.54  tff(215,plain,
% 0.22/0.54      (((~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat))) <=> ((~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)))),
% 0.22/0.54      inference(rewrite,[status(thm)],[])).
% 0.22/0.54  tff(216,plain,
% 0.22/0.54      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg))))),
% 0.22/0.54      inference(monotonicity,[status(thm)],[215])).
% 0.22/0.54  tff(217,plain,
% 0.22/0.54      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)))),
% 0.22/0.54      inference(transitivity,[status(thm)],[216, 214])).
% 0.22/0.54  tff(218,plain,
% 0.22/0.54      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))),
% 0.22/0.54      inference(quant_inst,[status(thm)],[])).
% 0.22/0.54  tff(219,plain,
% 0.22/0.54      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg))),
% 0.22/0.54      inference(modus_ponens,[status(thm)],[218, 217])).
% 0.22/0.54  tff(220,plain,
% 0.22/0.54      ((~c_lessequals(v_sko__urX(elem!1), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg))),
% 0.22/0.54      inference(unit_resolution,[status(thm)],[219, 24])).
% 0.22/0.54  tff(221,plain,
% 0.22/0.54      (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)),
% 0.22/0.54      inference(unit_resolution,[status(thm)],[220, 213])).
% 0.22/0.54  tff(222,plain,
% 0.22/0.54      (~c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.54      inference(modus_ponens,[status(thm)],[221, 208])).
% 0.22/0.54  tff(223,plain,
% 0.22/0.54      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) | c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) | c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.22/0.54      inference(rewrite,[status(thm)],[])).
% 0.22/0.54  tff(224,plain,
% 0.22/0.54      ((c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))) <=> (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) | c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.22/0.54      inference(rewrite,[status(thm)],[])).
% 0.22/0.54  tff(225,plain,
% 0.22/0.54      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) | c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)))),
% 0.22/0.54      inference(monotonicity,[status(thm)],[224])).
% 0.22/0.54  tff(226,plain,
% 0.22/0.54      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) | c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.22/0.54      inference(transitivity,[status(thm)],[225, 223])).
% 0.22/0.54  tff(227,plain,
% 0.22/0.54      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.54      inference(quant_inst,[status(thm)],[])).
% 0.22/0.54  tff(228,plain,
% 0.22/0.54      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) | c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.54      inference(modus_ponens,[status(thm)],[227, 226])).
% 0.22/0.54  tff(229,plain,
% 0.22/0.54      ((c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) | c_in(c_Message_Omsg_ONonce(c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.55      inference(unit_resolution,[status(thm)],[228, 44, 34])).
% 0.22/0.55  tff(230,plain,
% 0.22/0.55      (c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.55      inference(unit_resolution,[status(thm)],[229, 222])).
% 0.22/0.55  tff(231,plain,
% 0.22/0.55      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.55      inference(monotonicity,[status(thm)],[76, 230])).
% 0.22/0.55  tff(232,plain,
% 0.22/0.55      (inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) = inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.55      inference(symmetry,[status(thm)],[231])).
% 0.22/0.55  tff(233,plain,
% 0.22/0.55      (elem!1 = c_plus(tc_nat, c_List_Olist_ONil, tc_nat)),
% 0.22/0.55      inference(transitivity,[status(thm)],[165, 232, 205])).
% 0.22/0.55  tff(234,plain,
% 0.22/0.55      (c_Message_Omsg_ONonce(elem!1) = c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat))),
% 0.22/0.55      inference(monotonicity,[status(thm)],[233])).
% 0.22/0.55  tff(235,plain,
% 0.22/0.55      (c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(elem!1), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.55      inference(monotonicity,[status(thm)],[234, 203])).
% 0.22/0.55  tff(236,plain,
% 0.22/0.55      (c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(v_evs), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(elem!1), tc_Message_Omsg)),
% 0.22/0.55      inference(monotonicity,[status(thm)],[160])).
% 0.22/0.55  tff(237,plain,
% 0.22/0.55      (c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(v_evs), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.55      inference(transitivity,[status(thm)],[236, 235])).
% 0.22/0.55  tff(238,plain,
% 0.22/0.55      ((elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)) <=> (c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = elem!1)),
% 0.22/0.55      inference(commutativity,[status(thm)],[])).
