%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT272-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % 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 : 600s % DateTime : Sun Jul 17 06:05:45 EDT 2022 % Result : Unsatisfiable 0.19s 0.39s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : LAT272-2 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.13 % Command : moca.sh %s % 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 : 600 % 0.12/0.33 % DateTime : Wed Jun 29 06:19:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.39 % SZS status Unsatisfiable % 0.19/0.39 % SZS output start Proof % 0.19/0.39 The input problem is unsatisfiable because % 0.19/0.39 % 0.19/0.39 [1] the following set of Horn clauses is unsatisfiable: % 0.19/0.39 % 0.19/0.39 c_Tarski_OisLub(v_S, v_cl, v_L, t_a) % 0.19/0.39 c_in(v_x, v_S, t_a) % 0.19/0.39 c_in(c_Pair(v_x, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) ==> \bottom % 0.19/0.39 c_Tarski_OisLub(V_S, v_cl, V_L, t_a) & c_in(V_y, V_S, t_a) ==> c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) % 0.19/0.39 % 0.19/0.39 This holds because % 0.19/0.39 % 0.19/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.19/0.39 % 0.19/0.39 E: % 0.19/0.39 c_Tarski_OisLub(v_S, v_cl, v_L, t_a) = true__ % 0.19/0.39 c_in(v_x, v_S, t_a) = true__ % 0.19/0.39 f1(c_in(c_Pair(v_x, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) = true__ % 0.19/0.39 f1(true__) = false__ % 0.19/0.39 f2(true__, V_y, V_L) = c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) % 0.19/0.39 f3(c_in(V_y, V_S, t_a), V_S, V_L, V_y) = true__ % 0.19/0.39 f3(true__, V_S, V_L, V_y) = f2(c_Tarski_OisLub(V_S, v_cl, V_L, t_a), V_y, V_L) % 0.19/0.39 G: % 0.19/0.39 true__ = false__ % 0.19/0.39 % 0.19/0.39 This holds because % 0.19/0.39 % 0.19/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.19/0.39 % 0.19/0.39 % 0.19/0.39 c_Tarski_OisLub(v_S, v_cl, v_L, t_a) -> true__ % 0.19/0.39 c_in(c_Pair(V_y, V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> f2(true__, V_y, V_L) % 0.19/0.39 c_in(v_x, v_S, t_a) -> true__ % 0.19/0.39 f1(c_in(c_Pair(v_x, v_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) -> true__ % 0.19/0.39 f1(f2(true__, v_x, v_L)) -> true__ % 0.19/0.39 f1(true__) -> false__ % 0.19/0.39 f2(c_Tarski_OisLub(V_S, v_cl, V_L, t_a), V_y, V_L) -> f3(true__, V_S, V_L, V_y) % 0.19/0.39 f2(true__, Y2, v_L) -> f3(true__, v_S, v_L, Y2) % 0.19/0.39 f3(c_in(V_y, V_S, t_a), V_S, V_L, V_y) -> true__ % 0.19/0.39 f3(true__, v_S, Y2, v_x) -> true__ % 0.19/0.39 false__ -> true__ % 0.19/0.39 with the LPO induced by % 0.19/0.39 c_in > f2 > v_r > c_Pair > f3 > t_a > v_cl > tc_prod > f1 > v_x > v_L > v_S > c_Tarski_OisLub > false__ > true__ % 0.19/0.39 % 0.19/0.39 % SZS output end Proof % 0.19/0.39 %------------------------------------------------------------------------------