0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : run_Leo-III %s %d 0.11/0.31 % Computer : n011.cluster.edu 0.11/0.31 % Model : x86_64 x86_64 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.31 % Memory : 8042.1875MB 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.31 % CPULimit : 960 0.11/0.31 % WCLimit : 120 0.11/0.31 % DateTime : Tue Aug 9 05:33:51 EDT 2022 0.11/0.31 % CPUTime : 0.91/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 1.71/1.29 % [INFO] Parsing done (397ms). 1.71/1.30 % [INFO] Running in sequential loop mode. 2.59/1.64 % [INFO] eprover registered as external prover. 2.59/1.64 % [INFO] cvc4 registered as external prover. 2.59/1.65 % [INFO] Scanning for conjecture ... 2.88/1.80 % [INFO] Found a conjecture and 273 axioms. Running axiom selection ... 3.47/1.96 % [INFO] Axiom selection finished. Selected 273 axioms (removed 0 axioms). 4.10/2.23 % [INFO] Problem is higher-order (TPTP THF). 4.31/2.28 % [INFO] Type checking passed. 4.31/2.29 % [CONFIG] Using configuration: timeout(120) with strategy. Searching for refutation ... 21.18/7.46 % External prover 'cvc4' found a proof! 21.18/7.46 % [INFO] Killing All external provers ... 21.18/7.46 % Time passed: 7038ms (effective reasoning time: 6155ms) 21.18/7.46 % Solved by strategy 21.18/7.47 % Axioms used in derivation (273): fact_172_Graph_Omin__distI__eq, fact_80_ab__semigroup__add__class_Oadd__ac_I1_J, fact_37_le__trans, fact_22_isPath__distD, fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062, fact_142_Graph_OisShortestPath__alt, fact_229_dual__order_Oeq__iff, fact_124_Graph_Omin__dist__is__dist, fact_79_add__mono__thms__linordered__semiring_I4_J, fact_227_linorder__wlog, fact_42_add__le__imp__le__right, fact_36_le__refl, fact_30_add__le__cancel__right, fact_77_group__cancel_Oadd2, fact_6__C1_Oprems_C_I2_J, fact_258_neqE, fact_198_g_H_Omin__dist__def, fact_18_obtain__shortest__path, fact_168_Graph_Omin__dist__less, fact_170_Graph_Omin__dist__le, fact_146_Graph_Omin__dist_Ocong, fact_271_dual__order_Oorder__iff__strict, fact_268_order_Onot__eq__order__implies__strict, fact_221_order__class_Oorder_Oeq__iff, fact_251_less__linear, fact_29__092_060open_062connected_As_Au_092_060close_062, fact_3_nat__add__left__cancel__less, fact_269_dual__order_Ostrict__implies__order, fact_66_le__Suc__ex, fact_127_Graph_Omin__dist__split_I1_J, fact_157_Graph_Odist__trans, fact_50_add__left__mono, fact_93_add__mono__thms__linordered__field_I4_J, fact_112_min__dist__def, fact_71_add__leE, fact_11_add__left__cancel, fact_115_Graph_OisShortestPath__def, fact_95_add__less__imp__less__right, fact_234_dual__order_Ostrict__trans, fact_214_antisym, fact_74_add_Oleft__commute, fact_215_linear, fact_68_add__leD1, fact_184_g_H_OshortestPath__is__simple, fact_134_Graph_OisSPath__pathLE, fact_118_Graph_Omin__distI2, fact_149_Graph_Oconnected__refl, fact_262_ord__less__eq__subst, fact_106_add__less__mono1, fact_140_Graph_Omin__dist__def, fact_200_g_H_OisPath__distD, fact_223_ord__le__eq__trans, fact_97_add__strict__right__mono, fact_180_Least__le, fact_104_trans__less__add2, fact_49_less__eqE, fact_14_dist__trans, fact_150_Graph_Oconnected_Ocong, fact_108_not__add__less1, fact_8_min__dist__split_I2_J, fact_110_add__lessD1, fact_92_add__mono__thms__linordered__field_I3_J, fact_190_g_H_Omin__dist__minD, fact_246_less__imp__not__eq, fact_130_Graph_OreachableNodes_Ocong, fact_117_Graph_Omin__distI2, fact_33_P1, fact_87_less__not__refl, fact_167_Graph_Oobtain__shortest__path, fact_105_trans__less__add1, fact_114_Graph_OisShortestPath__min__dist__def, fact_60_nat__less__le, fact_169_Graph_Omin__dist__less, fact_94_mono__nat__linear__lb, fact_185_g_H_OreachableNodes__def, fact_84_less__irrefl__nat, fact_107_not__add__less2, fact_186_g_H_Omin__dist__less, fact_52_add__mono__thms__linordered__semiring_I1_J, fact_203_g_H_OisShortestPath__def, fact_56_le__neq__implies__less, fact_178__C1_Oprems_C_I3_J, fact_244_less__induct, fact_183_g_H_Oobtain__shortest__path, fact_211_ord__eq__le__subst, fact_236_exists__least__iff, fact_171_Graph_Omin__dist__le, fact_191_g_H_Omin__dist__split_I2_J, fact_23_dist__def, fact_96_add__less__imp__less__left, fact_90_add__less__le__mono, fact_125_Graph_Omin__dist__is__dist, fact_254_less__asym, fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062, fact_272_order_Ostrict__implies__order, fact_151_Graph_Oconnected_Ocong, fact_131_Graph_OreachableNodes_Ocong, fact_135_Graph_OisSPath__pathLE, fact_250_less__irrefl, fact_69_le__add2, fact_205__092_060open_062g_H_OisPath_Au_____Ap2_H_____At_092_060close_062, fact_41_Nat_Oex__has__greatest__nat, fact_152_Graph_Odist_Ocong, fact_46_Collect__mem__eq, fact_165_Graph_Oconnected__distI, fact_13__092_060open_062isPath_Au_Ap2_H_At_092_060close_062, fact_255_less__imp__neq, fact_109_add__less__mono, fact_55_less__mono__imp__le__mono, fact_72_add__right__imp__eq, fact_88_nat__neq__iff, fact_240_linorder__cases, fact_31_add__le__cancel__left, fact_164_Graph_Oconnected__distI, fact_133_Graph_OisSimplePath_Ocong, fact_225_order__trans, fact_62_trans__le__add2, fact_162_Graph_Oconnected__by__dist, fact_85_less__not__refl3, fact_195_g_H_OisSPath__pathLE, fact_179_not__less__Least, fact_81_linorder__neqE__nat, fact_76_add_Oassoc, fact_256_order_Oasym, fact_34_connected__refl, fact_245_less__not__sym, fact_182_g_H_Omin__dist__is__dist, fact_181_g_H_Oconnected__by__dist, fact_91_add__le__less__mono, fact_120_Graph_Odist__def, fact_228_dual__order_Otrans, fact_216_eq__refl, fact_202_order__refl, fact_148_Graph_Oconnected__refl, fact_261_order__less__subst1, fact_86_less__not__refl2, fact_158_Graph_Oconnected__def, fact_192_g_H_Omin__dist__split_I1_J, fact_243_antisym__conv3, fact_32_nat__add__left__cancel__le, fact_210_order__subst2, fact_99_add__strict__mono, fact_61_nat__le__iff__add, fact_231_dual__order_Ostrict__implies__not__eq, fact_98_add__strict__left__mono, fact_173_Graph_Omin__distI__eq, fact_206_g_H_Oconnected__distI, fact_270_dual__order_Ostrict__iff__order, fact_45_mem__Collect__eq, fact_73_add__left__imp__eq, fact_154_Graph_OisShortestPath_Ocong, fact_132_Graph_OisSimplePath_Ocong, fact_20_min__dist__minD, fact_4_add__less__cancel__left, fact_116_Graph_OisShortestPath__def, fact_103_less__add__eq__less, fact_51_add__mono, fact_64_add__le__mono1, fact_267_LeastI, fact_239_dual__order_Oirrefl, fact_226_dual__order_Orefl, fact_238_order_Ostrict__trans, fact_189_g_H_Omin__dist__le, fact_144_Graph_OisPath_Ocong, fact_137_Graph_OshortestPath__is__simple, fact_57_less__or__eq__imp__le, fact_242_less__imp__not__eq2, fact_197_g_H_OisShortestPath__alt, fact_208_P2_H, fact_204_assms_I5_J, fact_47_Collect__cong, fact_253_less__asym_H, fact_156_Graph_Odist__trans, fact_166_Graph_Oobtain__shortest__path, fact_16_shortestPath__is__path, fact_5_add__less__cancel__right, fact_175_Graph_Omin__dist__minD, fact_237_less__imp__not__less, fact_141_Graph_Omin__dist__def, fact_128_isSPath__pathLE, fact_143_Graph_OisShortestPath__alt, fact_75_add_Ocommute, fact_123_Graph_OisPath__distD, fact_59_less__imp__le__nat, fact_83_nat__less__induct, fact_27_min__distI2, fact_230_dual__order_Oantisym, fact_257_neq__iff, fact_122_Graph_OisPath__distD, fact_136_Graph_OshortestPath__is__simple, fact_266_LeastI2__ex, fact_247_dual__order_Oasym, fact_89_size__neq__size__imp__neq, fact_241_less__imp__triv, fact_264_LeastI2, fact_217_le__cases, fact_7_SP, fact_161_Graph_OshortestPath__is__path, fact_201_g_H_OisShortestPath__min__dist__def, fact_252_less__trans, fact_38_eq__imp__le, fact_194_g_H_Oconnected__def, fact_259_gt__ex, fact_39_le__antisym, fact_160_Graph_OshortestPath__is__path, fact_63_trans__le__add1, fact_220_antisym__conv, fact_67_add__leD2, fact_58_le__eq__less__or__eq, fact_213_eq__iff, fact_65_add__le__mono, fact_222_ord__eq__le__trans, fact_78_group__cancel_Oadd1, fact_19_min__dist__le, fact_249_ord__eq__less__trans, fact_163_Graph_Oconnected__by__dist, fact_224_order__class_Oorder_Oantisym, fact_196_g_H_OshortestPath__is__path, fact_176_Graph_Omin__dist__split_I2_J, fact_232_order_Ostrict__implies__not__eq, fact_119_isShortestPath__alt, fact_15_connected__def, fact_145_Graph_OisPath_Ocong, fact_129_shortestPath__is__simple, fact_219_le__cases3, fact_153_Graph_Odist_Ocong, fact_17_connected__by__dist, fact_25_min__dist__is__dist, fact_44_le__iff__add, fact_193_g_H_Odist__trans, fact_147_Graph_Omin__dist_Ocong, fact_121_Graph_Odist__def, fact_188_g_H_Omin__distI__eq, fact_101_add__mono__thms__linordered__field_I2_J, fact_48_add__right__mono, fact_174_Graph_Omin__dist__minD, fact_24__092_060open_062isPath_As_Ap1_____Av_____092_060close_062, fact_199_g_H_Odist__def, fact_155_Graph_OisShortestPath_Ocong, fact_218_order_Otrans, fact_21_min__distI__eq, fact_159_Graph_Oconnected__def, fact_111_reachableNodes__def, fact_138_Graph_OreachableNodes__def, fact_26_isShortestPath__def, fact_139_Graph_OreachableNodes__def, fact_82_infinite__descent, fact_207_g_H_Oconnected__refl, fact_177_Graph_Omin__dist__split_I2_J, fact_43_add__le__imp__le__left, fact_263_ord__eq__less__subst, fact_10_min__dist__less, fact_54_add__mono__thms__linordered__semiring_I3_J, fact_212_ord__le__eq__subst, fact_53_add__mono__thms__linordered__semiring_I2_J, fact_28_isShortestPath__min__dist__def, fact_235_linorder__less__wlog, fact_35_connected__distI, fact_248_ord__less__eq__trans, fact_9_min__dist__split_I1_J, fact_260_order__less__subst2, fact_102_add__mono__thms__linordered__field_I5_J, fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062, fact_233_not__less__iff__gr__or__eq, fact_265_LeastI__ex, fact_40_nat__le__linear, fact_70_le__add1, fact_113_Graph_OisShortestPath__min__dist__def, fact_12_add__right__cancel, fact_126_Graph_Omin__dist__split_I1_J, fact_209_order__subst1, fact_187_g_H_Omin__distI2, fact_100_add__mono__thms__linordered__field_I1_J 21.18/7.47 % No. of inferences in proof: 550 21.18/7.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7038 ms resp. 6155 ms w/o parsing 22.82/7.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 22.82/7.91 thf(list_P559422087at_nat_type, type, list_P559422087at_nat: $tType). 22.82/7.91 thf(product_prod_nat_nat_type, type, product_prod_nat_nat: $tType). 22.82/7.91 thf(set_nat_type, type, set_nat: $tType). 22.82/7.91 thf(capacity_type, type, capacity: $tType). 22.82/7.91 thf(nat_type, type, nat: $tType). 22.82/7.91 thf(a_type, type, a: $tType). 22.82/7.91 thf(connected_a_type, type, connected_a: ((product_prod_nat_nat > a) > (nat > (nat > $o)))). 22.82/7.91 thf(connected_capacity_type, type, connected_capacity: ((product_prod_nat_nat > capacity) > (nat > (nat > $o)))). 22.82/7.91 thf(dist_a_type, type, dist_a: ((product_prod_nat_nat > a) > (nat > (nat > (nat > $o))))). 22.82/7.91 thf(dist_capacity_type, type, dist_capacity: ((product_prod_nat_nat > capacity) > (nat > (nat > (nat > $o))))). 22.82/7.91 thf(isPath_a_type, type, isPath_a: ((product_prod_nat_nat > a) > (nat > (list_P559422087at_nat > (nat > $o))))). 22.82/7.91 thf(isPath_capacity_type, type, isPath_capacity: ((product_prod_nat_nat > capacity) > (nat > (list_P559422087at_nat > (nat > $o))))). 22.82/7.91 thf(isShortestPath_a_type, type, isShortestPath_a: ((product_prod_nat_nat > a) > (nat > (list_P559422087at_nat > (nat > $o))))). 22.82/7.91 thf(isShor1936442771pacity_type, type, isShor1936442771pacity: ((product_prod_nat_nat > capacity) > (nat > (list_P559422087at_nat > (nat > $o))))). 22.82/7.91 thf(isSimplePath_a_type, type, isSimplePath_a: ((product_prod_nat_nat > a) > (nat > (list_P559422087at_nat > (nat > $o))))). 22.82/7.91 thf(isSimp1359852763pacity_type, type, isSimp1359852763pacity: ((product_prod_nat_nat > capacity) > (nat > (list_P559422087at_nat > (nat > $o))))). 22.82/7.91 thf(min_dist_a_type, type, min_dist_a: ((product_prod_nat_nat > a) > (nat > (nat > nat)))). 22.82/7.91 thf(min_dist_capacity_type, type, min_dist_capacity: ((product_prod_nat_nat > capacity) > (nat > (nat > nat)))). 22.82/7.91 thf(reachableNodes_a_type, type, reachableNodes_a: ((product_prod_nat_nat > a) > (nat > set_nat))). 22.82/7.91 thf(reacha1693770334pacity_type, type, reacha1693770334pacity: ((product_prod_nat_nat > capacity) > (nat > set_nat))). 22.82/7.91 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 22.82/7.91 thf(size_s1990949619at_nat_type, type, size_s1990949619at_nat: (list_P559422087at_nat > nat)). 