0.00/0.00 % Leo-III: Strategy 1 (for '60') 84.93/23.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 84.93/23.94 % [INFO] Parsing done (369ms). 84.93/23.94 % [INFO] Running in sequential loop mode. 84.93/23.94 % [CONFIG] Using configuration: timeout(60) with strategy 84.93/23.94 % [INFO] eprover registered as external prover. 84.93/23.94 % [INFO] cvc4 registered as external prover. 84.93/23.94 % [INFO] Parsing finished. Scanning for conjecture ... 84.93/23.94 % [INFO] Found a conjecture and 353 axioms. Running axiom selection ... 84.93/23.94 % [INFO] Axiom selection finished. Selected 279 axioms (removed 74 axioms). 84.93/23.94 % [INFO] Problem is higher-order (TPTP THF). 84.93/23.94 % [INFO] Type checking passed. Searching for refutation ... 84.93/23.94 % External prover 'e' found a proof! 84.93/23.94 % [INFO] Killing All external provers ... 84.93/23.94 % Time passed: 21348ms (effective reasoning time: 20527ms) 84.93/23.94 % Solved by strategy 84.93/23.94 % Axioms used in derivation (279): fact_218_Vfin__imp__Efin, fact_91_ord__eq__le__subst, fact_332_card__subset__eq, fact_204_List_Ofinite__set, fact_61_order_Otrans, fact_89_ord__eq__le__subst, fact_60_order_Otrans, fact_216_finite__V, fact_81_ord__le__eq__subst, fact_228_Graph_OVfin__imp__Efin, fact_111_order__subst1, fact_116_set__eq__subset, fact_166_Graph_OreachableNodes_Ocong, fact_221_finite__incoming_H, fact_214_card__seteq, fact_146_Graph_OisPath__edgeset, fact_145_Graph_Ooutgoing__edges, fact_308_inf__le2, fact_327_finite__list, fact_191_Graph_OE_Ocong, fact_112_order__subst1, fact_238_finite__has__maximal2, fact_153_reachableNodes__append__edge, fact_22_ek__analysis_Ointro, fact_266_inf_OboundedE, fact_346_finite__nat__set__iff__bounded__le, fact_199_Graph_Oincoming_H_Ocong, fact_235_finite__has__minimal2, fact_1_SP__EDGES, fact_18_isPath__edgeset, fact_107_order__subst1, fact_76_ord__le__eq__subst, fact_302_le__infI, fact_119_subset__trans, fact_164_IntD2, fact_55_order__class_Oorder_Oeq__iff, fact_13_order__refl, fact_139_transfer__path, fact_138_reachable__ss__V, fact_6_incoming__edges, fact_350_isPath__fwd__cases, fact_85_ord__eq__le__subst, fact_102_mem__Collect__eq, fact_162_IntD1, fact_347_isPath_Oelims_I3_J, fact_59_le__cases3, fact_229_Graph_Ofinite__outgoing, fact_92_order__subst2, fact_168_Graph_Oreachable__ss__V, fact_212_card__mono, fact_106_order__subst1, fact_129_equalityD1, fact_124_subset__iff, fact_232_Graph_Ofinite__incoming_H, fact_21_ek__analysis__def, fact_342_impossible__Cons, fact_9_subsetI, fact_220_finite__outgoing, fact_135_subsetD, fact_51_ord__eq__le__trans, fact_27_ek__analysis_OE__ss__uE, fact_26_ek__analysis_OspEdges__ss__E, fact_208_inf_Obounded__iff, fact_43_order__trans, fact_177_Int__absorb2, fact_336_pathVertices__edgeset, fact_201_finite__Int, fact_31_dual__order_Oeq__iff, fact_95_order__subst2, fact_211_card__mono, fact_46_order__class_Oorder_Oantisym, fact_284_inf__unique, fact_103_Collect__mem__eq, fact_130_subset__eq, fact_343_list_Oset__cases, fact_222_finite__outgoing_H, fact_104_Collect__mem__eq, fact_109_order__subst1, fact_101_mem__Collect__eq, fact_200_Graph_OshortestPath__is__path, fact_29_dual__order_Oantisym, fact_32_dual__order_Oeq__iff, fact_340_isShortestPath__def, fact_196_Graph_Ooutgoing_Ocong, fact_156_finite__E, fact_217_adjacent__nodes__finite, fact_58_antisym__conv, fact_45_order__class_Oorder_Oantisym, fact_165_Graph_OreachableNodes__append__edge, fact_0_SP, fact_38_dual__order_Orefl, fact_37_linorder__wlog, fact_94_order__subst2, fact_181_Int__Collect__mono, fact_128_equalityD1, fact_333_card__subset__eq, fact_7_outgoing__edges, fact_90_ord__eq__le__subst, fact_19_shortestPath__is__path, fact_320_rev__finite__subset, fact_341_list_Oinject, fact_12_subset__antisym, fact_93_order__subst2, fact_338_obtain__subset__with__card__n, fact_331_infinite__arbitrarily__large, fact_314_inf__sup__ord_I1_J, fact_231_Graph_Ofinite__outgoing_H, fact_193_Graph_OV_Ocong, fact_69_antisym, fact_67_linear, fact_349_isPath_Osimps_I1_J, fact_344_list_Oset__cases, fact_281_le__iff__inf, fact_36_dual__order_Otrans, fact_184_Graph_OisPath__ex__edge2, fact_125_subset__iff, fact_2_ek__analysis__axioms, fact_5_E__ss__uE, fact_263_inf_OboundedI, fact_34_dual__order_Otrans, fact_223_Finite__Graph__def, fact_121_Collect__mono, fact_83_ord__eq__le__subst, fact_100_order__subst2, fact_236_finite__has__maximal2, fact_49_ord__le__eq__trans, fact_98_order__subst2, fact_175_Int__absorb1, fact_25_ek__analysis__defs_OuE_Ocong, fact_239_inf_OcoboundedI2, fact_152_isPath__ex__edge1, fact_194_ek__analysis_Ocard__spEdges__le, fact_185_Graph_OisPath__ex__edge1, fact_299_inf__mono, fact_99_order__subst2, fact_96_order__subst2, fact_115_Collect__mono__iff, fact_325_finite__subset, fact_149_IntI, fact_190_Graph_Otransfer__path, fact_230_Graph_Ofinite__incoming, fact_72_eq__iff, fact_296_le__infI1, fact_117_set__eq__subset, fact_225_Finite__Graph_Ofinite__V, fact_348_isPath_Oelims_I2_J, fact_186_Graph_OFinite__Graph__EI, fact_144_Graph_Oincoming__edges, fact_351_isPath_Oelims_I1_J, fact_11_subset__antisym, fact_337_obtain__subset__with__card__n, fact_97_order__subst2, fact_154_Int__subset__iff, fact_330_infinite__arbitrarily__large, fact_169_Int__mono, fact_74_ord__le__eq__subst, fact_213_card__seteq, fact_14_order__refl, fact_118_subset__trans, fact_269_inf__absorb2, fact_160_IntE, fact_23_ek__analysis_Oaxioms, fact_251_inf_Ocobounded2, fact_189_ek__analysis_Ofinite__uE, fact_105_order__subst1, fact_287_inf_OorderI, fact_73_eq__iff, fact_233_finite__has__minimal2, fact_167_Graph_Oadjacent__nodes_Ocong, fact_334_finite__if__finite__subsets__card__bdd, fact_4_outgoing_H__edges, fact_158_finite__spEdges, fact_197_Graph_Oincoming_Ocong, fact_33_dual__order_Oeq__iff, fact_41_order__trans, fact_57_antisym__conv, fact_134_subsetD, fact_326_finite__list, fact_122_subset__refl, fact_183_Graph_Oadjacent__nodes__ss__V, fact_260_inf__greatest, fact_254_inf_Ocobounded1, fact_339_isPath_Osimps_I2_J, fact_171_Int__lower1, fact_224_Finite__Graph_Ointro, fact_75_ord__le__eq__subst, fact_278_inf_Oabsorb1, fact_88_ord__eq__le__subst, fact_335_finite__if__finite__subsets__card__bdd, fact_203_List_Ofinite__set, fact_80_ord__le__eq__subst, fact_3_incoming_H__edges, fact_324_finite__subset, fact_195_Graph_OisShortestPath_Ocong, fact_20_adjacent__nodes__ss__V, fact_329_subset__code_I1_J, fact_328_subset__code_I1_J, fact_257_inf_Oorder__iff, fact_226_Finite__Graph_Oadjacent__nodes__finite, fact_219_finite__incoming, fact_179_Int__greatest, fact_40_dual__order_Orefl, fact_120_Collect__mono, fact_78_ord__le__eq__subst, fact_16_SV, fact_71_eq__iff, fact_137_in__mono, fact_311_inf__le1, fact_15_order__refl, fact_293_le__infI2, fact_133_equalityE, fact_132_equalityE, fact_198_Graph_Ooutgoing_H_Ocong, fact_39_dual__order_Orefl, fact_322_infinite__super, fact_352_Graph_OisPath_Oinduct, fact_173_Int__lower2, fact_317_inf__sup__ord_I2_J, fact_77_ord__le__eq__subst, fact_242_inf_OcoboundedI1, fact_84_ord__eq__le__subst, fact_63_le__cases, fact_68_antisym, fact_108_order__subst1, fact_82_ord__le__eq__subst, fact_272_inf__absorb1, fact_50_ord__eq__le__trans, fact_28_dual__order_Oantisym, fact_30_dual__order_Oantisym, fact_140_card__spEdges__le, fact_248_inf_Oabsorb__iff1, fact_127_equalityD2, fact_123_subset__refl, fact_62_order_Otrans, fact_53_order__class_Oorder_Oeq__iff, fact_87_ord__eq__le__subst, fact_64_eq__refl, fact_142_Graph_Oincoming_H__edges, fact_188_ek__analysis_Ofinite__spEdges, fact_215_Efin__imp__Vfin, fact_24_ek__analysis__defs_OspEdges_Ocong, fact_275_inf_Oabsorb2, fact_245_inf_Oabsorb__iff2, fact_126_equalityD2, fact_290_inf_OorderE, fact_47_ord__le__eq__trans, fact_323_infinite__super, fact_79_ord__le__eq__subst, fact_143_Graph_Ooutgoing_H__edges, fact_131_subset__eq, fact_54_order__class_Oorder_Oeq__iff, fact_113_order__subst1, fact_345_bounded__Max__nat, fact_114_Collect__mono__iff, fact_70_antisym, fact_192_Graph_OisPath_Ocong, fact_157_finite__uE, fact_66_eq__refl, fact_35_dual__order_Otrans, fact_187_Finite__Graph_Ofinite__E, fact_17_spEdges__ss__E, fact_321_rev__finite__subset, fact_147_isPath__ex__edge2, fact_42_order__trans, fact_8_Finite__Graph__axioms, fact_136_in__mono, fact_151_Int__iff, fact_56_antisym__conv, fact_48_ord__le__eq__trans, fact_44_order__class_Oorder_Oantisym, fact_10_subsetI, fact_305_le__infE, fact_86_ord__eq__le__subst, fact_227_Graph_OEfin__imp__Vfin, fact_52_ord__eq__le__trans, fact_205_le__inf__iff, fact_141_Finite__Graph__EI, fact_110_order__subst1, fact_65_eq__refl 84.93/23.94 % No. of inferences in proof: 679 84.93/23.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21348 ms resp. 20527 ms w/o parsing 84.93/23.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 84.93/23.94 thf(set_se1612935105at_nat_type, type, set_se1612935105at_nat: $tType). 