% 0.22/0.55  tff(239,plain,
% 0.22/0.55      ((c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = elem!1) <=> (elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.55      inference(symmetry,[status(thm)],[238])).
% 0.22/0.55  tff(240,plain,
% 0.22/0.55      (v_evs_H = c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat))),
% 0.22/0.55      inference(transitivity,[status(thm)],[112, 109, 137, 116])).
% 0.22/0.55  tff(241,plain,
% 0.22/0.55      (c_plus(v_evs_H, c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)),
% 0.22/0.55      inference(monotonicity,[status(thm)],[240])).
% 0.22/0.55  tff(242,plain,
% 0.22/0.55      (c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.55      inference(monotonicity,[status(thm)],[77])).
% 0.22/0.55  tff(243,plain,
% 0.22/0.55      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat) <=> c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.55      inference(symmetry,[status(thm)],[242])).
% 0.22/0.55  tff(244,plain,
% 0.22/0.55      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.55      inference(quant_inst,[status(thm)],[])).
% 0.22/0.55  tff(245,plain,
% 0.22/0.55      (c_lessequals(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.55      inference(unit_resolution,[status(thm)],[244, 15])).
% 0.22/0.55  tff(246,plain,
% 0.22/0.55      (c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)),
% 0.22/0.55      inference(modus_ponens,[status(thm)],[245, 243])).
% 0.22/0.55  tff(247,plain,
% 0.22/0.55      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))),
% 0.22/0.55      inference(rewrite,[status(thm)],[])).
% 0.22/0.55  tff(248,plain,
% 0.22/0.55      (((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat))) <=> ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))),
% 0.22/0.55      inference(rewrite,[status(thm)],[])).
% 0.22/0.55  tff(249,plain,
% 0.22/0.55      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))))),
% 0.22/0.55      inference(monotonicity,[status(thm)],[248])).
% 0.22/0.55  tff(250,plain,
% 0.22/0.55      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))),
% 0.22/0.55      inference(transitivity,[status(thm)],[249, 247])).
% 0.22/0.55  tff(251,plain,
% 0.22/0.55      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)))),
% 0.22/0.55      inference(quant_inst,[status(thm)],[])).
% 0.22/0.55  tff(252,plain,
% 0.22/0.55      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))),
% 0.22/0.55      inference(modus_ponens,[status(thm)],[251, 250])).
% 0.22/0.55  tff(253,plain,
% 0.22/0.55      ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))),
% 0.22/0.55      inference(unit_resolution,[status(thm)],[252, 24])).
% 0.22/0.55  tff(254,plain,
% 0.22/0.55      (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.55      inference(unit_resolution,[status(thm)],[253, 246])).
% 0.22/0.55  tff(255,plain,
% 0.22/0.55      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))),
% 0.22/0.55      inference(rewrite,[status(thm)],[])).
% 0.22/0.55  tff(256,plain,
% 0.22/0.55      ((c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))) <=> (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))),
% 0.22/0.55      inference(rewrite,[status(thm)],[])).
% 0.22/0.55  tff(257,plain,
% 0.22/0.55      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))))),
% 0.22/0.55      inference(monotonicity,[status(thm)],[256])).
% 0.22/0.55  tff(258,plain,
% 0.22/0.55      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))),
% 0.22/0.56      inference(transitivity,[status(thm)],[257, 255])).
% 0.22/0.56  tff(259,plain,
% 0.22/0.56      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)))),
% 0.22/0.56      inference(quant_inst,[status(thm)],[])).
% 0.22/0.56  tff(260,plain,
% 0.22/0.56      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.56      inference(modus_ponens,[status(thm)],[259, 258])).
% 0.22/0.56  tff(261,plain,
% 0.22/0.56      (c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.56      inference(unit_resolution,[status(thm)],[260, 44, 101, 254])).
% 0.22/0.56  tff(262,plain,
% 0.22/0.56      (c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(v_evs_H, c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.56      inference(symmetry,[status(thm)],[261])).
% 0.22/0.56  tff(263,plain,
% 0.22/0.56      (c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.56      inference(transitivity,[status(thm)],[262, 108])).
% 0.22/0.56  tff(264,plain,
% 0.22/0.56      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.56      inference(monotonicity,[status(thm)],[76, 263])).
