TSTP Solution File: SWV281-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV281-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Thu Sep 29 15:10:49 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV281-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 02:12:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(c_List_Olist_OCons_type, type, (
% 0.19/0.42 c_List_Olist_OCons: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(elem_1_type, type, (
% 0.19/0.42 elem_1: $i)).
% 0.19/0.42 tff(c_List_Olist_ONil_type, type, (
% 0.19/0.42 c_List_Olist_ONil: $i)).
% 0.19/0.42 tff(inj_0_type, type, (
% 0.19/0.42 inj_0: ( $i * $i ) > $i)).
% 0.19/0.42 tff(c_plus_type, type, (
% 0.19/0.42 c_plus: ( $i * $i * $i ) > $i)).
% 0.19/0.42 tff(tc_nat_type, type, (
% 0.19/0.42 tc_nat: $i)).
% 0.19/0.42 tff(v_sko__urX_type, type, (
% 0.19/0.42 v_sko__urX: $i > $i)).
% 0.19/0.42 tff(v_evs_type, type, (
% 0.19/0.42 v_evs: $i)).
% 0.19/0.42 tff(v_evs_H_type, type, (
% 0.19/0.42 v_evs_H: $i)).
% 0.19/0.42 tff(c_in_type, type, (
% 0.19/0.42 c_in: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(tc_Message_Omsg_type, type, (
% 0.19/0.42 tc_Message_Omsg: $i)).
% 0.19/0.42 tff(c_Event_Oused_type, type, (
% 0.19/0.42 c_Event_Oused: $i > $i)).
% 0.19/0.42 tff(c_Message_Omsg_ONonce_type, type, (
% 0.19/0.42 c_Message_Omsg_ONonce: $i > $i)).
% 0.19/0.42 tff(c_lessequals_type, type, (
% 0.19/0.42 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (![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)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 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/sandbox/benchmark/theBenchmark.p','cls_Nat_Onat__add__right__cancel_0')).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.42 tff(5,plain,(
% 0.19/0.42 ![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))),
% 0.19/0.42 inference(skolemize,[status(sab)],[4])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (![Xk!0: $i, Xk!1: $i] : (inj_0(Xk!0, c_plus(Xk!1, Xk!0, tc_nat)) = Xk!1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 ((~![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), c_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)) = c_List_Olist_OCons(elem!1, elem!1, elem!1))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (inj_0(v_sko__urX(v_evs), c_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)) = c_List_Olist_OCons(elem!1, elem!1, elem!1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (^[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))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (![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)),
% 0.19/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (![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)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 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/sandbox/benchmark/theBenchmark.p','cls_Nat_Ole__add2_0')).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.42 tff(14,plain,(
% 0.19/0.42 ![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)),
% 0.19/0.42 inference(skolemize,[status(sab)],[13])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (![V_n: $i, V_m: $i] : c_lessequals(V_n, c_plus(V_m, V_n, tc_nat), tc_nat)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 ((~![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(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat), tc_nat)),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (c_lessequals(v_sko__urX(v_evs), c_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat), tc_nat)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 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/sandbox/benchmark/theBenchmark.p','cls_Public_ONonce__supply__lemma_0')).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.43 tff(23,plain,(
% 0.19/0.43 ![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)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[22])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (((~![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_List_Olist_OCons(elem!1, elem!1, 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(c_List_Olist_OCons(elem!1, elem!1, 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(c_List_Olist_OCons(elem!1, elem!1, 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(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat), tc_nat)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 ((~![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_List_Olist_OCons(elem!1, elem!1, 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(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat), tc_nat)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 ((~![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_List_Olist_OCons(elem!1, elem!1, 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(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat), tc_nat))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (~c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[27, 24, 17])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 ((~![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)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (c_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), tc_nat)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[29, 15])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (((~![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(elem!1, v_sko__urX(v_evs_H), tc_nat), 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)))) <=> ((~![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(elem!1, v_sko__urX(v_evs_H), tc_nat), 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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (((~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))) <=> ((~c_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), 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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (((~![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_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), 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))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (((~![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_lessequals(v_sko__urX(v_evs_H), c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat), 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)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[33, 31])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 ((~![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(elem!1, v_sko__urX(v_evs_H), tc_nat), 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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (~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)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[36, 24, 30])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (^[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)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (^[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)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.43 tff(43,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/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.43 tff(46,plain,(
% 0.19/0.43 ![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))),
