%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n014.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 0.13s 0.40s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0. % 0.00/0.04 % Command : moca.sh %s % 0.10/0.36 % Computer : n014.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 17:22:27 UTC 2026 % 0.10/0.36 % CPUTime : % 0.13/0.40 % SZS status Unsatisfiable % 0.13/0.40 % SZS output start Proof % 0.13/0.40 The input problem is unsatisfiable because % 0.13/0.40 % 0.13/0.40 [1] the following set of Horn clauses is unsatisfiable: % 0.13/0.40 % 0.13/0.40 c_PropLog_Osat(c_emptyset, v_p, t_a) % 0.13/0.40 c_in(v_p, c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a)) ==> \bottom % 0.13/0.40 c_PropLog_Osat(c_emptyset, V_p, T_a) ==> c_in(V_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p, V_U, T_a), c_PropLog_Ohyps(V_p, V_t0, T_a), tc_set(tc_PropLog_Opl(T_a))), T_a), tc_PropLog_Opl(T_a)) % 0.13/0.40 c_minus(V_A, V_A, tc_set(T_a)) = c_emptyset % 0.13/0.40 % 0.13/0.40 This holds because % 0.13/0.40 % 0.13/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.13/0.40 % 0.13/0.40 E: % 0.13/0.40 c_PropLog_Osat(c_emptyset, v_p, t_a) = true__ % 0.13/0.40 c_minus(V_A, V_A, tc_set(T_a)) = c_emptyset % 0.13/0.40 f1(c_in(v_p, c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a))) = true__ % 0.13/0.40 f1(true__) = false__ % 0.13/0.40 f2(c_PropLog_Osat(c_emptyset, V_p, T_a), V_p, V_U, T_a, V_t0) = true__ % 0.13/0.40 f2(true__, V_p, V_U, T_a, V_t0) = c_in(V_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p, V_U, T_a), c_PropLog_Ohyps(V_p, V_t0, T_a), tc_set(tc_PropLog_Opl(T_a))), T_a), tc_PropLog_Opl(T_a)) % 0.13/0.40 G: % 0.13/0.40 true__ = false__ % 0.13/0.40 % 0.13/0.40 This holds because % 0.13/0.40 % 0.13/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.13/0.40 % 0.13/0.40 c_in(Y0, c_PropLog_Othms(c_emptyset, Y2), tc_PropLog_Opl(Y2)) = f2(true__, Y0, Y3, Y2, Y3) % 0.13/0.40 f2(true__, Y0, X2, Y1, X2) = f2(true__, Y0, Y2, Y1, Y2) % 0.13/0.40 f2(true__, Y0, true__, Y2, true__) = f2(true__, Y0, Y3, Y2, Y3) % 0.13/0.40 c_PropLog_Osat(c_emptyset, v_p, t_a) -> true__ % 0.13/0.40 c_in(V_p, c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p, V_U, T_a), c_PropLog_Ohyps(V_p, V_t0, T_a), tc_set(tc_PropLog_Opl(T_a))), T_a), tc_PropLog_Opl(T_a)) -> f2(true__, V_p, V_U, T_a, V_t0) % 0.13/0.40 c_minus(V_A, V_A, tc_set(T_a)) -> c_emptyset % 0.13/0.40 f1(c_in(v_p, c_PropLog_Othms(c_emptyset, t_a), tc_PropLog_Opl(t_a))) -> true__ % 0.13/0.40 f1(true__) -> false__ % 0.13/0.40 f2(c_PropLog_Osat(c_emptyset, V_p, T_a), V_p, V_U, T_a, V_t0) -> true__ % 0.13/0.40 f2(true__, v_p, Y2, t_a, Y3) -> true__ % 0.13/0.40 false__ -> true__ % 0.13/0.40 with the LPO induced by % 0.13/0.40 c_in > f2 > tc_set > c_emptyset > c_PropLog_Ohyps > c_minus > tc_PropLog_Opl > c_PropLog_Othms > f1 > t_a > v_p > c_PropLog_Osat > false__ > true__ % 0.13/0.40 % 0.13/0.40 % SZS output end Proof % 0.13/0.40 %------------------------------------------------------------------------------