%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV249-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 2.14s 2.32s
% Output : Proof 2.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV249-2 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:32:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.14/2.32 % SZS status Unsatisfiable
% 2.14/2.32 % SZS output start Proof
% 2.14/2.32 tff(c_lessequals_type, type, (
% 2.14/2.32 c_lessequals: ( $i * $i * $i ) > $o)).
% 2.14/2.32 tff(tc_set_type, type, (
% 2.14/2.32 tc_set: $i > $i)).
% 2.14/2.32 tff(tc_Message_Omsg_type, type, (
% 2.14/2.32 tc_Message_Omsg: $i)).
% 2.14/2.32 tff(c_insert_type, type, (
% 2.14/2.32 c_insert: ( $i * $i * $i ) > $i)).
% 2.14/2.32 tff(c_union_type, type, (
% 2.14/2.32 c_union: ( $i * $i * $i ) > $i)).
% 2.14/2.32 tff(c_Message_Osynth_type, type, (
% 2.14/2.32 c_Message_Osynth: $i > $i)).
% 2.14/2.32 tff(c_Message_Oanalz_type, type, (
% 2.14/2.32 c_Message_Oanalz: $i > $i)).
% 2.14/2.32 tff(v_G_type, type, (
% 2.14/2.32 v_G: $i)).
% 2.14/2.32 tff(v_H_type, type, (
% 2.14/2.32 v_H: $i)).
% 2.14/2.32 tff(v_X_type, type, (
% 2.14/2.32 v_X: $i)).
% 2.14/2.32 tff(class_Orderings_Oorder_type, type, (
% 2.14/2.32 class_Orderings_Oorder: $i > $o)).
% 2.14/2.32 tff(c_in_type, type, (
% 2.14/2.32 c_in: ( $i * $i * $i ) > $o)).
% 2.14/2.32 tff(c_minus_type, type, (
% 2.14/2.32 c_minus: ( $i * $i * $i ) > $i)).
% 2.14/2.32 tff(1,assumption,(~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.32 tff(2,plain,
% 2.14/2.32 (^[T_1: $i] : refl(class_Orderings_Oorder(tc_set(T_1)) <=> class_Orderings_Oorder(tc_set(T_1)))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(3,plain,
% 2.14/2.32 (![T_1: $i] : class_Orderings_Oorder(tc_set(T_1)) <=> ![T_1: $i] : class_Orderings_Oorder(tc_set(T_1))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[2])).
% 2.14/2.32 tff(4,plain,
% 2.14/2.32 (![T_1: $i] : class_Orderings_Oorder(tc_set(T_1)) <=> ![T_1: $i] : class_Orderings_Oorder(tc_set(T_1))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5,axiom,(![T_1: $i] : class_Orderings_Oorder(tc_set(T_1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clsarity_set_2')).
% 2.14/2.32 tff(6,plain,
% 2.14/2.32 (![T_1: $i] : class_Orderings_Oorder(tc_set(T_1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.14/2.32 tff(7,plain,(
% 2.14/2.32 ![T_1: $i] : class_Orderings_Oorder(tc_set(T_1))),
% 2.14/2.32 inference(skolemize,[status(sab)],[6])).
% 2.14/2.32 tff(8,plain,
% 2.14/2.32 (![T_1: $i] : class_Orderings_Oorder(tc_set(T_1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.14/2.32 tff(9,plain,
% 2.14/2.32 ((~![T_1: $i] : class_Orderings_Oorder(tc_set(T_1))) | class_Orderings_Oorder(tc_set(tc_Message_Omsg))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(10,plain,
% 2.14/2.32 (class_Orderings_Oorder(tc_set(tc_Message_Omsg))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[9, 8])).
% 2.14/2.32 tff(11,assumption,(~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.32 tff(12,plain,
% 2.14/2.32 (^[V_x: $i, T_a: $i] : refl(((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a)) <=> ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a)))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(13,plain,
% 2.14/2.32 (![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a)) <=> ![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[12])).
% 2.14/2.32 tff(14,plain,
% 2.14/2.32 (![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a)) <=> ![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(15,axiom,(![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Orderings_Oorder__class_Oaxioms__1_0')).
% 2.14/2.32 tff(16,plain,
% 2.14/2.32 (![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[15, 14])).
% 2.14/2.32 tff(17,plain,(
% 2.14/2.32 ![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))),
% 2.14/2.32 inference(skolemize,[status(sab)],[16])).
% 2.14/2.32 tff(18,plain,
% 2.14/2.32 (![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[17, 13])).
% 2.14/2.32 tff(19,plain,
% 2.14/2.32 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(20,plain,
% 2.14/2.32 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(21,plain,
% 2.14/2.32 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[20, 19])).
% 2.14/2.32 tff(22,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[21, 18, 11, 10])).
% 2.14/2.32 tff(23,plain,(c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(24,plain,
% 2.14/2.32 (^[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(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) | c_lessequals(V_A, V_C, tc_set(T_a))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(25,plain,
% 2.14/2.32 (![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))) <=> ![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)))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[24])).
% 2.14/2.32 tff(26,plain,
% 2.14/2.32 (![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))) <=> ![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)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(27,axiom,(![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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUn__subset__iff_0')).
% 2.14/2.32 tff(28,plain,
% 2.14/2.32 (![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)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[27, 26])).
% 2.14/2.32 tff(29,plain,(
% 2.14/2.32 ![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)))),
% 2.14/2.32 inference(skolemize,[status(sab)],[28])).
% 2.14/2.32 tff(30,plain,
% 2.14/2.32 (![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)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[29, 25])).
% 2.14/2.32 tff(31,plain,
% 2.14/2.32 (((~![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(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(v_G, c_union(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(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(32,plain,
% 2.14/2.32 ((~![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(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(33,plain,
% 2.14/2.32 ((~![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(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[32, 31])).
% 2.14/2.32 tff(34,plain,
% 2.14/2.32 (c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[33, 30, 23])).
