%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT281-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 06:05:51 EDT 2022 % Result : Unsatisfiable 1.36s 1.50s % Output : Proof 1.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : LAT281-2 : TPTP v8.1.0. Released v3.2.0. % 0.10/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 29 06:38:02 EDT 2022 % 0.12/0.33 % CPUTime : % 1.36/1.50 % SZS status Unsatisfiable % 1.36/1.50 % SZS output start Proof % 1.36/1.50 The input problem is unsatisfiable because % 1.36/1.50 % 1.36/1.50 [1] the following set of Horn clauses is unsatisfiable: % 1.36/1.50 % 1.36/1.50 c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) % 1.36/1.50 c_in(c_Pair(v_b, v_c, t_a, t_a), v_r, tc_prod(t_a, t_a)) % 1.36/1.50 c_in(c_Pair(v_a, v_c, t_a, t_a), v_r, tc_prod(t_a, t_a)) ==> \bottom % 1.36/1.50 c_Relation_Otrans(V_r, T_a) & c_in(c_Pair(V_V, V_W, T_a, T_a), V_r, tc_prod(T_a, T_a)) & c_in(c_Pair(V_U, V_V, T_a, T_a), V_r, tc_prod(T_a, T_a)) ==> c_in(c_Pair(V_U, V_W, T_a, T_a), V_r, tc_prod(T_a, T_a)) % 1.36/1.50 c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) ==> c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) % 1.36/1.50 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) % 1.36/1.50 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) % 1.36/1.50 % 1.36/1.50 This holds because % 1.36/1.50 % 1.36/1.50 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.36/1.50 % 1.36/1.50 E: % 1.36/1.50 c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true__ % 1.36/1.50 c_in(c_Pair(v_b, v_c, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true__ % 1.36/1.50 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true__ % 1.36/1.50 f1(c_in(c_Pair(v_a, v_c, t_a, t_a), v_r, tc_prod(t_a, t_a))) = true__ % 1.36/1.50 f1(true__) = false__ % 1.36/1.50 f2(true__, V_U, V_W, T_a, V_r) = c_in(c_Pair(V_U, V_W, T_a, T_a), V_r, tc_prod(T_a, T_a)) % 1.36/1.50 f3(true__, V_r, T_a, V_U, V_W) = f2(c_Relation_Otrans(V_r, T_a), V_U, V_W, T_a, V_r) % 1.36/1.50 f4(c_in(c_Pair(V_U, V_V, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_V, V_W, T_a, V_r, V_U) = true__ % 1.36/1.50 f4(true__, V_V, V_W, T_a, V_r, V_U) = f3(c_in(c_Pair(V_V, V_W, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_r, T_a, V_U, V_W) % 1.36/1.50 f5(c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_P, T_a) = true__ % 1.36/1.50 f5(true__, V_P, T_a) = c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) % 1.36/1.50 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) % 1.36/1.50 G: % 1.36/1.50 true__ = false__ % 1.36/1.50 % 1.36/1.50 This holds because % 1.36/1.50 % 1.36/1.50 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.36/1.50 % 1.36/1.50 % 1.36/1.50 c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) -> f5(true__, V_P, T_a) % 1.36/1.50 c_Relation_Otrans(v_r, t_a) -> f5(true__, v_cl, t_a) % 1.36/1.50 c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) -> v_r % 1.36/1.50 c_in(c_Pair(V_U, V_W, T_a, T_a), V_r, tc_prod(T_a, T_a)) -> f2(true__, V_U, V_W, T_a, V_r) % 1.36/1.50 c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> true__ % 1.36/1.50 c_in(c_Pair(v_b, v_c, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> true__ % 1.36/1.50 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) -> true__ % 1.36/1.50 f1(c_in(c_Pair(v_a, v_c, t_a, t_a), v_r, tc_prod(t_a, t_a))) -> true__ % 1.36/1.50 f1(f2(true__, v_a, v_c, t_a, v_r)) -> true__ % 1.36/1.50 f1(true__) -> false__ % 1.36/1.50 f2(c_Relation_Otrans(V_r, T_a), V_U, V_W, T_a, V_r) -> f3(true__, V_r, T_a, V_U, V_W) % 1.36/1.50 f2(f5(true__, X0, Y1), Y2, Y3, Y1, c_Tarski_Opotype_Oorder(X0, Y1, tc_Product__Type_Ounit)) -> f3(true__, c_Tarski_Opotype_Oorder(X0, Y1, tc_Product__Type_Ounit), Y1, Y2, Y3) % 1.36/1.50 f2(true__, Y2, Y3, t_a, v_r) -> f3(true__, v_r, t_a, Y2, Y3) % 1.36/1.50 f2(true__, v_a, v_b, t_a, v_r) -> true__ % 1.36/1.50 f2(true__, v_b, v_c, t_a, v_r) -> true__ % 1.36/1.50 f3(f2(true__, v_b, Y4, t_a, v_r), v_r, t_a, v_a, Y4) -> true__ % 1.36/1.50 f3(f2(true__, v_c, Y4, t_a, v_r), v_r, t_a, v_b, Y4) -> true__ % 1.36/1.50 f3(f3(true__, v_r, t_a, v_b, Y0), v_r, t_a, v_a, Y0) -> true__ % 1.36/1.50 f3(f3(true__, v_r, t_a, v_c, Y0), v_r, t_a, v_b, Y0) -> true__ % 1.36/1.50 f3(true__, v_r, t_a, v_a, v_b) -> true__ % 1.36/1.50 f3(true__, v_r, t_a, v_a, v_c) -> true__ % 1.36/1.50 f3(true__, v_r, t_a, v_b, v_c) -> true__ % 1.36/1.50 f4(c_in(c_Pair(V_U, V_V, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_V, V_W, T_a, V_r, V_U) -> true__ % 1.36/1.50 f4(f2(true__, Y0, Y1, Y2, Y3), Y1, Y4, Y2, Y3, Y0) -> true__ % 1.36/1.50 f4(f3(true__, v_r, t_a, Y0, Y1), Y1, Y4, t_a, v_r, Y0) -> true__ % 1.36/1.50 f4(true__, V_V, V_W, T_a, V_r, V_U) -> f3(c_in(c_Pair(V_V, V_W, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_r, T_a, V_U, V_W) % 1.36/1.50 f5(c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_P, T_a) -> true__ % 1.36/1.50 f5(true__, v_cl, t_a) -> true__ % 1.36/1.50 false__ -> true__ % 1.36/1.50 with the LPO induced by % 1.36/1.50 f4 > c_in > f2 > f3 > c_Relation_Otrans > f5 > c_Tarski_Opotype_Oorder > v_r > v_cl > tc_Product__Type_Ounit > c_Pair > tc_Tarski_Opotype_Opotype__ext__type > tc_prod > c_Tarski_OPartialOrder > f1 > v_c > t_a > v_b > v_a > false__ > true__ % 1.36/1.50 % 1.36/1.50 % SZS output end Proof % 1.36/1.50 %------------------------------------------------------------------------------