22.82/7.91 thf(ord_Least_nat_type, type, ord_Least_nat: ((nat > $o) > nat)). 22.82/7.91 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 22.82/7.91 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 22.82/7.91 thf(collect_nat_type, type, collect_nat: ((nat > $o) > set_nat)). 22.82/7.91 thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))). 22.82/7.91 thf(c_type, type, c: (product_prod_nat_nat > capacity)). 22.82/7.91 thf(c2_type, type, c2: (product_prod_nat_nat > a)). 22.82/7.91 thf(p_type, type, p: list_P559422087at_nat). 22.82/7.91 thf(p1_type, type, p1: list_P559422087at_nat). 22.82/7.91 thf(p1a_type, type, p1a: list_P559422087at_nat). 22.82/7.91 thf(p2_type, type, p2: list_P559422087at_nat). 22.82/7.91 thf(p2_a_type, type, p2_a: list_P559422087at_nat). 22.82/7.91 thf(p3_type, type, p3: list_P559422087at_nat). 22.82/7.91 thf(s_type, type, s: nat). 22.82/7.91 thf(t_type, type, t: nat). 22.82/7.91 thf(u_type, type, u: nat). 22.82/7.91 thf(ua_type, type, ua: nat). 22.82/7.91 thf(v_type, type, v: nat). 22.82/7.91 thf(va_type, type, va: nat). 22.82/7.91 thf(258,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_linorder__neqE__nat)). 22.82/7.91 thf(1036,plain,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 22.82/7.91 thf(171,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_nat__neq__iff)). 22.82/7.91 thf(760,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 22.82/7.91 thf(219,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__add2)). 22.82/7.91 thf(909,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 22.82/7.91 thf(214,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_antisym__conv3)). 22.82/7.91 thf(893,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 22.82/7.91 thf(87,axiom,((! [A:nat,B:nat,C:nat]: (((! [D:nat]: ((dist_a @ c2 @ A @ D @ C) => (ord_less_eq_nat @ B @ D))) => ((min_dist_a @ c2 @ A @ C) = B)) <= (dist_a @ c2 @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_g_H_Omin__distI__eq)). 22.82/7.91 thf(518,plain,((! [A:nat,B:nat,C:nat]: (((! [D:nat]: ((dist_a @ (c2) @ A @ D @ C) => (ord_less_eq_nat @ B @ D))) => ((min_dist_a @ (c2) @ A @ C) = B)) | ~ (dist_a @ (c2) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 22.82/7.91 thf(137,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_le__eq__less__or__eq)). 22.82/7.91 thf(666,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 22.82/7.91 thf(74,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: ((dist_a @ A @ B @ (min_dist_a @ A @ B @ C) @ C) <= (connected_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Graph_Omin__dist__is__dist)). 22.82/7.91 thf(481,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: ((dist_a @ (A) @ B @ (min_dist_a @ (A) @ B @ C) @ C) | ~ (connected_a @ (A) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 22.82/7.91 thf(271,axiom,((! [A:nat,B:(nat > $o)]: ((ord_less_nat @ A @ (ord_Least_nat @ B)) => (~ (B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_not__less__Least)). 22.82/7.91 thf(1083,plain,((! [A:nat,B:(nat > $o)]: ((ord_less_nat @ A @ (ord_Least_nat @ (B))) => (~ (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 22.82/7.91 thf(237,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_add__le__mono)). 22.82/7.91 thf(962,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 22.82/7.91 thf(14,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => (ord_less_eq_nat @ (ord_Least_nat @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Least__le)). 22.82/7.91 thf(308,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => (ord_less_eq_nat @ (ord_Least_nat @ (A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 22.82/7.91 thf(268,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_group__cancel_Oadd1)). 22.82/7.91 thf(1073,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 22.82/7.91 thf(64,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_order__trans)). 22.82/7.91 thf(449,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 22.82/7.91 thf(203,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((((min_dist_capacity @ c @ C @ E) = D) <= ((min_dist_capacity @ c @ A @ E) = (plus_plus_nat @ B @ D))) <= (dist_capacity @ c @ C @ D @ E)) <= (dist_capacity @ c @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_min__dist__split_I2_J)). 22.82/7.91 thf(861,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((min_dist_capacity @ (c) @ C @ E) = D) | ~ ((min_dist_capacity @ (c) @ A @ E) = (plus_plus_nat @ B @ D)) | ~ (dist_capacity @ (c) @ C @ D @ E) | ~ (dist_capacity @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 22.82/7.91 thf(88,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_le__cases)). 22.82/7.91 thf(523,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 22.82/7.91 thf(110,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__le__less__mono)). 22.82/7.91 thf(582,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 22.82/7.91 thf(160,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_capacity @ c @ A @ B @ C) => (dist_capacity @ c @ A @ (size_s1990949619at_nat @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_isPath__distD)). 22.82/7.91 thf(730,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_capacity @ (c) @ A @ B @ C) => (dist_capacity @ (c) @ A @ (size_s1990949619at_nat @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 22.82/7.91 thf(1,conjecture,((ord_less_nat @ (min_dist_capacity @ c @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)). 22.82/7.91 thf(2,negated_conjecture,((~ (ord_less_nat @ (min_dist_capacity @ c @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))))),inference(neg_conjecture,[status(cth)],[1])). 22.82/7.91 thf(276,plain,((~ (ord_less_nat @ (min_dist_capacity @ (c) @ s @ t) @ (plus_plus_nat @ (size_s1990949619at_nat @ p1a) @ (size_s1990949619at_nat @ p2_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 22.82/7.91 thf(60,axiom,((! [A:nat,B:nat,C:nat]: ((dist_a @ c2 @ A @ B @ C) => (connected_a @ c2 @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_g_H_Oconnected__distI)). 22.82/7.91 thf(440,plain,((! [A:nat,B:nat,C:nat]: ((dist_a @ (c2) @ A @ B @ C) => (connected_a @ (c2) @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 22.82/7.91 thf(134,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))) <= (~ (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_infinite__descent)). 22.82/7.91 thf(655,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)) | (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 22.82/7.91 thf(269,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_dual__order_Oasym)). 22.82/7.91 thf(1078,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 22.82/7.91 thf(153,axiom,((isShor1936442771pacity = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: (((size_s1990949619at_nat @ C) = (min_dist_capacity @ A @ B @ D)) & (isSimp1359852763pacity @ A @ B @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Graph_OisShortestPath__alt)). 22.82/7.91 thf(715,plain,(((isShor1936442771pacity) = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: (((size_s1990949619at_nat @ C) = (min_dist_capacity @ A @ B @ D)) & (isSimp1359852763pacity @ A @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 22.82/7.91 thf(71,axiom,((! [A:nat,B:nat]: ((connected_a @ c2 @ A @ B) = (? [C:list_P559422087at_nat]: (isPath_a @ c2 @ A @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_g_H_Oconnected__def)). 22.82/7.91 thf(472,plain,((! [A:nat,B:nat]: ((connected_a @ (c2) @ A @ B) = (? [C:list_P559422087at_nat]: (isPath_a @ (c2) @ A @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 22.82/7.91 thf(28,axiom,((isShor1936442771pacity = isShor1936442771pacity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Graph_OisShortestPath_Ocong)). 22.82/7.91 thf(340,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 22.82/7.91 thf(193,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__add1)). 22.82/7.91 thf(829,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 22.82/7.91 thf(177,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) <= (ord_less_nat @ (C @ B) @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_order__less__subst2)). 22.82/7.91 thf(782,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: (((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) | ~ (ord_less_nat @ (C @ B) @ D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 22.82/7.91 thf(52,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_linear)). 22.82/7.91 thf(417,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 22.82/7.91 thf(241,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add_Ocommute)). 22.82/7.91 thf(973,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 22.82/7.91 thf(42,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: ((isSimplePath_a @ A @ B @ C @ D) <= (isShortestPath_a @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Graph_OshortestPath__is__simple)). 22.82/7.91 thf(389,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: ((isSimplePath_a @ (A) @ B @ C @ D) | ~ (isShortestPath_a @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 22.82/7.91 thf(158,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((connected_capacity @ c @ A @ B) => ((! [D:nat]: ((dist_capacity @ c @ A @ D @ B) => ((C @ D) <= (! [E:nat]: ((ord_less_eq_nat @ D @ E) <= (dist_capacity @ c @ A @ E @ B)))))) => (C @ (min_dist_capacity @ c @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_min__distI2)). 22.82/7.91 thf(724,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((connected_capacity @ (c) @ A @ B) => ((! [D:nat]: ((dist_capacity @ (c) @ A @ D @ B) => ((C @ D) | ~ (! [E:nat]: ((ord_less_eq_nat @ D @ E) | ~ (dist_capacity @ (c) @ A @ E @ B)))))) => (C @ (min_dist_capacity @ (c) @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 22.82/7.91 thf(36,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: ((? [E:list_P559422087at_nat]: (isSimplePath_a @ A @ B @ E @ D)) <= (isPath_a @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Graph_OisSPath__pathLE)). 22.82/7.91 thf(372,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: (? [E:list_P559422087at_nat]: (isSimplePath_a @ (A) @ B @ E @ D) | ~ (isPath_a @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 22.82/7.91 thf(34,axiom,((isPath_a = isPath_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Graph_OisPath_Ocong)). 22.82/7.91 thf(357,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 22.82/7.91 thf(265,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_less__imp__le__nat)). 22.82/7.91 thf(1059,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 22.82/7.91 thf(234,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_not__less__iff__gr__or__eq)). 22.82/7.91 thf(949,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 22.82/7.91 thf(222,axiom,((! [A:nat,B:nat]: ((connected_capacity @ c @ A @ B) => (dist_capacity @ c @ A @ (min_dist_capacity @ c @ A @ B) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_min__dist__is__dist)). 22.82/7.91 thf(917,plain,((! [A:nat,B:nat]: ((connected_capacity @ (c) @ A @ B) => (dist_capacity @ (c) @ A @ (min_dist_capacity @ (c) @ A @ B) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 22.82/7.91 thf(168,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat,E:nat,F:nat]: ((dist_a @ A @ B @ C @ D) => ((dist_a @ A @ D @ E @ F) => (dist_a @ A @ B @ (plus_plus_nat @ C @ E) @ F))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Graph_Odist__trans)). 22.82/7.91 thf(751,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat,E:nat,F:nat]: ((dist_a @ (A) @ B @ C @ D) => ((dist_a @ (A) @ D @ E @ F) => (dist_a @ (A) @ B @ (plus_plus_nat @ C @ E) @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 22.82/7.91 thf(96,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: (((! [E:nat]: ((ord_less_eq_nat @ C @ E) <= (dist_capacity @ A @ B @ E @ D))) => ((min_dist_capacity @ A @ B @ D) = C)) <= (dist_capacity @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Graph_Omin__distI__eq)). 22.82/7.91 thf(542,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: (((! [E:nat]: ((ord_less_eq_nat @ C @ E) | ~ (dist_capacity @ (A) @ B @ E @ D))) => ((min_dist_capacity @ (A) @ B @ D) = C)) | ~ (dist_capacity @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 22.82/7.91 thf(68,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_le__trans)). 