% 2.14/2.32 tff(35,plain,
% 2.14/2.32 (^[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)))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(36,plain,
% 2.14/2.32 (![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))))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[35])).
% 2.14/2.32 tff(37,plain,
% 2.14/2.32 (![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))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(38,plain,
% 2.14/2.32 (^[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))))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(39,plain,
% 2.14/2.32 (![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))))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[38])).
% 2.14/2.32 tff(40,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/sandbox2/benchmark/theBenchmark.p','cls_Set_OUn__subset__iff_2')).
% 2.14/2.32 tff(41,plain,
% 2.14/2.32 (![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))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[40, 39])).
% 2.14/2.32 tff(42,plain,
% 2.14/2.32 (![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))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[41, 37])).
% 2.14/2.32 tff(43,plain,(
% 2.14/2.32 ![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))))),
% 2.14/2.32 inference(skolemize,[status(sab)],[42])).
% 2.14/2.32 tff(44,plain,
% 2.14/2.32 (![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))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[43, 36])).
% 2.14/2.32 tff(45,plain,
% 2.14/2.32 (((~![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(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(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(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(46,plain,
% 2.14/2.32 ((c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(47,plain,
% 2.14/2.32 (((~![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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(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(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[46])).
% 2.14/2.32 tff(48,plain,
% 2.14/2.32 (((~![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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(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(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[47, 45])).
% 2.14/2.32 tff(49,plain,
% 2.14/2.32 ((~![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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(50,plain,
% 2.14/2.32 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (~c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[49, 48])).
% 2.14/2.32 tff(51,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[50, 44, 34, 23, 1])).
% 2.14/2.32 tff(52,plain,(c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(53,assumption,(~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.32 tff(54,plain,
% 2.14/2.32 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(55,plain,
% 2.14/2.32 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(56,plain,
% 2.14/2.32 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[55, 54])).
% 2.14/2.32 tff(57,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[56, 18, 10, 53])).
% 2.14/2.32 tff(58,plain,(c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(59,plain,
% 2.14/2.32 (^[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_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_B, V_C, tc_set(T_a))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(60,plain,
% 2.14/2.32 (![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_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_B, V_C, tc_set(T_a)))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[59])).
% 2.14/2.32 tff(61,plain,
% 2.14/2.32 (![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_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_B, V_C, tc_set(T_a)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(62,axiom,(![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_B, V_C, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUn__subset__iff_1')).
% 2.14/2.32 tff(63,plain,
% 2.14/2.32 (![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_B, V_C, tc_set(T_a)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[62, 61])).
% 2.14/2.32 tff(64,plain,(
% 2.14/2.32 ![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_B, V_C, tc_set(T_a)))),
% 2.14/2.32 inference(skolemize,[status(sab)],[63])).
% 2.14/2.32 tff(65,plain,
% 2.14/2.32 (![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_B, V_C, tc_set(T_a)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[64, 60])).
% 2.14/2.32 tff(66,plain,
% 2.14/2.32 (((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), 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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(67,plain,
% 2.14/2.33 ((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(68,plain,
% 2.14/2.33 ((~![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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[67, 66])).
% 2.14/2.33 tff(69,plain,
% 2.14/2.33 (c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[68, 65, 58])).
% 2.14/2.33 tff(70,plain,
% 2.14/2.33 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(71,plain,
% 2.14/2.33 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[70])).
% 2.14/2.33 tff(72,plain,
% 2.14/2.33 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(73,plain,
% 2.14/2.33 (^[T_a: $i, V_B: $i, V_A: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> (((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)))), rewrite((((~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a)))) | (V_A = V_B)) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))), ((((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(74,plain,
% 2.14/2.33 (![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B)) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[73])).
% 2.14/2.33 tff(75,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (((~c_lessequals(V_B, V_A, tc_set(T_a))) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | (V_A = V_B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Osubset__antisym_0')).
% 2.14/2.33 tff(76,plain,
% 2.14/2.33 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[75, 74])).
% 2.14/2.33 tff(77,plain,
% 2.14/2.33 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[76, 72])).
% 2.14/2.33 tff(78,plain,(
% 2.14/2.33 ![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 2.14/2.33 inference(skolemize,[status(sab)],[77])).
% 2.14/2.33 tff(79,plain,
% 2.14/2.33 (![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[78, 71])).
% 2.14/2.33 tff(80,plain,
% 2.14/2.33 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(81,plain,
% 2.14/2.33 (((c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(82,plain,
% 2.14/2.33 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[81])).
% 2.14/2.33 tff(83,plain,
% 2.14/2.33 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[82, 80])).
% 2.14/2.33 tff(84,plain,
% 2.14/2.33 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(85,plain,
% 2.14/2.33 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[84, 83])).
% 2.14/2.33 tff(86,plain,
% 2.14/2.33 ((~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[85, 79, 69])).
% 2.14/2.33 tff(87,plain,
% 2.14/2.33 (c_union(v_G, v_H, tc_Message_Omsg) = c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[86, 52])).
% 2.14/2.33 tff(88,plain,
% 2.14/2.33 (c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[87])).
% 2.14/2.33 tff(89,plain,
% 2.14/2.33 (c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.33 inference(symmetry,[status(thm)],[88])).
% 2.14/2.33 tff(90,plain,
% 2.14/2.33 (c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[89])).
% 2.14/2.33 tff(91,plain,
% 2.14/2.33 (c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(v_G, v_H, tc_Message_Omsg)),
% 2.14/2.33 inference(symmetry,[status(thm)],[87])).
% 2.14/2.33 tff(92,plain,
% 2.14/2.33 (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.33 inference(monotonicity,[status(thm)],[91])).
% 2.14/2.33 tff(93,plain,
% 2.14/2.33 (c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[92])).
% 2.14/2.33 tff(94,plain,
% 2.14/2.33 (c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(symmetry,[status(thm)],[93])).
% 2.14/2.33 tff(95,assumption,(~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.33 tff(96,plain,
% 2.14/2.33 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(97,plain,
% 2.14/2.33 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(98,plain,
% 2.14/2.33 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[97, 96])).
