%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SWV242-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 : 600s % DateTime : Wed Jul 20 20:42:14 EDT 2022 % Result : Unsatisfiable 13.24s 13.23s % Output : Proof 13.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV242-2 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.13 % Command : moca.sh %s % 0.12/0.33 % Computer : n022.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 : 600 % 0.12/0.33 % DateTime : Wed Jun 15 22:02:47 EDT 2022 % 0.12/0.34 % CPUTime : % 13.24/13.23 % SZS status Unsatisfiable % 13.24/13.23 % SZS output start Proof % 13.24/13.23 The input problem is unsatisfiable because % 13.24/13.23 % 13.24/13.23 [1] the following set of Horn clauses is unsatisfiable: % 13.24/13.23 % 13.24/13.23 c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)) % 13.24/13.23 c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg)) % 13.24/13.23 c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) & c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) ==> \bottom % 13.24/13.23 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)) % 13.24/13.23 c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a)) % 13.24/13.23 c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a)) % 13.24/13.23 c_lessequals(V_B, V_C, tc_set(T_a)) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> c_lessequals(V_A, V_C, tc_set(T_a)) % 13.24/13.23 % 13.24/13.23 This holds because % 13.24/13.23 % 13.24/13.23 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 13.24/13.23 % 13.24/13.23 E: % 13.24/13.23 c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a)) = true__ % 13.24/13.23 c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a)) = true__ % 13.24/13.23 c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)) = true__ % 13.24/13.23 c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg)) = true__ % 13.24/13.23 f1(true__) = false__ % 13.24/13.23 f2(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) = true__ % 13.24/13.23 f2(true__) = f1(c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) % 13.24/13.23 f3(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) = true__ % 13.24/13.23 f3(true__, V_G, V_H) = c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)) % 13.24/13.23 f4(true__, V_A, V_C, T_a) = c_lessequals(V_A, V_C, tc_set(T_a)) % 13.24/13.23 f5(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_C, T_a, V_A) = true__ % 13.24/13.23 f5(true__, V_B, V_C, T_a, V_A) = f4(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_C, T_a) % 13.24/13.23 G: % 13.24/13.23 true__ = false__ % 13.24/13.23 % 13.24/13.23 This holds because % 13.24/13.23 % 13.24/13.23 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 13.24/13.23 % 13.24/13.23 % 13.24/13.23 c_lessequals(V_A, V_C, tc_set(T_a)) -> f4(true__, V_A, V_C, T_a) % 13.24/13.23 c_lessequals(V_A, c_union(V_A, V_B, T_a), tc_set(T_a)) -> true__ % 13.24/13.23 c_lessequals(V_B, c_union(V_A, V_B, T_a), tc_set(T_a)) -> true__ % 13.24/13.23 c_lessequals(v_G, c_Message_Oanalz(v_G_H), tc_set(tc_Message_Omsg)) -> true__ % 13.24/13.23 c_lessequals(v_H, c_Message_Oanalz(v_H_H), tc_set(tc_Message_Omsg)) -> true__ % 13.24/13.23 f1(f4(true__, v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg)) -> true__ % 13.24/13.23 f1(true__) -> false__ % 13.24/13.23 f2(c_lessequals(v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) -> true__ % 13.24/13.23 f2(f4(true__, v_G, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_Message_Omsg)) -> true__ % 13.24/13.23 f2(true__) -> f1(c_lessequals(v_H, c_Message_Oanalz(c_union(v_G_H, v_H_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) % 13.24/13.23 f3(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) -> true__ % 13.24/13.23 f3(f4(true__, Y0, Y1, tc_Message_Omsg), Y0, Y1) -> true__ % 13.24/13.23 f3(true__, V_G, V_H) -> c_lessequals(c_Message_Oanalz(V_G), c_Message_Oanalz(V_H), tc_set(tc_Message_Omsg)) % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G_H))), Y3, tc_Message_Omsg), c_Message_Oanalz(c_Message_Oanalz(v_G)), Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G_H)), Y3, tc_Message_Omsg), c_Message_Oanalz(v_G), Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H_H)), Y3, tc_Message_Omsg), c_Message_Oanalz(v_H), Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(X0, X1, tc_Message_Omsg)), Y3, tc_Message_Omsg), c_Message_Oanalz(X0), Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(X0, v_G_H, tc_Message_Omsg)), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(X0, v_H_H, tc_Message_Omsg)), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(X1, X0, tc_Message_Omsg)), Y3, tc_Message_Omsg), c_Message_Oanalz(X0), Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(v_G_H, X0, tc_Message_Omsg)), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(c_union(v_H_H, X0, tc_Message_Omsg)), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(v_G_H), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_Message_Oanalz(v_H_H), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_union(X0, c_Message_Oanalz(v_G_H), tc_Message_Omsg), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_union(X0, c_Message_Oanalz(v_H_H), tc_Message_Omsg), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_union(X1, Y0, Y2), Y3, Y2), Y0, Y3, Y2) -> true__ % 13.24/13.23 f4(f4(true__, c_union(Y0, X1, Y2), Y3, Y2), Y0, Y3, Y2) -> true__ % 13.24/13.23 