22.82/7.91 thf(460,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 22.82/7.91 thf(217,axiom,((! [A:nat,B:nat]: ((min_dist_capacity @ c @ A @ B) = (ord_Least_nat @ (^ [C:nat]: (dist_capacity @ c @ A @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_min__dist__def)). 22.82/7.91 thf(902,plain,((! [A:nat,B:nat]: ((min_dist_capacity @ (c) @ A @ B) = (ord_Least_nat @ (^ [C:nat]: (dist_capacity @ c @ A @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 22.82/7.91 thf(54,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_order__subst2)). 22.82/7.91 thf(421,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 22.82/7.91 thf(118,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_less__asym_H)). 22.82/7.91 thf(606,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 22.82/7.91 thf(209,axiom,((isShortestPath_a = (^ [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: ((isPath_a @ A @ B @ C @ D) & ! [E:list_P559422087at_nat]: ((isPath_a @ A @ B @ E @ D) => (ord_less_eq_nat @ (size_s1990949619at_nat @ C) @ (size_s1990949619at_nat @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Graph_OisShortestPath__def)). 22.82/7.91 thf(881,plain,(((isShortestPath_a) = (^ [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: ((isPath_a @ A @ B @ C @ D) & ! [E:list_P559422087at_nat]: ((isPath_a @ A @ B @ E @ D) => (ord_less_eq_nat @ (size_s1990949619at_nat @ C) @ (size_s1990949619at_nat @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 22.82/7.91 thf(7,axiom,((! [A:nat,B:nat]: ((min_dist_a @ c2 @ A @ B) = (ord_Least_nat @ (^ [C:nat]: (dist_a @ c2 @ A @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_g_H_Omin__dist__def)). 22.82/7.91 thf(289,plain,((! [A:nat,B:nat]: ((min_dist_a @ (c2) @ A @ B) = (ord_Least_nat @ (^ [C:nat]: (dist_a @ c2 @ A @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 22.82/7.91 thf(72,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((connected_a @ c2 @ A @ B) => ((C @ (min_dist_a @ c2 @ A @ B)) <= (! [D:nat]: (((! [E:nat]: ((ord_less_eq_nat @ D @ E) <= (dist_a @ c2 @ A @ E @ B))) => (C @ D)) <= (dist_a @ c2 @ A @ D @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_g_H_Omin__distI2)). 22.82/7.91 thf(475,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((connected_a @ (c2) @ A @ B) => ((C @ (min_dist_a @ (c2) @ A @ B)) | ~ (! [D:nat]: (((! [E:nat]: ((ord_less_eq_nat @ D @ E) | ~ (dist_a @ (c2) @ A @ E @ B))) => (C @ D)) | ~ (dist_a @ (c2) @ A @ D @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 22.82/7.91 thf(113,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_less__linear)). 22.82/7.91 thf(591,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 22.82/7.91 thf(21,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((isPath_capacity @ A @ B @ C @ D) => (? [E:list_P559422087at_nat]: (isSimp1359852763pacity @ A @ B @ E @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Graph_OisSPath__pathLE)). 22.82/7.91 thf(321,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((isPath_capacity @ (A) @ B @ C @ D) => (? [E:list_P559422087at_nat]: (isSimp1359852763pacity @ (A) @ B @ E @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 22.82/7.91 thf(38,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_nat__le__linear)). 22.82/7.91 thf(376,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 22.82/7.91 thf(125,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__less__le__mono)). 22.82/7.91 thf(623,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 22.82/7.91 thf(229,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ C @ D) & (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__mono__thms__linordered__field_I3_J)). 22.82/7.91 thf(937,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ C @ D) & (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 22.82/7.91 thf(107,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_less__not__sym)). 22.82/7.91 thf(574,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 22.82/7.91 thf(263,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__strict__right__mono)). 22.82/7.91 thf(1051,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 22.82/7.91 thf(218,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) & (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__mono__thms__linordered__semiring_I3_J)). 22.82/7.91 thf(905,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) & (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 22.82/7.91 thf(73,axiom,((isShortestPath_a = isShortestPath_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Graph_OisShortestPath_Ocong)). 22.82/7.91 thf(480,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 22.82/7.91 thf(143,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_add__less__cancel__left)). 22.82/7.91 thf(687,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 22.82/7.91 thf(208,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_less__imp__not__eq)). 22.82/7.91 thf(877,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 22.82/7.91 thf(44,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_eq__imp__le)). 22.82/7.91 thf(396,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 22.82/7.91 thf(251,axiom,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_ord__less__eq__trans)). 22.82/7.91 thf(998,plain,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 22.82/7.91 thf(247,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_order_Ostrict__implies__order)). 22.82/7.91 thf(988,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 22.82/7.91 thf(199,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_less__or__eq__imp__le)). 22.82/7.91 thf(849,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 22.82/7.91 thf(90,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((isPath_capacity @ A @ B @ C @ D) <= (isShor1936442771pacity @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Graph_OshortestPath__is__path)). 22.82/7.91 thf(527,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((isPath_capacity @ (A) @ B @ C @ D) | ~ (isShor1936442771pacity @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 22.82/7.91 thf(244,axiom,((ord_less_eq_nat @ (min_dist_capacity @ c @ ua @ t) @ (size_s1990949619at_nat @ p2_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062)). 22.82/7.91 thf(981,plain,((ord_less_eq_nat @ (min_dist_capacity @ (c) @ ua @ t) @ (size_s1990949619at_nat @ p2_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 22.82/7.91 thf(173,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ab__semigroup__add__class_Oadd__ac_I1_J)). 22.82/7.91 thf(766,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 22.82/7.91 thf(13,axiom,((dist_capacity = dist_capacity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_Graph_Odist_Ocong)). 22.82/7.91 thf(307,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 22.82/7.91 thf(8,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_a @ c2 @ A @ B @ C) => (? [D:list_P559422087at_nat]: (isSimplePath_a @ c2 @ A @ D @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_g_H_OisSPath__pathLE)). 22.82/7.91 thf(292,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_a @ (c2) @ A @ B @ C) => (? [D:list_P559422087at_nat]: (isSimplePath_a @ (c2) @ A @ D @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 22.82/7.91 thf(65,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: ((isShortestPath_a @ A @ B @ C @ D) => (isPath_a @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Graph_OshortestPath__is__path)). 22.82/7.91 thf(452,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: ((isShortestPath_a @ (A) @ B @ C @ D) => (isPath_a @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 22.82/7.91 thf(91,axiom,((min_dist_a = min_dist_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Graph_Omin__dist_Ocong)). 22.82/7.91 thf(529,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 22.82/7.91 thf(225,axiom,((! [A:nat,B:nat,C:nat]: ((dist_a @ c2 @ A @ B @ C) = (? [D:list_P559422087at_nat]: ((isPath_a @ c2 @ A @ D @ C) & ((size_s1990949619at_nat @ D) = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_g_H_Odist__def)). 22.82/7.91 thf(925,plain,((! [A:nat,B:nat,C:nat]: ((dist_a @ (c2) @ A @ B @ C) = (? [D:list_P559422087at_nat]: ((isPath_a @ (c2) @ A @ D @ C) & ((size_s1990949619at_nat @ D) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 22.82/7.91 thf(187,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_not__add__less2)). 22.82/7.91 thf(810,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 22.82/7.91 thf(152,axiom,((isPath_a @ c2 @ s @ p3 @ t)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_assms_I5_J)). 22.82/7.91 thf(714,plain,((isPath_a @ (c2) @ s @ p3 @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 22.82/7.91 thf(183,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_dual__order_Oirrefl)). 22.82/7.91 thf(798,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 22.82/7.91 thf(27,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) <= (ord_less_eq_nat @ D @ E))) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_linorder__wlog)). 22.82/7.91 thf(334,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) | ~ (ord_less_eq_nat @ D @ E))) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 22.82/7.91 thf(166,axiom,((dist_a = (^ [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ? [E:list_P559422087at_nat]: ((isPath_a @ A @ B @ E @ D) & ((size_s1990949619at_nat @ E) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Graph_Odist__def)). 22.82/7.91 thf(746,plain,(((dist_a) = (^ [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ? [E:list_P559422087at_nat]: ((isPath_a @ A @ B @ E @ D) & ((size_s1990949619at_nat @ E) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 22.82/7.91 thf(235,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((connected_a @ c2 @ A @ B) => (((ord_less_nat @ D @ C) => (? [E:nat]: (((min_dist_a @ c2 @ A @ E) = D) & (connected_a @ c2 @ A @ E)))) <= ((min_dist_a @ c2 @ A @ B) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_g_H_Omin__dist__less)). 22.82/7.91 thf(952,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((connected_a @ (c2) @ A @ B) => (((ord_less_nat @ D @ C) => (? [E:nat]: (((min_dist_a @ (c2) @ A @ E) = D) & (connected_a @ (c2) @ A @ E)))) | ~ ((min_dist_a @ (c2) @ A @ B) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 22.82/7.91 thf(12,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_ord__eq__le__trans)). 22.82/7.91 thf(302,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 22.82/7.91 thf(116,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShor1936442771pacity @ c @ A @ B @ C) = (((size_s1990949619at_nat @ B) = (min_dist_capacity @ c @ A @ C)) & (isSimp1359852763pacity @ c @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_isShortestPath__alt)). 22.82/7.91 thf(598,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShor1936442771pacity @ (c) @ A @ B @ C) = (((size_s1990949619at_nat @ B) = (min_dist_capacity @ (c) @ A @ C)) & (isSimp1359852763pacity @ (c) @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 22.82/7.91 thf(190,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_less__imp__not__less)). 22.82/7.91 thf(820,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 22.82/7.91 thf(102,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_add__right__mono)). 22.82/7.91 thf(561,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 22.82/7.91 thf(10,axiom,((reachableNodes_a = (^ [A:(product_prod_nat_nat > a),B:nat]: (collect_nat @ (connected_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Graph_OreachableNodes__def)). 22.82/7.91 thf(297,plain,(((reachableNodes_a) = (^ [A:(product_prod_nat_nat > a),B:nat]: (collect_nat @ (connected_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 22.82/7.91 thf(159,axiom,((isPath_a @ c2 @ ua @ p2_a @ t)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_P2_H)). 22.82/7.91 thf(729,plain,((isPath_a @ (c2) @ ua @ p2_a @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 22.82/7.91 thf(48,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isSimplePath_a @ c2 @ A @ B @ C) <= (isShortestPath_a @ c2 @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_g_H_OshortestPath__is__simple)). 