% 2.14/2.33 tff(99,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[98, 18, 10, 95])).
% 2.14/2.33 tff(100,plain,(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(101,plain,
% 2.14/2.33 (c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[100, 94])).
% 2.14/2.33 tff(102,plain,
% 2.14/2.33 (((~![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(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), 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(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(103,plain,
% 2.14/2.33 ((~![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(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(104,plain,
% 2.14/2.33 ((~![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(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[103, 102])).
% 2.14/2.33 tff(105,plain,
% 2.14/2.33 ((~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[104, 30])).
% 2.14/2.33 tff(106,plain,
% 2.14/2.33 (c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[105, 101])).
% 2.14/2.33 tff(107,assumption,(~c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.33 tff(108,plain,
% 2.14/2.33 (((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), 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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(109,plain,
% 2.14/2.33 ((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(110,plain,
% 2.14/2.33 ((~![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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[109, 108])).
% 2.14/2.33 tff(111,plain,
% 2.14/2.33 ((~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[110, 65])).
% 2.14/2.33 tff(112,plain,
% 2.14/2.33 (c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[111, 101])).
% 2.14/2.33 tff(113,plain,
% 2.14/2.33 (((~![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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), 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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(114,plain,
% 2.14/2.33 ((c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(115,plain,
% 2.14/2.33 (((~![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_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), 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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[114])).
% 2.14/2.33 tff(116,plain,
% 2.14/2.33 (((~![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_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), 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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[115, 113])).
% 2.14/2.34 tff(117,plain,
% 2.14/2.34 ((~![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_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(118,plain,
% 2.14/2.34 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[117, 116])).
% 2.14/2.34 tff(119,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[118, 44, 112, 107, 106])).
% 2.14/2.34 tff(120,plain,(c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(121,plain,
% 2.14/2.34 (c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[120, 90])).
% 2.14/2.34 tff(122,plain,
% 2.14/2.34 (c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[92])).
% 2.14/2.34 tff(123,plain,
% 2.14/2.34 (c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(symmetry,[status(thm)],[122])).
% 2.14/2.34 tff(124,plain,
% 2.14/2.34 ((~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[123])).
% 2.14/2.34 tff(125,assumption,(~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.34 tff(126,plain,
% 2.14/2.34 (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[125, 124])).
% 2.14/2.34 tff(127,assumption,(~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.34 tff(128,plain,
% 2.14/2.34 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(129,plain,
% 2.14/2.34 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(130,plain,
% 2.14/2.34 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[129, 128])).
% 2.14/2.34 tff(131,plain,
% 2.14/2.34 (c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[130, 18, 10])).
% 2.14/2.34 tff(132,plain,
% 2.14/2.34 (((~![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(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), 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(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(133,plain,
% 2.14/2.34 ((~![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(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(134,plain,
% 2.14/2.34 ((~![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(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[133, 132])).
% 2.14/2.34 tff(135,plain,
% 2.14/2.34 (c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[134, 30, 131])).
% 2.14/2.34 tff(136,plain,
% 2.14/2.34 (((~![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(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), 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(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(137,plain,
% 2.14/2.34 ((~![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(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(138,plain,
% 2.14/2.34 ((~![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(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[137, 136])).
% 2.14/2.34 tff(139,plain,
% 2.14/2.34 (c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[138, 30, 135])).
% 2.14/2.34 tff(140,plain,
% 2.14/2.34 (((~![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_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), 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_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(141,plain,
% 2.14/2.34 ((c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(142,plain,
% 2.14/2.34 (((~![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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), 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_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[141])).
% 2.14/2.34 tff(143,plain,
% 2.14/2.34 (((~![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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), 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_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[142, 140])).
% 2.14/2.34 tff(144,plain,
% 2.14/2.34 ((~![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, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(145,plain,
% 2.14/2.34 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(v_G, c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[144, 143])).
% 2.14/2.34 tff(146,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[145, 44, 135, 139, 127])).
% 2.14/2.34 tff(147,plain,(c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(148,plain,
% 2.14/2.34 (((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), 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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(149,plain,
% 2.14/2.34 ((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(150,plain,
% 2.14/2.34 ((~![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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[149, 148])).
% 2.14/2.34 tff(151,plain,
% 2.14/2.34 (c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[150, 65, 131])).
% 2.14/2.34 tff(152,plain,
% 2.14/2.34 (((~![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_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), 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_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(153,plain,
% 2.14/2.34 ((c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(154,plain,
% 2.14/2.34 (((~![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_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), 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_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[153])).
% 2.14/2.34 tff(155,plain,
% 2.14/2.34 (((~![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_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), 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_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[154, 152])).
% 2.14/2.34 tff(156,plain,
% 2.14/2.34 ((~![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_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(157,plain,
% 2.14/2.34 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[156, 155])).
% 2.14/2.34 tff(158,plain,
% 2.14/2.34 (c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[157, 44, 151, 147])).
% 2.14/2.34 tff(159,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[158, 126])).
% 2.14/2.34 tff(160,plain,(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(161,plain,
% 2.14/2.35 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(162,plain,
% 2.14/2.35 (((c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(163,plain,
% 2.14/2.35 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[162])).
% 2.14/2.35 tff(164,plain,
% 2.14/2.35 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[163, 161])).
% 2.14/2.35 tff(165,plain,
% 2.14/2.35 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(166,plain,
% 2.14/2.35 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[165, 164])).
% 2.14/2.35 tff(167,plain,
% 2.14/2.35 ((~c_lessequals(c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[166, 79, 160])).
% 2.14/2.35 tff(168,plain,
% 2.14/2.35 (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[167, 121])).
% 2.14/2.35 tff(169,plain,
% 2.14/2.35 (c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.35 inference(symmetry,[status(thm)],[168])).
% 2.14/2.35 tff(170,assumption,(~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.35 tff(171,plain,
% 2.14/2.35 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(172,plain,
% 2.14/2.35 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(173,plain,
% 2.14/2.35 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[172, 171])).