84.93/23.94 thf(list_P559422087at_nat_type, type, list_P559422087at_nat: $tType). 84.93/23.94 thf(set_Pr1986765409at_nat_type, type, set_Pr1986765409at_nat: $tType). 84.93/23.94 thf(product_prod_nat_nat_type, type, product_prod_nat_nat: $tType). 84.93/23.94 thf(set_set_nat_type, type, set_set_nat: $tType). 84.93/23.94 thf(list_nat_type, type, list_nat: $tType). 84.93/23.94 thf(set_nat_type, type, set_nat: $tType). 84.93/23.94 thf(nat_type, type, nat: $tType). 84.93/23.94 thf(a_type, type, a: $tType). 84.93/23.94 thf(edmond1517640972ysis_a_type, type, edmond1517640972ysis_a: ((product_prod_nat_nat > a) > $o)). 84.93/23.94 thf(edmond475474835dges_a_type, type, edmond475474835dges_a: ((product_prod_nat_nat > a) > (nat > (nat > set_Pr1986765409at_nat)))). 84.93/23.94 thf(edmond771116670s_uE_a_type, type, edmond771116670s_uE_a: ((product_prod_nat_nat > a) > set_Pr1986765409at_nat)). 84.93/23.94 thf(finite_card_nat_type, type, finite_card_nat: (set_nat > nat)). 84.93/23.94 thf(finite447719721at_nat_type, type, finite447719721at_nat: (set_Pr1986765409at_nat > nat)). 84.93/23.94 thf(finite_finite_nat_type, type, finite_finite_nat: (set_nat > $o)). 84.93/23.94 thf(finite772653738at_nat_type, type, finite772653738at_nat: (set_Pr1986765409at_nat > $o)). 84.93/23.94 thf(finite1457549322at_nat_type, type, finite1457549322at_nat: (set_se1612935105at_nat > $o)). 84.93/23.94 thf(finite_Graph_a_type, type, finite_Graph_a: ((product_prod_nat_nat > a) > $o)). 84.93/23.94 thf(e_a_type, type, e_a: ((product_prod_nat_nat > a) > set_Pr1986765409at_nat)). 84.93/23.94 thf(v_a_type, type, v_a: ((product_prod_nat_nat > a) > set_nat)). 84.93/23.94 thf(adjacent_nodes_a_type, type, adjacent_nodes_a: ((product_prod_nat_nat > a) > (nat > set_nat))). 84.93/23.94 thf(incoming_a_type, type, incoming_a: ((product_prod_nat_nat > a) > (nat > set_Pr1986765409at_nat))). 84.93/23.94 thf(incoming_a2_type, type, incoming_a2: ((product_prod_nat_nat > a) > (set_nat > set_Pr1986765409at_nat))). 84.93/23.94 thf(isPath_a_type, type, isPath_a: ((product_prod_nat_nat > a) > (nat > (list_P559422087at_nat > (nat > $o))))). 84.93/23.94 thf(isShortestPath_a_type, type, isShortestPath_a: ((product_prod_nat_nat > a) > (nat > (list_P559422087at_nat > (nat > $o))))). 84.93/23.94 thf(outgoing_a_type, type, outgoing_a: ((product_prod_nat_nat > a) > (nat > set_Pr1986765409at_nat))). 84.93/23.94 thf(outgoing_a2_type, type, outgoing_a2: ((product_prod_nat_nat > a) > (set_nat > set_Pr1986765409at_nat))). 84.93/23.94 thf(pathVertices_type, type, pathVertices: (nat > (list_P559422087at_nat > list_nat))). 84.93/23.94 thf(reachableNodes_a_type, type, reachableNodes_a: ((product_prod_nat_nat > a) > (nat > set_nat))). 84.93/23.94 thf(inf_in586391887at_nat_type, type, inf_in586391887at_nat: (set_Pr1986765409at_nat > (set_Pr1986765409at_nat > set_Pr1986765409at_nat))). 84.93/23.94 thf(cons_nat_type, type, cons_nat: (nat > (list_nat > list_nat))). 84.93/23.94 thf(cons_P66992567at_nat_type, type, cons_P66992567at_nat: (product_prod_nat_nat > (list_P559422087at_nat > list_P559422087at_nat))). 84.93/23.94 thf(nil_Pr1308055047at_nat_type, type, nil_Pr1308055047at_nat: list_P559422087at_nat). 84.93/23.94 thf(set_nat2_type, type, set_nat2: (list_nat > set_nat)). 84.93/23.94 thf(set_Pr2131844118at_nat_type, type, set_Pr2131844118at_nat: (list_P559422087at_nat > set_Pr1986765409at_nat)). 84.93/23.94 thf(size_s1990949619at_nat_type, type, size_s1990949619at_nat: (list_P559422087at_nat > nat)). 84.93/23.94 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 84.93/23.94 thf(ord_less_eq_set_nat_type, type, ord_less_eq_set_nat: (set_nat > (set_nat > $o))). 84.93/23.94 thf(ord_le841296385at_nat_type, type, ord_le841296385at_nat: (set_Pr1986765409at_nat > (set_Pr1986765409at_nat > $o))). 84.93/23.94 thf(product_Pair_nat_nat_type, type, product_Pair_nat_nat: (nat > (nat > product_prod_nat_nat))). 84.93/23.94 thf(collect_nat_type, type, collect_nat: ((nat > $o) > set_nat)). 84.93/23.94 thf(collec7649004at_nat_type, type, collec7649004at_nat: ((product_prod_nat_nat > $o) > set_Pr1986765409at_nat)). 84.93/23.94 thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))). 84.93/23.94 thf(member701585322at_nat_type, type, member701585322at_nat: (product_prod_nat_nat > (set_Pr1986765409at_nat > $o))). 84.93/23.94 thf(member298845450at_nat_type, type, member298845450at_nat: (set_Pr1986765409at_nat > (set_se1612935105at_nat > $o))). 84.93/23.94 thf(c_type, type, c: (product_prod_nat_nat > a)). 84.93/23.94 thf(edges_type, type, edges: set_Pr1986765409at_nat). 84.93/23.94 thf(p_type, type, p: list_P559422087at_nat). 84.93/23.94 thf(s_type, type, s: nat). 84.93/23.94 thf(t_type, type, t: nat). 84.93/23.94 thf(sk2_type, type, sk2: (set_nat > ((nat > set_nat) > (nat > (nat > nat))))). 84.93/23.94 thf(sk3_type, type, sk3: (set_nat > ((nat > set_nat) > (nat > (nat > nat))))). 84.93/23.94 thf(sk47_type, type, sk47: (nat > (set_nat > nat))). 84.93/23.94 thf(sk91_type, type, sk91: ($o > (nat > (list_P559422087at_nat > (nat > nat))))). 84.93/23.94 thf(sk92_type, type, sk92: ($o > (nat > (list_P559422087at_nat > (nat > nat))))). 84.93/23.94 thf(sk93_type, type, sk93: ($o > (nat > (list_P559422087at_nat > (nat > list_P559422087at_nat))))). 84.93/23.94 thf(sk94_type, type, sk94: (nat > (set_Pr1986765409at_nat > $o))). 84.93/23.94 thf(sk95_type, type, sk95: (nat > (set_Pr1986765409at_nat > set_Pr1986765409at_nat))). 84.93/23.94 thf(237,axiom,((member_nat @ s @ (v_a @ c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_SV)). 84.93/23.94 thf(1076,plain,((member_nat @ s @ (v_a @ (c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 84.93/23.94 thf(64,axiom,((! [A:set_nat,B:nat]: (((member_nat @ B @ A) => (? [C:nat]: ((ord_less_eq_nat @ C @ B) & ! [D:nat]: ((member_nat @ D @ A) => ((C = D) <= (ord_less_eq_nat @ D @ C))) & (member_nat @ C @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_finite__has__minimal2)). 84.93/23.94 thf(504,plain,((! [A:set_nat,B:nat]: (((member_nat @ B @ A) => (? [C:nat]: ((ord_less_eq_nat @ C @ B) & ! [D:nat]: ((member_nat @ D @ A) => ((C = D) | ~ (ord_less_eq_nat @ D @ C))) & (member_nat @ C @ A)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 84.93/23.94 thf(505,plain,((! [A:set_nat]: (! [B:nat]: ((member_nat @ B @ A) => (? [C:nat]: ((ord_less_eq_nat @ C @ B) & ! [D:nat]: ((member_nat @ D @ A) => ((C = D) | ~ (ord_less_eq_nat @ D @ C))) & (member_nat @ C @ A)))) | ~ (finite_finite_nat @ A)))),inference(miniscope,[status(thm)],[504])). 84.93/23.94 thf(507,plain,(! [C:nat,B:nat,A:set_nat] : ((~ (member_nat @ B @ A)) | (~ (member_nat @ C @ A)) | ((sk47 @ B @ A) = C) | (~ (ord_less_eq_nat @ C @ (sk47 @ B @ A))) | (~ (finite_finite_nat @ A)))),inference(cnf,[status(esa)],[505])). 84.93/23.94 thf(509,plain,(! [C:nat,B:nat,A:set_nat] : (((sk47 @ B @ A) = C) | (~ (member_nat @ B @ A)) | (~ (member_nat @ C @ A)) | (~ (ord_less_eq_nat @ C @ (sk47 @ B @ A))) | (~ (finite_finite_nat @ A)))),inference(lifteq,[status(thm)],[507])). 84.93/23.94 thf(23,axiom,((! [A:list_P559422087at_nat,B:list_P559422087at_nat,C:product_prod_nat_nat]: ((ord_less_eq_nat @ (size_s1990949619at_nat @ A) @ (size_s1990949619at_nat @ B)) => (A != (cons_P66992567at_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_impossible__Cons)). 84.93/23.94 thf(352,plain,((! [A:list_P559422087at_nat,B:list_P559422087at_nat,C:product_prod_nat_nat]: ((ord_less_eq_nat @ (size_s1990949619at_nat @ A) @ (size_s1990949619at_nat @ B)) => (~ (A = (cons_P66992567at_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 84.93/23.94 thf(353,plain,((! [A:list_P559422087at_nat,B:list_P559422087at_nat]: ((ord_less_eq_nat @ (size_s1990949619at_nat @ A) @ (size_s1990949619at_nat @ B)) => (~ (? [C:product_prod_nat_nat]: (A = (cons_P66992567at_nat @ C @ B))))))),inference(miniscope,[status(thm)],[352])). 84.93/23.94 thf(354,plain,(! [C:product_prod_nat_nat,B:list_P559422087at_nat,A:list_P559422087at_nat] : ((~ (ord_less_eq_nat @ (size_s1990949619at_nat @ A) @ (size_s1990949619at_nat @ B))) | (~ (A = (cons_P66992567at_nat @ C @ B))))),inference(cnf,[status(esa)],[353])). 84.93/23.94 thf(355,plain,(! [C:product_prod_nat_nat,B:list_P559422087at_nat,A:list_P559422087at_nat] : ((A != (cons_P66992567at_nat @ C @ B)) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ A) @ (size_s1990949619at_nat @ B))))),inference(lifteq,[status(thm)],[354])). 84.93/23.94 thf(356,plain,(! [B:product_prod_nat_nat,A:list_P559422087at_nat] : ((~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ B @ A)) @ (size_s1990949619at_nat @ A))))),inference(simp,[status(thm)],[355])). 