22.82/7.91 thf(407,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isSimplePath_a @ (c2) @ A @ B @ C) | ~ (isShortestPath_a @ (c2) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 22.82/7.91 thf(145,axiom,((ord_less_nat @ (min_dist_capacity @ c @ s @ ua) @ (size_s1990949619at_nat @ p1a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062)). 22.82/7.91 thf(693,plain,((ord_less_nat @ (min_dist_capacity @ (c) @ s @ ua) @ (size_s1990949619at_nat @ p1a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 22.82/7.91 thf(127,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_order_Oasym)). 22.82/7.91 thf(630,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 22.82/7.91 thf(104,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_trans__le__add2)). 22.82/7.91 thf(566,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 22.82/7.91 thf(24,axiom,((isSimp1359852763pacity = isSimp1359852763pacity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_Graph_OisSimplePath_Ocong)). 22.82/7.91 thf(329,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 22.82/7.91 thf(79,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_le__antisym)). 22.82/7.91 thf(493,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 22.82/7.91 thf(151,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => (((ord_less_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F))))) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_order__less__subst1)). 22.82/7.91 thf(710,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 22.82/7.91 thf(196,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__le__iff__add)). 22.82/7.91 thf(842,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 22.82/7.91 thf(255,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_nat__less__induct)). 22.82/7.91 thf(1012,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 22.82/7.91 thf(164,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) <= (~ (ord_less_nat @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_neqE)). 22.82/7.91 thf(742,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 22.82/7.91 thf(147,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E)))) => (ord_less_eq_nat @ (plus_plus_nat @ (A @ B) @ C) @ (A @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_mono__nat__linear__lb)). 22.82/7.91 thf(697,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E)))) => (ord_less_eq_nat @ (plus_plus_nat @ (A @ B) @ C) @ (A @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 22.82/7.91 thf(19,axiom,((! [A:(nat > $o)]: ((A @ (ord_Least_nat @ A)) <= (? [B:nat]: (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_LeastI__ex)). 22.82/7.91 thf(317,plain,((! [A:(nat > $o)]: ((A @ (ord_Least_nat @ (A))) | ~ (? [B:nat]: (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 22.82/7.91 thf(133,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_group__cancel_Oadd2)). 22.82/7.91 thf(650,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 22.82/7.91 thf(41,axiom,((dist_a = dist_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Graph_Odist_Ocong)). 22.82/7.91 thf(388,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 22.82/7.91 thf(201,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: ((dist_capacity @ A @ B @ C @ D) => (ord_less_eq_nat @ (min_dist_capacity @ A @ B @ D) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Graph_Omin__dist__minD)). 22.82/7.91 thf(857,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: ((dist_capacity @ (A) @ B @ C @ D) => (ord_less_eq_nat @ (min_dist_capacity @ (A) @ B @ D) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 22.82/7.91 thf(100,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_less__not__refl2)). 22.82/7.91 thf(554,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 22.82/7.91 thf(77,axiom,((! [A:nat,B:nat,C:nat]: ((dist_a @ c2 @ A @ B @ C) => (ord_less_eq_nat @ (min_dist_a @ c2 @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_g_H_Omin__dist__minD)). 22.82/7.91 thf(489,plain,((! [A:nat,B:nat,C:nat]: ((dist_a @ (c2) @ A @ B @ C) => (ord_less_eq_nat @ (min_dist_a @ (c2) @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 22.82/7.91 thf(256,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat]: (A @ D @ D)) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_linorder__less__wlog)). 22.82/7.91 thf(1016,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat]: (A @ D @ D)) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 22.82/7.91 thf(97,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_gt__ex)). 22.82/7.91 thf(547,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 22.82/7.91 thf(259,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat,E:nat,F:nat]: (((((min_dist_a @ A @ B @ F) = (plus_plus_nat @ C @ E)) => ((min_dist_a @ A @ D @ F) = E)) <= (dist_a @ A @ D @ E @ F)) <= (dist_a @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Graph_Omin__dist__split_I2_J)). 22.82/7.91 thf(1039,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat,E:nat,F:nat]: ((((min_dist_a @ (A) @ B @ F) = (plus_plus_nat @ C @ E)) => ((min_dist_a @ (A) @ D @ F) = E)) | ~ (dist_a @ (A) @ D @ E @ F) | ~ (dist_a @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 22.82/7.91 thf(240,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_add__le__mono1)). 22.82/7.91 thf(970,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 22.82/7.91 thf(124,axiom,((isPath_capacity @ c @ s @ p1a @ va)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__C1_Oprems_C_I2_J)). 22.82/7.91 thf(622,plain,((isPath_capacity @ (c) @ s @ p1a @ va)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 22.82/7.91 thf(132,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat,E:nat,F:nat]: (((dist_capacity @ A @ B @ (plus_plus_nat @ C @ E) @ F) <= (dist_capacity @ A @ D @ E @ F)) <= (dist_capacity @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Graph_Odist__trans)). 22.82/7.91 thf(647,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat,E:nat,F:nat]: ((dist_capacity @ (A) @ B @ (plus_plus_nat @ C @ E) @ F) | ~ (dist_capacity @ (A) @ D @ E @ F) | ~ (dist_capacity @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 22.82/7.91 thf(148,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) & (A = B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add__mono__thms__linordered__field_I2_J)). 22.82/7.91 thf(701,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) & (A = B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 22.82/7.91 thf(163,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((dist_capacity @ c @ A @ B @ C) => ((((min_dist_capacity @ c @ A @ C) = B) <= ((min_dist_capacity @ c @ A @ E) = (plus_plus_nat @ B @ D))) <= (dist_capacity @ c @ C @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_min__dist__split_I1_J)). 22.82/7.91 thf(738,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((dist_capacity @ (c) @ A @ B @ C) => (((min_dist_capacity @ (c) @ A @ C) = B) | ~ ((min_dist_capacity @ (c) @ A @ E) = (plus_plus_nat @ B @ D)) | ~ (dist_capacity @ (c) @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 22.82/7.91 thf(67,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_order_Otrans)). 22.82/7.91 thf(457,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 22.82/7.91 thf(220,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_add__left__cancel)). 22.82/7.91 thf(911,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 22.82/7.91 thf(105,axiom,((! [A:nat,B:nat]: ((~ (! [C:list_P559422087at_nat]: ~ (isShor1936442771pacity @ c @ A @ C @ B))) <= (connected_capacity @ c @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_obtain__shortest__path)). 22.82/7.91 thf(569,plain,((! [A:nat,B:nat]: (~ (! [C:list_P559422087at_nat]: ~ (isShor1936442771pacity @ (c) @ A @ C @ B)) | ~ (connected_capacity @ (c) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 22.82/7.91 thf(30,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: ((~ (! [D:list_P559422087at_nat]: ~ (isShor1936442771pacity @ A @ B @ D @ C))) <= (connected_capacity @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_Graph_Oobtain__shortest__path)). 22.82/7.91 thf(343,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: (~ (! [D:list_P559422087at_nat]: ~ (isShor1936442771pacity @ (A) @ B @ D @ C)) | ~ (connected_capacity @ (A) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 22.82/7.91 thf(180,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: ((dist_a @ A @ B @ (size_s1990949619at_nat @ C) @ D) <= (isPath_a @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Graph_OisPath__distD)). 22.82/7.91 thf(792,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: ((dist_a @ (A) @ B @ (size_s1990949619at_nat @ C) @ D) | ~ (isPath_a @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 22.82/7.91 thf(185,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_add__strict__mono)). 22.82/7.91 thf(805,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 22.82/7.91 thf(16,axiom,((reacha1693770334pacity = (^ [A:(product_prod_nat_nat > capacity),B:nat]: (collect_nat @ (connected_capacity @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Graph_OreachableNodes__def)). 22.82/7.91 thf(311,plain,(((reacha1693770334pacity) = (^ [A:(product_prod_nat_nat > capacity),B:nat]: (collect_nat @ (connected_capacity @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 22.82/7.91 thf(224,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) <= ((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_less__add__eq__less)). 22.82/7.91 thf(921,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) | ~ ((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 22.82/7.91 thf(264,axiom,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_ord__eq__less__trans)). 22.82/7.91 thf(1054,plain,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 22.82/7.91 thf(101,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShor1936442771pacity @ c @ A @ B @ C) = ((isPath_capacity @ c @ A @ B @ C) & ((size_s1990949619at_nat @ B) = (min_dist_capacity @ c @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_isShortestPath__min__dist__def)). 22.82/7.91 thf(558,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShor1936442771pacity @ (c) @ A @ B @ C) = ((isPath_capacity @ (c) @ A @ B @ C) & ((size_s1990949619at_nat @ B) = (min_dist_capacity @ (c) @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 22.82/7.91 thf(92,axiom,((connected_capacity @ c @ s @ ua)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29__092_060open_062connected_As_Au_092_060close_062)). 22.82/7.91 thf(530,plain,((connected_capacity @ (c) @ s @ ua)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 22.82/7.91 thf(181,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((dist_a @ c2 @ A @ (size_s1990949619at_nat @ B) @ C) <= (isPath_a @ c2 @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_g_H_OisPath__distD)). 22.82/7.91 thf(794,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((dist_a @ (c2) @ A @ (size_s1990949619at_nat @ B) @ C) | ~ (isPath_a @ (c2) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 22.82/7.91 thf(155,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_dual__order_Ostrict__implies__order)). 22.82/7.91 thf(718,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 22.82/7.91 thf(212,axiom,((isShortestPath_a = (^ [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: (((size_s1990949619at_nat @ C) = (min_dist_a @ A @ B @ D)) & (isPath_a @ A @ B @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Graph_OisShortestPath__min__dist__def)). 22.82/7.91 thf(888,plain,(((isShortestPath_a) = (^ [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: (((size_s1990949619at_nat @ C) = (min_dist_a @ A @ B @ D)) & (isPath_a @ A @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 22.82/7.91 thf(238,axiom,((isShor1936442771pacity = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: (((size_s1990949619at_nat @ C) = (min_dist_capacity @ A @ B @ D)) & (isPath_capacity @ A @ B @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Graph_OisShortestPath__min__dist__def)). 22.82/7.91 thf(965,plain,(((isShor1936442771pacity) = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: (((size_s1990949619at_nat @ C) = (min_dist_capacity @ A @ B @ D)) & (isPath_capacity @ A @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 22.82/7.91 thf(122,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add_Oleft__commute)). 