% 0.22/0.56  tff(265,plain,
% 0.22/0.56      ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)) | (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)))),
% 0.22/0.56      inference(quant_inst,[status(thm)],[])).
% 0.22/0.56  tff(266,plain,
% 0.22/0.56      (inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)) = c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.56      inference(unit_resolution,[status(thm)],[265, 6])).
% 0.22/0.56  tff(267,plain,
% 0.22/0.56      (c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)) = inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.56      inference(symmetry,[status(thm)],[266])).
% 0.22/0.56  tff(268,plain,
% 0.22/0.56      (c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)) = v_evs_H),
% 0.22/0.56      inference(transitivity,[status(thm)],[267, 264, 164, 111])).
% 0.22/0.56  tff(269,plain,
% 0.22/0.56      (c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = c_plus(v_evs_H, c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)),
% 0.22/0.56      inference(monotonicity,[status(thm)],[268])).
% 0.22/0.56  tff(270,plain,
% 0.22/0.56      (c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)),
% 0.22/0.56      inference(transitivity,[status(thm)],[269, 241])).
% 0.22/0.56  tff(271,plain,
% 0.22/0.56      ((c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = elem!1) <=> (c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = elem!1)),
% 0.22/0.56      inference(monotonicity,[status(thm)],[270])).
% 0.22/0.56  tff(272,plain,
% 0.22/0.56      ((c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = elem!1) <=> (c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = elem!1)),
% 0.22/0.56      inference(symmetry,[status(thm)],[271])).
% 0.22/0.56  tff(273,plain,
% 0.22/0.56      ((elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)) <=> (c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = elem!1)),
% 0.22/0.56      inference(commutativity,[status(thm)],[])).
% 0.22/0.56  tff(274,plain,
% 0.22/0.56      (c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)) = c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat))),
% 0.22/0.56      inference(transitivity,[status(thm)],[267, 264, 137, 116])).
% 0.22/0.56  tff(275,plain,
% 0.22/0.56      (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.56      inference(monotonicity,[status(thm)],[274])).
% 0.22/0.56  tff(276,plain,
% 0.22/0.56      (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.56      inference(symmetry,[status(thm)],[275])).
% 0.22/0.56  tff(277,plain,
% 0.22/0.56      (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)),
% 0.22/0.56      inference(monotonicity,[status(thm)],[114])).
% 0.22/0.56  tff(278,plain,
% 0.22/0.56      (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.56      inference(symmetry,[status(thm)],[277])).
% 0.22/0.56  tff(279,plain,
% 0.22/0.56      (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.56      inference(transitivity,[status(thm)],[278, 276])).
% 0.22/0.56  tff(280,plain,
% 0.22/0.56      ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))),
% 0.22/0.56      inference(monotonicity,[status(thm)],[279])).
% 0.22/0.56  tff(281,plain,
% 0.22/0.56      (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.56      inference(modus_ponens,[status(thm)],[201, 280])).
% 0.22/0.56  tff(282,plain,
% 0.22/0.56      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)))),
% 0.22/0.56      inference(rewrite,[status(thm)],[])).
% 0.22/0.56  tff(283,plain,
% 0.22/0.56      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)))),
% 0.22/0.56      inference(quant_inst,[status(thm)],[])).
% 0.22/0.56  tff(284,plain,
% 0.22/0.56      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.56      inference(modus_ponens,[status(thm)],[283, 282])).
% 0.22/0.56  tff(285,plain,
% 0.22/0.56      (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.56      inference(unit_resolution,[status(thm)],[284, 44, 72])).
% 0.22/0.56  tff(286,plain,
% 0.22/0.56      (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)),
% 0.22/0.56      inference(unit_resolution,[status(thm)],[285, 281])).
% 0.22/0.56  tff(287,plain,
% 0.22/0.56      ((elem!1 = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) <=> (elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.56      inference(monotonicity,[status(thm)],[286])).
% 0.22/0.56  tff(288,plain,
% 0.22/0.56      ((elem!1 = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) <=> (c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = elem!1)),
% 0.22/0.56      inference(transitivity,[status(thm)],[287, 273])).
% 0.22/0.56  tff(289,plain,
% 0.22/0.56      (c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.56      inference(symmetry,[status(thm)],[286])).
% 0.22/0.56  tff(290,plain,
% 0.22/0.56      (c_0 = v_evs_H),
% 0.22/0.56      inference(transitivity,[status(thm)],[82, 79, 164, 111])).