84.93/23.94 thf(1419,plain,(! [E:product_prod_nat_nat,D:list_P559422087at_nat,C:nat,B:nat,A:set_nat] : ((~ (member_nat @ B @ A)) | (~ (member_nat @ C @ A)) | (~ (ord_less_eq_nat @ C @ (sk47 @ B @ A))) | (~ (finite_finite_nat @ A)) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ E @ D)) @ (sk47 @ B @ A))) | (C != (size_s1990949619at_nat @ D)))),inference(paramod_ordered,[status(thm)],[509,356])). 84.93/23.94 thf(1420,plain,(! [D:list_P559422087at_nat,C:product_prod_nat_nat,B:nat,A:set_nat] : ((~ (member_nat @ B @ A)) | (~ (member_nat @ (size_s1990949619at_nat @ D) @ A)) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ D) @ (sk47 @ B @ A))) | (~ (finite_finite_nat @ A)) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ C @ D)) @ (sk47 @ B @ A))))),inference(pattern_uni,[status(thm)],[1419:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(size_s1990949619at_nat @ F)),bind(D, $thf(F))]])). 84.93/23.94 thf(1433,plain,(! [D:list_P559422087at_nat,C:product_prod_nat_nat,B:nat,A:set_nat] : ((~ (member_nat @ B @ A)) | (~ (member_nat @ (size_s1990949619at_nat @ D) @ A)) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ D) @ (sk47 @ B @ A))) | (~ (finite_finite_nat @ A)) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ C @ D)) @ (sk47 @ B @ A))))),inference(simp,[status(thm)],[1420])). 84.93/23.94 thf(1648,plain,(! [D:list_P559422087at_nat,C:product_prod_nat_nat,B:nat,A:set_nat] : ((~ (member_nat @ (size_s1990949619at_nat @ D) @ A)) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ D) @ (sk47 @ B @ A))) | (~ (finite_finite_nat @ A)) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ C @ D)) @ (sk47 @ B @ A))) | ((member_nat @ s @ (v_a @ (c))) != (member_nat @ B @ A)))),inference(paramod_ordered,[status(thm)],[1076,1433])). 84.93/23.94 thf(1649,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (member_nat @ (size_s1990949619at_nat @ B) @ (v_a @ (c)))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | (~ (finite_finite_nat @ (v_a @ (c)))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) @ (sk47 @ s @ (v_a @ (c))))))),inference(pattern_uni,[status(thm)],[1648:[bind(A, $thf(v_a @ (c))),bind(B, $thf(s)),bind(C, $thf(C)),bind(D, $thf(D))]])). 84.93/23.94 thf(1658,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (member_nat @ (size_s1990949619at_nat @ B) @ (v_a @ (c)))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | (~ (finite_finite_nat @ (v_a @ (c)))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) @ (sk47 @ s @ (v_a @ (c))))))),inference(simp,[status(thm)],[1649])). 84.93/23.94 thf(215,axiom,((finite_finite_nat @ (v_a @ c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_finite__V)). 84.93/23.94 thf(1005,plain,((finite_finite_nat @ (v_a @ (c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 84.93/23.94 thf(1664,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (member_nat @ (size_s1990949619at_nat @ B) @ (v_a @ (c)))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | ~ ($true) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) @ (sk47 @ s @ (v_a @ (c))))))),inference(rewrite,[status(thm)],[1658,1005])). 84.93/23.94 thf(1665,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (member_nat @ (size_s1990949619at_nat @ B) @ (v_a @ (c)))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) @ (sk47 @ s @ (v_a @ (c))))))),inference(simp,[status(thm)],[1664])). 84.93/23.94 thf(162,axiom,((ord_less_eq_nat @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t)) @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_card__spEdges__le)). 84.93/23.94 thf(826,plain,((ord_less_eq_nat @ (finite447719721at_nat @ (edmond475474835dges_a @ (c) @ s @ t)) @ (finite447719721at_nat @ (edmond771116670s_uE_a @ (c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 84.93/23.94 thf(198,axiom,((! [A:set_Pr1986765409at_nat,B:nat]: (((finite772653738at_nat @ A) & (ord_less_eq_nat @ (finite447719721at_nat @ A) @ B)) <= (! [C:set_Pr1986765409at_nat]: (((ord_less_eq_nat @ (finite447719721at_nat @ C) @ B) <= (finite772653738at_nat @ C)) <= (ord_le841296385at_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_finite__if__finite__subsets__card__bdd)). 84.93/23.94 thf(953,plain,((! [A:set_Pr1986765409at_nat,B:nat]: (((finite772653738at_nat @ A) & (ord_less_eq_nat @ (finite447719721at_nat @ A) @ B)) | ~ (! [C:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ (finite447719721at_nat @ C) @ B) | ~ (finite772653738at_nat @ C) | ~ (ord_le841296385at_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 84.93/23.94 thf(958,plain,(! [B:nat,A:set_Pr1986765409at_nat] : ((~ (sk94 @ B @ A)) | (~ (ord_less_eq_nat @ (finite447719721at_nat @ (sk95 @ B @ A)) @ B)))),inference(cnf,[status(esa)],[953])). 84.93/23.94 thf(2606,plain,(! [B:nat,A:set_Pr1986765409at_nat] : ((~ (sk94 @ B @ A)) | ((ord_less_eq_nat @ (finite447719721at_nat @ (edmond475474835dges_a @ (c) @ s @ t)) @ (finite447719721at_nat @ (edmond771116670s_uE_a @ (c)))) != (ord_less_eq_nat @ (finite447719721at_nat @ (sk95 @ B @ A)) @ B)))),inference(paramod_ordered,[status(thm)],[826,958])). 84.93/23.94 thf(2626,plain,(! [B:nat,A:set_Pr1986765409at_nat] : ((~ (sk94 @ B @ A)) | ((finite447719721at_nat @ (edmond475474835dges_a @ (c) @ s @ t)) != (finite447719721at_nat @ (sk95 @ B @ A))) | ((finite447719721at_nat @ (edmond771116670s_uE_a @ (c))) != B))),inference(simp,[status(thm)],[2606])). 84.93/23.94 thf(2630,plain,(! [A:set_Pr1986765409at_nat] : ((~ (sk94 @ (finite447719721at_nat @ (edmond771116670s_uE_a @ (c))) @ A)) | ((finite447719721at_nat @ (edmond475474835dges_a @ (c) @ s @ t)) != (finite447719721at_nat @ (sk95 @ (finite447719721at_nat @ (edmond771116670s_uE_a @ (c))) @ A))))),inference(simp,[status(thm)],[2626])). 84.93/23.94 thf(155,axiom,(((finite_finite_nat @ (v_a @ c)) => (finite772653738at_nat @ (e_a @ c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_Vfin__imp__Efin)). 84.93/23.94 thf(809,plain,(((finite_finite_nat @ (v_a @ (c))) => (finite772653738at_nat @ (e_a @ (c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 84.93/23.94 thf(100,axiom,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C)) => (member701585322at_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_IntD2)). 84.93/23.94 thf(629,plain,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C)) => (member701585322at_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 84.93/23.94 thf(269,axiom,((! [A:nat]: (ord_le841296385at_nat @ (outgoing_a @ c @ A) @ (e_a @ c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_outgoing__edges)). 84.93/23.94 thf(1190,plain,((! [A:nat]: (ord_le841296385at_nat @ (outgoing_a @ (c) @ A) @ (e_a @ (c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 84.93/23.94 thf(222,axiom,((! [A:list_P559422087at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (set_Pr2131844118at_nat @ A) @ B) = (! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ (set_Pr2131844118at_nat @ A)) => (member701585322at_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_subset__code_I1_J)). 84.93/23.94 thf(1031,plain,((! [A:list_P559422087at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (set_Pr2131844118at_nat @ A) @ B) = (! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ (set_Pr2131844118at_nat @ A)) => (member701585322at_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 84.93/23.94 thf(239,axiom,(((= @ set_Pr1986765409at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_order__class_Oorder_Oeq__iff)). 84.93/23.94 thf(1083,plain,(((= @ set_Pr1986765409at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 84.93/23.94 thf(264,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_inf_Ocobounded2)). 84.93/23.94 thf(1179,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 84.93/23.94 thf(112,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_equalityD2)). 84.93/23.94 thf(666,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 84.93/23.94 thf(260,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ A @ C) => (ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_inf__greatest)). 84.93/23.94 thf(1168,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ A @ C) => (ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 84.93/23.94 thf(141,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((((finite447719721at_nat @ B) = (finite447719721at_nat @ A)) => (B = A)) <= (ord_le841296385at_nat @ B @ A)) <= (finite772653738at_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_card__subset__eq)). 84.93/23.94 thf(760,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((((finite447719721at_nat @ B) = (finite447719721at_nat @ A)) => (B = A)) | ~ (ord_le841296385at_nat @ B @ A) | ~ (finite772653738at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 84.93/23.94 thf(148,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ B @ A) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_dual__order_Oantisym)). 