22.82/7.91 thf(618,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 22.82/7.91 thf(55,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_eq__iff)). 22.82/7.91 thf(425,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 22.82/7.91 thf(165,axiom,((isPath_a @ c2 @ u @ p2 @ t)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205__092_060open_062g_H_OisPath_Au_____Ap2_H_____At_092_060close_062)). 22.82/7.91 thf(745,plain,((isPath_a @ (c2) @ u @ p2 @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 22.82/7.91 thf(117,axiom,((! [A:nat,B:nat,C:nat]: (((? [D:nat]: ((connected_capacity @ c @ A @ D) & ((min_dist_capacity @ c @ A @ D) = C))) <= (ord_less_eq_nat @ C @ (min_dist_capacity @ c @ A @ B))) <= (connected_capacity @ c @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_min__dist__le)). 22.82/7.91 thf(601,plain,((! [A:nat,B:nat,C:nat]: (? [D:nat]: ((connected_capacity @ (c) @ A @ D) & ((min_dist_capacity @ (c) @ A @ D) = C)) | ~ (ord_less_eq_nat @ C @ (min_dist_capacity @ (c) @ A @ B)) | ~ (connected_capacity @ (c) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 22.82/7.91 thf(84,axiom,((! [A:nat]: ((reachableNodes_a @ c2 @ A) = (collect_nat @ (connected_a @ c2 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_g_H_OreachableNodes__def)). 22.82/7.91 thf(513,plain,((! [A:nat]: ((reachableNodes_a @ (c2) @ A) = (collect_nat @ (connected_a @ c2 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 22.82/7.91 thf(57,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ((dist_a @ A @ B @ C @ D) => (ord_less_eq_nat @ (min_dist_a @ A @ B @ D) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Graph_Omin__dist__minD)). 22.82/7.91 thf(430,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ((dist_a @ (A) @ B @ C @ D) => (ord_less_eq_nat @ (min_dist_a @ (A) @ B @ D) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 22.82/7.91 thf(242,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add_Oassoc)). 22.82/7.91 thf(975,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 22.82/7.91 thf(161,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ c2 @ A @ B @ C) = (((size_s1990949619at_nat @ B) = (min_dist_a @ c2 @ A @ C)) & (isPath_a @ c2 @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_g_H_OisShortestPath__min__dist__def)). 22.82/7.91 thf(732,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ (c2) @ A @ B @ C) = (((size_s1990949619at_nat @ B) = (min_dist_a @ (c2) @ A @ C)) & (isPath_a @ (c2) @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 22.82/7.91 thf(175,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_ord__less__eq__subst)). 22.82/7.91 thf(772,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 22.82/7.91 thf(109,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((dist_capacity @ c @ C @ D @ E) => (dist_capacity @ c @ A @ (plus_plus_nat @ B @ D) @ E)) <= (dist_capacity @ c @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_dist__trans)). 22.82/7.91 thf(579,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((dist_capacity @ (c) @ C @ D @ E) => (dist_capacity @ (c) @ A @ (plus_plus_nat @ B @ D) @ E)) | ~ (dist_capacity @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 22.82/7.91 thf(253,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: ((connected_capacity @ A @ B @ C) => (dist_capacity @ A @ B @ (min_dist_capacity @ A @ B @ C) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Graph_Omin__dist__is__dist)). 22.82/7.91 thf(1007,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: ((connected_capacity @ (A) @ B @ C) => (dist_capacity @ (A) @ B @ (min_dist_capacity @ (A) @ B @ C) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 22.82/7.91 thf(146,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__le__cancel__left)). 22.82/7.91 thf(694,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 22.82/7.91 thf(207,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_dual__order_Oorder__iff__strict)). 22.82/7.91 thf(875,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 22.82/7.91 thf(192,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__le__cancel__right)). 22.82/7.91 thf(826,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 22.82/7.91 thf(130,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_add__leE)). 22.82/7.91 thf(641,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 22.82/7.91 thf(43,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ((dist_a @ A @ B @ C @ D) => (((min_dist_a @ A @ B @ D) = C) <= (! [E:nat]: ((ord_less_eq_nat @ C @ E) <= (dist_a @ A @ B @ E @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Graph_Omin__distI__eq)). 22.82/7.91 thf(391,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ((dist_a @ (A) @ B @ C @ D) => (((min_dist_a @ (A) @ B @ D) = C) | ~ (! [E:nat]: ((ord_less_eq_nat @ C @ E) | ~ (dist_a @ (A) @ B @ E @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 22.82/7.91 thf(62,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat]: (connected_capacity @ A @ B @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Graph_Oconnected__refl)). 22.82/7.91 thf(445,plain,((! [A:(product_prod_nat_nat > capacity),B:nat]: (connected_capacity @ (A) @ B @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 22.82/7.91 thf(106,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_add__leD2)). 22.82/7.91 thf(572,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 22.82/7.91 thf(17,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ c2 @ A @ B @ C) => (isPath_a @ c2 @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_g_H_OshortestPath__is__path)). 22.82/7.91 thf(313,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ (c2) @ A @ B @ C) => (isPath_a @ (c2) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 22.82/7.91 thf(81,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_ord__eq__le__subst)). 22.82/7.91 thf(498,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 22.82/7.91 thf(274,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_add__le__imp__le__left)). 22.82/7.91 thf(1090,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 22.82/7.91 thf(223,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_capacity @ c @ A @ B @ C) <= (isShor1936442771pacity @ c @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_shortestPath__is__path)). 22.82/7.91 thf(919,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_capacity @ (c) @ A @ B @ C) | ~ (isShor1936442771pacity @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 22.82/7.91 thf(95,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_dual__order_Ostrict__iff__order)). 22.82/7.91 thf(540,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 22.82/7.91 thf(70,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_Nat_Oex__has__greatest__nat)). 22.82/7.91 thf(466,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 22.82/7.91 thf(275,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_ord__eq__less__subst)). 22.82/7.91 thf(1092,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 22.82/7.91 thf(216,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_add__lessD1)). 22.82/7.91 thf(900,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 22.82/7.91 thf(194,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat,E:nat]: ((connected_a @ A @ B @ C) => (((min_dist_a @ A @ B @ C) = D) => ((? [F:nat]: ((connected_a @ A @ B @ F) & ((min_dist_a @ A @ B @ F) = E))) <= (ord_less_nat @ E @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Graph_Omin__dist__less)). 22.82/7.91 thf(831,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat,E:nat]: ((connected_a @ (A) @ B @ C) => (((min_dist_a @ (A) @ B @ C) = D) => (? [F:nat]: ((connected_a @ (A) @ B @ F) & ((min_dist_a @ (A) @ B @ F) = E)) | ~ (ord_less_nat @ E @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 22.82/7.91 thf(141,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_less__imp__neq)). 22.82/7.91 thf(681,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 22.82/7.91 thf(53,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_dual__order_Oeq__iff)). 22.82/7.91 thf(419,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 22.82/7.91 thf(262,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_add__less__cancel__right)). 22.82/7.91 thf(1048,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 22.82/7.91 thf(260,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isSimp1359852763pacity @ c @ A @ B @ C) <= (isShor1936442771pacity @ c @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_shortestPath__is__simple)). 22.82/7.91 thf(1043,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isSimp1359852763pacity @ (c) @ A @ B @ C) | ~ (isShor1936442771pacity @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 22.82/7.91 thf(248,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_less__not__refl)). 22.82/7.91 thf(990,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 22.82/7.91 thf(250,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ A @ B) & (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add__mono__thms__linordered__field_I4_J)). 22.82/7.91 thf(996,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ A @ B) & (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 22.82/7.91 thf(213,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShor1936442771pacity @ c @ A @ B @ C) = (! [D:list_P559422087at_nat]: ((ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (size_s1990949619at_nat @ D)) <= (isPath_capacity @ c @ A @ D @ C)) & (isPath_capacity @ c @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_isShortestPath__def)). 22.82/7.91 thf(890,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShor1936442771pacity @ (c) @ A @ B @ C) = (! [D:list_P559422087at_nat]: ((ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (size_s1990949619at_nat @ D)) | ~ (isPath_capacity @ (c) @ A @ D @ C)) & (isPath_capacity @ (c) @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 22.82/7.91 thf(270,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__mono)). 22.82/7.91 thf(1080,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 22.82/7.91 thf(170,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_nat @ A @ B) & (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_add__mono__thms__linordered__field_I5_J)). 22.82/7.91 thf(758,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_nat @ A @ B) & (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 22.82/7.91 thf(99,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_less__asym)). 22.82/7.91 thf(552,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 22.82/7.91 thf(189,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((dist_a @ c2 @ C @ D @ E) => (((min_dist_a @ c2 @ A @ E) = (plus_plus_nat @ B @ D)) => ((min_dist_a @ c2 @ A @ C) = B))) <= (dist_a @ c2 @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_g_H_Omin__dist__split_I1_J)). 22.82/7.91 thf(816,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((dist_a @ (c2) @ C @ D @ E) => (((min_dist_a @ (c2) @ A @ E) = (plus_plus_nat @ B @ D)) => ((min_dist_a @ (c2) @ A @ C) = B))) | ~ (dist_a @ (c2) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 22.82/7.91 thf(120,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_order_Ostrict__implies__not__eq)). 22.82/7.91 thf(609,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 22.82/7.91 thf(22,axiom,((! [A:(nat > $o),B:nat,C:(nat > $o)]: (((! [D:nat]: ((A @ D) => (C @ D))) => (C @ (ord_Least_nat @ A))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_LeastI2)). 22.82/7.91 thf(323,plain,((! [A:(nat > $o),B:nat,C:(nat > $o)]: (((! [D:nat]: ((A @ D) => (C @ D))) => (C @ (ord_Least_nat @ (A)))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 22.82/7.91 thf(114,axiom,(((min_dist_capacity @ c @ s @ t) = (plus_plus_nat @ (min_dist_capacity @ c @ s @ ua) @ (min_dist_capacity @ c @ ua @ t)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062)). 22.82/7.91 thf(594,plain,(((min_dist_capacity @ (c) @ s @ t) = (plus_plus_nat @ (min_dist_capacity @ (c) @ s @ ua) @ (min_dist_capacity @ (c) @ ua @ t)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 22.82/7.91 thf(123,axiom,((isPath_capacity @ c @ ua @ p2_a @ t)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062isPath_Au_Ap2_H_At_092_060close_062)). 