%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 06:05:41 EDT 2022 % Result : Unsatisfiable 36.82s 36.76s % Output : Proof 36.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0. % 0.06/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n020.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 : Wed Jun 29 19:39:01 EDT 2022 % 0.13/0.34 % CPUTime : % 36.82/36.76 % SZS status Unsatisfiable % 36.82/36.76 % SZS output start Proof % 36.82/36.76 The input problem is unsatisfiable because % 36.82/36.76 % 36.82/36.76 [1] the following set of Horn clauses is unsatisfiable: % 36.82/36.76 % 36.82/36.76 ifeq(A, A, B, C) = B % 36.82/36.76 c_lessequals(v_S, v_A, tc_set(t_a)) = true % 36.82/36.76 c_in(v_x, v_S, t_a) = true % 36.82/36.76 c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true ==> \bottom % 36.82/36.76 v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) % 36.82/36.76 ifeq(c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), tc_set(T_a)), true, ifeq(c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), true, ifeq(c_in(V_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), true, ifeq(c_in(V_x, V_S, T_a), true, c_in(c_Pair(V_x, c_Tarski_Olub(V_S, V_cl, T_a), T_a, T_a), c_Tarski_Opotype_Oorder(V_cl, T_a, tc_Product__Type_Ounit), tc_prod(T_a, T_a)), true), true), true), true) = true % 36.82/36.76 ifeq(c_in(c_Pair(V_x, V_y, T_a, T_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit), tc_prod(T_a, T_a)), true, c_in(c_Pair(V_y, V_x, T_a, T_a), c_Tarski_Opotype_Oorder(V_cl, T_a, tc_Product__Type_Ounit), tc_prod(T_a, T_a)), true) = true % 36.82/36.76 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 % 36.82/36.76 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 % 36.82/36.76 c_Tarski_Oglb(V_S, V_cl, T_a) = c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a) % 36.82/36.76 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) % 36.82/36.76 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) % 36.82/36.76 % 36.82/36.76 This holds because % 36.82/36.76 % 36.82/36.76 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 36.82/36.76 % 36.82/36.76 E: % 36.82/36.76 c_Tarski_Oglb(V_S, V_cl, T_a) = c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a) % 36.82/36.76 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) % 36.82/36.76 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 % 36.82/36.76 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 % 36.82/36.76 c_in(v_x, v_S, t_a) = true % 36.82/36.76 c_lessequals(v_S, v_A, tc_set(t_a)) = true % 36.82/36.76 f1(c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))) = true__ % 36.82/36.76 f1(true) = false__ % 36.82/36.76 ifeq(A, A, B, C) = B % 36.82/36.76 ifeq(c_in(c_Pair(V_x, V_y, T_a, T_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit), tc_prod(T_a, T_a)), true, c_in(c_Pair(V_y, V_x, T_a, T_a), c_Tarski_Opotype_Oorder(V_cl, T_a, tc_Product__Type_Ounit), tc_prod(T_a, T_a)), true) = true % 36.82/36.76 ifeq(c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), tc_set(T_a)), true, ifeq(c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), true, ifeq(c_in(V_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), true, ifeq(c_in(V_x, V_S, T_a), true, c_in(c_Pair(V_x, c_Tarski_Olub(V_S, V_cl, T_a), T_a, T_a), c_Tarski_Opotype_Oorder(V_cl, T_a, tc_Product__Type_Ounit), tc_prod(T_a, T_a)), true), true), true), true) = true % 36.82/36.76 v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) % 36.82/36.76 v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) % 36.82/36.76 G: % 36.82/36.76 true__ = false__ % 36.82/36.76 % 36.82/36.76 This holds because % 36.82/36.76 % 36.82/36.76 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 36.82/36.76 % 36.82/36.76 % 36.82/36.76 c_Tarski_Oglb(V_S, V_cl, T_a) -> c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a) % 36.82/36.76 c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) -> v_r % 36.82/36.76 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) % 36.82/36.76 c_in(c_Pair(c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), v_x, t_a, t_a), v_r, tc_prod(t_a, t_a)) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 c_in(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 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 % 36.82/36.76 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 % 36.82/36.76 c_in(v_x, v_S, t_a) -> true % 36.82/36.76 f1(c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, t_a), v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))) -> true__ % 36.82/36.76 f1(c_in(c_Pair(c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), v_x, t_a, t_a), v_r, tc_prod(t_a, t_a))) -> true__ % 36.82/36.76 f1(c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> false__ % 36.82/36.76 f1(true) -> false__ % 36.82/36.76 ifeq(A, A, B, C) -> B % 36.82/36.76 ifeq(c_in(Y1, v_S, t_a), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y1, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_in(c_Pair(V_x, V_y, T_a, T_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit), tc_prod(T_a, T_a)), true, c_in(c_Pair(V_y, V_x, T_a, T_a), c_Tarski_Opotype_Oorder(V_cl, T_a, tc_Product__Type_Ounit), tc_prod(T_a, T_a)), true) -> true % 36.82/36.76 ifeq(c_in(c_Pair(Y0, Y1, Y2, Y2), c_Tarski_Opotype_Oorder(c_Tarski_Odual(Y3, Y2), Y2, tc_Product__Type_Ounit), tc_prod(Y2, Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y1, Y0, Y2, Y2), c_Tarski_Opotype_Oorder(Y3, Y2, tc_Product__Type_Ounit), tc_prod(Y2, Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_in(c_Pair(Y0, Y1, t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y1, Y0, t_a, t_a), v_r, tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_in(c_Pair(c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), v_x, t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), c_Tarski_OCompleteLattice, 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)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), 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_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), c_Tarski_OCompleteLattice, 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)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), 