%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LCL441-2 : TPTP v9.3.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 12:46:08 PM UTC 2026 % Result : Unsatisfiable 0.13s 0.42s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL441-2 : TPTP v9.3.1. Released v3.2.0. % 0.00/0.04 % Command : moca.sh %s % 0.09/0.35 % Computer : n020.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 08:06:27 UTC 2026 % 0.09/0.35 % CPUTime : % 0.13/0.42 % SZS status Unsatisfiable % 0.13/0.42 % SZS output start Proof % 0.13/0.42 The input problem is unsatisfiable because % 0.13/0.42 % 0.13/0.42 [1] the following set of Horn clauses is unsatisfiable: % 0.13/0.42 % 0.13/0.42 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) & c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a)) ==> \bottom % 0.13/0.42 c_in(V_p, V_H, tc_PropLog_Opl(T_a)) ==> c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) % 0.13/0.42 c_in(V_x, c_insert(V_x, V_B, T_a), T_a) % 0.13/0.42 % 0.13/0.42 This holds because % 0.13/0.42 % 0.13/0.42 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.13/0.42 % 0.13/0.42 E: % 0.13/0.42 c_in(V_x, c_insert(V_x, V_B, T_a), T_a) = true__ % 0.13/0.42 f1(true__) = false__ % 0.13/0.42 f2(c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) = true__ % 0.13/0.42 f2(true__) = f1(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) % 0.13/0.42 f3(c_in(V_p, V_H, tc_PropLog_Opl(T_a)), V_p, V_H, T_a) = true__ % 0.13/0.42 f3(true__, V_p, V_H, T_a) = c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) % 0.13/0.42 G: % 0.13/0.42 true__ = false__ % 0.13/0.42 % 0.13/0.42 This holds because % 0.13/0.42 % 0.13/0.42 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.13/0.42 % 0.13/0.42 % 0.13/0.42 c_in(V_p, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) -> f3(true__, V_p, V_H, T_a) % 0.13/0.42 c_in(V_x, c_insert(V_x, V_B, T_a), T_a) -> true__ % 0.13/0.42 f1(true__) -> false__ % 0.13/0.42 f2(c_in(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) -> true__ % 0.13/0.42 f2(f3(true__, c_PropLog_Opl_Ovar(v_a, t_a), c_insert(c_PropLog_Opl_Ovar(v_a, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a)) -> true__ % 0.13/0.42 f2(true__) -> f1(c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a, t_a), c_PropLog_Opl_Ofalse, t_a), c_emptyset, tc_PropLog_Opl(t_a)), t_a), tc_PropLog_Opl(t_a))) % 0.13/0.42 f3(c_in(V_p, V_H, tc_PropLog_Opl(T_a)), V_p, V_H, T_a) -> true__ % 0.13/0.42 f3(f3(true__, Y0, X1, Y2), Y0, c_PropLog_Othms(X1, Y2), Y2) -> true__ % 0.13/0.42 f3(true__, Y0, c_PropLog_Othms(c_insert(Y0, X1, tc_PropLog_Opl(Y2)), Y2), Y2) -> true__ % 0.13/0.42 f3(true__, Y0, c_insert(Y0, X1, tc_PropLog_Opl(Y2)), Y2) -> true__ % 0.13/0.42 true__ -> false__ % 0.13/0.42 with the LPO induced by % 0.13/0.42 f2 > c_emptyset > c_in > f3 > f1 > tc_PropLog_Opl > c_insert > c_PropLog_Othms > c_PropLog_Opl_Ofalse > t_a > v_a > c_PropLog_Opl_Ovar > c_PropLog_Opl_Oop_A_N_62 > true__ > false__ % 0.13/0.42 % 0.13/0.42 % SZS output end Proof % 0.13/0.42 %------------------------------------------------------------------------------