%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SET829-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n024.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 : Tue Jul 19 03:44:57 EDT 2022 % Result : Unsatisfiable 0.62s 0.82s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET829-2 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n024.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 : 600 % 0.12/0.34 % DateTime : Sat Jul 9 23:23:43 EDT 2022 % 0.12/0.34 % CPUTime : % 0.62/0.82 % SZS status Unsatisfiable % 0.62/0.82 % SZS output start Proof % 0.62/0.82 The input problem is unsatisfiable because % 0.62/0.82 % 0.62/0.82 [1] the following set of Horn clauses is unsatisfiable: % 0.62/0.82 % 0.62/0.82 c_in(V_c, V_A, T_a) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> c_in(V_c, V_B, T_a) % 0.62/0.82 c_lessequals(v_X, v_Z, tc_set(t_a)) % 0.62/0.82 c_in(v_x, v_X, t_a) % 0.62/0.82 c_in(v_x, v_Z, t_a) ==> \bottom % 0.62/0.82 % 0.62/0.82 This holds because % 0.62/0.82 % 0.62/0.82 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.62/0.82 % 0.62/0.82 E: % 0.62/0.82 c_in(v_x, v_X, t_a) = true__ % 0.62/0.82 c_lessequals(v_X, v_Z, tc_set(t_a)) = true__ % 0.62/0.82 f1(true__, V_c, V_B, T_a) = c_in(V_c, V_B, T_a) % 0.62/0.82 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_c, V_A, T_a, V_B) = true__ % 0.62/0.82 f2(true__, V_c, V_A, T_a, V_B) = f1(c_in(V_c, V_A, T_a), V_c, V_B, T_a) % 0.62/0.82 f3(c_in(v_x, v_Z, t_a)) = true__ % 0.62/0.82 f3(true__) = false__ % 0.62/0.82 G: % 0.62/0.82 true__ = false__ % 0.62/0.82 % 0.62/0.82 This holds because % 0.62/0.82 % 0.62/0.82 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.62/0.82 % 0.62/0.82 % 0.62/0.82 c_in(V_c, V_B, T_a) -> f1(true__, V_c, V_B, T_a) % 0.62/0.82 c_in(v_x, Y3, t_a) -> f2(true__, v_x, v_X, t_a, Y3) % 0.62/0.82 c_lessequals(v_X, v_Z, tc_set(t_a)) -> true__ % 0.62/0.82 f1(f1(true__, Y3, v_X, t_a), Y3, v_Z, t_a) -> true__ % 0.62/0.82 f1(true__, v_x, v_X, t_a) -> true__ % 0.62/0.82 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_c, V_A, T_a, V_B) -> true__ % 0.62/0.82 f2(true__, V_c, V_A, T_a, V_B) -> f1(f1(true__, V_c, V_A, T_a), V_c, V_B, T_a) % 0.62/0.82 f2(true__, v_x, v_X, t_a, v_X) -> true__ % 0.62/0.82 f3(c_in(v_x, v_Z, t_a)) -> true__ % 0.62/0.82 f3(f1(true__, v_x, v_Z, t_a)) -> true__ % 0.62/0.82 f3(true__) -> false__ % 0.62/0.82 false__ -> true__ % 0.62/0.82 with the LPO induced by % 0.62/0.82 v_Z > v_x > c_lessequals > v_X > c_in > f2 > f1 > f3 > tc_set > t_a > false__ > true__ % 0.62/0.82 % 0.62/0.82 % SZS output end Proof % 0.62/0.82 %------------------------------------------------------------------------------