22.82/7.91 thf(621,plain,((isPath_capacity @ (c) @ ua @ p2_a @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 22.82/7.91 thf(75,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => (A @ (ord_Least_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_LeastI)). 22.82/7.91 thf(483,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => (A @ (ord_Least_nat @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 22.82/7.91 thf(198,axiom,((isPath_capacity @ c @ s @ p1a @ va)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_P1)). 22.82/7.91 thf(848,plain,((isPath_capacity @ (c) @ s @ p1a @ va)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 22.82/7.91 thf(126,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((dist_a @ c2 @ A @ B @ C) => ((dist_a @ c2 @ C @ D @ E) => (((min_dist_a @ c2 @ A @ E) = (plus_plus_nat @ B @ D)) => ((min_dist_a @ c2 @ C @ E) = D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_g_H_Omin__dist__split_I2_J)). 22.82/7.91 thf(626,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((dist_a @ (c2) @ A @ B @ C) => ((dist_a @ (c2) @ C @ D @ E) => (((min_dist_a @ (c2) @ A @ E) = (plus_plus_nat @ B @ D)) => ((min_dist_a @ (c2) @ C @ E) = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 22.82/7.91 thf(174,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__left__mono)). 22.82/7.91 thf(769,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 22.82/7.91 thf(232,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_less__irrefl)). 22.82/7.91 thf(943,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 22.82/7.91 thf(138,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat,E:nat]: ((((min_dist_capacity @ A @ B @ C) = D) => ((? [F:nat]: ((connected_capacity @ A @ B @ F) & ((min_dist_capacity @ A @ B @ F) = E))) <= (ord_less_nat @ E @ D))) <= (connected_capacity @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_Graph_Omin__dist__less)). 22.82/7.91 thf(668,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat,E:nat]: ((((min_dist_capacity @ (A) @ B @ C) = D) => (? [F:nat]: ((connected_capacity @ (A) @ B @ F) & ((min_dist_capacity @ (A) @ B @ F) = E)) | ~ (ord_less_nat @ E @ D))) | ~ (connected_capacity @ (A) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 22.82/7.91 thf(25,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_order__refl)). 22.82/7.91 thf(330,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 22.82/7.91 thf(266,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((connected_capacity @ c @ A @ B) => (((ord_less_nat @ D @ C) => (? [E:nat]: (((min_dist_capacity @ c @ A @ E) = D) & (connected_capacity @ c @ A @ E)))) <= ((min_dist_capacity @ c @ A @ B) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_min__dist__less)). 22.82/7.91 thf(1061,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((connected_capacity @ (c) @ A @ B) => (((ord_less_nat @ D @ C) => (? [E:nat]: (((min_dist_capacity @ (c) @ A @ E) = D) & (connected_capacity @ (c) @ A @ E)))) | ~ ((min_dist_capacity @ (c) @ A @ B) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 22.82/7.91 thf(142,axiom,((dist_capacity = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: ? [E:list_P559422087at_nat]: ((isPath_capacity @ A @ B @ E @ D) & ((size_s1990949619at_nat @ E) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Graph_Odist__def)). 22.82/7.91 thf(685,plain,(((dist_capacity) = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: ? [E:list_P559422087at_nat]: ((isPath_capacity @ A @ B @ E @ D) & ((size_s1990949619at_nat @ E) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 22.82/7.91 thf(129,axiom,((! [A:nat,B:nat,C:nat]: (((! [D:nat]: ((dist_capacity @ c @ A @ D @ C) => (ord_less_eq_nat @ B @ D))) => ((min_dist_capacity @ c @ A @ C) = B)) <= (dist_capacity @ c @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_min__distI__eq)). 22.82/7.91 thf(636,plain,((! [A:nat,B:nat,C:nat]: (((! [D:nat]: ((dist_capacity @ (c) @ A @ D @ C) => (ord_less_eq_nat @ B @ D))) => ((min_dist_capacity @ (c) @ A @ C) = B)) | ~ (dist_capacity @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 22.82/7.91 thf(176,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_nat__less__le)). 22.82/7.91 thf(780,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 22.82/7.91 thf(210,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (B = (plus_plus_nat @ A @ C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_le__Suc__ex)). 22.82/7.91 thf(883,plain,((! [A:nat,B:nat]: (? [C:nat]: (B = (plus_plus_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 22.82/7.91 thf(119,axiom,((min_dist_capacity = min_dist_capacity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Graph_Omin__dist_Ocong)). 22.82/7.91 thf(608,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 22.82/7.91 thf(246,axiom,((! [A:nat,B:nat,C:nat]: ((dist_capacity @ c @ A @ B @ C) => (connected_capacity @ c @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_connected__distI)). 22.82/7.91 thf(986,plain,((! [A:nat,B:nat,C:nat]: ((dist_capacity @ (c) @ A @ B @ C) => (connected_capacity @ (c) @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 22.82/7.91 thf(11,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_antisym__conv)). 22.82/7.91 thf(299,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 22.82/7.91 thf(4,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((? [C:nat]: (A @ C)) => ((B @ (ord_Least_nat @ A)) <= (! [C:nat]: ((A @ C) => (B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_LeastI2__ex)). 22.82/7.91 thf(278,plain,((! [A:(nat > $o),B:(nat > $o)]: ((? [C:nat]: (A @ C)) => ((B @ (ord_Least_nat @ (A))) | ~ (! [C:nat]: ((A @ C) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 22.82/7.91 thf(205,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_add__right__cancel)). 22.82/7.91 thf(868,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 22.82/7.91 thf(157,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add__le__imp__le__right)). 22.82/7.91 thf(722,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 22.82/7.91 thf(257,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_add__leD1)). 22.82/7.91 thf(1034,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 22.82/7.91 thf(93,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: ((connected_capacity @ A @ B @ C) => ((? [E:nat]: (((min_dist_capacity @ A @ B @ E) = D) & (connected_capacity @ A @ B @ E))) <= (ord_less_eq_nat @ D @ (min_dist_capacity @ A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Graph_Omin__dist__le)). 22.82/7.91 thf(531,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: ((connected_capacity @ (A) @ B @ C) => (? [E:nat]: (((min_dist_capacity @ (A) @ B @ E) = D) & (connected_capacity @ (A) @ B @ E)) | ~ (ord_less_eq_nat @ D @ (min_dist_capacity @ (A) @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 22.82/7.91 thf(140,axiom,((isPath_capacity @ c @ s @ p1 @ v)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24__092_060open_062isPath_As_Ap1_____Av_____092_060close_062)). 22.82/7.91 thf(680,plain,((isPath_capacity @ (c) @ s @ p1 @ v)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 22.82/7.91 thf(136,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((dist_a @ c2 @ A @ (plus_plus_nat @ B @ D) @ E) <= (dist_a @ c2 @ C @ D @ E)) <= (dist_a @ c2 @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_g_H_Odist__trans)). 22.82/7.91 thf(663,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((dist_a @ (c2) @ A @ (plus_plus_nat @ B @ D) @ E) | ~ (dist_a @ (c2) @ C @ D @ E) | ~ (dist_a @ (c2) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 22.82/7.91 thf(37,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ((connected_a @ A @ B @ D) <= (dist_a @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_Graph_Oconnected__distI)). 22.82/7.91 thf(374,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ((connected_a @ (A) @ B @ D) | ~ (dist_a @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 22.82/7.91 thf(85,axiom,((isSimplePath_a = isSimplePath_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Graph_OisSimplePath_Ocong)). 22.82/7.91 thf(516,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 22.82/7.91 thf(230,axiom,((isPath_a @ c2 @ ua @ p2_a @ t)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178__C1_Oprems_C_I3_J)). 22.82/7.91 thf(939,plain,((isPath_a @ (c2) @ ua @ p2_a @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 22.82/7.91 thf(169,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_dual__order_Ostrict__implies__not__eq)). 22.82/7.91 thf(754,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 22.82/7.91 thf(89,axiom,((min_dist_a = (^ [A:(product_prod_nat_nat > a),B:nat,C:nat]: (ord_Least_nat @ (^ [D:nat]: (dist_a @ A @ B @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Graph_Omin__dist__def)). 22.82/7.91 thf(525,plain,(((min_dist_a) = (^ [A:(product_prod_nat_nat > a),B:nat,C:nat]: (ord_Least_nat @ (^ [D:nat]: (dist_a @ A @ B @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 22.82/7.91 thf(252,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_less__mono__imp__le__mono)). 22.82/7.91 thf(1003,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 22.82/7.91 thf(144,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_nat__add__left__cancel__less)). 22.82/7.91 thf(690,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 22.82/7.91 thf(50,axiom,((isPath_capacity = isPath_capacity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Graph_OisPath_Ocong)). 22.82/7.91 thf(414,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 22.82/7.91 thf(23,axiom,((connected_capacity = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: ? [D:list_P559422087at_nat]: (isPath_capacity @ A @ B @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_Graph_Oconnected__def)). 22.82/7.91 thf(327,plain,(((connected_capacity) = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: ? [D:list_P559422087at_nat]: (isPath_capacity @ A @ B @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 22.82/7.91 thf(49,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ((connected_a @ A @ B @ C) => ((? [E:nat]: (((min_dist_a @ A @ B @ E) = D) & (connected_a @ A @ B @ E))) <= (ord_less_eq_nat @ D @ (min_dist_a @ A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Graph_Omin__dist__le)). 22.82/7.91 thf(409,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat]: ((connected_a @ (A) @ B @ C) => (? [E:nat]: (((min_dist_a @ (A) @ B @ E) = D) & (connected_a @ (A) @ B @ E)) | ~ (ord_less_eq_nat @ D @ (min_dist_a @ (A) @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 22.82/7.91 thf(15,axiom,((connected_a = connected_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Graph_Oconnected_Ocong)). 22.82/7.91 thf(310,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 22.82/7.91 thf(249,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__irrefl__nat)). 22.82/7.91 thf(993,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 22.82/7.91 thf(149,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_add__less__mono)). 22.82/7.91 thf(705,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 22.82/7.91 thf(5,axiom,((! [A:nat,B:nat,C:nat]: (((? [D:nat]: ((connected_a @ c2 @ A @ D) & ((min_dist_a @ c2 @ A @ D) = C))) <= (ord_less_eq_nat @ C @ (min_dist_a @ c2 @ A @ B))) <= (connected_a @ c2 @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_g_H_Omin__dist__le)). 22.82/7.91 thf(282,plain,((! [A:nat,B:nat,C:nat]: (? [D:nat]: ((connected_a @ (c2) @ A @ D) & ((min_dist_a @ (c2) @ A @ D) = C)) | ~ (ord_less_eq_nat @ C @ (min_dist_a @ (c2) @ A @ B)) | ~ (connected_a @ (c2) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 22.82/7.91 thf(111,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_add__strict__left__mono)). 22.82/7.91 thf(585,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 22.82/7.91 thf(154,axiom,((isShor1936442771pacity @ c @ s @ p @ t)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_SP)). 22.82/7.91 thf(717,plain,((isShor1936442771pacity @ (c) @ s @ p @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 22.82/7.91 thf(69,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: ((~ (! [D:list_P559422087at_nat]: ~ (isShortestPath_a @ A @ B @ D @ C))) <= (connected_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_Graph_Oobtain__shortest__path)). 