% 0.19/0.43 inference(skolemize,[status(sab)],[45])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (![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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (((~![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_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), 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_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), 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_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), 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_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 ((c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_OCons(elem!1, elem!1, 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(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))) <=> ((c_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), 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_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (((~![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_List_Olist_OCons(elem!1, elem!1, 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(c_List_Olist_OCons(elem!1, elem!1, 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_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), 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_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (((~![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_List_Olist_OCons(elem!1, elem!1, 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(c_List_Olist_OCons(elem!1, elem!1, 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_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), 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_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.19/0.44 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 ((~![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_List_Olist_OCons(elem!1, elem!1, 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(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 ((~![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_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), 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_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.44 tff(54,plain,
% 0.19/0.44 (c_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[53, 47, 37, 28])).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 (c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat) = c_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)),
% 0.19/0.44 inference(symmetry,[status(thm)],[54])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 ((~![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(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(57,plain,
% 0.19/0.44 (c_lessequals(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[56, 15])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 (((~![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(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), 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(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (((~c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat))) <=> ((~c_lessequals(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 (((~![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_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, 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_lessequals(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (((~![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_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, 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_lessequals(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 ((~![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_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)) | (~c_lessequals(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 ((~![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(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat), tc_nat)) | (~c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 (~c_in(c_Message_Omsg_ONonce(c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)), c_Event_Oused(v_evs), tc_Message_Omsg)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[63, 24, 57])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (((~![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_List_Olist_ONil, 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(c_List_Olist_ONil, 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(c_List_Olist_ONil, 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(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 ((~![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_List_Olist_ONil, 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(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 ((~![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_List_Olist_ONil, 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(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat) = c_plus(elem!1, v_sko__urX(v_evs_H), tc_nat)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[67, 47, 37, 64])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat) = c_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat)),
% 0.19/0.44 inference(transitivity,[status(thm)],[68, 55])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (inj_0(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)) = inj_0(v_sko__urX(v_evs), c_plus(c_List_Olist_OCons(elem!1, elem!1, elem!1), v_sko__urX(v_evs), tc_nat))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 ((~![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), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)) = c_List_Olist_ONil)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (inj_0(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat)) = c_List_Olist_ONil),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[71, 6])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (c_List_Olist_ONil = inj_0(v_sko__urX(v_evs), c_plus(c_List_Olist_ONil, v_sko__urX(v_evs), tc_nat))),
% 0.19/0.44 inference(symmetry,[status(thm)],[72])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (c_List_Olist_ONil = c_List_Olist_OCons(elem!1, elem!1, elem!1)),
% 0.19/0.44 inference(transitivity,[status(thm)],[73, 70, 8])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (^[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))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(78,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/sandbox/benchmark/theBenchmark.p','cls_List_Olist_Odistinct__1_0')).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.44 tff(80,plain,(
% 0.19/0.44 ![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)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[79])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (![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)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 ((~![V_a_H: $i, V_list_H: $i, T_a: $i] : (~(c_List_Olist_ONil = c_List_Olist_OCons(V_a_H, V_list_H, T_a)))) | (~(c_List_Olist_ONil = c_List_Olist_OCons(elem!1, elem!1, elem!1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (~(c_List_Olist_ONil = c_List_Olist_OCons(elem!1, elem!1, elem!1))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[83, 74])).
% 0.19/0.45 % SZS output end Proof
%------------------------------------------------------------------------------