84.93/23.94 thf(777,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 84.93/23.94 thf(77,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)) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_order__subst1)). 84.93/23.94 thf(555,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) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 84.93/23.94 thf(58,axiom,((v_a = v_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Graph_OV_Ocong)). 84.93/23.94 thf(481,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 84.93/23.94 thf(206,axiom,((! [A:set_nat,B:(set_Pr1986765409at_nat > set_nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((A = (B @ C)) => (((ord_less_eq_set_nat @ A @ (B @ D)) <= (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) <= (ord_le841296385at_nat @ E @ F)))) <= (ord_le841296385at_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_ord__eq__le__subst)). 84.93/23.94 thf(977,plain,((! [A:set_nat,B:(set_Pr1986765409at_nat > set_nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((A = (B @ C)) => ((ord_less_eq_set_nat @ A @ (B @ D)) | ~ (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) | ~ (ord_le841296385at_nat @ E @ F))) | ~ (ord_le841296385at_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 84.93/23.94 thf(11,axiom,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((member701585322at_nat @ A @ C) => (member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C))) <= (member701585322at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_IntI)). 84.93/23.94 thf(308,plain,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((member701585322at_nat @ A @ C) => (member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C))) | ~ (member701585322at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 84.93/23.94 thf(27,axiom,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_mem__Collect__eq)). 84.93/23.94 thf(379,plain,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 84.93/23.94 thf(115,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: ((((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))) <= ((C @ B) = D)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_ord__le__eq__subst)). 84.93/23.94 thf(677,plain,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 84.93/23.94 thf(87,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_order_Otrans)). 84.93/23.94 thf(597,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 84.93/23.94 thf(173,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_inf__sup__ord_I1_J)). 84.93/23.94 thf(861,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 84.93/23.94 thf(178,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_inf__le2)). 84.93/23.94 thf(878,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 84.93/23.94 thf(49,axiom,((! [A:(product_prod_nat_nat > a)]: ((edmond1517640972ysis_a @ A) => (finite_Graph_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_ek__analysis_Oaxioms)). 84.93/23.94 thf(440,plain,((! [A:(product_prod_nat_nat > a)]: ((edmond1517640972ysis_a @ (A)) => (finite_Graph_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 84.93/23.94 thf(108,axiom,(((= @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_eq__iff)). 84.93/23.94 thf(654,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)],[108])). 84.93/23.94 thf(655,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = (= @ nat))),inference(lifteq,[status(thm)],[654])). 84.93/23.94 thf(65,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_subset__iff)). 84.93/23.94 thf(510,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 84.93/23.94 thf(511,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B))))),inference(lifteq,[status(thm)],[510])). 84.93/23.94 thf(33,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_dual__order_Orefl)). 84.93/23.94 thf(393,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 84.93/23.94 thf(394,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ A))),inference(cnf,[status(esa)],[393])). 84.93/23.94 thf(2168,plain,(! [C:nat,B:set_Pr1986765409at_nat,A:nat] : ((~ (sk94 @ C @ B)) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ (finite447719721at_nat @ (sk95 @ C @ B)) @ C)))),inference(paramod_ordered,[status(thm)],[394,958])). 84.93/23.94 thf(2179,plain,(! [C:nat,B:set_Pr1986765409at_nat,A:nat] : ((~ (sk94 @ C @ B)) | (A != (finite447719721at_nat @ (sk95 @ C @ B))) | (A != C))),inference(simp,[status(thm)],[2168])). 84.93/23.94 thf(2195,plain,(! [B:nat,A:set_Pr1986765409at_nat] : ((~ (sk94 @ B @ A)) | ((finite447719721at_nat @ (sk95 @ B @ A)) != B))),inference(simp,[status(thm)],[2179])). 84.93/23.94 thf(29,axiom,((edmond1517640972ysis_a = finite_Graph_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_ek__analysis__def)). 84.93/23.94 thf(385,plain,(((edmond1517640972ysis_a) = (finite_Graph_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 84.93/23.94 thf(128,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_order__trans)). 84.93/23.94 thf(715,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 84.93/23.94 thf(121,axiom,((! [A:(product_prod_nat_nat > a)]: ((finite_Graph_a @ A) <= (finite_finite_nat @ (v_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Finite__Graph_Ointro)). 84.93/23.94 thf(698,plain,((! [A:(product_prod_nat_nat > a)]: ((finite_Graph_a @ (A)) | ~ (finite_finite_nat @ (v_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 84.93/23.94 thf(251,axiom,((ord_le841296385at_nat = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_subset__iff)). 84.93/23.94 thf(1126,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 84.93/23.94 thf(1127,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))))),inference(lifteq,[status(thm)],[1126])). 84.93/23.94 thf(151,axiom,((ord_le841296385at_nat = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_inf_Oabsorb__iff2)). 84.93/23.94 thf(792,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 84.93/23.94 thf(793,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)))),inference(lifteq,[status(thm)],[792])). 84.93/23.94 thf(1919,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))))),inference(rewrite,[status(thm)],[1127,793])). 84.93/23.94 thf(190,axiom,((! [A:(product_prod_nat_nat > a)]: ((ord_le841296385at_nat @ (e_a @ A) @ (edmond771116670s_uE_a @ A)) <= (edmond1517640972ysis_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_ek__analysis_OE__ss__uE)). 84.93/23.94 thf(913,plain,((! [A:(product_prod_nat_nat > a)]: ((ord_le841296385at_nat @ (e_a @ (A)) @ (edmond771116670s_uE_a @ (A))) | ~ (edmond1517640972ysis_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 84.93/23.94 thf(195,axiom,((! [A:nat]: ((ord_less_eq_set_nat @ (reachableNodes_a @ c @ A) @ (v_a @ c)) <= (member_nat @ A @ (v_a @ c))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_reachable__ss__V)). 84.93/23.94 thf(945,plain,((! [A:nat]: ((ord_less_eq_set_nat @ (reachableNodes_a @ (c) @ A) @ (v_a @ (c))) | ~ (member_nat @ A @ (v_a @ (c)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 84.93/23.94 thf(20,axiom,((! [A:set_nat,B:set_nat,C:nat]: (((member_nat @ C @ A) => (member_nat @ C @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_subsetD)). 84.93/23.94 thf(340,plain,((! [A:set_nat,B:set_nat,C:nat]: (((member_nat @ C @ A) => (member_nat @ C @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 84.93/23.94 thf(73,axiom,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_ord__eq__le__trans)). 84.93/23.94 thf(538,plain,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 84.93/23.94 thf(193,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat,D:$o]: (((~ (! [E:nat,F:nat,G:list_P559422087at_nat]: ((D = (~ ((A = E) & (isPath_a @ c @ F @ G @ C) & (member701585322at_nat @ (product_Pair_nat_nat @ E @ F) @ (e_a @ c))))) <= (B = (cons_P66992567at_nat @ (product_Pair_nat_nat @ E @ F) @ G))))) <= ((D = (A != C)) <= (B = nil_Pr1308055047at_nat))) <= ((isPath_a @ c @ A @ B @ C) = D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_isPath_Oelims_I1_J)). 84.93/23.94 thf(930,plain,((! [A:nat,B:list_P559422087at_nat,C:nat,D:$o]: (~ (! [E:nat,F:nat,G:list_P559422087at_nat]: ((D = (~ ((A = E) & (isPath_a @ (c) @ F @ G @ C) & (member701585322at_nat @ (product_Pair_nat_nat @ E @ F) @ (e_a @ (c)))))) | ~ (B = (cons_P66992567at_nat @ (product_Pair_nat_nat @ E @ F) @ G)))) | ~ ((D = (~ (A = C))) | ~ (B = nil_Pr1308055047at_nat)) | ~ ((isPath_a @ (c) @ A @ B @ C) = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 84.93/23.94 thf(113,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((A = B) => ((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_ord__eq__le__trans)). 