% 2.14/2.35 tff(174,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[173, 18, 10, 170])).
% 2.14/2.35 tff(175,plain,(c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(176,assumption,(~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.35 tff(177,plain,
% 2.14/2.35 (^[V_x: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 2.14/2.35 inference(bind,[status(th)],[])).
% 2.14/2.35 tff(178,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 2.14/2.35 inference(quant_intro,[status(thm)],[177])).
% 2.14/2.35 tff(179,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(180,axiom,(![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Oinsert__subset_1')).
% 2.14/2.35 tff(181,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[180, 179])).
% 2.14/2.35 tff(182,plain,(
% 2.14/2.35 ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 2.14/2.35 inference(skolemize,[status(sab)],[181])).
% 2.14/2.35 tff(183,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[182, 178])).
% 2.14/2.35 tff(184,plain,
% 2.14/2.35 (((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(185,plain,
% 2.14/2.35 ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(186,plain,
% 2.14/2.35 ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[185, 184])).
% 2.14/2.35 tff(187,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[186, 183, 176, 175])).
% 2.14/2.35 tff(188,plain,(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(189,assumption,(~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.35 tff(190,plain,
% 2.14/2.35 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(191,plain,
% 2.14/2.35 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(192,plain,
% 2.14/2.35 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[191, 190])).
% 2.14/2.35 tff(193,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[192, 18, 10, 189])).
% 2.14/2.35 tff(194,plain,(c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(195,plain,
% 2.14/2.35 (^[V_x: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a))) <=> (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a))))),
% 2.14/2.35 inference(bind,[status(th)],[])).
% 2.14/2.35 tff(196,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a))) <=> ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))),
% 2.14/2.35 inference(quant_intro,[status(thm)],[195])).
% 2.14/2.35 tff(197,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a))) <=> ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(198,plain,
% 2.14/2.35 (^[V_x: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_x, V_B, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) <=> (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a))))),
% 2.14/2.35 inference(bind,[status(th)],[])).
% 2.14/2.35 tff(199,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_x, V_B, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a))) <=> ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))),
% 2.14/2.35 inference(quant_intro,[status(thm)],[198])).
% 2.14/2.35 tff(200,axiom,(![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_x, V_B, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Oinsert__subset_2')).
% 2.14/2.35 tff(201,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[200, 199])).
% 2.14/2.35 tff(202,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[201, 197])).
% 2.14/2.35 tff(203,plain,(
% 2.14/2.35 ![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))),
% 2.14/2.35 inference(skolemize,[status(sab)],[202])).
% 2.14/2.35 tff(204,plain,
% 2.14/2.35 (![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[203, 196])).
% 2.14/2.35 tff(205,plain,
% 2.14/2.35 (c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) <=> c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(206,axiom,(c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 2.14/2.35 tff(207,plain,
% 2.14/2.35 (c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[206, 205])).
% 2.14/2.35 tff(208,plain,
% 2.14/2.35 (((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))) | ((~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(209,plain,
% 2.14/2.35 ((c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))) <=> ((~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(210,plain,
% 2.14/2.35 (((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))) | (c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))) | ((~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[209])).
% 2.14/2.35 tff(211,plain,
% 2.14/2.35 (((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))) | (c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[210, 208])).
% 2.14/2.35 tff(212,plain,
% 2.14/2.35 ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))) | (c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(213,plain,
% 2.14/2.35 ((~![V_x: $i, T_a: $i, V_B: $i, V_A: $i] : (c_lessequals(c_insert(V_x, V_A, T_a), V_B, tc_set(T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_x, V_B, T_a)))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | (~c_in(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[212, 211])).
% 2.14/2.35 tff(214,plain,
% 2.14/2.35 (c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[213, 207, 204, 194])).
% 2.14/2.35 tff(215,plain,
% 2.14/2.35 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(216,plain,
% 2.14/2.35 (((c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(217,plain,
% 2.14/2.35 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[216])).
% 2.14/2.35 tff(218,plain,
% 2.14/2.35 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[217, 215])).
% 2.14/2.35 tff(219,plain,
% 2.14/2.35 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(220,plain,
% 2.14/2.35 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[219, 218])).
% 2.14/2.35 tff(221,plain,
% 2.14/2.35 ((c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[220, 79, 214])).
% 2.14/2.35 tff(222,plain,
% 2.14/2.35 (c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Osynth(c_Message_Oanalz(v_G))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[221, 188])).
% 2.14/2.35 tff(223,plain,
% 2.14/2.35 (c_Message_Osynth(c_Message_Oanalz(v_G)) = c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.35 inference(symmetry,[status(thm)],[222])).
% 2.14/2.35 tff(224,plain,
% 2.14/2.35 (c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.35 inference(monotonicity,[status(thm)],[223])).
% 2.14/2.35 tff(225,plain,
% 2.14/2.35 (c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.35 inference(symmetry,[status(thm)],[224])).
% 2.14/2.35 tff(226,plain,
% 2.14/2.35 (^[V_a: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a)) <=> (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a)))),
% 2.14/2.35 inference(bind,[status(th)],[])).
% 2.14/2.35 tff(227,plain,
% 2.14/2.35 (![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a)) <=> ![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a))),
% 2.14/2.35 inference(quant_intro,[status(thm)],[226])).
% 2.14/2.35 tff(228,plain,
% 2.14/2.35 (![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a)) <=> ![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(229,axiom,(![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUn__insert__right_0')).
% 2.14/2.36 tff(230,plain,
% 2.14/2.36 (![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[229, 228])).
% 2.14/2.36 tff(231,plain,(
% 2.14/2.36 ![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a))),
% 2.14/2.36 inference(skolemize,[status(sab)],[230])).
% 2.14/2.36 tff(232,plain,
% 2.14/2.36 (![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[231, 227])).
% 2.14/2.36 tff(233,plain,
% 2.14/2.36 ((~![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a))) | (c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg) = c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(234,plain,
% 2.14/2.36 (c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg) = c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[233, 232])).
