%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV240-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:31:49 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV240-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:32:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(c_in_type, type, (
% 0.20/0.38 c_in: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(tc_Message_Omsg_type, type, (
% 0.20/0.38 tc_Message_Omsg: $i)).
% 0.20/0.38 tff(c_Message_Oanalz_type, type, (
% 0.20/0.38 c_Message_Oanalz: $i > $i)).
% 0.20/0.38 tff(v_G_type, type, (
% 0.20/0.38 v_G: $i)).
% 0.20/0.38 tff(c_Main_OsubsetI__1_type, type, (
% 0.20/0.38 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(c_lessequals_type, type, (
% 0.20/0.38 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(tc_set_type, type, (
% 0.20/0.38 tc_set: $i > $i)).
% 0.20/0.38 tff(v_H_type, type, (
% 0.20/0.38 v_H: $i)).
% 0.20/0.38 tff(c_union_type, type, (
% 0.20/0.38 c_union: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(1,assumption,(~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[T_a: $i, V_A: $i] : refl(c_lessequals(V_A, V_A, tc_set(T_a)) <=> c_lessequals(V_A, V_A, tc_set(T_a)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,(![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Osubset__refl_0')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,(
% 0.20/0.38 ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.20/0.38 inference(skolemize,[status(sab)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))) | c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.38 tff(11,plain,(c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : refl((c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), 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_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg)))) <=> ![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg)))) <=> ![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : trans(monotonicity(rewrite(((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg)))) <=> ((~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))), ((((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), 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_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (((~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), 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_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))))), rewrite((((~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), 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_H, V_H_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_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))), ((((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), 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_H, V_H_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_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), 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_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> ![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,axiom,(![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (((~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), 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_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz__subset__cong_0')).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.38 tff(20,plain,(
% 0.20/0.38 ![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[19])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~c_lessequals(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)), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,axiom,(~c_lessequals(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)), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (~c_lessequals(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)), tc_set(tc_Message_Omsg))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))))) <=> ((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((c_lessequals(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)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg)))) <=> (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))))) <=> ((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))))) <=> ((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | (c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 ((~![V_G_H: $i, V_H_H: $i, V_H: $i, V_G: $i] : (c_lessequals(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(V_G_H, V_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_G_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(V_H), c_Message_Oanalz(V_H_H), tc_set(tc_Message_Omsg))))) | c_lessequals(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G), v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 ((~c_lessequals(c_Message_Oanalz(v_H), c_Message_Oanalz(v_H), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[30, 24, 21])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (~c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[31, 11])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(36,axiom,(![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_1')).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.38 tff(38,plain,(
% 0.20/0.38 ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[37])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[42, 39, 32])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (^[T_a: $i, V_B: $i, V_A: $i] : refl((c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(47,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetI_0')).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,(
% 0.20/0.39 ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[48])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg))) <=> (c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg))),
% 0.20/0.39 inference(transitivity,[status(thm)],[53, 51])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[56, 50, 32])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(61,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz_OInj_0')).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.39 tff(63,plain,(
% 0.20/0.39 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(skolemize,[status(sab)],[62])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(v_G), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), tc_Message_Omsg)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[67, 64, 57, 43])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------