84.93/23.94 thf(670,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((A = B) => ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 84.93/23.94 thf(271,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: (((~ (! [D:list_P559422087at_nat,E:nat]: ((B = (cons_P66992567at_nat @ (product_Pair_nat_nat @ A @ E) @ D)) => ((~ (isPath_a @ c @ E @ D @ C)) <= (member701585322at_nat @ (product_Pair_nat_nat @ A @ E) @ (e_a @ c)))))) <= ((B = nil_Pr1308055047at_nat) => (C != A))) <= (isPath_a @ c @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_isPath__fwd__cases)). 84.93/23.94 thf(1196,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: (~ (! [D:list_P559422087at_nat,E:nat]: ((B = (cons_P66992567at_nat @ (product_Pair_nat_nat @ A @ E) @ D)) => (~ (isPath_a @ (c) @ E @ D @ C) | ~ (member701585322at_nat @ (product_Pair_nat_nat @ A @ E) @ (e_a @ (c)))))) | ~ ((B = nil_Pr1308055047at_nat) => (~ (C = A))) | ~ (isPath_a @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 84.93/23.94 thf(185,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ C) => (ord_le841296385at_nat @ A @ C)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_order_Otrans)). 84.93/23.94 thf(898,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ C) => (ord_le841296385at_nat @ A @ C)) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 84.93/23.94 thf(213,axiom,((finite772653738at_nat @ (edmond475474835dges_a @ c @ s @ t))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_finite__spEdges)). 84.93/23.94 thf(1001,plain,((finite772653738at_nat @ (edmond475474835dges_a @ (c) @ s @ t))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 84.93/23.94 thf(208,axiom,((ord_le841296385at_nat @ (e_a @ c) @ (edmond771116670s_uE_a @ c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_E__ss__uE)). 84.93/23.94 thf(989,plain,((ord_le841296385at_nat @ (e_a @ (c)) @ (edmond771116670s_uE_a @ (c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 84.93/23.94 thf(1,conjecture,((ord_le841296385at_nat @ edges @ (e_a @ c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 84.93/23.94 thf(2,negated_conjecture,((~ (ord_le841296385at_nat @ edges @ (e_a @ c)))),inference(neg_conjecture,[status(cth)],[1])). 84.93/23.94 thf(282,plain,((~ (ord_le841296385at_nat @ edges @ (e_a @ (c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 84.93/23.94 thf(1912,plain,(((ord_le841296385at_nat @ (e_a @ (c)) @ (edmond771116670s_uE_a @ (c))) != (ord_le841296385at_nat @ edges @ (e_a @ (c))))),inference(paramod_ordered,[status(thm)],[989,282])). 84.93/23.94 thf(1914,plain,(((e_a @ (c)) != edges) | ((e_a @ (c)) != (edmond771116670s_uE_a @ (c)))),inference(simp,[status(thm)],[1912])). 84.93/23.94 thf(281,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_inf_Ocobounded1)). 84.93/23.94 thf(1243,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 84.93/23.94 thf(126,axiom,((! [A:set_Pr1986765409at_nat]: ((? [B:list_P559422087at_nat]: ((set_Pr2131844118at_nat @ B) = A)) <= (finite772653738at_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_finite__list)). 84.93/23.94 thf(709,plain,((! [A:set_Pr1986765409at_nat]: (? [B:list_P559422087at_nat]: ((set_Pr2131844118at_nat @ B) = A) | ~ (finite772653738at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 84.93/23.94 thf(4,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (A @ C))) => (ord_less_eq_set_nat @ (collect_nat @ A) @ (collect_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Collect__mono)). 84.93/23.94 thf(286,plain,((! [A:(nat > $o),B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (A @ C))) => (ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 84.93/23.94 thf(288,plain,(! [B:(nat > $o),A:(nat > $o)] : ((A @ (sk1 @ (B) @ (A))) | (ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))))),inference(cnf,[status(esa)],[286])). 84.93/23.94 thf(47,axiom,(((= @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_dual__order_Oeq__iff)). 84.93/23.94 thf(435,plain,(((= @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 84.93/23.94 thf(436,plain,(((^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))) = (= @ set_nat))),inference(lifteq,[status(thm)],[435])). 84.93/23.94 thf(107,axiom,((! [A:(product_prod_nat_nat > a),B:nat]: ((finite_finite_nat @ (v_a @ A)) => (finite772653738at_nat @ (outgoing_a @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_Graph_Ofinite__outgoing)). 84.93/23.94 thf(651,plain,((! [A:(product_prod_nat_nat > a),B:nat]: ((finite_finite_nat @ (v_a @ (A))) => (finite772653738at_nat @ (outgoing_a @ (A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 84.93/23.94 thf(164,axiom,((! [A:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_dual__order_Orefl)). 84.93/23.94 thf(829,plain,((! [A:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 84.93/23.94 thf(38,axiom,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((~ ((member701585322at_nat @ A @ B) => (~ (member701585322at_nat @ A @ C)))) <= (member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_IntE)). 84.93/23.94 thf(404,plain,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (~ ((member701585322at_nat @ A @ B) => (~ (member701585322at_nat @ A @ C))) | ~ (member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 84.93/23.94 thf(229,axiom,((! [A:set_Pr1986765409at_nat,B:(set_Pr1986765409at_nat > set_Pr1986765409at_nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (B @ C)) => ((ord_le841296385at_nat @ C @ D) => ((ord_le841296385at_nat @ A @ (B @ D)) <= (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) <= (ord_le841296385at_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_order__subst1)). 84.93/23.94 thf(1055,plain,((! [A:set_Pr1986765409at_nat,B:(set_Pr1986765409at_nat > set_Pr1986765409at_nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (B @ C)) => ((ord_le841296385at_nat @ C @ D) => ((ord_le841296385at_nat @ A @ (B @ D)) | ~ (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) | ~ (ord_le841296385at_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 84.93/23.94 thf(129,axiom,(((= @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_dual__order_Oeq__iff)). 84.93/23.94 thf(718,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)],[129])). 84.93/23.94 thf(719,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = (= @ nat))),inference(lifteq,[status(thm)],[718])). 84.93/23.94 thf(153,axiom,((! [A:(product_prod_nat_nat > a)]: ((finite_finite_nat @ (v_a @ A)) => (finite772653738at_nat @ (e_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_Graph_OVfin__imp__Efin)). 84.93/23.94 thf(802,plain,((! [A:(product_prod_nat_nat > a)]: ((finite_finite_nat @ (v_a @ (A))) => (finite772653738at_nat @ (e_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 84.93/23.94 thf(24,axiom,((! [A:set_nat,B:nat]: ((~ (finite_finite_nat @ A)) => (? [C:set_nat]: ((finite_finite_nat @ C) & ((finite_card_nat @ C) = B) & (ord_less_eq_set_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_infinite__arbitrarily__large)). 84.93/23.94 thf(357,plain,((! [A:set_nat,B:nat]: ((~ (finite_finite_nat @ A)) => (? [C:set_nat]: ((finite_finite_nat @ C) & ((finite_card_nat @ C) = B) & (ord_less_eq_set_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 84.93/23.94 thf(53,axiom,((finite_Graph_a = (^ [A:(product_prod_nat_nat > a)]: (finite_finite_nat @ (v_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_Finite__Graph__def)). 84.93/23.94 thf(460,plain,(((finite_Graph_a) = (^ [A:(product_prod_nat_nat > a)]: (finite_finite_nat @ (v_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 84.93/23.94 thf(230,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ A @ C) => (ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C))) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_Int__greatest)). 84.93/23.94 thf(1059,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ A @ C) => (ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C))) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 84.93/23.94 thf(254,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((((A != C) <= (B = nil_Pr1308055047at_nat)) => (~ (! [D:nat,E:nat,F:list_P559422087at_nat]: ((B = (cons_P66992567at_nat @ (product_Pair_nat_nat @ D @ E) @ F)) => (~ ((isPath_a @ c @ E @ F @ C) & (member701585322at_nat @ (product_Pair_nat_nat @ D @ E) @ (e_a @ c)) & (A = D))))))) <= (isPath_a @ c @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_isPath_Oelims_I2_J)). 84.93/23.94 thf(1132,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: (((~ (A = C) | ~ (B = nil_Pr1308055047at_nat)) => (~ (! [D:nat,E:nat,F:list_P559422087at_nat]: ((B = (cons_P66992567at_nat @ (product_Pair_nat_nat @ D @ E) @ F)) => (~ ((isPath_a @ (c) @ E @ F @ C) & (member701585322at_nat @ (product_Pair_nat_nat @ D @ E) @ (e_a @ (c))) & (A = D))))))) | ~ (isPath_a @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 84.93/23.94 thf(78,axiom,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)) => ((((~ (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ C)) => (((~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B)))) <= ((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A)))) <= ((~ (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ C @ B)))) <= ((~ (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_le__cases3)). 