%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT271-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 06:05:44 EDT 2022 % Result : Unsatisfiable 0.14s 0.41s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : LAT271-2 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n026.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Wed Jun 29 18:21:33 EDT 2022 % 0.14/0.34 % CPUTime : % 0.14/0.41 % SZS status Unsatisfiable % 0.14/0.41 % SZS output start Proof % 0.14/0.41 The input problem is unsatisfiable because % 0.14/0.41 % 0.14/0.41 [1] the following set of Horn clauses is unsatisfiable: % 0.14/0.41 % 0.14/0.41 c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) % 0.14/0.41 c_in(v_x, v_S, t_a) % 0.14/0.41 c_in(c_Pair(v_a, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a)) ==> \bottom % 0.14/0.41 c_in(V_x, V_S, T_a) & c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)) ==> c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) % 0.14/0.41 % 0.14/0.41 This holds because % 0.14/0.41 % 0.14/0.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.14/0.41 % 0.14/0.41 E: % 0.14/0.41 c_in(v_x, v_S, t_a) = true__ % 0.14/0.41 c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) = true__ % 0.14/0.41 f1(c_in(c_Pair(v_a, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))) = true__ % 0.14/0.41 f1(true__) = false__ % 0.14/0.41 f2(true__, V_a, V_x, T_a, V_r) = c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) % 0.14/0.41 f3(c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)), V_x, V_S, T_a, V_a, V_r) = true__ % 0.14/0.41 f3(true__, V_x, V_S, T_a, V_a, V_r) = f2(c_in(V_x, V_S, T_a), V_a, V_x, T_a, V_r) % 0.14/0.41 G: % 0.14/0.41 true__ = false__ % 0.14/0.41 % 0.14/0.41 This holds because % 0.14/0.41 % 0.14/0.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.14/0.41 % 0.14/0.41 % 0.14/0.41 c_in(c_Pair(V_a, V_x, T_a, T_a), V_r, tc_prod(T_a, T_a)) -> f2(true__, V_a, V_x, T_a, V_r) % 0.14/0.41 c_in(v_x, v_S, t_a) -> true__ % 0.14/0.41 c_lessequals(v_S, c_Tarski_Ointerval(v_r, v_a, v_b, t_a), tc_set(t_a)) -> true__ % 0.14/0.41 f1(c_in(c_Pair(v_a, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))) -> true__ % 0.14/0.41 f1(f2(true__, v_a, v_x, t_a, v_r)) -> true__ % 0.14/0.41 f1(true__) -> false__ % 0.14/0.41 f2(c_in(V_x, V_S, T_a), V_a, V_x, T_a, V_r) -> f3(true__, V_x, V_S, T_a, V_a, V_r) % 0.14/0.41 f2(f2(true__, X0, X1, X2, Y1), Y3, c_Pair(X0, X1, X2, X2), tc_prod(X2, X2), Y4) -> f3(true__, c_Pair(X0, X1, X2, X2), Y1, tc_prod(X2, X2), Y3, Y4) % 0.14/0.41 f2(f3(true__, v_x, v_S, t_a, Y0, Y3), Y4, c_Pair(Y0, v_x, t_a, t_a), tc_prod(t_a, t_a), Y5) -> f3(true__, c_Pair(Y0, v_x, t_a, t_a), Y3, tc_prod(t_a, t_a), Y4, Y5) % 0.14/0.41 f2(true__, Y3, v_x, t_a, Y4) -> f3(true__, v_x, v_S, t_a, Y3, Y4) % 0.14/0.41 f3(c_lessequals(V_S, c_Tarski_Ointerval(V_r, V_a, V_b, T_a), tc_set(T_a)), V_x, V_S, T_a, V_a, V_r) -> true__ % 0.14/0.41 f3(true__, Y5, v_S, t_a, v_a, v_r) -> true__ % 0.14/0.41 false__ -> true__ % 0.14/0.41 with the LPO induced by % 0.14/0.41 c_in > f2 > f3 > c_Pair > tc_prod > f1 > v_x > tc_set > t_a > v_b > v_a > v_r > c_Tarski_Ointerval > v_S > c_lessequals > false__ > true__ % 0.14/0.41 % 0.14/0.41 % SZS output end Proof % 0.14/0.41 %------------------------------------------------------------------------------