% 2.14/2.36 tff(235,plain,
% 2.14/2.36 (c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg) = c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.36 inference(symmetry,[status(thm)],[234])).
% 2.14/2.36 tff(236,plain,
% 2.14/2.36 (c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.36 inference(transitivity,[status(thm)],[235, 225, 89, 169])).
% 2.14/2.36 tff(237,plain,
% 2.14/2.36 (c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[236])).
% 2.14/2.36 tff(238,plain,
% 2.14/2.36 (c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(symmetry,[status(thm)],[237])).
% 2.14/2.36 tff(239,plain,
% 2.14/2.36 ((~c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[238])).
% 2.14/2.36 tff(240,plain,
% 2.14/2.36 (^[V_H: $i, V_G: $i] : refl((c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = 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)) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Osynth(V_G), tc_Message_Omsg)))),
% 2.14/2.36 inference(bind,[status(th)],[])).
% 2.14/2.36 tff(241,plain,
% 2.14/2.36 (![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Osynth(V_G), tc_Message_Omsg)) <=> ![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Osynth(V_G), tc_Message_Omsg))),
% 2.14/2.36 inference(quant_intro,[status(thm)],[240])).
% 2.14/2.36 tff(242,plain,
% 2.14/2.36 (![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Osynth(V_G), tc_Message_Omsg)) <=> ![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Osynth(V_G), tc_Message_Omsg))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(243,axiom,(![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Osynth(V_G), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz__synth__Un_0')).
% 2.14/2.36 tff(244,plain,
% 2.14/2.36 (![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Osynth(V_G), tc_Message_Omsg))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[243, 242])).
% 2.14/2.36 tff(245,plain,(
% 2.14/2.36 ![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Osynth(V_G), tc_Message_Omsg))),
% 2.14/2.36 inference(skolemize,[status(sab)],[244])).
% 2.14/2.36 tff(246,plain,
% 2.14/2.36 (![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Osynth(V_G), tc_Message_Omsg))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[245, 241])).
% 2.14/2.36 tff(247,plain,
% 2.14/2.36 ((~![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg)) = 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(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(248,plain,
% 2.14/2.36 (c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[247, 246])).
% 2.14/2.36 tff(249,plain,
% 2.14/2.36 (c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.36 inference(symmetry,[status(thm)],[248])).
% 2.14/2.36 tff(250,assumption,(~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.36 tff(251,plain,
% 2.14/2.36 (^[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))))),
% 2.14/2.36 inference(bind,[status(th)],[])).
% 2.14/2.36 tff(252,plain,
% 2.14/2.36 (![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)))),
% 2.14/2.36 inference(quant_intro,[status(thm)],[251])).
% 2.14/2.36 tff(253,plain,
% 2.14/2.36 (![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)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(254,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/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz__mono_0')).
% 2.14/2.36 tff(255,plain,
% 2.14/2.36 (![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)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[254, 253])).
% 2.14/2.36 tff(256,plain,(
% 2.14/2.36 ![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)))),
% 2.14/2.36 inference(skolemize,[status(sab)],[255])).
% 2.14/2.36 tff(257,plain,
% 2.14/2.36 (![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)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[256, 252])).
% 2.14/2.36 tff(258,plain,
% 2.14/2.36 (((~![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(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(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(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(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(259,plain,
% 2.14/2.36 ((~![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(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(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(260,plain,
% 2.14/2.36 ((~![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(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(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[259, 258])).
% 2.14/2.36 tff(261,plain,
% 2.14/2.36 ((~c_lessequals(c_union(v_G, v_H, tc_Message_Omsg), c_union(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(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[260, 257])).
% 2.14/2.36 tff(262,plain,
% 2.14/2.36 (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[261, 23])).
% 2.14/2.36 tff(263,plain,
% 2.14/2.36 (((~![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(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(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(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(264,plain,
% 2.14/2.36 ((~![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(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(265,plain,
% 2.14/2.36 ((~![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(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[264, 263])).
% 2.14/2.36 tff(266,plain,
% 2.14/2.36 ((~c_lessequals(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[265, 257])).
% 2.14/2.36 tff(267,plain,
% 2.14/2.36 (c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[266, 34])).
% 2.14/2.36 tff(268,plain,
% 2.14/2.36 (((~![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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(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(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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(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(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(269,plain,
% 2.14/2.36 ((~![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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(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(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(270,plain,
% 2.14/2.36 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[269, 268])).
% 2.14/2.36 tff(271,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[270, 44, 267, 262, 250])).
% 2.14/2.36 tff(272,plain,(c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(273,assumption,(~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.36 tff(274,plain,
% 2.14/2.36 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(275,plain,
% 2.14/2.36 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(276,plain,
% 2.14/2.36 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[275, 274])).
% 2.14/2.36 tff(277,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[276, 18, 10, 273])).
% 2.14/2.36 tff(278,plain,(c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(279,plain,
% 2.14/2.36 (((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), 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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(280,plain,
% 2.14/2.36 ((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(281,plain,
% 2.14/2.36 ((~![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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[280, 279])).
% 2.14/2.36 tff(282,plain,
% 2.14/2.36 (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[281, 65, 278])).
% 2.14/2.36 tff(283,plain,
% 2.14/2.36 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(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_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(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_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(284,plain,
% 2.14/2.36 (((c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(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_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(285,plain,
% 2.14/2.36 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(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_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[284])).
% 2.14/2.36 tff(286,plain,
% 2.14/2.36 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(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_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[285, 283])).
% 2.14/2.36 tff(287,plain,
% 2.14/2.36 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(288,plain,
% 2.14/2.36 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(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_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[287, 286])).
% 2.14/2.36 tff(289,plain,
% 2.14/2.36 ((c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[288, 79, 282])).
% 2.14/2.36 tff(290,plain,
% 2.14/2.36 (c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[289, 272])).