84.93/23.94 thf(559,plain,((! [A:nat,B:nat,C:nat]: ((~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)) => (((~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ A @ C)) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))) | ~ ((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))) | ~ (~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ C @ B)))) | ~ (~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 84.93/23.94 thf(170,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_inf__sup__ord_I2_J)). 84.93/23.94 thf(853,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 84.93/23.94 thf(203,axiom,((! [A:set_nat]: (ord_le841296385at_nat @ (incoming_a2 @ c @ A) @ (e_a @ c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_incoming_H__edges)). 84.93/23.94 thf(969,plain,((! [A:set_nat]: (ord_le841296385at_nat @ (incoming_a2 @ (c) @ A) @ (e_a @ (c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 84.93/23.94 thf(218,axiom,((! [A:set_Pr1986765409at_nat,B:(set_Pr1986765409at_nat > set_Pr1986765409at_nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ C @ D) => ((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) <= (ord_le841296385at_nat @ E @ F))) => (ord_le841296385at_nat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_ord__eq__le__subst)). 84.93/23.94 thf(1013,plain,((! [A:set_Pr1986765409at_nat,B:(set_Pr1986765409at_nat > set_Pr1986765409at_nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ C @ D) => ((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) | ~ (ord_le841296385at_nat @ E @ F))) => (ord_le841296385at_nat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 84.93/23.94 thf(247,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) = ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_le__inf__iff)). 84.93/23.94 thf(1115,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) = ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 84.93/23.94 thf(5,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_order_Otrans)). 84.93/23.94 thf(289,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 84.93/23.94 thf(277,axiom,((ord_le841296385at_nat = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) <= (member701585322at_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_subset__eq)). 84.93/23.94 thf(1232,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) | ~ (member701585322at_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 84.93/23.94 thf(43,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: (((ord_less_eq_set_nat @ (C @ B) @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_set_nat @ (C @ A) @ D))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_order__subst2)). 84.93/23.94 thf(421,plain,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: (((ord_less_eq_set_nat @ (C @ B) @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_set_nat @ (C @ A) @ D))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 84.93/23.94 thf(176,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > nat),D:nat]: ((ord_le841296385at_nat @ A @ B) => (((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_le841296385at_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_order__subst2)). 84.93/23.94 thf(870,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > nat),D:nat]: ((ord_le841296385at_nat @ A @ B) => (((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_le841296385at_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 84.93/23.94 thf(202,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) = ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_inf_Obounded__iff)). 84.93/23.94 thf(966,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) = ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 84.93/23.94 thf(160,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_inf__le1)). 84.93/23.94 thf(821,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 84.93/23.94 thf(224,axiom,((! [A:set_nat]: ((finite772653738at_nat @ (outgoing_a2 @ c @ A)) <= (finite_finite_nat @ (v_a @ c))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_finite__outgoing_H)). 84.93/23.94 thf(1040,plain,((! [A:set_nat]: ((finite772653738at_nat @ (outgoing_a2 @ (c) @ A)) | ~ (finite_finite_nat @ (v_a @ (c)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 84.93/23.94 thf(245,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ C) @ (inf_in586391887at_nat @ B @ D)) <= (ord_le841296385at_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_Int__mono)). 84.93/23.94 thf(1109,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ C) @ (inf_in586391887at_nat @ B @ D)) | ~ (ord_le841296385at_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 84.93/23.94 thf(15,axiom,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: ((A = (B @ C)) => ((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_ord__eq__le__subst)). 84.93/23.94 thf(321,plain,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: ((A = (B @ C)) => ((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 84.93/23.94 thf(60,axiom,((edmond475474835dges_a = edmond475474835dges_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_ek__analysis__defs_OspEdges_Ocong)). 84.93/23.94 thf(485,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 84.93/23.94 thf(166,axiom,((! [A:set_Pr1986765409at_nat,B:(set_nat > set_Pr1986765409at_nat),C:set_nat,D:set_nat]: ((A = (B @ C)) => (((! [E:set_nat,F:set_nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_le841296385at_nat @ A @ (B @ D))) <= (ord_less_eq_set_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_ord__eq__le__subst)). 84.93/23.94 thf(834,plain,((! [A:set_Pr1986765409at_nat,B:(set_nat > set_Pr1986765409at_nat),C:set_nat,D:set_nat]: ((A = (B @ C)) => (((! [E:set_nat,F:set_nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_le841296385at_nat @ A @ (B @ D))) | ~ (ord_less_eq_set_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 84.93/23.94 thf(144,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) = ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Int__subset__iff)). 84.93/23.94 thf(766,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) = ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 84.93/23.94 thf(2160,plain,(! [C:product_prod_nat_nat,B:list_P559422087at_nat,A:nat] : (((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ C @ B)) @ (size_s1990949619at_nat @ B))))),inference(paramod_ordered,[status(thm)],[394,356])). 84.93/23.94 thf(2192,plain,(! [C:product_prod_nat_nat,B:list_P559422087at_nat,A:nat] : ((A != (size_s1990949619at_nat @ (cons_P66992567at_nat @ C @ B))) | (A != (size_s1990949619at_nat @ B)))),inference(simp,[status(thm)],[2160])). 84.93/23.94 thf(2206,plain,(! [B:product_prod_nat_nat,A:list_P559422087at_nat] : (((size_s1990949619at_nat @ (cons_P66992567at_nat @ B @ A)) != (size_s1990949619at_nat @ A)))),inference(simp,[status(thm)],[2192])). 84.93/23.94 thf(2281,plain,(! [B:product_prod_nat_nat,A:list_P559422087at_nat] : (((cons_P66992567at_nat @ B @ A) != A))),inference(simp,[status(thm)],[2206])). 84.93/23.94 thf(102,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_antisym)). 84.93/23.94 thf(634,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)],[102])). 84.93/23.94 thf(119,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: ((finite772653738at_nat @ (edmond475474835dges_a @ A @ B @ C)) <= (edmond1517640972ysis_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_ek__analysis_Ofinite__spEdges)). 84.93/23.94 thf(692,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: ((finite772653738at_nat @ (edmond475474835dges_a @ (A) @ B @ C)) | ~ (edmond1517640972ysis_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 84.93/23.94 thf(134,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => (((ord_le841296385at_nat @ (C @ A) @ D) <= (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ E @ F) => (ord_le841296385at_nat @ (C @ E) @ (C @ F))))) <= (ord_le841296385at_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_order__subst2)). 84.93/23.94 thf(734,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ (C @ A) @ D) | ~ (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ E @ F) => (ord_le841296385at_nat @ (C @ E) @ (C @ F)))) | ~ (ord_le841296385at_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 84.93/23.94 thf(6,axiom,(((= @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_set__eq__subset)). 84.93/23.94 thf(292,plain,(((= @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 84.93/23.94 thf(293,plain,(((^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))) = (= @ set_nat))),inference(lifteq,[status(thm)],[292])). 