%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL120-2 : 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 : Fri Jul 15 00:38:02 EDT 2022 % Result : Unsatisfiable 0.18s 0.39s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COL120-2 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n026.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 : Tue May 31 13:28:26 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.39 % SZS status Unsatisfiable % 0.18/0.39 % SZS output start Proof % 0.18/0.39 The input problem is unsatisfiable because % 0.18/0.39 % 0.18/0.39 [1] the following set of Horn clauses is unsatisfiable: % 0.18/0.39 % 0.18/0.39 c_in(c_Pair(v_y, v_x, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) % 0.18/0.39 c_in(c_Pair(v_x, V_U, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) & c_in(c_Pair(v_y, V_U, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) ==> \bottom % 0.18/0.39 c_in(c_Pair(V_a, V_a, T_a, T_a), c_Transitive__Closure_Ortrancl(V_r, T_a), tc_prod(T_a, T_a)) % 0.18/0.39 % 0.18/0.39 This holds because % 0.18/0.39 % 0.18/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.18/0.39 % 0.18/0.39 E: % 0.18/0.39 c_in(c_Pair(V_a, V_a, T_a, T_a), c_Transitive__Closure_Ortrancl(V_r, T_a), tc_prod(T_a, T_a)) = true__ % 0.18/0.39 c_in(c_Pair(v_y, v_x, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) = true__ % 0.18/0.39 f1(true__) = false__ % 0.18/0.39 f2(c_in(c_Pair(v_y, V_U, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), V_U) = true__ % 0.18/0.39 f2(true__, V_U) = f1(c_in(c_Pair(v_x, V_U, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a))) % 0.18/0.39 G: % 0.18/0.39 true__ = false__ % 0.18/0.39 % 0.18/0.39 This holds because % 0.18/0.39 % 0.18/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.18/0.39 % 0.18/0.39 % 0.18/0.39 c_in(c_Pair(V_a, V_a, T_a, T_a), c_Transitive__Closure_Ortrancl(V_r, T_a), tc_prod(T_a, T_a)) -> true__ % 0.18/0.39 c_in(c_Pair(v_y, v_x, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)) -> true__ % 0.18/0.39 f1(c_in(c_Pair(v_x, V_U, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a))) -> f2(true__, V_U) % 0.18/0.39 f1(true__) -> false__ % 0.18/0.39 f2(c_in(c_Pair(v_y, V_U, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), V_U) -> true__ % 0.18/0.39 f2(true__, v_x) -> false__ % 0.18/0.39 f2(true__, v_x) -> true__ % 0.18/0.39 f2(true__, v_y) -> true__ % 0.18/0.39 false__ -> true__ % 0.18/0.39 with the LPO induced by % 0.18/0.39 c_in > f2 > tc_prod > v_r > t_a > v_x > f1 > c_Transitive__Closure_Ortrancl > v_y > c_Pair > false__ > true__ % 0.18/0.39 % 0.18/0.39 % SZS output end Proof % 0.18/0.39 %------------------------------------------------------------------------------