% 0.22/0.56  tff(291,plain,
% 0.22/0.56      (c_plus(c_0, c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = c_plus(v_evs_H, c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)),
% 0.22/0.56      inference(monotonicity,[status(thm)],[290])).
% 0.22/0.56  tff(292,plain,
% 0.22/0.56      ((~![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)) | (c_plus(c_0, c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = c_List_Olist_OCons(elem!1, elem!1, elem!1))),
% 0.22/0.56      inference(quant_inst,[status(thm)],[])).
% 0.22/0.56  tff(293,plain,
% 0.22/0.56      (c_plus(c_0, c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat) = c_List_Olist_OCons(elem!1, elem!1, elem!1)),
% 0.22/0.56      inference(unit_resolution,[status(thm)],[292, 55])).
% 0.22/0.56  tff(294,plain,
% 0.22/0.56      (c_List_Olist_OCons(elem!1, elem!1, elem!1) = c_plus(c_0, c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)),
% 0.22/0.56      inference(symmetry,[status(thm)],[293])).
% 0.22/0.56  tff(295,plain,
% 0.22/0.56      (c_List_Olist_OCons(elem!1, elem!1, elem!1) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.56      inference(transitivity,[status(thm)],[294, 291, 241, 289])).
% 0.22/0.56  tff(296,plain,
% 0.22/0.56      (c_plus(tc_nat, c_List_Olist_ONil, tc_nat) = inj_0(c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), c_plus(c_plus(tc_nat, c_List_Olist_ONil, tc_nat), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat))),
% 0.22/0.56      inference(symmetry,[status(thm)],[205])).
% 0.22/0.56  tff(297,plain,
% 0.22/0.56      ((~![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)) | (inj_0(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)) = tc_nat)),
% 0.22/0.56      inference(quant_inst,[status(thm)],[])).
% 0.22/0.56  tff(298,plain,
% 0.22/0.56      (inj_0(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)) = tc_nat),
% 0.22/0.56      inference(unit_resolution,[status(thm)],[297, 6])).
% 0.22/0.56  tff(299,plain,
% 0.22/0.56      ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)) | c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.56      inference(quant_inst,[status(thm)],[])).
% 0.22/0.56  tff(300,plain,
% 0.22/0.56      (c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.22/0.56      inference(unit_resolution,[status(thm)],[299, 15])).
% 0.22/0.56  tff(301,plain,
% 0.22/0.56      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))),
% 0.22/0.56      inference(rewrite,[status(thm)],[])).
% 0.22/0.56  tff(302,plain,
% 0.22/0.56      (((~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat))) <=> ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))),
% 0.22/0.56      inference(rewrite,[status(thm)],[])).
% 0.22/0.56  tff(303,plain,
% 0.22/0.56      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))))),
% 0.22/0.56      inference(monotonicity,[status(thm)],[302])).
% 0.22/0.56  tff(304,plain,
% 0.22/0.56      (((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)))) <=> ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)))),
% 0.22/0.56      inference(transitivity,[status(thm)],[303, 301])).
% 0.22/0.56  tff(305,plain,
% 0.22/0.56      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | ((~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)))),
% 0.22/0.56      inference(quant_inst,[status(thm)],[])).
% 0.22/0.56  tff(306,plain,
% 0.22/0.56      ((~![V_U: $i, V_evs: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(V_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(V_evs), V_U, tc_nat)))) | (~c_lessequals(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))),
% 0.22/0.56      inference(modus_ponens,[status(thm)],[305, 304])).
% 0.22/0.56  tff(307,plain,
% 0.22/0.56      (~c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.56      inference(unit_resolution,[status(thm)],[306, 24, 300])).
% 0.22/0.56  tff(308,plain,
% 0.22/0.56      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.56      inference(rewrite,[status(thm)],[])).
% 0.22/0.56  tff(309,plain,
% 0.22/0.56      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)))),
% 0.22/0.56      inference(quant_inst,[status(thm)],[])).
% 0.22/0.56  tff(310,plain,
% 0.22/0.56      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.56      inference(modus_ponens,[status(thm)],[309, 308])).
