%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LCL432-2 : TPTP v9.3.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:46:07 PM UTC 2026 % Result : Unsatisfiable 0.10s 0.41s % Output : Proof 0.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL432-2 : TPTP v9.3.1. Released v3.2.0. % 0.00/0.04 % Command : moca.sh %s % 0.10/0.36 % Computer : n003.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Fri Sep 4 15:50:04 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.41 % SZS status Unsatisfiable % 0.10/0.41 % SZS output start Proof % 0.10/0.41 The input problem is unsatisfiable because % 0.10/0.41 % 0.10/0.41 [1] the following set of Horn clauses is unsatisfiable: % 0.10/0.41 % 0.10/0.41 c_PropLog_Osat(c_emptyset, v_x, t_a) % 0.10/0.41 c_in(v_x, c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a)) ==> \bottom % 0.10/0.41 c_PropLog_Osat(c_emptyset, V_p, T_a) ==> c_in(V_p, c_PropLog_Othms(c_emptyset, T_a), tc_PropLog_Opl(T_a)) % 0.10/0.41 % 0.10/0.41 This holds because % 0.10/0.41 % 0.10/0.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.10/0.41 % 0.10/0.41 E: % 0.10/0.41 c_PropLog_Osat(c_emptyset, v_x, t_a) = true__ % 0.10/0.41 f1(c_in(v_x, c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a))) = true__ % 0.10/0.41 f1(true__) = false__ % 0.10/0.41 f2(c_PropLog_Osat(c_emptyset, V_p, T_a), V_p, T_a) = true__ % 0.10/0.41 f2(true__, V_p, T_a) = c_in(V_p, c_PropLog_Othms(c_emptyset, T_a), tc_PropLog_Opl(T_a)) % 0.10/0.41 G: % 0.10/0.41 true__ = false__ % 0.10/0.41 % 0.10/0.41 This holds because % 0.10/0.41 % 0.10/0.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.10/0.41 % 0.10/0.41 % 0.10/0.41 c_PropLog_Osat(c_emptyset, v_x, t_a) -> true__ % 0.10/0.41 c_in(V_p, c_PropLog_Othms(c_emptyset, T_a), tc_PropLog_Opl(T_a)) -> f2(true__, V_p, T_a) % 0.10/0.41 f1(c_in(v_x, c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a))) -> true__ % 0.10/0.41 f1(f2(true__, v_x, t_a)) -> true__ % 0.10/0.41 f1(true__) -> false__ % 0.10/0.41 f2(c_PropLog_Osat(c_emptyset, V_p, T_a), V_p, T_a) -> true__ % 0.10/0.41 f2(true__, v_x, t_a) -> true__ % 0.10/0.41 false__ -> true__ % 0.10/0.41 with the LPO induced by % 0.10/0.41 c_in > f2 > c_emptyset > tc_PropLog_Opl > c_PropLog_Othms > f1 > t_a > v_x > c_PropLog_Osat > false__ > true__ % 0.10/0.41 % 0.10/0.41 % SZS output end Proof % 0.10/0.41 %------------------------------------------------------------------------------