22.82/7.91 thf(463,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: (~ (! [D:list_P559422087at_nat]: ~ (isShortestPath_a @ (A) @ B @ D @ C)) | ~ (connected_a @ (A) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 22.82/7.91 thf(186,axiom,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((~ (A @ C)) <= (ord_less_nat @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_exists__least__iff)). 22.82/7.91 thf(808,plain,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: (~ (A @ C) | ~ (ord_less_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 22.82/7.91 thf(272,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_add__less__mono1)). 22.82/7.91 thf(1085,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 22.82/7.91 thf(108,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_nat__add__left__cancel__le)). 22.82/7.91 thf(576,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 22.82/7.91 thf(121,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:(nat > $o)]: (((D @ (min_dist_capacity @ A @ B @ C)) <= (! [E:nat]: ((dist_capacity @ A @ B @ E @ C) => ((D @ E) <= (! [F:nat]: ((dist_capacity @ A @ B @ F @ C) => (ord_less_eq_nat @ E @ F))))))) <= (connected_capacity @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Graph_Omin__distI2)). 22.82/7.91 thf(613,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:(nat > $o)]: ((D @ (min_dist_capacity @ (A) @ B @ C)) | ~ (! [E:nat]: ((dist_capacity @ (A) @ B @ E @ C) => ((D @ E) | ~ (! [F:nat]: ((dist_capacity @ (A) @ B @ F @ C) => (ord_less_eq_nat @ E @ F)))))) | ~ (connected_capacity @ (A) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 22.82/7.91 thf(202,axiom,((! [A:nat]: (connected_capacity @ c @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_connected__refl)). 22.82/7.91 thf(859,plain,((! [A:nat]: (connected_capacity @ (c) @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 22.82/7.91 thf(243,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_not__add__less1)). 22.82/7.91 thf(978,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 22.82/7.91 thf(40,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((isSimp1359852763pacity @ A @ B @ C @ D) <= (isShor1936442771pacity @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Graph_OshortestPath__is__simple)). 22.82/7.91 thf(386,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((isSimp1359852763pacity @ (A) @ B @ C @ D) | ~ (isShor1936442771pacity @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 22.82/7.91 thf(227,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_less__not__refl3)). 22.82/7.91 thf(931,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 22.82/7.91 thf(197,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_add__mono__thms__linordered__semiring_I4_J)). 22.82/7.91 thf(844,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 22.82/7.91 thf(112,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) <= (A != B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_linorder__cases)). 22.82/7.91 thf(588,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (A = B) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 22.82/7.91 thf(188,axiom,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((C) <= (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_less__imp__triv)). 22.82/7.91 thf(813,plain,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((C) | ~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 22.82/7.91 thf(86,axiom,((reacha1693770334pacity = reacha1693770334pacity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Graph_OreachableNodes_Ocong)). 22.82/7.91 thf(517,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 22.82/7.91 thf(20,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: ((dist_capacity @ A @ B @ C @ D) => (connected_capacity @ A @ B @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_Graph_Oconnected__distI)). 22.82/7.91 thf(319,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat]: ((dist_capacity @ (A) @ B @ C @ D) => (connected_capacity @ (A) @ B @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 22.82/7.91 thf(233,axiom,((! [A:nat,B:nat]: ((connected_capacity @ c @ A @ B) = (? [C:list_P559422087at_nat]: (isPath_capacity @ c @ A @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_connected__def)). 22.82/7.91 thf(946,plain,((! [A:nat,B:nat]: ((connected_capacity @ (c) @ A @ B) = (? [C:list_P559422087at_nat]: (isPath_capacity @ (c) @ A @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 22.82/7.91 thf(32,axiom,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq)). 22.82/7.91 thf(351,plain,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 22.82/7.91 thf(128,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat,E:nat,F:nat]: (((((min_dist_capacity @ A @ B @ F) = (plus_plus_nat @ C @ E)) => ((min_dist_capacity @ A @ B @ D) = C)) <= (dist_capacity @ A @ D @ E @ F)) <= (dist_capacity @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Graph_Omin__dist__split_I1_J)). 22.82/7.91 thf(632,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat,E:nat,F:nat]: ((((min_dist_capacity @ (A) @ B @ F) = (plus_plus_nat @ C @ E)) => ((min_dist_capacity @ (A) @ B @ D) = C)) | ~ (dist_capacity @ (A) @ D @ E @ F) | ~ (dist_capacity @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 22.82/7.91 thf(46,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_eq__refl)). 22.82/7.91 thf(401,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 22.82/7.91 thf(178,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat,E:nat,F:nat]: (((((min_dist_capacity @ A @ B @ F) = (plus_plus_nat @ C @ E)) => ((min_dist_capacity @ A @ D @ F) = E)) <= (dist_capacity @ A @ D @ E @ F)) <= (dist_capacity @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_Graph_Omin__dist__split_I2_J)). 22.82/7.91 thf(786,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:nat,D:nat,E:nat,F:nat]: ((((min_dist_capacity @ (A) @ B @ F) = (plus_plus_nat @ C @ E)) => ((min_dist_capacity @ (A) @ D @ F) = E)) | ~ (dist_capacity @ (A) @ D @ E @ F) | ~ (dist_capacity @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 22.82/7.91 thf(215,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_add__left__imp__eq)). 22.82/7.91 thf(896,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 22.82/7.91 thf(167,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_trans__less__add2)). 22.82/7.91 thf(748,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 22.82/7.91 thf(83,axiom,((! [A:nat,B:nat]: ((connected_a @ c2 @ A @ B) = (? [C:nat]: (dist_a @ c2 @ A @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_g_H_Oconnected__by__dist)). 22.82/7.91 thf(510,plain,((! [A:nat,B:nat]: ((connected_a @ (c2) @ A @ B) = (? [C:nat]: (dist_a @ (c2) @ A @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 22.82/7.91 thf(172,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_trans__less__add1)). 22.82/7.91 thf(763,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 22.82/7.91 thf(31,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_ord__le__eq__trans)). 22.82/7.91 thf(346,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 22.82/7.91 thf(98,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ c2 @ A @ B @ C) = (! [D:list_P559422087at_nat]: ((isPath_a @ c2 @ A @ D @ C) => (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (size_s1990949619at_nat @ D))) & (isPath_a @ c2 @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_g_H_OisShortestPath__def)). 22.82/7.91 thf(549,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ (c2) @ A @ B @ C) = (! [D:list_P559422087at_nat]: ((isPath_a @ (c2) @ A @ D @ C) => (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (size_s1990949619at_nat @ D))) & (isPath_a @ (c2) @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 22.82/7.91 thf(94,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_less__induct)). 22.82/7.91 thf(536,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 22.82/7.91 thf(261,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_trans__le__add1)). 22.82/7.91 thf(1045,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 22.82/7.91 thf(6,axiom,((! [A:(product_prod_nat_nat > a),B:nat]: (connected_a @ A @ B @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_Graph_Oconnected__refl)). 22.82/7.91 thf(287,plain,((! [A:(product_prod_nat_nat > a),B:nat]: (connected_a @ (A) @ B @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 22.82/7.91 thf(221,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_less__trans)). 22.82/7.91 thf(914,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 22.82/7.91 thf(39,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_ord__le__eq__subst)). 22.82/7.91 thf(378,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 22.82/7.91 thf(63,axiom,((connected_a = (^ [A:(product_prod_nat_nat > a),B:nat,C:nat]: ? [D:nat]: (dist_a @ A @ B @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_Graph_Oconnected__by__dist)). 22.82/7.91 thf(447,plain,(((connected_a) = (^ [A:(product_prod_nat_nat > a),B:nat,C:nat]: ? [D:nat]: (dist_a @ A @ B @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 22.82/7.91 thf(18,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_dual__order_Orefl)). 22.82/7.91 thf(315,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 22.82/7.91 thf(58,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:(nat > $o)]: (((! [E:nat]: ((dist_a @ A @ B @ E @ C) => ((D @ E) <= (! [F:nat]: ((ord_less_eq_nat @ E @ F) <= (dist_a @ A @ B @ F @ C)))))) => (D @ (min_dist_a @ A @ B @ C))) <= (connected_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Graph_Omin__distI2)). 22.82/7.91 thf(432,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:(nat > $o)]: (((! [E:nat]: ((dist_a @ (A) @ B @ E @ C) => ((D @ E) | ~ (! [F:nat]: ((ord_less_eq_nat @ E @ F) | ~ (dist_a @ (A) @ B @ F @ C)))))) => (D @ (min_dist_a @ (A) @ B @ C))) | ~ (connected_a @ (A) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 22.82/7.91 thf(239,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_neq__iff)). 22.82/7.91 thf(967,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 22.82/7.91 thf(47,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_le__refl)). 22.82/7.91 thf(405,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 22.82/7.91 thf(200,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) <= (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_dual__order_Ostrict__trans)). 22.82/7.91 thf(854,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) | ~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 22.82/7.91 thf(179,axiom,((! [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((dist_capacity @ A @ B @ (size_s1990949619at_nat @ C) @ D) <= (isPath_capacity @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Graph_OisPath__distD)). 22.82/7.91 thf(790,plain,((! [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((dist_capacity @ (A) @ B @ (size_s1990949619at_nat @ C) @ D) | ~ (isPath_capacity @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 22.82/7.91 thf(204,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) <= (ord_less_eq_nat @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_order_Onot__eq__order__implies__strict)). 22.82/7.91 thf(865,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_eq_nat @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 22.82/7.91 thf(162,axiom,((! [A:nat,B:nat]: ((connected_capacity @ c @ A @ B) = (? [C:nat]: (dist_capacity @ c @ A @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_connected__by__dist)). 22.82/7.91 thf(735,plain,((! [A:nat,B:nat]: ((connected_capacity @ (c) @ A @ B) = (? [C:nat]: (dist_capacity @ (c) @ A @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 22.82/7.91 thf(103,axiom,((! [A:nat,B:nat,C:nat]: ((dist_capacity @ c @ A @ B @ C) => (ord_less_eq_nat @ (min_dist_capacity @ c @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_min__dist__minD)). 22.82/7.91 thf(564,plain,((! [A:nat,B:nat,C:nat]: ((dist_capacity @ (c) @ A @ B @ C) => (ord_less_eq_nat @ (min_dist_capacity @ (c) @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 22.82/7.91 thf(29,axiom,((connected_a = (^ [A:(product_prod_nat_nat > a),B:nat,C:nat]: ? [D:list_P559422087at_nat]: (isPath_a @ A @ B @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Graph_Oconnected__def)). 