% 0.22/0.56  tff(311,plain,
% 0.22/0.56      (c_plus(elem!1, v_sko__urX(v_evs), tc_nat) = c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.56      inference(unit_resolution,[status(thm)],[310, 44, 307, 28])).
% 0.22/0.56  tff(312,plain,
% 0.22/0.56      (c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs), tc_nat)),
% 0.22/0.56      inference(symmetry,[status(thm)],[311])).
% 0.22/0.56  tff(313,plain,
% 0.22/0.56      (c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.22/0.56      inference(transitivity,[status(thm)],[312, 48])).
% 0.22/0.56  tff(314,plain,
% 0.22/0.56      (inj_0(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat)) = inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.56      inference(monotonicity,[status(thm)],[313])).
% 0.22/0.56  tff(315,plain,
% 0.22/0.56      (inj_0(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)) = inj_0(v_sko__urX(v_evs_H), c_plus(tc_nat, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.56      inference(symmetry,[status(thm)],[314])).
% 0.22/0.56  tff(316,plain,
% 0.22/0.56      (c_0 = tc_nat),
% 0.22/0.56      inference(transitivity,[status(thm)],[82, 79, 315, 298])).
% 0.22/0.56  tff(317,plain,
% 0.22/0.56      (c_plus(c_0, c_List_Olist_ONil, tc_nat) = c_plus(tc_nat, c_List_Olist_ONil, tc_nat)),
% 0.22/0.56      inference(monotonicity,[status(thm)],[316])).
% 0.22/0.56  tff(318,plain,
% 0.22/0.56      ((~![V_y: $i] : (c_plus(c_0, V_y, tc_nat) = V_y)) | (c_plus(c_0, c_List_Olist_ONil, tc_nat) = c_List_Olist_ONil)),
% 0.22/0.57      inference(quant_inst,[status(thm)],[])).
% 0.22/0.57  tff(319,plain,
% 0.22/0.57      (c_plus(c_0, c_List_Olist_ONil, tc_nat) = c_List_Olist_ONil),
% 0.22/0.57      inference(unit_resolution,[status(thm)],[318, 55])).
% 0.22/0.57  tff(320,plain,
% 0.22/0.57      (c_List_Olist_ONil = c_plus(c_0, c_List_Olist_ONil, tc_nat)),
% 0.22/0.57      inference(symmetry,[status(thm)],[319])).
% 0.22/0.57  tff(321,plain,
% 0.22/0.57      (c_List_Olist_ONil = elem!1),
% 0.22/0.57      inference(transitivity,[status(thm)],[320, 317, 296, 231, 8])).
% 0.22/0.57  tff(322,plain,
% 0.22/0.57      ((c_List_Olist_ONil = c_List_Olist_OCons(elem!1, elem!1, elem!1)) <=> (elem!1 = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.22/0.57      inference(monotonicity,[status(thm)],[321, 295])).
% 0.22/0.57  tff(323,plain,
% 0.22/0.57      ((c_List_Olist_ONil = c_List_Olist_OCons(elem!1, elem!1, elem!1)) <=> (elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.57      inference(transitivity,[status(thm)],[322, 288, 272, 239])).
% 0.22/0.57  tff(324,plain,
% 0.22/0.57      ((~(c_List_Olist_ONil = c_List_Olist_OCons(elem!1, elem!1, elem!1))) <=> (~(elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)))),
% 0.22/0.57      inference(monotonicity,[status(thm)],[323])).
% 0.22/0.57  tff(325,plain,
% 0.22/0.57      (^[V_a_H: $i, V_list_H: $i, T_a: $i] : refl((~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a))) <=> (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a))))),
% 0.22/0.57      inference(bind,[status(th)],[])).
% 0.22/0.57  tff(326,plain,
% 0.22/0.57      (![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a))) <=> ![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a)))),
% 0.22/0.57      inference(quant_intro,[status(thm)],[325])).
% 0.22/0.57  tff(327,plain,
% 0.22/0.57      (![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a))) <=> ![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a)))),
% 0.22/0.57      inference(rewrite,[status(thm)],[])).
% 0.22/0.57  tff(328,axiom,(![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_List_Olist_Odistinct__1_0')).
% 0.22/0.57  tff(329,plain,
% 0.22/0.57      (![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a)))),
% 0.22/0.57      inference(modus_ponens,[status(thm)],[328, 327])).
