%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV280-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV280-2 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:37:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(c_in_type, type, (
% 0.11/0.37 c_in: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(tc_Message_Omsg_type, type, (
% 0.11/0.37 tc_Message_Omsg: $i)).
% 0.11/0.37 tff(c_Event_Oused_type, type, (
% 0.11/0.37 c_Event_Oused: $i > $i)).
% 0.11/0.37 tff(v_evs_type, type, (
% 0.11/0.37 v_evs: $i)).
% 0.11/0.37 tff(c_Message_Omsg_ONonce_type, type, (
% 0.11/0.37 c_Message_Omsg_ONonce: $i > $i)).
% 0.11/0.37 tff(c_plus_type, type, (
% 0.11/0.37 c_plus: ( $i * $i * $i ) > $i)).
% 0.11/0.37 tff(tc_nat_type, type, (
% 0.11/0.37 tc_nat: $i)).
% 0.11/0.37 tff(elem_0_type, type, (
% 0.11/0.37 elem_0: $i)).
% 0.11/0.37 tff(v_sko__urX_type, type, (
% 0.11/0.37 v_sko__urX: $i > $i)).
% 0.11/0.37 tff(c_lessequals_type, type, (
% 0.11/0.37 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[V_n: $i, V_m: $i] : refl(c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat) <=> c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat) <=> ![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat) <=> ![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,axiom,(![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Nat_Ole__add1_0')).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.37 tff(6,plain,(
% 0.11/0.37 ![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat)),
% 0.11/0.37 inference(skolemize,[status(sab)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 ((~![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_n, V_m, tc_nat), tc_nat)) | c_lessequals(v_sko__urX(v_evs), c_plus(v_sko__urX(v_evs), elem!0, tc_nat), tc_nat)),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (c_lessequals(v_sko__urX(v_evs), c_plus(v_sko__urX(v_evs), elem!0, tc_nat), tc_nat)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (^[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))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(13,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')).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.11/0.37 tff(15,plain,(
% 0.11/0.37 ![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)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[14])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![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)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (((~![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_sko__urX(v_evs), elem!0, tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_sko__urX(v_evs), elem!0, 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_sko__urX(v_evs), elem!0, tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_sko__urX(v_evs), elem!0, tc_nat), tc_nat)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 ((~![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_sko__urX(v_evs), elem!0, tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_sko__urX(v_evs), elem!0, tc_nat), tc_nat)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 ((~![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_sko__urX(v_evs), elem!0, tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(v_sko__urX(v_evs), elem!0, tc_nat), tc_nat))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (~c_in(c_Message_Omsg_ONonce(c_plus(v_sko__urX(v_evs), elem!0, tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (^[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_U), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![V_U: $i] : c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) <=> ![V_U: $i] : c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![V_U: $i] : c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg) <=> ![V_U: $i] : c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(24,axiom,(![V_U: $i] : 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')).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![V_U: $i] : c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.37 tff(26,plain,(
% 0.11/0.37 ![V_U: $i] : c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.11/0.37 inference(skolemize,[status(sab)],[25])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![V_U: $i] : c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~![V_U: $i] : c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_evs), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(c_plus(v_sko__urX(v_evs), elem!0, tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[28, 27, 20])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------