%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LCL436-2 : TPTP v9.3.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n002.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 0.39s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL436-2 : TPTP v9.3.1. Released v3.2.0. % 0.00/0.03 % Command : moca.sh %s % 0.09/0.34 % Computer : n002.cluster.edu % 0.09/0.34 % Model : x86_64 x86_64 % 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.34 % Memory : 8046.5625MB % 0.09/0.34 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Fri Sep 4 15:08:35 UTC 2026 % 0.09/0.35 % CPUTime : % 0.13/0.39 % SZS status Unsatisfiable % 0.13/0.39 % SZS output start Proof % 0.13/0.39 The input problem is unsatisfiable because % 0.13/0.39 % 0.13/0.39 [1] the following set of Horn clauses is unsatisfiable: % 0.13/0.39 % 0.13/0.39 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(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a)) ==> \bottom % 0.13/0.39 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Oop_A_N_62(V_q, V_r, T_a), T_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Oop_A_N_62(V_p, V_r, T_a), T_a), T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) % 0.13/0.39 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)) % 0.13/0.39 % 0.13/0.39 This holds because % 0.13/0.39 % 0.13/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.13/0.39 % 0.13/0.39 E: % 0.13/0.39 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Oop_A_N_62(V_q, V_r, T_a), T_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Oop_A_N_62(V_p, V_r, T_a), T_a), T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) = true__ % 0.13/0.39 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(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))) = true__ % 0.13/0.39 f1(true__) = false__ % 0.13/0.39 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__ % 0.13/0.39 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)) % 0.13/0.39 G: % 0.13/0.39 true__ = false__ % 0.13/0.39 % 0.13/0.39 This holds because % 0.13/0.39 % 0.13/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.13/0.39 % 0.13/0.39 % 0.13/0.39 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)) -> f2(true__, V_p, V_q, T_a, V_H) % 0.13/0.39 c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, c_PropLog_Opl_Oop_A_N_62(V_q, V_r, T_a), T_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p, V_q, T_a), c_PropLog_Opl_Oop_A_N_62(V_p, V_r, T_a), T_a), T_a), c_PropLog_Othms(V_H, T_a), tc_PropLog_Opl(T_a)) -> true__ % 0.13/0.39 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(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), t_a), c_PropLog_Othms(v_H, t_a), tc_PropLog_Opl(t_a))) -> true__ % 0.13/0.39 f1(f2(true__, v_p, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, c_PropLog_Opl_Oop_A_N_62(v_q, v_r, t_a), t_a), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_pa, v_q, t_a), c_PropLog_Opl_Oop_A_N_62(v_pa, v_r, t_a), t_a), t_a), t_a, v_H)) -> true__ % 0.13/0.39 f1(true__) -> false__ % 0.13/0.39 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__ % 0.13/0.39 f2(f2(true__, X0, X1, Y2, Y1), Y3, c_PropLog_Opl_Oop_A_N_62(X0, X1, Y2), Y2, Y1) -> true__ % 0.13/0.39 f2(true__, Y3, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0, c_PropLog_Opl_Oop_A_N_62(X1, X2, Y2), Y2), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0, X1, Y2), c_PropLog_Opl_Oop_A_N_62(X0, X2, Y2), Y2), Y2), Y2, Y1) -> true__ % 0.13/0.39 f2(true__, Y4, c_PropLog_Opl_Oop_A_N_62(Y0, c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1, c_PropLog_Opl_Oop_A_N_62(X2, X3, Y2), Y2), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1, X2, Y2), c_PropLog_Opl_Oop_A_N_62(X1, X3, Y2), Y2), Y2), Y2), Y2, Y3) -> true__ % 0.13/0.39 f2(true__, c_PropLog_Opl_Oop_A_N_62(Y0, c_PropLog_Opl_Oop_A_N_62(Y1, Y2, Y3), Y3), c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(Y0, Y1, Y3), c_PropLog_Opl_Oop_A_N_62(Y0, Y2, Y3), Y3), Y3, Y4) -> true__ % 0.13/0.39 false__ -> true__ % 0.13/0.39 with the LPO induced by % 0.13/0.39 v_pa > c_in > f2 > c_PropLog_Opl_Oop_A_N_62 > tc_PropLog_Opl > v_H > c_PropLog_Othms > t_a > v_r > v_q > v_p > f1 > false__ > true__ % 0.13/0.39 % 0.13/0.39 % SZS output end Proof % 0.13/0.39 %------------------------------------------------------------------------------