84.93/23.94 thf(175,axiom,((! [A:nat,B:(set_Pr1986765409at_nat > nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_le841296385at_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_order__subst1)). 84.93/23.94 thf(866,plain,((! [A:nat,B:(set_Pr1986765409at_nat > nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_le841296385at_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 84.93/23.94 thf(147,axiom,((! [A:list_P559422087at_nat,B:(product_prod_nat_nat > a),C:(product_prod_nat_nat > a),D:nat,E:nat]: ((ord_le841296385at_nat @ (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ A) @ (e_a @ B)) @ (e_a @ C)) => ((isPath_a @ B @ D @ A @ E) => (isPath_a @ C @ D @ A @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Graph_Otransfer__path)). 84.93/23.94 thf(774,plain,((! [A:list_P559422087at_nat,B:(product_prod_nat_nat > a),C:(product_prod_nat_nat > a),D:nat,E:nat]: ((ord_le841296385at_nat @ (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ A) @ (e_a @ (B))) @ (e_a @ (C))) => ((isPath_a @ (B) @ D @ A @ E) => (isPath_a @ (C) @ D @ A @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 84.93/23.94 thf(40,axiom,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => ((B = A) <= (ord_less_eq_nat @ (finite_card_nat @ A) @ (finite_card_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_card__seteq)). 84.93/23.94 thf(411,plain,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => ((B = A) | ~ (ord_less_eq_nat @ (finite_card_nat @ A) @ (finite_card_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 84.93/23.94 thf(10,axiom,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => (((finite_card_nat @ B) = (finite_card_nat @ A)) => (B = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_card__subset__eq)). 84.93/23.94 thf(304,plain,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => (((finite_card_nat @ B) = (finite_card_nat @ A)) => (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 84.93/23.94 thf(305,plain,((! [A:set_nat]: ((finite_finite_nat @ A) => (! [B:set_nat]: ((ord_less_eq_set_nat @ B @ A) => (((finite_card_nat @ B) = (finite_card_nat @ A)) => (B = A))))))),inference(miniscope,[status(thm)],[304])). 84.93/23.94 thf(306,plain,(! [B:set_nat,A:set_nat] : ((~ (finite_finite_nat @ A)) | (~ (ord_less_eq_set_nat @ B @ A)) | (~ ((finite_card_nat @ B) = (finite_card_nat @ A))) | (B = A))),inference(cnf,[status(esa)],[305])). 84.93/23.94 thf(307,plain,(! [B:set_nat,A:set_nat] : (((finite_card_nat @ B) != (finite_card_nat @ A)) | (B = A) | (~ (finite_finite_nat @ A)) | (~ (ord_less_eq_set_nat @ B @ A)))),inference(lifteq,[status(thm)],[306])). 84.93/23.94 thf(236,axiom,((! [A:(product_prod_nat_nat > a)]: ((finite_finite_nat @ (v_a @ A)) <= (finite772653738at_nat @ (e_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_Graph_OEfin__imp__Vfin)). 84.93/23.94 thf(1074,plain,((! [A:(product_prod_nat_nat > a)]: ((finite_finite_nat @ (v_a @ (A))) | ~ (finite772653738at_nat @ (e_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 84.93/23.94 thf(66,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((finite772653738at_nat @ (inf_in586391887at_nat @ A @ B)) <= ((finite772653738at_nat @ A) | (finite772653738at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_finite__Int)). 84.93/23.94 thf(512,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((finite772653738at_nat @ (inf_in586391887at_nat @ A @ B)) | ~ ((finite772653738at_nat @ A) | (finite772653738at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 84.93/23.94 thf(110,axiom,((! [A:(product_prod_nat_nat > a),B:nat]: ((finite772653738at_nat @ (incoming_a @ A @ B)) <= (finite_finite_nat @ (v_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Graph_Ofinite__incoming)). 84.93/23.94 thf(661,plain,((! [A:(product_prod_nat_nat > a),B:nat]: ((finite772653738at_nat @ (incoming_a @ (A) @ B)) | ~ (finite_finite_nat @ (v_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 84.93/23.94 thf(71,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_order__refl)). 84.93/23.94 thf(534,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 84.93/23.94 thf(233,axiom,((ord_le841296385at_nat = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_inf_Oorder__iff)). 84.93/23.94 thf(1067,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 84.93/23.94 thf(227,axiom,((! [A:nat,B:nat,C:nat]: ((member_nat @ A @ (reachableNodes_a @ c @ B)) => ((member_nat @ C @ (reachableNodes_a @ c @ B)) <= (member701585322at_nat @ (product_Pair_nat_nat @ A @ C) @ (e_a @ c)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_reachableNodes__append__edge)). 84.93/23.94 thf(1047,plain,((! [A:nat,B:nat,C:nat]: ((member_nat @ A @ (reachableNodes_a @ (c) @ B)) => ((member_nat @ C @ (reachableNodes_a @ (c) @ B)) | ~ (member701585322at_nat @ (product_Pair_nat_nat @ A @ C) @ (e_a @ (c))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 84.93/23.94 thf(17,axiom,((! [A:(product_prod_nat_nat > a),B:set_nat]: ((finite772653738at_nat @ (outgoing_a2 @ A @ B)) <= (finite_finite_nat @ (v_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_Graph_Ofinite__outgoing_H)). 84.93/23.94 thf(334,plain,((! [A:(product_prod_nat_nat > a),B:set_nat]: ((finite772653738at_nat @ (outgoing_a2 @ (A) @ B)) | ~ (finite_finite_nat @ (v_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 84.93/23.94 thf(189,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ A) = (B = A)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_antisym__conv)). 84.93/23.94 thf(910,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ A) = (B = A)) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 84.93/23.94 thf(275,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((inf_in586391887at_nat @ B @ A) = A) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_inf__absorb2)). 84.93/23.94 thf(1223,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((inf_in586391887at_nat @ B @ A) = A) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 84.93/23.94 thf(138,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > set_nat),D:set_nat]: ((((ord_less_eq_set_nat @ (C @ A) @ D) <= (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) <= (ord_le841296385at_nat @ E @ F)))) <= ((C @ B) = D)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ord__le__eq__subst)). 84.93/23.94 thf(746,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > set_nat),D:set_nat]: ((ord_less_eq_set_nat @ (C @ A) @ D) | ~ (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_le841296385at_nat @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 84.93/23.94 thf(219,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat,D:nat,E:nat]: ((isPath_a @ c @ A @ B @ C) => ((member701585322at_nat @ (product_Pair_nat_nat @ D @ E) @ (set_Pr2131844118at_nat @ B)) => ((D != A) => (? [F:nat]: (member701585322at_nat @ (product_Pair_nat_nat @ F @ D) @ (set_Pr2131844118at_nat @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_isPath__ex__edge1)). 84.93/23.94 thf(1021,plain,((! [A:nat,B:list_P559422087at_nat,C:nat,D:nat,E:nat]: ((isPath_a @ (c) @ A @ B @ C) => ((member701585322at_nat @ (product_Pair_nat_nat @ D @ E) @ (set_Pr2131844118at_nat @ B)) => ((~ (D = A)) => (? [F:nat]: (member701585322at_nat @ (product_Pair_nat_nat @ F @ D) @ (set_Pr2131844118at_nat @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 84.93/23.94 thf(262,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_inf_OcoboundedI1)). 84.93/23.94 thf(1174,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 84.93/23.94 thf(273,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (inf_in586391887at_nat @ C @ A) @ B) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_le__infI2)). 84.93/23.94 thf(1217,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (inf_in586391887at_nat @ C @ A) @ B) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 84.93/23.94 thf(32,axiom,((outgoing_a = outgoing_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_Graph_Ooutgoing_Ocong)). 84.93/23.94 thf(392,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 84.93/23.94 thf(39,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [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)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_order__subst2)). 84.93/23.94 thf(407,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 84.93/23.94 thf(158,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ C) @ (inf_in586391887at_nat @ B @ D)) <= (ord_le841296385at_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_inf__mono)). 