% 2.14/2.36 tff(291,plain,
% 2.14/2.36 (c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) = c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))),
% 2.14/2.36 inference(symmetry,[status(thm)],[290])).
% 2.14/2.36 tff(292,plain,
% 2.14/2.36 (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[291])).
% 2.14/2.36 tff(293,plain,
% 2.14/2.36 (c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[292])).
% 2.14/2.36 tff(294,plain,
% 2.14/2.36 (c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.36 inference(symmetry,[status(thm)],[293])).
% 2.14/2.36 tff(295,plain,
% 2.14/2.36 ((~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[294])).
% 2.14/2.37 tff(296,assumption,(~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.37 tff(297,plain,
% 2.14/2.37 (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[296, 295])).
% 2.14/2.37 tff(298,plain,
% 2.14/2.37 (^[V_H: $i, V_G: $i] : refl((c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg))) <=> (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg))))),
% 2.14/2.37 inference(bind,[status(th)],[])).
% 2.14/2.37 tff(299,plain,
% 2.14/2.37 (![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)))),
% 2.14/2.37 inference(quant_intro,[status(thm)],[298])).
% 2.14/2.37 tff(300,plain,
% 2.14/2.37 (![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(301,axiom,(![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz__analz__Un_0')).
% 2.14/2.37 tff(302,plain,
% 2.14/2.37 (![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[301, 300])).
% 2.14/2.37 tff(303,plain,(
% 2.14/2.37 ![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)))),
% 2.14/2.37 inference(skolemize,[status(sab)],[302])).
% 2.14/2.37 tff(304,plain,
% 2.14/2.37 (![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[303, 299])).
% 2.14/2.37 tff(305,plain,
% 2.14/2.37 ((~![V_H: $i, V_G: $i] : (c_Message_Oanalz(c_union(c_Message_Oanalz(V_G), V_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)))) | (c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) = c_Message_Oanalz(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(306,plain,
% 2.14/2.37 (c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) = c_Message_Oanalz(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[305, 304])).
% 2.14/2.37 tff(307,plain,
% 2.14/2.37 (c_Message_Oanalz(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) = c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.37 inference(symmetry,[status(thm)],[306])).
% 2.14/2.37 tff(308,plain,
% 2.14/2.37 (c_Message_Oanalz(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) = c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[91])).
% 2.14/2.37 tff(309,plain,
% 2.14/2.37 (c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)) = c_Message_Oanalz(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.37 inference(symmetry,[status(thm)],[308])).
% 2.14/2.37 tff(310,plain,
% 2.14/2.37 (c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.37 inference(transitivity,[status(thm)],[291, 309, 307])).
% 2.14/2.37 tff(311,plain,
% 2.14/2.37 (c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[310])).
% 2.14/2.37 tff(312,plain,
% 2.14/2.37 (c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.37 inference(transitivity,[status(thm)],[311, 249])).
% 2.14/2.37 tff(313,plain,
% 2.14/2.37 (c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[312, 249])).
% 2.14/2.37 tff(314,plain,
% 2.14/2.37 (c_lessequals(c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(symmetry,[status(thm)],[313])).
% 2.14/2.37 tff(315,plain,
% 2.14/2.37 (c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[249, 249])).
% 2.14/2.37 tff(316,plain,
% 2.14/2.37 (c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(transitivity,[status(thm)],[315, 314])).
% 2.14/2.37 tff(317,assumption,(~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.37 tff(318,plain,
% 2.14/2.37 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(319,plain,
% 2.14/2.37 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(320,plain,
% 2.14/2.37 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[319, 318])).
% 2.14/2.37 tff(321,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[320, 18, 10, 317])).
% 2.14/2.37 tff(322,plain,(c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(323,plain,
% 2.14/2.37 (c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[322, 316])).
% 2.14/2.37 tff(324,plain,
% 2.14/2.37 (((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), 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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(325,plain,
% 2.14/2.37 ((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(326,plain,
% 2.14/2.37 ((~![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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[325, 324])).
% 2.14/2.37 tff(327,plain,
% 2.14/2.37 (c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[326, 65, 323])).
% 2.14/2.37 tff(328,plain,
% 2.14/2.37 (((~![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(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), 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(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(329,plain,
% 2.14/2.37 ((~![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(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(330,plain,
% 2.14/2.37 ((~![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(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[329, 328])).
% 2.14/2.37 tff(331,plain,
% 2.14/2.37 (c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[330, 30, 323])).
% 2.14/2.37 tff(332,plain,
% 2.14/2.37 (((~![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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), 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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(333,plain,
% 2.14/2.37 ((c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(334,plain,
% 2.14/2.37 (((~![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_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), 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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[333])).
% 2.14/2.37 tff(335,plain,
% 2.14/2.37 (((~![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_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), 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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[334, 332])).
% 2.14/2.37 tff(336,plain,
% 2.14/2.37 ((~![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_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(337,plain,
% 2.14/2.37 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[336, 335])).
% 2.14/2.37 tff(338,plain,
% 2.14/2.37 (c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[337, 44, 331, 327])).
% 2.14/2.37 tff(339,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[338, 297])).
% 2.14/2.37 tff(340,plain,(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(341,plain,
% 2.14/2.37 (c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[311])).
% 2.14/2.38 tff(342,assumption,(~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.38 tff(343,plain,
% 2.14/2.38 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(344,plain,
% 2.14/2.38 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(345,plain,
% 2.14/2.38 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[344, 343])).
% 2.14/2.38 tff(346,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[345, 18, 10, 342])).
% 2.14/2.38 tff(347,plain,(c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(348,plain,
% 2.14/2.38 (((~![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(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), 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(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(349,plain,
% 2.14/2.38 ((~![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(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(350,plain,
% 2.14/2.38 ((~![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(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[349, 348])).
% 2.14/2.38 tff(351,plain,
% 2.14/2.38 (c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[350, 30, 347])).
% 2.14/2.38 tff(352,assumption,(~c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.14/2.38 tff(353,plain,
% 2.14/2.38 (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[290])).
