%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT277-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.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 06:05:48 EDT 2022 % Result : Unsatisfiable 1.68s 1.76s % Output : Proof 1.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : LAT277-2 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.14 % Command : moca.sh %s % 0.14/0.36 % Computer : n021.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Thu Jun 30 00:32:57 EDT 2022 % 0.14/0.36 % CPUTime : % 1.68/1.76 % SZS status Unsatisfiable % 1.68/1.76 % SZS output start Proof % 1.68/1.76 The input problem is unsatisfiable because % 1.68/1.76 % 1.68/1.76 [1] the following set of Horn clauses is unsatisfiable: % 1.68/1.76 % 1.68/1.76 c_in(v_x, v_A, t_a) % 1.68/1.76 c_in(c_Pair(v_x, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a)) ==> \bottom % 1.68/1.76 c_Relation_Orefl(V_A, V_r, T_a) & c_in(V_a, V_A, T_a) ==> c_in(c_Pair(V_a, V_a, T_a, T_a), V_r, tc_prod(T_a, T_a)) % 1.68/1.76 v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) % 1.68/1.76 c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) ==> c_Relation_Orefl(c_Tarski_Opotype_Opset(V_P, T_a, tc_Product__Type_Ounit), c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) % 1.68/1.76 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) % 1.68/1.76 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) % 1.68/1.76 % 1.68/1.76 This holds because % 1.68/1.76 % 1.68/1.76 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.68/1.76 % 1.68/1.76 E: % 1.68/1.76 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true__ % 1.68/1.76 c_in(v_x, v_A, t_a) = true__ % 1.68/1.76 f1(c_in(c_Pair(v_x, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))) = true__ % 1.68/1.76 f1(true__) = false__ % 1.68/1.76 f2(true__, V_a, T_a, V_r) = c_in(c_Pair(V_a, V_a, T_a, T_a), V_r, tc_prod(T_a, T_a)) % 1.68/1.76 f3(c_in(V_a, V_A, T_a), V_A, V_r, T_a, V_a) = true__ % 1.68/1.76 f3(true__, V_A, V_r, T_a, V_a) = f2(c_Relation_Orefl(V_A, V_r, T_a), V_a, T_a, V_r) % 1.68/1.76 f4(c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_P, T_a) = true__ % 1.68/1.76 f4(true__, V_P, T_a) = c_Relation_Orefl(c_Tarski_Opotype_Opset(V_P, T_a, tc_Product__Type_Ounit), c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) % 1.68/1.76 v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) % 1.68/1.76 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) % 1.68/1.76 G: % 1.68/1.76 true__ = false__ % 1.68/1.76 % 1.68/1.76 This holds because % 1.68/1.76 % 1.68/1.76 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.68/1.76 % 1.68/1.76 f2(f4(true__, X0, Y2), Y3, Y2, c_Tarski_Opotype_Oorder(X0, Y2, tc_Product__Type_Ounit)) = f3(true__, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), c_Tarski_Opotype_Oorder(X0, Y2, tc_Product__Type_Ounit), Y2, Y3) % 1.68/1.76 f3(true__, v_A, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), t_a, Y2) = f2(true__, Y2, t_a, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)) % 1.68/1.76 c_Relation_Orefl(c_Tarski_Opotype_Opset(V_P, T_a, tc_Product__Type_Ounit), c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a) -> f4(true__, V_P, T_a) % 1.68/1.76 c_Relation_Orefl(v_A, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), t_a) -> f4(true__, v_cl, t_a) % 1.68/1.76 c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) -> v_A % 1.68/1.76 c_in(c_Pair(V_a, V_a, T_a, T_a), V_r, tc_prod(T_a, T_a)) -> f2(true__, V_a, T_a, V_r) % 1.68/1.76 c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) -> true__ % 1.68/1.76 c_in(v_x, v_A, t_a) -> true__ % 1.68/1.76 f1(c_in(c_Pair(v_x, v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))) -> true__ % 1.68/1.76 f1(f2(true__, v_x, t_a, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit))) -> true__ % 1.68/1.76 f1(true__) -> false__ % 1.68/1.76 f2(c_Relation_Orefl(V_A, V_r, T_a), V_a, T_a, V_r) -> f3(true__, V_A, V_r, T_a, V_a) % 1.68/1.76 f2(true__, v_x, t_a, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)) -> true__ % 1.68/1.76 f3(c_in(V_a, V_A, T_a), V_A, V_r, T_a, V_a) -> true__ % 1.68/1.76 f3(f2(true__, X0, X1, Y1), Y1, Y3, tc_prod(X1, X1), c_Pair(X0, X0, X1, X1)) -> true__ % 1.68/1.76 f3(f3(true__, v_A, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), t_a, Y0), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), Y3, tc_prod(t_a, t_a), c_Pair(Y0, Y0, t_a, t_a)) -> true__ % 1.68/1.76 f3(true__, c_Tarski_OPartialOrder, Y3, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), v_cl) -> true__ % 1.68/1.76 f3(true__, c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), Y3, tc_prod(t_a, t_a), c_Pair(v_x, v_x, t_a, t_a)) -> true__ % 1.68/1.76 f3(true__, v_A, Y3, t_a, v_x) -> true__ % 1.68/1.76 f4(c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), V_P, T_a) -> true__ % 1.68/1.76 f4(true__, v_cl, t_a) -> true__ % 1.68/1.76 false__ -> true__ % 1.68/1.76 v_r -> c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) % 1.68/1.76 with the LPO induced by % 1.68/1.76 tc_Tarski_Opotype_Opotype__ext__type > c_Tarski_OPartialOrder > v_r > c_Tarski_Opotype_Opset > v_A > t_a > v_cl > f4 > tc_Product__Type_Ounit > c_Tarski_Opotype_Oorder > c_in > f2 > f3 > c_Relation_Orefl > c_Pair > v_x > tc_prod > f1 > false__ > true__ % 1.68/1.76 % 1.68/1.76 % SZS output end Proof % 1.68/1.76 %------------------------------------------------------------------------------