f4(f4(true__, c_union(c_Message_Oanalz(v_G_H), X0, tc_Message_Omsg), Y3, tc_Message_Omsg), v_G, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(f4(true__, c_union(c_Message_Oanalz(v_H_H), X0, tc_Message_Omsg), Y3, tc_Message_Omsg), v_H, Y3, tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, Y0, c_union(X1, Y0, Y2), Y2) -> true__ % 13.24/13.23 f4(true__, Y0, c_union(X1, c_union(Y0, Y1, Y2), Y2), Y2) -> true__ % 13.24/13.23 f4(true__, Y0, c_union(Y0, X1, Y2), Y2) -> true__ % 13.24/13.23 f4(true__, Y0, c_union(c_union(Y0, Y1, Y2), X1, Y2), Y2) -> true__ % 13.24/13.23 f4(true__, Y1, c_union(X1, c_union(Y0, Y1, Y2), Y2), Y2) -> true__ % 13.24/13.23 f4(true__, Y1, c_union(c_union(Y0, Y1, Y2), X1, Y2), Y2) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(X1, Y0, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(X1, c_union(X2, Y0, tc_Message_Omsg), tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(X1, c_union(Y0, X2, tc_Message_Omsg), tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(Y0, X1, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(c_union(X1, Y0, tc_Message_Omsg), X3, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(Y0), c_Message_Oanalz(c_union(c_union(Y0, X1, tc_Message_Omsg), X3, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(X0)), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, X1, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(X0)), c_Message_Oanalz(c_Message_Oanalz(c_union(X1, X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(X0))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(X0, X1, tc_Message_Omsg)))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(X0))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(X1, X0, tc_Message_Omsg)))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G)))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G_H))))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G_H)))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_H))), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_H_H)))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(X0, v_G_H, tc_Message_Omsg)))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(v_G_H, X0, tc_Message_Omsg)))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_G_H))), tc_Message_Omsg) -> true__ % 13.24/13.23 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, c_Message_Oanalz(v_G_H), tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_G)), c_Message_Oanalz(c_Message_Oanalz(c_union(c_Message_Oanalz(v_G_H), X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(c_union(v_H_H, X0, tc_Message_Omsg)))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H)), c_Message_Oanalz(c_Message_Oanalz(c_Message_Oanalz(v_H_H))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H)), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, c_Message_Oanalz(v_H_H), tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(c_Message_Oanalz(v_H)), c_Message_Oanalz(c_Message_Oanalz(c_union(c_Message_Oanalz(v_H_H), X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, v_G_H, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(c_union(v_G_H, X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_Message_Oanalz(v_G_H)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(X0, c_Message_Oanalz(v_G_H), tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_G), c_Message_Oanalz(c_union(c_Message_Oanalz(v_G_H), X0, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_Message_Oanalz(c_union(X0, v_H_H, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_Message_Oanalz(c_union(v_H_H, X0, tc_Message_Omsg))), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_Message_Oanalz(v_H_H)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_union(X0, c_Message_Oanalz(v_H_H), tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, c_Message_Oanalz(v_H), c_Message_Oanalz(c_union(c_Message_Oanalz(v_H_H), X0, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_G, c_Message_Oanalz(c_union(X1, v_G_H, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_G, c_Message_Oanalz(c_union(v_G_H, X1, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_G, c_Message_Oanalz(v_G_H), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_G, c_union(X1, c_Message_Oanalz(v_G_H), tc_Message_Omsg), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_G, c_union(c_Message_Oanalz(v_G_H), X1, tc_Message_Omsg), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_H, c_Message_Oanalz(c_union(X1, v_H_H, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_H, c_Message_Oanalz(c_union(v_H_H, X1, tc_Message_Omsg)), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_H, c_Message_Oanalz(v_H_H), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_H, c_union(X1, c_Message_Oanalz(v_H_H), tc_Message_Omsg), tc_Message_Omsg) -> true__ % 13.24/13.24 f4(true__, v_H, c_union(c_Message_Oanalz(v_H_H), X1, tc_Message_Omsg), tc_Message_Omsg) -> true__ % 13.24/13.24 f5(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_C, T_a, V_A) -> true__ % 13.24/13.24 f5(f4(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__ % 13.24/13.24 f5(true__, V_B, V_C, T_a, V_A) -> f4(c_lessequals(V_B, V_C, tc_set(T_a)), V_A, V_C, T_a) % 13.24/13.24 false__ -> true__ % 13.24/13.24 with the LPO induced by % 13.24/13.24 f5 > v_G > f2 > c_union > f3 > c_lessequals > f4 > tc_set > v_G_H > c_Message_Oanalz > tc_Message_Omsg > f1 > v_H_H > v_H > false__ > true__ % 13.24/13.24 % 13.24/13.24 % SZS output end Proof % 13.24/13.24 %------------------------------------------------------------------------------