% 2.14/2.38 tff(354,plain,
% 2.14/2.38 (((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), 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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(355,plain,
% 2.14/2.38 ((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(356,plain,
% 2.14/2.38 ((~![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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[355, 354])).
% 2.14/2.38 tff(357,plain,
% 2.14/2.38 (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[356, 65, 347])).
% 2.14/2.38 tff(358,plain,
% 2.14/2.38 (c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[357, 353])).
% 2.14/2.38 tff(359,plain,
% 2.14/2.38 (((~![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(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), 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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(360,plain,
% 2.14/2.38 ((c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(361,plain,
% 2.14/2.38 (((~![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(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), 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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[360])).
% 2.14/2.38 tff(362,plain,
% 2.14/2.38 (((~![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(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), 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(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[361, 359])).
% 2.14/2.38 tff(363,plain,
% 2.14/2.38 ((~![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(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(364,plain,
% 2.14/2.38 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (~c_lessequals(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[363, 362])).
% 2.14/2.38 tff(365,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[364, 44, 358, 352, 351])).
% 2.14/2.38 tff(366,plain,(c_lessequals(c_union(c_union(c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(367,plain,
% 2.14/2.38 (c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[366, 341])).
% 2.14/2.38 tff(368,plain,
% 2.14/2.38 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(369,plain,
% 2.14/2.38 (((c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(370,plain,
% 2.14/2.38 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[369])).
% 2.14/2.38 tff(371,plain,
% 2.14/2.38 (((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[370, 368])).
% 2.14/2.38 tff(372,plain,
% 2.14/2.38 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | ((c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | (~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(373,plain,
% 2.14/2.38 ((~![T_a: $i, V_B: $i, V_A: $i] : ((V_A = V_B) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_lessequals(V_B, V_A, tc_set(T_a))))) | (~c_lessequals(c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[372, 371])).
% 2.14/2.38 tff(374,plain,
% 2.14/2.38 ((~c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | (c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[373, 79, 367])).
% 2.14/2.39 tff(375,plain,
% 2.14/2.39 (c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[374, 340])).
% 2.14/2.39 tff(376,plain,
% 2.14/2.39 (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) = c_union(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.39 inference(symmetry,[status(thm)],[375])).
% 2.14/2.39 tff(377,plain,
% 2.14/2.39 (c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.39 inference(transitivity,[status(thm)],[376, 249])).
% 2.14/2.39 tff(378,plain,
% 2.14/2.39 (c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[377])).
% 2.14/2.39 tff(379,plain,
% 2.14/2.39 ((~c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[378])).
% 2.14/2.39 tff(380,plain,
% 2.14/2.39 ((~c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(381,axiom,(~c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 2.14/2.39 tff(382,plain,
% 2.14/2.39 (~c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[381, 380])).
% 2.14/2.39 tff(383,plain,
% 2.14/2.39 (~c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[382, 379])).
% 2.14/2.39 tff(384,plain,
% 2.14/2.39 (((~![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_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), 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_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(385,plain,
% 2.14/2.39 ((~![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_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(386,plain,
% 2.14/2.39 ((~![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_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[385, 384])).
% 2.14/2.39 tff(387,plain,
% 2.14/2.39 ((~c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oanalz(c_insert(v_X, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[386, 257])).
% 2.14/2.39 tff(388,plain,
% 2.14/2.39 (~c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_union(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[387, 383])).
% 2.14/2.39 tff(389,plain,
% 2.14/2.39 (~c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[388, 239])).
% 2.14/2.39 tff(390,plain,
% 2.14/2.39 (c_insert(v_X, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[87])).
% 2.14/2.39 tff(391,plain,
% 2.14/2.39 ((~![V_a: $i, T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_insert(V_a, V_B, T_a), T_a) = c_insert(V_a, c_union(V_A, V_B, T_a), T_a))) | (c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_insert(v_X, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(392,plain,
% 2.14/2.39 (c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_insert(v_X, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[391, 232])).
% 2.14/2.39 tff(393,plain,
% 2.14/2.39 (c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg) = c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.39 inference(transitivity,[status(thm)],[392, 390])).
% 2.14/2.39 tff(394,plain,
% 2.14/2.39 (c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[393])).
% 2.14/2.39 tff(395,plain,
% 2.14/2.39 (c_lessequals(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.14/2.39 inference(symmetry,[status(thm)],[394])).
% 2.14/2.39 tff(396,plain,
% 2.14/2.39 (^[T_a: $i, V_B: $i, V_A: $i] : refl((c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a)) <=> (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a)))),
% 2.14/2.39 inference(bind,[status(th)],[])).
% 2.14/2.39 tff(397,plain,
% 2.14/2.39 (![T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a)) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a))),
% 2.14/2.39 inference(quant_intro,[status(thm)],[396])).
% 2.14/2.39 tff(398,plain,
% 2.14/2.39 (![T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a)) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(399,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUn__Diff__cancel_0')).
% 2.14/2.39 tff(400,plain,
% 2.14/2.39 (![T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[399, 398])).
% 2.14/2.39 tff(401,plain,(
% 2.14/2.39 ![T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a))),
% 2.14/2.39 inference(skolemize,[status(sab)],[400])).
% 2.14/2.39 tff(402,plain,
% 2.14/2.39 (![T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[401, 397])).
% 2.14/2.39 tff(403,plain,
% 2.14/2.39 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_union(V_A, c_minus(V_B, V_A, tc_set(T_a)), T_a) = c_union(V_A, V_B, T_a))) | (c_union(c_union(v_G, v_H, tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(404,plain,
% 2.14/2.39 (c_union(c_union(v_G, v_H, tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[403, 402])).
% 2.14/2.39 tff(405,plain,
% 2.14/2.39 (c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg) = c_union(c_union(v_G, v_H, tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[91])).
% 2.14/2.39 tff(406,plain,
% 2.14/2.39 (c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg) = c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 2.14/2.39 inference(transitivity,[status(thm)],[405, 404, 88])).