% 0.22/0.57  tff(330,plain,(
% 0.22/0.57      ![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a)))),
% 0.22/0.57      inference(skolemize,[status(sab)],[329])).
% 0.22/0.57  tff(331,plain,
% 0.22/0.57      (![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a)))),
% 0.22/0.57      inference(modus_ponens,[status(thm)],[330, 326])).
% 0.22/0.57  tff(332,plain,
% 0.22/0.57      ((~![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a)))) | (~(c_List_Olist_ONil = c_List_Olist_OCons(elem!1, elem!1, elem!1)))),
% 0.22/0.57      inference(quant_inst,[status(thm)],[])).
% 0.22/0.57  tff(333,plain,
% 0.22/0.57      (~(c_List_Olist_ONil = c_List_Olist_OCons(elem!1, elem!1, elem!1))),
% 0.22/0.57      inference(unit_resolution,[status(thm)],[332, 331])).
% 0.22/0.57  tff(334,plain,
% 0.22/0.57      (~(elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.57      inference(modus_ponens,[status(thm)],[333, 324])).
% 0.22/0.57  tff(335,plain,
% 0.22/0.57      (c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)) = c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.57      inference(monotonicity,[status(thm)],[270])).
% 0.22/0.57  tff(336,plain,
% 0.22/0.57      (c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)) = c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat))),
% 0.22/0.57      inference(transitivity,[status(thm)],[335, 267, 264, 137, 116])).
% 0.22/0.57  tff(337,plain,
% 0.22/0.57      (c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)),
% 0.22/0.57      inference(monotonicity,[status(thm)],[336, 114])).
% 0.22/0.57  tff(338,plain,
% 0.22/0.57      (c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg) <=> c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.57      inference(symmetry,[status(thm)],[337])).
% 0.22/0.57  tff(339,plain,
% 0.22/0.57      ((~c_in(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_Event_Oused(elem!1), tc_Message_Omsg)) <=> (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg))),
% 0.22/0.57      inference(monotonicity,[status(thm)],[338])).
% 0.22/0.57  tff(340,plain,
% 0.22/0.57      (~c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.57      inference(modus_ponens,[status(thm)],[201, 339])).
% 0.22/0.57  tff(341,plain,
% 0.22/0.57      (((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)))) <=> ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)))),
% 0.22/0.57      inference(rewrite,[status(thm)],[])).
% 0.22/0.57  tff(342,plain,
% 0.22/0.57      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | (c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)))),
% 0.22/0.57      inference(quant_inst,[status(thm)],[])).
% 0.22/0.57  tff(343,plain,
% 0.22/0.57      ((~![V_V: $i, V_U: $i] : (c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(V_V), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (V_U = V_V))) | c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.57      inference(modus_ponens,[status(thm)],[342, 341])).
% 0.22/0.57  tff(344,plain,
% 0.22/0.57      (c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(v_evs), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg) | (elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.57      inference(unit_resolution,[status(thm)],[343, 44])).
% 0.22/0.57  tff(345,plain,
% 0.22/0.57      (c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(v_evs), tc_Message_Omsg) | (elem!1 = c_plus(c_Message_Omsg_ONonce(c_plus(c_Message_Omsg_ONonce(c_plus(elem!1, v_sko__urX(elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat)), c_List_Olist_OCons(elem!1, elem!1, elem!1), tc_nat))),
% 0.22/0.57      inference(unit_resolution,[status(thm)],[344, 340])).
% 0.22/0.57  tff(346,plain,
% 0.22/0.57      (c_in(c_Message_Omsg_ONonce(elem!1), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.22/0.57      inference(unit_resolution,[status(thm)],[345, 334])).
% 0.22/0.57  tff(347,plain,
% 0.22/0.57      (c_in(c_Message_Omsg_ONonce(c_plus(tc_nat, c_List_Olist_ONil, tc_nat)), c_Event_Oused(v_evs_H), tc_Message_Omsg)),
% 0.22/0.57      inference(modus_ponens,[status(thm)],[346, 237])).
% 0.22/0.57  tff(348,plain,
% 0.22/0.57      ($false),
% 0.22/0.57      inference(unit_resolution,[status(thm)],[347, 202])).
% 0.22/0.57  % SZS output end Proof
% 0.22/0.57  % E exiting
%------------------------------------------------------------------------------