%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV248-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:31:51 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV248-2 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 09:32:10 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.36 % SZS status Unsatisfiable
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(c_in_type, type, (
% 0.12/0.36 c_in: ( $i * $i * $i ) > $o)).
% 0.12/0.36 tff(tc_Message_Omsg_type, type, (
% 0.12/0.36 tc_Message_Omsg: $i)).
% 0.12/0.36 tff(c_union_type, type, (
% 0.12/0.36 c_union: ( $i * $i * $i ) > $i)).
% 0.12/0.36 tff(v_H_type, type, (
% 0.12/0.36 v_H: $i)).
% 0.12/0.36 tff(c_Message_Osynth_type, type, (
% 0.12/0.36 c_Message_Osynth: $i > $i)).
% 0.12/0.36 tff(v_G_type, type, (
% 0.12/0.36 v_G: $i)).
% 0.12/0.36 tff(c_Main_OsubsetI__1_type, type, (
% 0.12/0.36 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 0.12/0.36 tff(c_Message_Oanalz_type, type, (
% 0.12/0.36 c_Message_Oanalz: $i > $i)).
% 0.12/0.36 tff(c_lessequals_type, type, (
% 0.12/0.36 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.12/0.36 tff(tc_set_type, type, (
% 0.12/0.36 tc_set: $i > $i)).
% 0.12/0.36 tff(1,assumption,(~c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(5,axiom,(![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.36 tff(7,plain,(
% 0.12/0.36 ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.36 inference(skolemize,[status(sab)],[6])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OUnCI_1')).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,(
% 0.12/0.37 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.37 inference(skolemize,[status(sab)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[22, 19, 12])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (^[T_a: $i, V_B: $i, V_A: $i] : refl((c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(27,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.37 tff(29,plain,(
% 0.12/0.37 ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ((c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg))),
% 0.12/0.37 inference(transitivity,[status(thm)],[33, 31])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[36, 30, 1])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(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_Osynth(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(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_Osynth(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(41,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Osynth_OInj_0')).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.37 tff(43,plain,(
% 0.12/0.37 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(skolemize,[status(sab)],[42])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_G, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[47, 44, 37, 23])).
% 0.12/0.37 tff(49,plain,(c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(50,assumption,(~c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (~c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[53, 8, 50])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(56,plain,
% 0.12/0.37 ((c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[56])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))),
% 0.12/0.38 inference(transitivity,[status(thm)],[57, 55])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[60, 30, 50])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[62])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(65,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OUnCI_0')).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.12/0.38 tff(67,plain,(
% 0.12/0.38 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(skolemize,[status(sab)],[66])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, 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_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.38 tff(72,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[71, 68, 61, 54])).
% 0.12/0.38 tff(73,plain,(c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(74,assumption,(~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 0.12/0.38 tff(75,plain,
% 0.12/0.38 (^[T_a: $i, V_B: $i, V_A: $i, V_C: $i] : refl((c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(76,plain,
% 0.12/0.38 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[75])).
% 0.12/0.38 tff(77,plain,
% 0.12/0.38 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(78,plain,
% 0.12/0.38 (^[T_a: $i, V_B: $i, V_A: $i, V_C: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))), ((((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) <=> (((~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))))), rewrite((((~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) <=> (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))), ((((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) <=> (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(79,plain,
% 0.12/0.38 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[78])).
% 0.12/0.38 tff(80,axiom,(![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OUn__least_0')).
% 0.12/0.38 tff(81,plain,
% 0.12/0.38 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.12/0.38 tff(82,plain,
% 0.12/0.38 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.12/0.38 tff(83,plain,(
% 0.12/0.38 ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[82])).
% 0.12/0.38 tff(84,plain,
% 0.12/0.38 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.12/0.38 tff(85,plain,
% 0.12/0.38 (((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(86,plain,
% 0.12/0.38 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(87,plain,
% 0.12/0.38 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_H, c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.12/0.38 tff(88,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[87, 84, 74, 73, 49])).
% 0.12/0.38 tff(89,plain,(c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(90,plain,
% 0.12/0.38 (^[V_H: $i, V_G: $i] : refl(((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))) <=> ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(91,plain,
% 0.12/0.38 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[90])).
% 0.12/0.38 tff(92,plain,
% 0.12/0.38 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(93,axiom,(![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Oanalz__mono_0')).
% 0.12/0.38 tff(94,plain,
% 0.12/0.38 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.12/0.38 tff(95,plain,(
% 0.12/0.38 ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[94])).
% 0.12/0.38 tff(96,plain,
% 0.12/0.38 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.12/0.38 tff(97,plain,
% 0.12/0.38 (((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 ((~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[100, 89])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 ((~c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(103,axiom,(~c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 (~c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 (((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.12/0.39 tff(108,plain,
% 0.12/0.39 ((~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[107, 104, 84])).
% 0.12/0.39 tff(109,plain,
% 0.12/0.39 (~c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[108, 101])).
% 0.12/0.39 tff(110,plain,
% 0.12/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(111,plain,
% 0.12/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(112,plain,
% 0.12/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.12/0.39 tff(113,plain,
% 0.12/0.39 (~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[112, 8, 109])).
% 0.12/0.39 tff(114,plain,
% 0.12/0.39 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(115,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(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_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[114])).
% 0.12/0.39 tff(116,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(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_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(117,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Oanalz_OInj_0')).
% 0.12/0.39 tff(118,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.12/0.39 tff(119,plain,(
% 0.12/0.39 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.39 inference(skolemize,[status(sab)],[118])).
% 0.12/0.39 tff(120,plain,
% 0.12/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.12/0.39 tff(121,plain,
% 0.12/0.39 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, 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_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(122,plain,
% 0.12/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(123,plain,
% 0.12/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.12/0.39 tff(124,plain,
% 0.12/0.39 (~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[123, 120, 113])).
% 0.12/0.39 tff(125,plain,
% 0.12/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(126,plain,
% 0.12/0.39 ((c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(127,plain,
% 0.12/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[126])).
% 0.12/0.39 tff(128,plain,
% 0.12/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg))),
% 0.12/0.40 inference(transitivity,[status(thm)],[127, 125])).
% 0.12/0.40 tff(129,plain,
% 0.12/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(130,plain,
% 0.12/0.40 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.12/0.40 tff(131,plain,
% 0.12/0.40 (c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[130, 30, 109])).
% 0.12/0.40 tff(132,plain,
% 0.12/0.40 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(133,plain,
% 0.12/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(134,plain,
% 0.12/0.40 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Osynth(v_G), c_Message_Oanalz(c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(v_G), v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.12/0.40 tff(135,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[134, 19, 131, 124])).
% 0.12/0.40 % SZS output end Proof
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------