%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT259-2 : TPTP v8.1.0. 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 : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sun Jul 17 06:05:35 EDT 2022 % Result : Unsatisfiable 1.39s 1.47s % Output : Proof 1.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : LAT259-2 : TPTP v8.1.0. Released v3.2.0. % 0.04/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n019.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Thu Jun 30 12:19:23 EDT 2022 % 0.13/0.34 % CPUTime : % 1.39/1.47 % SZS status Unsatisfiable % 1.39/1.47 % SZS output start Proof % 1.39/1.47 The input problem is unsatisfiable because % 1.39/1.47 % 1.39/1.47 [1] the following set of Horn clauses is unsatisfiable: % 1.39/1.47 % 1.39/1.47 c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) % 1.39/1.47 c_in(c_Pair(v_b, v_a, t_a, t_a), v_r, tc_prod(t_a, t_a)) % 1.39/1.47 v_a = v_b ==> \bottom % 1.39/1.47 c_Relation_Oantisym(V_r, T_a) & c_in(c_Pair(V_V, V_U, 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)) ==> V_U = V_V % 1.39/1.47 c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) ==> c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) % 1.39/1.47 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) % 1.39/1.47 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) % 1.39/1.47 % 1.39/1.47 This holds because % 1.39/1.47 % 1.39/1.47 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.39/1.47 % 1.39/1.47 E: % 1.39/1.47 c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true__ % 1.39/1.47 c_in(c_Pair(v_b, v_a, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true__ % 1.39/1.47 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true__ % 1.39/1.47 f1(v_a) = true__ % 1.39/1.47 f1(v_b) = false__ % 1.39/1.47 f2(true__, V_U, V_V) = V_U % 1.39/1.47 f3(true__, V_r, T_a, V_U, V_V) = f2(c_Relation_Oantisym(V_r, T_a), V_U, V_V) % 1.39/1.47 f4(c_in(c_Pair(V_U, V_V, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_V, V_U, T_a, V_r) = V_V % 1.39/1.47 f4(true__, V_V, V_U, T_a, V_r) = f3(c_in(c_Pair(V_V, V_U, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_r, T_a, V_U, V_V) % 1.39/1.47 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__ % 1.39/1.47 f5(true__, V_P, T_a) = c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) % 1.39/1.47 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) % 1.39/1.47 G: % 1.39/1.47 true__ = false__ % 1.39/1.47 % 1.39/1.47 This holds because % 1.39/1.47 % 1.39/1.47 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.39/1.47 % 1.39/1.47 % 1.39/1.47 c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) -> f5(true__, V_P, T_a) % 1.39/1.47 c_Relation_Oantisym(v_r, t_a) -> f5(true__, v_cl, t_a) % 1.39/1.47 c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) -> v_r % 1.39/1.47 c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> true__ % 1.39/1.47 c_in(c_Pair(v_b, v_a, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> true__ % 1.39/1.47 c_in(c_Pair(v_b, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> true__ % 1.39/1.47 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) -> true__ % 1.39/1.47 f1(v_a) -> true__ % 1.39/1.47 f1(v_b) -> false__ % 1.39/1.47 f2(c_Relation_Oantisym(V_r, T_a), V_U, V_V) -> f3(true__, V_r, T_a, V_U, V_V) % 1.39/1.47 f2(f5(true__, X0, Y1), Y2, Y3) -> f3(true__, c_Tarski_Opotype_Oorder(X0, Y1, tc_Product__Type_Ounit), Y1, Y2, Y3) % 1.39/1.47 f2(true__, V_U, V_V) -> V_U % 1.39/1.47 f3(c_in(c_Pair(V_V, V_U, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_r, T_a, V_U, V_V) -> f4(true__, V_V, V_U, T_a, V_r) % 1.39/1.47 f3(true__, v_r, t_a, Y2, Y3) -> Y2 % 1.39/1.47 f3(true__, v_r, t_a, v_a, v_b) -> f4(true__, v_b, v_a, t_a, v_r) % 1.39/1.47 f3(true__, v_r, t_a, v_b, v_a) -> f4(true__, v_a, v_b, t_a, v_r) % 1.39/1.47 f4(c_in(c_Pair(V_U, V_V, T_a, T_a), V_r, tc_prod(T_a, T_a)), V_V, V_U, T_a, V_r) -> V_V % 1.39/1.47 f4(true__, v_a, v_b, t_a, v_r) -> v_a % 1.39/1.47 f4(true__, v_b, v_a, t_a, v_r) -> v_b % 1.39/1.47 f4(true__, v_b, v_b, t_a, v_r) -> v_b % 1.39/1.47 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__ % 1.39/1.47 f5(true__, v_cl, t_a) -> true__ % 1.39/1.47 false__ -> true__ % 1.39/1.47 v_a -> v_b % 1.39/1.47 with the LPO induced by % 1.39/1.47 f2 > f3 > f4 > c_Relation_Oantisym > f5 > c_Tarski_Opotype_Oorder > v_r > v_cl > tc_Tarski_Opotype_Opotype__ext__type > c_Tarski_OPartialOrder > tc_Product__Type_Ounit > v_a > c_in > c_Pair > f1 > tc_prod > t_a > v_b > false__ > true__ % 1.39/1.47 % 1.39/1.47 % SZS output end Proof % 1.39/1.47 %------------------------------------------------------------------------------