%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sun Jul 17 06:05:38 EDT 2022 % Result : Unsatisfiable 1.42s 1.54s % Output : Proof 1.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0. % 0.10/0.10 % Command : moca.sh %s % 0.10/0.29 % Computer : n032.cluster.edu % 0.10/0.29 % Model : x86_64 x86_64 % 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.29 % Memory : 8042.1875MB % 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.29 % CPULimit : 300 % 0.10/0.29 % WCLimit : 600 % 0.10/0.29 % DateTime : Wed Jun 29 05:42:58 EDT 2022 % 0.10/0.29 % CPUTime : % 1.42/1.54 % SZS status Unsatisfiable % 1.42/1.54 % SZS output start Proof % 1.42/1.54 The input problem is unsatisfiable because % 1.42/1.54 % 1.42/1.54 [1] the following set of Horn clauses is unsatisfiable: % 1.42/1.54 % 1.42/1.54 c_lessequals(v_S, v_A, tc_set(t_a)) % 1.42/1.54 c_in(c_Tarski_Oglb(v_S, v_cl, t_a), v_A, t_a) ==> \bottom % 1.42/1.54 v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) % 1.42/1.54 c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) & c_in(V_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) & c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), tc_set(T_a)) ==> c_in(c_Tarski_Olub(V_S, V_cl, T_a), c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), T_a) % 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) % 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) % 1.42/1.54 c_Tarski_Oglb(V_S, V_cl, T_a) = c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a) % 1.42/1.54 c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit) % 1.42/1.54 % 1.42/1.54 This holds because % 1.42/1.54 % 1.42/1.54 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.42/1.54 % 1.42/1.54 E: % 1.42/1.54 c_Tarski_Oglb(V_S, V_cl, T_a) = c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a) % 1.42/1.54 c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit) % 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true__ % 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true__ % 1.42/1.54 c_lessequals(v_S, v_A, tc_set(t_a)) = true__ % 1.42/1.54 f1(c_in(c_Tarski_Oglb(v_S, v_cl, t_a), v_A, t_a)) = true__ % 1.42/1.54 f1(true__) = false__ % 1.42/1.54 f2(true__, V_S, V_cl, T_a) = c_in(c_Tarski_Olub(V_S, V_cl, T_a), c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), T_a) % 1.42/1.54 f3(true__, V_cl, T_a, V_S) = f2(c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_S, V_cl, T_a) % 1.42/1.54 f4(c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), tc_set(T_a)), V_cl, T_a, V_S) = true__ % 1.42/1.54 f4(true__, V_cl, T_a, V_S) = f3(c_in(V_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_cl, T_a, V_S) % 1.42/1.54 v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) % 1.42/1.54 G: % 1.42/1.54 true__ = false__ % 1.42/1.54 % 1.42/1.54 This holds because % 1.42/1.54 % 1.42/1.54 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.42/1.54 % 1.42/1.54 c_in(c_Tarski_Oglb(Y0, X0, Y2), c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), Y2) = f2(true__, Y0, c_Tarski_Odual(X0, Y2), Y2) % 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(X0, Y2), Y2), c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), Y2) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2) % 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), Y2) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2) % 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2), c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), Y2) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2), Y2) % 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), v_A, t_a) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), t_a) % 1.42/1.54 c_in(c_Tarski_Oglb(Y0, c_Tarski_Odual(v_cl, t_a), t_a), v_A, t_a) = f2(true__, Y0, c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a) % 1.42/1.54 c_in(c_Tarski_Oglb(Y0, v_cl, t_a), v_A, t_a) = f4(true__, c_Tarski_Odual(v_cl, t_a), t_a, Y0) % 1.42/1.54 c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a) -> c_Tarski_Oglb(V_S, V_cl, T_a) % 1.42/1.54 c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit) -> c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit) % 1.42/1.54 c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) -> v_A % 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) -> true__ % 1.42/1.54 c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) -> true__ % 1.42/1.54 c_in(c_Tarski_Oglb(v_S, v_cl, t_a), v_A, t_a) -> true__ % 1.42/1.54 c_in(c_Tarski_Olub(V_S, V_cl, T_a), c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), T_a) -> f2(true__, V_S, V_cl, T_a) % 1.42/1.54 c_in(c_Tarski_Olub(Y0, v_cl, t_a), v_A, t_a) -> f2(true__, Y0, v_cl, t_a) % 1.42/1.54 c_lessequals(v_S, v_A, tc_set(t_a)) -> true__ % 1.42/1.54 f1(c_in(c_Tarski_Oglb(v_S, v_cl, t_a), v_A, t_a)) -> true__ % 1.42/1.54 f1(true__) -> false__ % 1.42/1.54 f2(c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_S, V_cl, T_a) -> f3(true__, V_cl, T_a, V_S) % 1.42/1.54 f2(true__, Y2, c_Tarski_Odual(v_cl, t_a), t_a) -> f3(true__, c_Tarski_Odual(v_cl, t_a), t_a, Y2) % 1.42/1.54 f3(c_in(V_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_cl, T_a, V_S) -> f4(true__, V_cl, T_a, V_S) % 1.42/1.54 f3(true__, c_Tarski_Odual(v_cl, t_a), t_a, Y2) -> f4(true__, c_Tarski_Odual(v_cl, t_a), t_a, Y2) % 1.42/1.54 f4(c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), tc_set(T_a)), V_cl, T_a, V_S) -> true__ % 1.42/1.54 f4(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_Tarski_Odual(X0, Y2), Y2, Y0) -> true__ % 1.42/1.54 f4(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2, Y0) -> true__ % 1.42/1.54 f4(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2, Y0) -> true__ % 1.42/1.54 f4(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2), Y2, Y0) -> true__ % 1.42/1.54 f4(c_lessequals(Y0, v_A, tc_set(t_a)), c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), t_a, Y0) -> true__ % 1.42/1.54 f4(c_lessequals(Y0, v_A, tc_set(t_a)), c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a, Y0) -> true__ % 1.42/1.54 f4(c_lessequals(Y0, v_A, tc_set(t_a)), c_Tarski_Odual(v_cl, t_a), t_a, Y0) -> true__ % 1.42/1.54 f4(c_lessequals(Y0, v_A, tc_set(t_a)), v_cl, t_a, Y0) -> true__ % 1.42/1.54 f4(true__, c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a, v_S) -> true__ % 1.42/1.54 f4(true__, v_cl, t_a, v_S) -> true__ % 1.42/1.54 false__ -> true__ % 1.42/1.54 with the LPO induced by % 1.42/1.54 c_Tarski_Odual > c_in > f2 > f3 > c_Tarski_OCompleteLattice > f4 > tc_Product__Type_Ounit > v_A > t_a > c_Tarski_Opotype_Opset > c_Tarski_OPartialOrder > tc_Tarski_Opotype_Opotype__ext__type > c_Tarski_Olub > c_Tarski_Oglb > v_cl > f1 > tc_set > v_S > c_lessequals > false__ > true__ % 1.42/1.54 % 1.42/1.54 % SZS output end Proof % 1.42/1.54 %------------------------------------------------------------------------------