%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT270-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 : Sun Jul 17 06:05:43 EDT 2022 % Result : Unsatisfiable 0.86s 1.06s % Output : Proof 0.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : LAT270-2 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.35 % Computer : n007.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Tue Jun 28 22:20:22 EDT 2022 % 0.13/0.35 % CPUTime : % 0.86/1.06 % SZS status Unsatisfiable % 0.86/1.06 % SZS output start Proof % 0.86/1.06 The input problem is unsatisfiable because % 0.86/1.06 % 0.86/1.06 [1] the following set of Horn clauses is unsatisfiable: % 0.86/1.06 % 0.86/1.06 c_in(v_a, v_A, t_a) % 0.86/1.06 c_in(v_b, v_A, t_a) % 0.86/1.06 c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) % 0.86/1.06 c_lessequals(v_S, v_A, tc_set(t_a)) ==> \bottom % 0.86/1.06 c_in(V_b, v_A, t_a) & c_in(V_a, v_A, t_a) & c_lessequals(V_S, c_Tarski_Ointerval(v_r, V_a, V_b, t_a), tc_set(t_a)) ==> c_lessequals(V_S, v_A, tc_set(t_a)) % 0.86/1.06 % 0.86/1.06 This holds because % 0.86/1.06 % 0.86/1.06 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.86/1.06 % 0.86/1.06 E: % 0.86/1.06 c_in(v_a, v_A, t_a) = true__ % 0.86/1.06 c_in(v_b, v_A, t_a) = true__ % 0.86/1.06 c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) = true__ % 0.86/1.06 f1(c_lessequals(v_S, v_A, tc_set(t_a))) = true__ % 0.86/1.06 f1(true__) = false__ % 0.86/1.06 f2(true__, V_S) = c_lessequals(V_S, v_A, tc_set(t_a)) % 0.86/1.06 f3(true__, V_b, V_S) = f2(c_in(V_b, v_A, t_a), V_S) % 0.86/1.06 f4(c_lessequals(V_S, c_Tarski_Ointerval(v_r, V_a, V_b, t_a), tc_set(t_a)), V_a, V_b, V_S) = true__ % 0.86/1.06 f4(true__, V_a, V_b, V_S) = f3(c_in(V_a, v_A, t_a), V_b, V_S) % 0.86/1.06 G: % 0.86/1.06 true__ = false__ % 0.86/1.06 % 0.86/1.06 This holds because % 0.86/1.06 % 0.86/1.06 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.86/1.06 % 0.86/1.06 % 0.86/1.06 c_in(v_a, v_A, t_a) -> true__ % 0.86/1.06 c_in(v_b, v_A, t_a) -> true__ % 0.86/1.06 c_lessequals(V_S, v_A, tc_set(t_a)) -> f2(true__, V_S) % 0.86/1.06 c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) -> true__ % 0.86/1.06 f1(c_lessequals(v_S, v_A, tc_set(t_a))) -> true__ % 0.86/1.06 f1(f2(true__, v_S)) -> true__ % 0.86/1.06 f1(f4(true__, v_a, v_a, v_S)) -> true__ % 0.86/1.06 f1(f4(true__, v_b, v_a, v_S)) -> true__ % 0.86/1.06 f1(f4(true__, v_b, v_b, v_S)) -> true__ % 0.86/1.06 f1(true__) -> false__ % 0.86/1.06 f2(c_in(V_b, v_A, t_a), V_S) -> f3(true__, V_b, V_S) % 0.86/1.06 f2(true__, Y1) -> f3(true__, v_a, Y1) % 0.86/1.06 f2(true__, Y1) -> f3(true__, v_b, Y1) % 0.86/1.06 f3(c_in(V_a, v_A, t_a), V_b, V_S) -> f4(true__, V_a, V_b, V_S) % 0.86/1.06 f3(true__, Y1, Y2) -> f4(true__, v_a, Y1, Y2) % 0.86/1.06 f3(true__, Y1, Y2) -> f4(true__, v_b, Y1, Y2) % 0.86/1.06 f4(c_lessequals(V_S, c_Tarski_Ointerval(v_r, V_a, V_b, t_a), tc_set(t_a)), V_a, V_b, V_S) -> true__ % 0.86/1.06 f4(true__, v_a, v_b, Y0) -> f4(true__, v_a, v_a, Y0) % 0.86/1.06 f4(true__, v_a, v_b, v_S) -> true__ % 0.86/1.06 f4(true__, v_b, Y1, Y2) -> f4(true__, v_a, Y1, Y2) % 0.86/1.06 f4(true__, v_b, v_b, Y1) -> f4(true__, v_b, v_a, Y1) % 0.86/1.06 false__ -> true__ % 0.86/1.06 with the LPO induced by % 0.86/1.06 c_lessequals > f2 > f3 > tc_set > f4 > t_a > v_A > f1 > v_r > c_Tarski_Ointerval > v_S > v_b > v_a > c_in > false__ > true__ % 0.86/1.06 % 0.86/1.06 % SZS output end Proof % 0.86/1.06 %------------------------------------------------------------------------------