%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LCL437-2 : TPTP v9.3.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 0.02s 0.41s % Output : Proof 0.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL437-2 : TPTP v9.3.1. Released v3.2.0. % 0.00/0.04 % Command : moca.sh %s % 0.08/0.36 % Computer : n019.cluster.edu % 0.08/0.36 % Model : x86_64 x86_64 % 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.36 % Memory : 8046.5625MB % 0.08/0.36 % OS : Linux 6.8.0-71-generic % 0.08/0.36 % CPULimit : 300 % 0.08/0.36 % WCLimit : 300 % 0.08/0.36 % DateTime : Fri Sep 4 16:01:08 UTC 2026 % 0.02/0.36 % CPUTime : % 0.02/0.41 % SZS status Unsatisfiable % 0.02/0.41 % SZS output start Proof % 0.02/0.41 The input problem is unsatisfiable because % 0.02/0.41 % 0.02/0.41 [1] the following set of Horn clauses is unsatisfiable: % 0.02/0.41 % 0.02/0.41 c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Opl_Ofalse, t_a), v_pa, t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)) ==> \bottom % 0.02/0.41 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Opl_Ofalse, T_a), V_p, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) % 0.02/0.41 c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) ==> c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) % 0.02/0.41 % 0.02/0.41 This holds because % 0.02/0.41 % 0.02/0.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.02/0.41 % 0.02/0.41 E: % 0.02/0.41 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Opl_Ofalse, T_a), V_p, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) = true__ % 0.02/0.41 f1(c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Opl_Ofalse, t_a), v_pa, t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))) = true__ % 0.02/0.41 f1(true__) = false__ % 0.02/0.41 f2(c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)), V_p, V_q, T_a, V_H) = true__ % 0.02/0.41 f2(true__, V_p, V_q, T_a, V_H) = c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) % 0.02/0.41 G: % 0.02/0.41 true__ = false__ % 0.02/0.41 % 0.02/0.41 This holds because % 0.02/0.41 % 0.02/0.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.02/0.41 % 0.02/0.41 % 0.02/0.41 c_in(c_PropLog_Opl_Oop_A_N_62(Y3, c_PropLog_Opl_Oop_A_N_62(X0, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1, c_PropLog_Opl_Ofalse, Y2), c_PropLog_Opl_Ofalse, Y2), X1, Y2), Y2), Y2), c_PropLog_Othms(Y1, Y2), tc_PropLog_Opl(Y2)) -> true__ % 0.02/0.41 c_in(c_PropLog_Opl_Oop_A_N_62(Y3, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0, c_PropLog_Opl_Ofalse, Y2), c_PropLog_Opl_Ofalse, Y2), X0, Y2), Y2), c_PropLog_Othms(Y1, Y2), tc_PropLog_Opl(Y2)) -> true__ % 0.02/0.41 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Ofalse, T_a), c_PropLog_Opl_Ofalse, T_a), V_p, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) -> true__ % 0.02/0.41 f1(c_in(c_PropLog_Opl_Oop_A_N_62(v_p, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Ofalse, t_a), c_PropLog_Opl_Ofalse, t_a), v_pa, t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))) -> true__ % 0.02/0.41 f1(true__) -> false__ % 0.02/0.41 f2(c_in(V_q, c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)), V_p, V_q, T_a, V_H) -> true__ % 0.02/0.41 f2(true__, V_p, V_q, T_a, V_H) -> c_in(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) % 0.02/0.41 false__ -> true__ % 0.02/0.41 with the LPO induced by % 0.02/0.41 f2 > tc_PropLog_Opl > v_H > c_PropLog_Othms > t_a > c_PropLog_Opl_Ofalse > v_pa > v_p > c_PropLog_Opl_Oop_A_N_62 > c_in > f1 > false__ > true__ % 0.02/0.41 % 0.02/0.41 % SZS output end Proof % 0.02/0.41 %------------------------------------------------------------------------------