%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV283-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:31:59 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.46s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWV283-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 09:35:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.46 % SZS status Unsatisfiable
% 0.22/0.46 % SZS output start Proof
% 0.22/0.46 tff(c_lessequals_type, type, (
% 0.22/0.46 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.22/0.46 tff(tc_nat_type, type, (
% 0.22/0.46 tc_nat: $i)).
% 0.22/0.46 tff(v_xd_type, type, (
% 0.22/0.46 v_xd: $i > $i)).
% 0.22/0.46 tff(c_plus_type, type, (
% 0.22/0.46 c_plus: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(v_sko__upX_type, type, (
% 0.22/0.46 v_sko__upX: $i > $i)).
% 0.22/0.46 tff(v_xc_type, type, (
% 0.22/0.46 v_xc: $i)).
% 0.22/0.46 tff(elem_0_type, type, (
% 0.22/0.46 elem_0: $i)).
% 0.22/0.46 tff(v_x_type, type, (
% 0.22/0.46 v_x: $i)).
% 0.22/0.46 tff(c_in_type, type, (
% 0.22/0.46 c_in: ( $i * $i * $i ) > $o)).
% 0.22/0.46 tff(tc_Message_Omsg_type, type, (
% 0.22/0.46 tc_Message_Omsg: $i)).
% 0.22/0.46 tff(c_Message_Oparts_type, type, (
% 0.22/0.46 c_Message_Oparts: $i > $i)).
% 0.22/0.46 tff(c_insert_type, type, (
% 0.22/0.46 c_insert: ( $i * $i * $i ) > $i)).
% 0.22/0.46 tff(c_emptyset_type, type, (
% 0.22/0.46 c_emptyset: $i)).
% 0.22/0.46 tff(c_Message_Omsg_ONonce_type, type, (
% 0.22/0.46 c_Message_Omsg_ONonce: $i > $i)).
% 0.22/0.46 tff(c_Event_Oused_type, type, (
% 0.22/0.46 c_Event_Oused: $i > $i)).
% 0.22/0.46 tff(v_list_type, type, (
% 0.22/0.46 v_list: $i)).
% 0.22/0.46 tff(1,plain,
% 0.22/0.46 (^[V_W: $i, V_U: $i] : refl((c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat)) <=> (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat)))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(2,plain,
% 0.22/0.46 (![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat)) <=> ![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.46 tff(3,plain,
% 0.22/0.46 (![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat)) <=> ![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(4,plain,
% 0.22/0.46 (^[V_W: $i, V_U: $i] : rewrite((c_lessequals(V_W, v_xd(V_W), tc_nat) | c_lessequals(V_U, v_xd(V_U), tc_nat)) <=> (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat)))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(5,plain,
% 0.22/0.46 (![V_W: $i, V_U: $i] : (c_lessequals(V_W, v_xd(V_W), tc_nat) | c_lessequals(V_U, v_xd(V_U), tc_nat)) <=> ![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[4])).
% 0.22/0.46 tff(6,axiom,(![V_W: $i, V_U: $i] : (c_lessequals(V_W, v_xd(V_W), tc_nat) | c_lessequals(V_U, v_xd(V_U), tc_nat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.22/0.46 tff(7,plain,
% 0.22/0.46 (![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.22/0.46 tff(8,plain,
% 0.22/0.46 (![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.22/0.46 tff(9,plain,(
% 0.22/0.46 ![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))),
% 0.22/0.46 inference(skolemize,[status(sab)],[8])).
% 0.22/0.46 tff(10,plain,
% 0.22/0.46 (![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.22/0.46 tff(11,plain,
% 0.22/0.46 (((~![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))) | c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) <=> ((~![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))) | c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(12,plain,
% 0.22/0.46 ((c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat) | c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) <=> c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(13,plain,
% 0.22/0.47 (((~![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))) | (c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat) | c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))) <=> ((~![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))) | c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[12])).
% 0.22/0.47 tff(14,plain,
% 0.22/0.47 (((~![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))) | (c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat) | c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))) <=> ((~![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))) | c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.47 inference(transitivity,[status(thm)],[13, 11])).
% 0.22/0.47 tff(15,plain,
% 0.22/0.47 ((~![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))) | (c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat) | c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(16,plain,
% 0.22/0.47 ((~![V_W: $i, V_U: $i] : (c_lessequals(V_U, v_xd(V_U), tc_nat) | c_lessequals(V_W, v_xd(V_W), tc_nat))) | c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.22/0.47 tff(17,plain,
% 0.22/0.47 (c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.22/0.47 tff(18,plain,
% 0.22/0.47 (^[V_n: $i, V_m: $i, V_k: $i] : refl(((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat)) <=> ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(19,plain,
% 0.22/0.47 (![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat)) <=> ![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[18])).
