%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV279-2 : 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 05:31:58 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV279-2 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.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 09:35:25 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(c_in_type, type, (
% 0.18/0.37 c_in: ( $i * $i * $i ) > $o)).
% 0.18/0.37 tff(tc_Message_Omsg_type, type, (
% 0.18/0.37 tc_Message_Omsg: $i)).
% 0.18/0.37 tff(c_Message_Oparts_type, type, (
% 0.18/0.37 c_Message_Oparts: $i > $i)).
% 0.18/0.37 tff(c_insert_type, type, (
% 0.18/0.37 c_insert: ( $i * $i * $i ) > $i)).
% 0.18/0.37 tff(c_emptyset_type, type, (
% 0.18/0.37 c_emptyset: $i)).
% 0.18/0.37 tff(c_Message_Omsg_OMPair_type, type, (
% 0.18/0.37 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.18/0.37 tff(v_Y_type, type, (
% 0.18/0.37 v_Y: $i)).
% 0.18/0.37 tff(v_X_type, type, (
% 0.18/0.37 v_X: $i)).
% 0.18/0.37 tff(c_lessequals_type, type, (
% 0.18/0.37 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.18/0.37 tff(tc_set_type, type, (
% 0.18/0.37 tc_set: $i > $i)).
% 0.18/0.37 tff(c_Event_Oused_type, type, (
% 0.18/0.37 c_Event_Oused: $i > $i)).
% 0.18/0.37 tff(v_H_type, type, (
% 0.18/0.37 v_H: $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[V_x: $i, T_a: $i, V_A: $i] : refl(c_in(V_x, c_insert(V_x, V_A, T_a), T_a) <=> c_in(V_x, c_insert(V_x, V_A, T_a), T_a))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![V_x: $i, T_a: $i, V_A: $i] : c_in(V_x, c_insert(V_x, V_A, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_A: $i] : c_in(V_x, c_insert(V_x, V_A, T_a), T_a)),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![V_x: $i, T_a: $i, V_A: $i] : c_in(V_x, c_insert(V_x, V_A, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_A: $i] : c_in(V_x, c_insert(V_x, V_A, T_a), T_a)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(4,axiom,(![V_x: $i, T_a: $i, V_A: $i] : c_in(V_x, c_insert(V_x, V_A, T_a), T_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Oinsert__iff_1')).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![V_x: $i, T_a: $i, V_A: $i] : c_in(V_x, c_insert(V_x, V_A, T_a), T_a)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.37 tff(6,plain,(
% 0.18/0.37 ![V_x: $i, T_a: $i, V_A: $i] : c_in(V_x, c_insert(V_x, V_A, T_a), T_a)),
% 0.18/0.37 inference(skolemize,[status(sab)],[5])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![V_x: $i, T_a: $i, V_A: $i] : c_in(V_x, c_insert(V_x, V_A, T_a), T_a)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 ((~![V_x: $i, T_a: $i, V_A: $i] : c_in(V_x, c_insert(V_x, V_A, T_a), T_a)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg), tc_Message_Omsg)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg), tc_Message_Omsg)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.37 tff(10,assumption,(~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)), introduced(assumption)).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(14,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oparts_OInj_0')).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.37 tff(16,plain,(
% 0.18/0.37 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(skolemize,[status(sab)],[15])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[20, 17, 10, 9])).
% 0.18/0.37 tff(22,plain,(c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(26,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__parts_0')).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.37 tff(28,plain,(
% 0.18/0.37 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(skolemize,[status(sab)],[27])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_Y, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[32, 29])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (^[V_X: $i, V_evs: $i] : refl(((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg))) <=> ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg))) <=> ![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[35])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg))) <=> ![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(38,axiom,(![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Public_Oused__parts__subset__parts_0')).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.18/0.38 tff(40,plain,(
% 0.18/0.38 ![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[39])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Event_Oused(v_H), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Event_Oused(v_H), tc_Message_Omsg)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(43,axiom,(c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Event_Oused(v_H), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Event_Oused(v_H), tc_Message_Omsg)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (((~![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Event_Oused(v_H), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg)))) <=> ((~![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Event_Oused(v_H), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 ((~![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Event_Oused(v_H), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 ((~![V_X: $i, V_evs: $i] : ((~c_in(V_X, c_Event_Oused(V_evs), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(V_X, c_emptyset, tc_Message_Omsg)), c_Event_Oused(V_evs), tc_set(tc_Message_Omsg)))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Event_Oused(v_H), tc_Message_Omsg)) | c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[47, 44, 41])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.38 tff(54,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetD_0')).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.18/0.38 tff(57,plain,(
% 0.18/0.38 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[56])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(62,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__parts_1')).
% 0.18/0.38 tff(63,plain,
% 0.18/0.38 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.38 tff(64,plain,(
% 0.18/0.38 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.38 inference(skolemize,[status(sab)],[63])).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(67,plain,
% 0.18/0.38 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oparts(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oparts(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 (c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[69, 22])).
% 0.18/0.38 tff(71,assumption,(~c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg)), introduced(assumption)).
% 0.18/0.38 tff(72,plain,
% 0.18/0.38 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg) | (~c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))) | (~c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg) | (~c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))) | (~c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg) | (~c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))) | (~c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(74,plain,
% 0.18/0.38 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg) | (~c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))) | (~c_in(v_X, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.38 tff(75,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[74, 71, 58, 48, 70])).
% 0.18/0.38 tff(76,plain,(c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 (((~c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg)) | (~c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg))) <=> ((~c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg)) | (~c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(78,axiom,((~c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg)) | (~c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.18/0.38 tff(79,plain,
% 0.18/0.38 ((~c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg)) | (~c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.38 tff(80,plain,
% 0.18/0.38 ((~c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg)) | (~c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 ((~c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg)) | (~c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.18/0.38 tff(82,plain,
% 0.18/0.38 ((~c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg)) | (~c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.18/0.38 tff(83,plain,
% 0.18/0.38 ((~c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg)) | (~c_in(v_X, c_Event_Oused(v_H), tc_Message_Omsg))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[82, 77])).
% 0.18/0.38 tff(84,plain,
% 0.18/0.38 (~c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[83, 76])).
% 0.18/0.38 tff(85,plain,
% 0.18/0.38 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg) | (~c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))) | (~c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg) | (~c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))) | (~c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(86,plain,
% 0.18/0.38 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg) | (~c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))) | (~c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_Y, c_Event_Oused(v_H), tc_Message_Omsg) | (~c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), c_Event_Oused(v_H), tc_set(tc_Message_Omsg))) | (~c_in(v_Y, c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(v_X, v_Y), c_emptyset, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[87, 84, 58, 48, 34])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------