% 2.14/2.39 tff(407,plain,
% 2.14/2.39 (c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg) = c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.39 inference(monotonicity,[status(thm)],[406])).
% 2.14/2.39 tff(408,plain,
% 2.14/2.39 (^[V_a: $i, T_a: $i, V_B: $i, V_C: $i] : refl((c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a)) <=> (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a)))),
% 2.14/2.39 inference(bind,[status(th)],[])).
% 2.14/2.39 tff(409,plain,
% 2.14/2.39 (![V_a: $i, T_a: $i, V_B: $i, V_C: $i] : (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a)) <=> ![V_a: $i, T_a: $i, V_B: $i, V_C: $i] : (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a))),
% 2.14/2.39 inference(quant_intro,[status(thm)],[408])).
% 2.14/2.39 tff(410,plain,
% 2.14/2.39 (![V_a: $i, T_a: $i, V_B: $i, V_C: $i] : (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a)) <=> ![V_a: $i, T_a: $i, V_B: $i, V_C: $i] : (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(411,axiom,(![V_a: $i, T_a: $i, V_B: $i, V_C: $i] : (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUn__insert__left_0')).
% 2.14/2.39 tff(412,plain,
% 2.14/2.39 (![V_a: $i, T_a: $i, V_B: $i, V_C: $i] : (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[411, 410])).
% 2.14/2.39 tff(413,plain,(
% 2.14/2.39 ![V_a: $i, T_a: $i, V_B: $i, V_C: $i] : (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a))),
% 2.14/2.39 inference(skolemize,[status(sab)],[412])).
% 2.14/2.39 tff(414,plain,
% 2.14/2.39 (![V_a: $i, T_a: $i, V_B: $i, V_C: $i] : (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[413, 409])).
% 2.14/2.39 tff(415,plain,
% 2.14/2.39 ((~![V_a: $i, T_a: $i, V_B: $i, V_C: $i] : (c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a))) | (c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg) = c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(416,plain,
% 2.14/2.39 (c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg) = c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), tc_Message_Omsg)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[415, 414])).
% 2.14/2.39 tff(417,plain,
% 2.14/2.39 (c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg) = c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg)),
% 2.23/2.39 inference(transitivity,[status(thm)],[416, 407, 235])).
% 2.23/2.39 tff(418,plain,
% 2.23/2.39 (c_lessequals(c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[417, 235])).
% 2.23/2.39 tff(419,plain,
% 2.23/2.39 (c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.39 inference(symmetry,[status(thm)],[418])).
% 2.23/2.39 tff(420,plain,
% 2.23/2.39 (c_lessequals(c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[235, 235])).
% 2.23/2.39 tff(421,plain,
% 2.23/2.39 (c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)) <=> c_lessequals(c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.39 inference(symmetry,[status(thm)],[420])).
% 2.23/2.39 tff(422,plain,
% 2.23/2.39 ((~c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.23/2.39 inference(monotonicity,[status(thm)],[421])).
% 2.23/2.39 tff(423,assumption,(~c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 2.23/2.39 tff(424,plain,
% 2.23/2.39 (~c_lessequals(c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[423, 422])).
% 2.23/2.39 tff(425,plain,
% 2.23/2.39 (((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(426,plain,
% 2.23/2.39 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | ((~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(427,plain,
% 2.23/2.39 ((~![V_x: $i, T_a: $i] : ((~class_Orderings_Oorder(T_a)) | c_lessequals(V_x, V_x, T_a))) | (~class_Orderings_Oorder(tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[426, 425])).
% 2.23/2.39 tff(428,plain,
% 2.23/2.39 (c_lessequals(c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[427, 18, 10])).
% 2.23/2.39 tff(429,plain,
% 2.23/2.39 ($false),
% 2.23/2.39 inference(unit_resolution,[status(thm)],[428, 424])).
% 2.23/2.39 tff(430,plain,(c_lessequals(c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.39 tff(431,plain,
% 2.23/2.39 (c_lessequals(c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.39 inference(modus_ponens,[status(thm)],[430, 419])).
% 2.23/2.39 tff(432,plain,
% 2.23/2.39 (((~![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(c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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(c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.23/2.39 inference(rewrite,[status(thm)],[])).
% 2.23/2.39 tff(433,plain,
% 2.23/2.39 ((~![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(c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.23/2.39 inference(quant_inst,[status(thm)],[])).
% 2.23/2.39 tff(434,plain,
% 2.23/2.39 ((~![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(c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[433, 432])).
% 2.23/2.40 tff(435,plain,
% 2.23/2.40 ((~c_lessequals(c_union(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_minus(c_Message_Osynth(c_Message_Oanalz(v_G)), c_union(v_G, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[434, 30])).
% 2.23/2.40 tff(436,plain,
% 2.23/2.40 (c_lessequals(c_insert(v_X, c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[435, 431])).
% 2.23/2.40 tff(437,plain,
% 2.23/2.40 (c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[436, 395])).
% 2.23/2.40 tff(438,plain,
% 2.23/2.40 (((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), 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_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(439,plain,
% 2.23/2.40 ((~![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_B, V_C, tc_set(T_a)))) | ((~c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(440,plain,
% 2.23/2.40 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : ((~c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) | c_lessequals(V_B, V_C, tc_set(T_a)))) | (~c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[439, 438])).
% 2.23/2.40 tff(441,plain,
% 2.23/2.40 ((~c_lessequals(c_union(v_G, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[440, 65])).
% 2.23/2.40 tff(442,plain,
% 2.23/2.40 (c_lessequals(c_insert(v_X, v_H, tc_Message_Omsg), c_insert(v_X, c_union(c_union(v_G, c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg), c_Message_Osynth(c_Message_Oanalz(v_G)), tc_Message_Omsg), tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[441, 437])).
% 2.23/2.40 tff(443,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[442, 389])).
% 2.23/2.40 % SZS output end Proof
% 2.24/2.40 % E exiting
%------------------------------------------------------------------------------