% 0.22/0.47 tff(20,plain,
% 0.22/0.47 (![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat)) <=> ![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(21,axiom,(![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Nat_Oadd__leE_0')).
% 0.22/0.47 tff(22,plain,
% 0.22/0.47 (![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.22/0.47 tff(23,plain,(
% 0.22/0.47 ![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))),
% 0.22/0.47 inference(skolemize,[status(sab)],[22])).
% 0.22/0.47 tff(24,plain,
% 0.22/0.47 (![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.22/0.47 tff(25,plain,
% 0.22/0.47 (((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))) | ((~c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(c_plus(elem!0, v_sko__upX(v_xc), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))) <=> ((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))) | (~c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(c_plus(elem!0, v_sko__upX(v_xc), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(26,plain,
% 0.22/0.47 ((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))) | ((~c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(c_plus(elem!0, v_sko__upX(v_xc), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(27,plain,
% 0.22/0.47 ((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))) | (~c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(c_plus(elem!0, v_sko__upX(v_xc), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.22/0.47 tff(28,plain,
% 0.22/0.47 (c_lessequals(c_plus(elem!0, v_sko__upX(v_xc), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[27, 24, 17])).
% 0.22/0.47 tff(29,plain,
% 0.22/0.47 (((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))) | ((~c_lessequals(c_plus(elem!0, v_sko__upX(v_xc), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(v_sko__upX(v_xc), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))) <=> ((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))) | (~c_lessequals(c_plus(elem!0, v_sko__upX(v_xc), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(v_sko__upX(v_xc), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(30,plain,
% 0.22/0.47 ((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))) | ((~c_lessequals(c_plus(elem!0, v_sko__upX(v_xc), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(v_sko__upX(v_xc), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(31,plain,
% 0.22/0.47 ((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_k, V_n, tc_nat))) | (~c_lessequals(c_plus(elem!0, v_sko__upX(v_xc), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(v_sko__upX(v_xc), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.22/0.47 tff(32,plain,
% 0.22/0.47 (c_lessequals(v_sko__upX(v_xc), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[31, 24, 28])).
% 0.22/0.47 tff(33,plain,
% 0.22/0.47 (^[V_n: $i, V_m: $i, V_k: $i] : refl(((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat)) <=> ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat)))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(34,plain,
% 0.22/0.47 (![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat)) <=> ![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[33])).
% 0.22/0.47 tff(35,plain,
% 0.22/0.47 (![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat)) <=> ![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(36,axiom,(![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Nat_Oadd__leE_1')).
% 0.22/0.47 tff(37,plain,
% 0.22/0.47 (![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.22/0.47 tff(38,plain,(
% 0.22/0.47 ![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))),
% 0.22/0.47 inference(skolemize,[status(sab)],[37])).
% 0.22/0.47 tff(39,plain,
% 0.22/0.47 (![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.22/0.47 tff(40,plain,
% 0.22/0.47 (((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))) | ((~c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(v_x, v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))) <=> ((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))) | (~c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(v_x, v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(41,plain,
% 0.22/0.47 ((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))) | ((~c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(v_x, v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(42,plain,
% 0.22/0.47 ((~![V_n: $i, V_m: $i, V_k: $i] : ((~c_lessequals(c_plus(V_m, V_k, tc_nat), V_n, tc_nat)) | c_lessequals(V_m, V_n, tc_nat))) | (~c_lessequals(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | c_lessequals(v_x, v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.22/0.47 tff(43,plain,
% 0.22/0.47 (c_lessequals(v_x, v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[42, 39, 17])).
% 0.22/0.47 tff(44,plain,
% 0.22/0.47 (^[V_U: $i] : refl(((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg))) <=> ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(45,plain,
% 0.22/0.47 (![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg))) <=> ![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.48 tff(46,plain,
% 0.22/0.48 (![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg))) <=> ![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(47,plain,
% 0.22/0.48 (^[V_U: $i] : rewrite(((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)) | (~c_lessequals(v_x, V_U, tc_nat))) <=> ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(48,plain,
% 0.22/0.48 (![V_U: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)) | (~c_lessequals(v_x, V_U, tc_nat))) <=> ![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[47])).
% 0.22/0.48 tff(49,axiom,(![V_U: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)) | (~c_lessequals(v_x, V_U, tc_nat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.22/0.48 tff(50,plain,
% 0.22/0.48 (![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.22/0.48 tff(51,plain,
% 0.22/0.48 (![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.22/0.48 tff(52,plain,(
% 0.22/0.48 ![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(skolemize,[status(sab)],[51])).