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_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), c_Tarski_OCompleteLattice, 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)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), 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)), ifeq(c_in(Y3, v_S, t_a), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y3, c_Tarski_Olub(v_S, c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(v_cl, t_a), t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_in(v_cl, c_Tarski_OCompleteLattice, 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)), ifeq(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_Pair(v_x, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_in(v_cl, c_Tarski_OCompleteLattice, 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)), ifeq(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)), ifeq(c_in(Y1, v_S, t_a), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y1, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit), tc_set(T_a)), true, ifeq(c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), true, ifeq(c_in(V_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)), true, ifeq(c_in(V_x, V_S, T_a), true, c_in(c_Pair(V_x, c_Tarski_Olub(V_S, V_cl, T_a), T_a, T_a), c_Tarski_Opotype_Oorder(V_cl, T_a, tc_Product__Type_Ounit), tc_prod(T_a, T_a)), true), true), true), true) -> true % 36.82/36.76 ifeq(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(X0, Y2), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(Y2, tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(X0, Y2), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(Y2, tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y3, Y0, Y2), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y3, c_Tarski_Olub(Y0, c_Tarski_Odual(X0, Y2), Y2), Y2, Y2), c_Tarski_Opotype_Oorder(c_Tarski_Odual(X0, Y2), Y2, tc_Product__Type_Ounit), tc_prod(Y2, Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(Y2, tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(Y2, tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y3, Y0, Y2), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y3, c_Tarski_Olub(Y0, c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2, Y2), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2, tc_Product__Type_Ounit), tc_prod(Y2, Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(Y0, c_Tarski_Opotype_Opset(X0, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(Y2, tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(Y2, tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y3, Y0, Y2), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y3, c_Tarski_Olub(Y0, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2), Y2, Y2), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, Y2), Y2), Y2), Y2, tc_Product__Type_Ounit), tc_prod(Y2, Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(Y0, c_Tarski_Opotype_Opset(Y1, Y2, tc_Product__Type_Ounit), tc_set(Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y1, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(Y2, tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y1, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(Y2, tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y3, Y0, Y2), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y3, c_Tarski_Olub(Y0, Y1, Y2), Y2, Y2), c_Tarski_Opotype_Oorder(Y1, Y2, tc_Product__Type_Ounit), tc_prod(Y2, Y2)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(Y0, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y3, Y0, t_a), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y3, c_Tarski_Olub(Y0, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(Y0, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(v_cl, c_Tarski_OCompleteLattice, 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)), ifeq(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)), ifeq(c_in(Y3, Y0, t_a), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_in(c_Pair(Y3, c_Tarski_Olub(Y0, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(c_Tarski_OCompleteLattice, c_Tarski_Opotype_Opset(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_set(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)), ifeq(c_in(Y1, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y1, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_Pair(c_Tarski_Odual(v_cl, t_a), c_Tarski_Olub(c_Tarski_OCompleteLattice, Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_Opotype_Oorder(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_prod(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(c_Tarski_OCompleteLattice, c_Tarski_Opotype_Opset(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_set(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)), ifeq(c_in(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_Pair(c_Tarski_Odual(v_cl, t_a), c_Tarski_Olub(c_Tarski_OCompleteLattice, c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_Opotype_Oorder(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_prod(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(c_Tarski_OCompleteLattice, c_Tarski_Opotype_Opset(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_set(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)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_Pair(c_Tarski_Odual(v_cl, t_a), c_Tarski_Olub(c_Tarski_OCompleteLattice, c_Tarski_Odual(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_prod(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(c_Tarski_OPartialOrder, c_Tarski_Opotype_Opset(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_set(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)), ifeq(c_in(Y1, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y1, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_Pair(c_Tarski_Odual(v_cl, t_a), c_Tarski_Olub(c_Tarski_OPartialOrder, Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_Opotype_Oorder(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_prod(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(c_Tarski_OPartialOrder, c_Tarski_Opotype_Opset(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_set(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)), ifeq(c_in(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_Pair(c_Tarski_Odual(v_cl, t_a), c_Tarski_Olub(c_Tarski_OPartialOrder, c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_Opotype_Oorder(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_prod(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(c_Tarski_OPartialOrder, c_Tarski_Opotype_Opset(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_set(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)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_Pair(c_Tarski_Odual(v_cl, t_a), c_Tarski_Olub(c_Tarski_OPartialOrder, c_Tarski_Odual(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(Y1, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), tc_Product__Type_Ounit), tc_prod(tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit), 