22.82/7.91 thf(341,plain,(((connected_a) = (^ [A:(product_prod_nat_nat > a),B:nat,C:nat]: ? [D:list_P559422087at_nat]: (isPath_a @ A @ B @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 22.82/7.91 thf(82,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_order__subst1)). 22.82/7.91 thf(506,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 22.82/7.91 thf(35,axiom,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => ((~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B)))) <= ((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_le__cases3)). 22.82/7.91 thf(358,plain,((! [A:nat,B:nat,C:nat]: ((~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))) | ~ ((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 22.82/7.91 thf(59,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((! [C:nat]: ((A @ C) = (B @ C))) => ((collect_nat @ A) = (collect_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong)). 22.82/7.91 thf(437,plain,((! [A:(nat > $o),B:(nat > $o)]: ((! [C:nat]: ((A @ C) = (B @ C))) => ((collect_nat @ (A)) = (collect_nat @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 22.82/7.91 thf(45,axiom,((connected_capacity = connected_capacity)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Graph_Oconnected_Ocong)). 22.82/7.91 thf(400,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 22.82/7.91 thf(236,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__less__imp__less__right)). 22.82/7.91 thf(960,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 22.82/7.91 thf(156,axiom,((isShortestPath_a = (^ [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: (((size_s1990949619at_nat @ C) = (min_dist_a @ A @ B @ D)) & (isSimplePath_a @ A @ B @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Graph_OisShortestPath__alt)). 22.82/7.91 thf(720,plain,(((isShortestPath_a) = (^ [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat]: (((size_s1990949619at_nat @ C) = (min_dist_a @ A @ B @ D)) & (isSimplePath_a @ A @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 22.82/7.91 thf(182,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_capacity @ c @ A @ B @ C) => (? [D:list_P559422087at_nat]: (isSimp1359852763pacity @ c @ A @ D @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_isSPath__pathLE)). 22.82/7.91 thf(796,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_capacity @ (c) @ A @ B @ C) => (? [D:list_P559422087at_nat]: (isSimp1359852763pacity @ (c) @ A @ D @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 22.82/7.91 thf(9,axiom,((! [A:nat,B:nat]: (((B = A) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_dual__order_Oantisym)). 22.82/7.91 thf(294,plain,((! [A:nat,B:nat]: ((B = A) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 22.82/7.91 thf(184,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ C @ D) & (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__mono__thms__linordered__semiring_I2_J)). 22.82/7.91 thf(801,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ C @ D) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 22.82/7.91 thf(211,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add__mono__thms__linordered__semiring_I1_J)). 22.82/7.91 thf(886,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 22.82/7.91 thf(226,axiom,((! [A:nat]: ((reacha1693770334pacity @ c @ A) = (collect_nat @ (connected_capacity @ c @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_reachableNodes__def)). 22.82/7.91 thf(928,plain,((! [A:nat]: ((reacha1693770334pacity @ (c) @ A) = (collect_nat @ (connected_capacity @ c @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 22.82/7.91 thf(51,axiom,((! [A:nat,B:nat]: ((dist_a @ c2 @ A @ (min_dist_a @ c2 @ A @ B) @ B) <= (connected_a @ c2 @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_g_H_Omin__dist__is__dist)). 22.82/7.91 thf(415,plain,((! [A:nat,B:nat]: ((dist_a @ (c2) @ A @ (min_dist_a @ (c2) @ A @ B) @ B) | ~ (connected_a @ (c2) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 22.82/7.91 thf(195,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ c2 @ A @ B @ C) = ((isSimplePath_a @ c2 @ A @ B @ C) & ((size_s1990949619at_nat @ B) = (min_dist_a @ c2 @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_g_H_OisShortestPath__alt)). 22.82/7.91 thf(839,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ (c2) @ A @ B @ C) = ((isSimplePath_a @ (c2) @ A @ B @ C) & ((size_s1990949619at_nat @ B) = (min_dist_a @ (c2) @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 22.82/7.91 thf(26,axiom,((connected_capacity = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: ? [D:nat]: (dist_capacity @ A @ B @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Graph_Oconnected__by__dist)). 22.82/7.91 thf(332,plain,(((connected_capacity) = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: ? [D:nat]: (dist_capacity @ A @ B @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 22.82/7.91 thf(56,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) <= (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_dual__order_Otrans)). 22.82/7.91 thf(427,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 22.82/7.91 thf(115,axiom,((isShor1936442771pacity = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((isPath_capacity @ A @ B @ C @ D) & ! [E:list_P559422087at_nat]: ((ord_less_eq_nat @ (size_s1990949619at_nat @ C) @ (size_s1990949619at_nat @ E)) <= (isPath_capacity @ A @ B @ E @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Graph_OisShortestPath__def)). 22.82/7.91 thf(596,plain,(((isShor1936442771pacity) = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:list_P559422087at_nat,D:nat]: ((isPath_capacity @ A @ B @ C @ D) & ! [E:list_P559422087at_nat]: ((ord_less_eq_nat @ (size_s1990949619at_nat @ C) @ (size_s1990949619at_nat @ E)) | ~ (isPath_capacity @ A @ B @ E @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 22.82/7.91 thf(131,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) <= (A != B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_le__neq__implies__less)). 22.82/7.91 thf(644,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 22.82/7.91 thf(191,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_less__imp__not__eq2)). 22.82/7.91 thf(822,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 22.82/7.91 thf(245,axiom,((! [A:list_P559422087at_nat,B:list_P559422087at_nat]: (((size_s1990949619at_nat @ A) != (size_s1990949619at_nat @ B)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_size__neq__size__imp__neq)). 22.82/7.91 thf(982,plain,((! [A:list_P559422087at_nat,B:list_P559422087at_nat]: ((~ ((size_s1990949619at_nat @ A) = (size_s1990949619at_nat @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 22.82/7.91 thf(3,axiom,((reachableNodes_a = reachableNodes_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Graph_OreachableNodes_Ocong)). 22.82/7.91 thf(277,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 22.82/7.91 thf(61,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_order__class_Oorder_Oantisym)). 22.82/7.91 thf(442,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 22.82/7.91 thf(206,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__right__imp__eq)). 22.82/7.91 thf(871,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 22.82/7.91 thf(76,axiom,((! [A:nat,B:nat]: ((connected_a @ c2 @ A @ B) => (~ (! [C:list_P559422087at_nat]: ~ (isShortestPath_a @ c2 @ A @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_g_H_Oobtain__shortest__path)). 22.82/7.91 thf(486,plain,((! [A:nat,B:nat]: ((connected_a @ (c2) @ A @ B) => (~ (! [C:list_P559422087at_nat]: ~ (isShortestPath_a @ (c2) @ A @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 22.82/7.91 thf(231,axiom,((! [A:nat,B:nat,C:nat]: ((dist_capacity @ c @ A @ B @ C) = (? [D:list_P559422087at_nat]: ((isPath_capacity @ c @ A @ D @ C) & ((size_s1990949619at_nat @ D) = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_dist__def)). 22.82/7.91 thf(940,plain,((! [A:nat,B:nat,C:nat]: ((dist_capacity @ (c) @ A @ B @ C) = (? [D:list_P559422087at_nat]: ((isPath_capacity @ (c) @ A @ D @ C) & ((size_s1990949619at_nat @ D) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 22.82/7.91 thf(33,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_antisym)). 22.82/7.91 thf(354,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 22.82/7.91 thf(135,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat,E:nat,F:nat]: (((((min_dist_a @ A @ B @ D) = C) <= ((min_dist_a @ A @ B @ F) = (plus_plus_nat @ C @ E))) <= (dist_a @ A @ D @ E @ F)) <= (dist_a @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_Graph_Omin__dist__split_I1_J)). 22.82/7.91 thf(659,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat,D:nat,E:nat,F:nat]: (((min_dist_a @ (A) @ B @ D) = C) | ~ ((min_dist_a @ (A) @ B @ F) = (plus_plus_nat @ C @ E)) | ~ (dist_a @ (A) @ D @ E @ F) | ~ (dist_a @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 22.82/7.91 thf(139,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: (B != (plus_plus_nat @ A @ C)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_less__eqE)). 22.82/7.91 thf(676,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ~ (B = (plus_plus_nat @ A @ C))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 22.82/7.91 thf(150,axiom,((min_dist_capacity = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: (ord_Least_nat @ (^ [D:nat]: (dist_capacity @ A @ B @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Graph_Omin__dist__def)). 22.82/7.91 thf(708,plain,(((min_dist_capacity) = (^ [A:(product_prod_nat_nat > capacity),B:nat,C:nat]: (ord_Least_nat @ (^ [D:nat]: (dist_capacity @ A @ B @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 22.82/7.91 thf(228,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_le__iff__add)). 22.82/7.91 thf(935,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 22.82/7.91 thf(254,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_order_Ostrict__trans)). 22.82/7.91 thf(1009,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 22.82/7.91 thf(78,axiom,((! [A:nat]: (connected_a @ c2 @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_g_H_Oconnected__refl)). 22.82/7.91 thf(491,plain,((! [A:nat]: (connected_a @ (c2) @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 22.82/7.91 thf(273,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__less__imp__less__left)). 22.82/7.91 thf(1088,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 22.82/7.91 thf(80,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_order__class_Oorder_Oeq__iff)). 22.82/7.91 thf(496,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 22.82/7.91 thf(66,axiom,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq)). 22.82/7.91 thf(454,plain,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 22.82/7.91 thf(267,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) & (ord_less_nat @ A @ B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_add__mono__thms__linordered__field_I1_J)). 22.82/7.91 thf(1069,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) & (ord_less_nat @ A @ B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 22.82/7.91 thf(1408,plain,(($false)),inference(cvc4,[status(thm)],[1036,760,909,893,518,666,481,1083,962,308,1073,449,861,523,582,730,276,440,655,1078,715,472,340,829,782,417,973,389,724,372,357,1059,949,917,751,542,460,902,421,606,881,289,475,591,321,376,623,937,574,1051,905,480,687,877,396,998,988,849,527,981,766,307,292,452,529,925,810,714,798,334,746,952,302,598,820,561,297,729,407,693,630,566,329,493,710,842,1012,742,697,317,650,388,857,554,489,1016,547,1039,970,622,647,701,738,457,911,569,343,792,805,311,921,1054,558,530,794,718,888,965,618,425,745,601,513,430,975,732,772,579,1007,694,875,826,641,391,445,572,313,498,1090,919,540,466,1092,900,831,681,419,1048,1043,990,996,890,1080,758,552,816,609,323,594,621,483,848,626,769,943,668,330,1061,685,636,780,883,608,986,299,278,868,722,1034,531,680,663,374,516,939,754,525,1003,690,414,327,409,310,993,705,282,585,717,463,808,1085,576,613,859,978,386,931,844,588,813,517,319,946,351,632,401,786,896,748,510,763,346,549,536,1045,287,914,378,447,315,432,967,405,854,790,865,735,564,341,506,358,437,400,960,720,796,294,801,886,928,415,839,332,427,596,644,822,982,277,442,871,486,940,354,659,676,708,935,1009,491,1088,496,454,1069])). 22.82/7.91 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 22.82/7.91 % [INFO] Killing All external provers ... 22.82/7.98 EOF