% 0.22/0.48 tff(53,plain,
% 0.22/0.48 (![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.22/0.48 tff(54,plain,
% 0.22/0.48 (((~![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))) | ((~c_lessequals(v_x, v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg)))) <=> ((~![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))) | (~c_lessequals(v_x, v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(55,plain,
% 0.22/0.48 ((~![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))) | ((~c_lessequals(v_x, v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(56,plain,
% 0.22/0.48 ((~![V_U: $i] : ((~c_lessequals(v_x, V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Event_Oused(v_list), tc_Message_Omsg)))) | (~c_lessequals(v_x, v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.22/0.48 tff(57,plain,
% 0.22/0.48 (~c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.22/0.48 tff(58,plain,
% 0.22/0.48 (^[V_U: $i, V_X: $i] : refl((c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(59,plain,
% 0.22/0.48 (![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg)) <=> ![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[58])).
% 0.22/0.48 tff(60,plain,
% 0.22/0.48 (![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg)) <=> ![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(61,plain,
% 0.22/0.48 (^[V_U: $i, V_X: $i] : trans(monotonicity(rewrite(((c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))), ((((c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) <=> ((c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))), rewrite(((c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))), ((((c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(62,plain,
% 0.22/0.48 (![V_U: $i, V_X: $i] : (((c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) <=> ![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[61])).
% 0.22/0.48 tff(63,axiom,(![V_U: $i, V_X: $i] : (((c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg)) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_9')).
% 0.22/0.48 tff(64,plain,
% 0.22/0.48 (![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.22/0.48 tff(65,plain,
% 0.22/0.48 (![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.22/0.48 tff(66,plain,(
% 0.22/0.48 ![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(skolemize,[status(sab)],[65])).
% 0.22/0.48 tff(67,plain,
% 0.22/0.48 (![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.22/0.48 tff(68,plain,
% 0.22/0.48 (((~![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))) | (c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg))) <=> ((~![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(69,plain,
% 0.22/0.48 ((c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(70,plain,
% 0.22/0.48 (((~![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))) | (c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg))) <=> ((~![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))) | (c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg)))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[69])).
% 0.22/0.49 tff(71,plain,
% 0.22/0.49 (((~![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))) | (c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg))) <=> ((~![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.49 inference(transitivity,[status(thm)],[70, 68])).
% 0.22/0.49 tff(72,plain,
% 0.22/0.49 ((~![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))) | (c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(73,plain,
% 0.22/0.49 ((~![V_U: $i, V_X: $i] : (c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_U)), c_Event_Oused(v_list), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(V_X)), c_Event_Oused(v_list), tc_Message_Omsg))) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg)),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.49 tff(74,plain,
% 0.22/0.49 (c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg) | c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Event_Oused(v_list), tc_Message_Omsg)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[73, 67])).
% 0.22/0.49 tff(75,plain,
% 0.22/0.49 (c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[74, 57])).
% 0.22/0.49 tff(76,plain,
% 0.22/0.49 (^[V_U: $i, V_msg: $i] : refl(((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(77,plain,
% 0.22/0.49 (![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))) <=> ![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[76])).
% 0.22/0.49 tff(78,plain,
% 0.22/0.49 (![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))) <=> ![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(79,plain,
% 0.22/0.49 (^[V_U: $i, V_msg: $i] : rewrite(((~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat))) <=> ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(80,plain,
% 0.22/0.49 (![V_U: $i, V_msg: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat))) <=> ![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[79])).
% 0.22/0.49 tff(81,axiom,(![V_U: $i, V_msg: $i] : ((~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Omsg__Nonce__supply_0')).
% 0.22/0.49 tff(82,plain,
% 0.22/0.49 (![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.22/0.49 tff(83,plain,
% 0.22/0.49 (![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.22/0.49 tff(84,plain,(
% 0.22/0.49 ![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.22/0.49 inference(skolemize,[status(sab)],[83])).
% 0.22/0.49 tff(85,plain,
% 0.22/0.49 (![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.22/0.49 tff(86,plain,
% 0.22/0.49 (((~![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))) | ((~c_lessequals(v_sko__upX(v_xc), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))) <=> ((~![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))) | (~c_lessequals(v_sko__upX(v_xc), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(87,plain,
% 0.22/0.49 ((~![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))) | ((~c_lessequals(v_sko__upX(v_xc), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(88,plain,
% 0.22/0.49 ((~![V_U: $i, V_msg: $i] : ((~c_lessequals(v_sko__upX(V_msg), V_U, tc_nat)) | (~c_in(c_Message_Omsg_ONonce(V_U), c_Message_Oparts(c_insert(V_msg, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))) | (~c_lessequals(v_sko__upX(v_xc), v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat)), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(v_xd(c_plus(v_x, c_plus(elem!0, v_sko__upX(v_xc), tc_nat), tc_nat))), c_Message_Oparts(c_insert(v_xc, c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.22/0.49 tff(89,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[88, 85, 75, 32])).
% 0.22/0.49 % SZS output end Proof
% 0.22/0.49 % E exiting
%------------------------------------------------------------------------------