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_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), c_Tarski_Opotype_Opset(X0, tc_prod(t_a, t_a), tc_Product__Type_Ounit), tc_set(tc_prod(t_a, t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(X0, tc_prod(t_a, t_a)), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(tc_prod(t_a, 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)), ifeq(c_in(c_Tarski_Odual(X0, tc_prod(t_a, t_a)), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(tc_prod(t_a, 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_Pair(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Olub(c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), c_Tarski_Odual(X0, tc_prod(t_a, t_a)), tc_prod(t_a, t_a)), tc_prod(t_a, t_a), tc_prod(t_a, t_a)), c_Tarski_Opotype_Oorder(c_Tarski_Odual(X0, tc_prod(t_a, t_a)), tc_prod(t_a, t_a), tc_Product__Type_Ounit), tc_prod(tc_prod(t_a, t_a), tc_prod(t_a, t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), c_Tarski_Opotype_Opset(Y1, tc_prod(t_a, t_a), tc_Product__Type_Ounit), tc_set(tc_prod(t_a, t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y1, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(tc_prod(t_a, 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)), ifeq(c_in(Y1, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(tc_prod(t_a, 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_Pair(c_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, t_a), c_Tarski_Olub(c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl, t_a), t_a, tc_Product__Type_Ounit), Y1, tc_prod(t_a, t_a)), tc_prod(t_a, t_a), tc_prod(t_a, t_a)), c_Tarski_Opotype_Oorder(Y1, tc_prod(t_a, t_a), tc_Product__Type_Ounit), tc_prod(tc_prod(t_a, t_a), tc_prod(t_a, t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(v_S, c_Tarski_Opotype_Opset(X0, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), c_Tarski_OCompleteLattice, 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)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), 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_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(v_S, c_Tarski_Opotype_Opset(X0, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a), c_Tarski_OCompleteLattice, 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)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a), 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_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(v_S, c_Tarski_Opotype_Opset(X0, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a), t_a), c_Tarski_OCompleteLattice, 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)), ifeq(c_in(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a), t_a), 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_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a), t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(c_Tarski_Odual(X0, t_a), t_a), t_a), t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.76 ifeq(c_lessequals(v_S, c_Tarski_Opotype_Opset(Y1, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y1, c_Tarski_OCompleteLattice, 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)), ifeq(c_in(Y1, 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_Pair(v_x, c_Tarski_Olub(v_S, Y1, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(Y1, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.77 ifeq(c_lessequals(v_S, c_Tarski_Opotype_Opset(Y1, t_a, tc_Product__Type_Ounit), tc_set(t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(c_Tarski_Odual(Y1, t_a), c_Tarski_OCompleteLattice, 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)), ifeq(c_in(c_Tarski_Odual(Y1, t_a), 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_Pair(v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(Y1, t_a), t_a), t_a, t_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(Y1, t_a), t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.77 ifeq(c_lessequals(v_r, c_Tarski_Opotype_Opset(Y1, tc_prod(t_a, t_a), tc_Product__Type_Ounit), tc_set(tc_prod(t_a, t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), ifeq(c_in(Y1, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(tc_prod(t_a, 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)), ifeq(c_in(Y1, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(tc_prod(t_a, 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_Pair(c_Pair(c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), v_x, t_a, t_a), c_Tarski_Olub(v_r, Y1, tc_prod(t_a, t_a)), tc_prod(t_a, t_a), tc_prod(t_a, t_a)), c_Tarski_Opotype_Oorder(Y1, tc_prod(t_a, t_a), tc_Product__Type_Ounit), tc_prod(tc_prod(t_a, t_a), tc_prod(t_a, t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) -> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) % 36.82/36.77 true -> c_lessequals(v_S, v_A, tc_set(t_a)) % 36.82/36.77 true__ -> false__ % 36.82/36.77 v_A -> c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) % 36.82/36.77 with the LPO induced by % 36.82/36.77 c_Tarski_Opotype_Oorder > v_r > c_Tarski_OPartialOrder > c_Tarski_OCompleteLattice > v_x > true > tc_set > c_lessequals > v_A > c_Tarski_Opotype_Opset > v_cl > c_Tarski_Oglb > c_Tarski_Odual > c_Tarski_Olub > t_a > tc_Tarski_Opotype_Opotype__ext__type > tc_Product__Type_Ounit > tc_prod > c_Pair > f1 > c_in > v_S > ifeq > true__ > false__ % 36.82/36.77 % 36.82/36.77 % SZS output end Proof % 36.82/36.77 %------------------------------------------------------------------------------