84.93/23.94 thf(815,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ C) @ (inf_in586391887at_nat @ B @ D)) | ~ (ord_le841296385at_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 84.93/23.94 thf(280,axiom,((! [A:nat,B:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ A @ (finite447719721at_nat @ B)) => (~ (! [C:set_Pr1986765409at_nat]: ((((finite447719721at_nat @ C) = A) => (~ (finite772653738at_nat @ C))) <= (ord_le841296385at_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_obtain__subset__with__card__n)). 84.93/23.94 thf(1238,plain,((! [A:nat,B:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ A @ (finite447719721at_nat @ B)) => (~ (! [C:set_Pr1986765409at_nat]: ((((finite447719721at_nat @ C) = A) => (~ (finite772653738at_nat @ C))) | ~ (ord_le841296385at_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 84.93/23.94 thf(1506,plain,(! [B:(nat > $o),A:(nat > $o)] : ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) | ((A @ (sk1 @ (B) @ (A))) != (ord_le841296385at_nat @ edges @ (e_a @ (c)))))),inference(paramod_ordered,[status(thm)],[288,282])). 84.93/23.94 thf(1574,plain,(! [A:(nat > $o)] : ((ord_less_eq_set_nat @ (collect_nat @ (^ [B:nat]: (ord_le841296385at_nat @ edges @ (e_a @ c)))) @ (collect_nat @ (A))))),inference(pre_uni,[status(thm)],[1506:[bind(A, $thf(^ [C:nat]: (ord_le841296385at_nat @ edges @ (e_a @ c)))),bind(B, $thf(B))]])). 84.93/23.94 thf(1619,plain,(! [A:(nat > $o)] : ((ord_less_eq_set_nat @ (collect_nat @ (^ [B:nat]: (ord_le841296385at_nat @ edges @ (e_a @ c)))) @ (collect_nat @ (A))))),inference(simp,[status(thm)],[1574])). 84.93/23.94 thf(1739,plain,(! [A:(nat > $o)] : ((ord_less_eq_set_nat @ (collect_nat @ (^ [B:nat]: ($false))) @ (collect_nat @ (A))))),inference(rewrite,[status(thm)],[1619,282])). 84.93/23.94 thf(287,plain,(! [B:(nat > $o),A:(nat > $o)] : ((~ (B @ (sk1 @ (B) @ (A)))) | (ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))))),inference(cnf,[status(esa)],[286])). 84.93/23.94 thf(1744,plain,(! [C:(nat > $o),B:(nat > $o),A:(nat > $o)] : ((ord_less_eq_set_nat @ (collect_nat @ (B)) @ (collect_nat @ (C))) | ((ord_less_eq_set_nat @ (collect_nat @ (^ [D:nat]: ($false))) @ (collect_nat @ (A))) != (C @ (sk1 @ (C) @ (B)))))),inference(paramod_ordered,[status(thm)],[1739,287])). 84.93/23.94 thf(1746,plain,(! [B:(nat > (nat > $o)),A:(nat > $o)] : ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (^ [C:nat]: (ord_less_eq_set_nat @ (collect_nat @ (^ [D:nat]: ($false))) @ (collect_nat @ (B @ C)))))))),inference(pre_uni,[status(thm)],[1744:[bind(A, $thf(F @ (sk1 @ (^ [E:nat]: (ord_less_eq_set_nat @ (collect_nat @ (^ [F:nat]: ($false))) @ (collect_nat @ (F @ E)))) @ B))),bind(B, $thf(B)),bind(C, $thf(^ [E:nat]: (ord_less_eq_set_nat @ (collect_nat @ (^ [F:nat]: ($false))) @ (collect_nat @ (F @ E)))))]])). 84.93/23.94 thf(1748,plain,(! [B:(nat > (nat > $o)),A:(nat > $o)] : ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (^ [C:nat]: (ord_less_eq_set_nat @ (collect_nat @ (^ [D:nat]: ($false))) @ (collect_nat @ (B @ C)))))))),inference(simp,[status(thm)],[1746])). 84.93/23.94 thf(1883,plain,(! [A:(nat > $o)] : ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (^ [B:nat]: ($true)))))),inference(rewrite,[status(thm)],[1748,1739])). 84.93/23.94 thf(181,axiom,((ord_le841296385at_nat = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_le__iff__inf)). 84.93/23.94 thf(886,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 84.93/23.94 thf(887,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A)))),inference(lifteq,[status(thm)],[886])). 84.93/23.94 thf(1255,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A)))),inference(rewrite,[status(thm)],[887,793])). 84.93/23.94 thf(9,axiom,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_set_nat @ (C @ B) @ D) => ((ord_less_eq_set_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_order__subst2)). 84.93/23.94 thf(300,plain,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_set_nat @ (C @ B) @ D) => ((ord_less_eq_set_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 84.93/23.94 thf(301,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:(nat > set_nat),D:set_nat]: ((ord_less_eq_set_nat @ (C @ B) @ D) => ((ord_less_eq_set_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))))))))),inference(miniscope,[status(thm)],[300])). 84.93/23.94 thf(302,plain,(! [D:set_nat,C:(nat > set_nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_set_nat @ (C @ B) @ D)) | (ord_less_eq_set_nat @ (C @ A) @ D) | (~ (ord_less_eq_set_nat @ (C @ (sk2 @ D @ (C) @ B @ A)) @ (C @ (sk3 @ D @ (C) @ B @ A)))))),inference(cnf,[status(esa)],[301])). 84.93/23.94 thf(168,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_le__infI1)). 84.93/23.94 thf(847,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 84.93/23.94 thf(98,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/sandbox2/benchmark/theBenchmark.p',fact_200_Graph_OshortestPath__is__path)). 84.93/23.94 thf(625,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)],[98])). 84.93/23.94 thf(16,axiom,((! [A:nat,B:set_nat]: ((ord_less_eq_nat @ A @ (finite_card_nat @ B)) => (~ (! [C:set_nat]: (((~ (finite_finite_nat @ C)) <= ((finite_card_nat @ C) = A)) <= (ord_less_eq_set_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_obtain__subset__with__card__n)). 84.93/23.94 thf(329,plain,((! [A:nat,B:set_nat]: ((ord_less_eq_nat @ A @ (finite_card_nat @ B)) => (~ (! [C:set_nat]: (~ (finite_finite_nat @ C) | ~ ((finite_card_nat @ C) = A) | ~ (ord_less_eq_set_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 84.93/23.94 thf(69,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((~ (! [D:nat]: ((~ (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))) <= (A @ D)))) <= (! [D:nat]: ((ord_less_eq_nat @ D @ C) <= (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_bounded__Max__nat)). 84.93/23.94 thf(522,plain,((! [A:(nat > $o),B:nat,C:nat]: (~ (! [D:nat]: (~ (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D))) | ~ (A @ D))) | ~ (! [D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (A @ D))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 84.93/23.94 thf(62,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_antisym__conv)). 84.93/23.94 thf(493,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)],[62])). 84.93/23.94 thf(221,axiom,((! [A:set_Pr1986765409at_nat,B:(set_nat > set_Pr1986765409at_nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_le841296385at_nat @ A @ (B @ D)))) <= (ord_le841296385at_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_order__subst1)). 84.93/23.94 thf(1027,plain,((! [A:set_Pr1986765409at_nat,B:(set_nat > set_Pr1986765409at_nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_le841296385at_nat @ A @ (B @ D)))) | ~ (ord_le841296385at_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 84.93/23.94 thf(252,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat,E:product_prod_nat_nat]: ((isPath_a @ A @ B @ C @ D) => ((member701585322at_nat @ E @ (e_a @ A)) <= (member701585322at_nat @ E @ (set_Pr2131844118at_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Graph_OisPath__edgeset)). 84.93/23.94 thf(1128,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat,E:product_prod_nat_nat]: ((isPath_a @ (A) @ B @ C @ D) => ((member701585322at_nat @ E @ (e_a @ (A))) | ~ (member701585322at_nat @ E @ (set_Pr2131844118at_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 84.93/23.94 thf(167,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ C) => (ord_le841296385at_nat @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_ord__eq__le__trans)). 84.93/23.94 thf(842,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ C) => (ord_le841296385at_nat @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 84.93/23.94 thf(205,axiom,((! [A:nat,B:nat,C:nat,D:list_P559422087at_nat,E:nat]: ((isPath_a @ c @ A @ (cons_P66992567at_nat @ (product_Pair_nat_nat @ B @ C) @ D) @ E) = ((member701585322at_nat @ (product_Pair_nat_nat @ B @ C) @ (e_a @ c)) & (isPath_a @ c @ C @ D @ E) & (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_isPath_Osimps_I2_J)). 84.93/23.94 thf(974,plain,((! [A:nat,B:nat,C:nat,D:list_P559422087at_nat,E:nat]: ((isPath_a @ (c) @ A @ (cons_P66992567at_nat @ (product_Pair_nat_nat @ B @ C) @ D) @ E) = ((member701585322at_nat @ (product_Pair_nat_nat @ B @ C) @ (e_a @ (c))) & (isPath_a @ (c) @ C @ D @ E) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 84.93/23.94 thf(3,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ A) @ (collect_nat @ B)) = (! [C:nat]: ((B @ C) <= (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Collect__mono__iff)). 84.93/23.94 thf(283,plain,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) = (! [C:nat]: ((B @ C) | ~ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 84.93/23.94 thf(284,plain,(! [B:(nat > $o),A:(nat > $o)] : (((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) = (! [C:nat]: ((B @ C) | ~ (A @ C)))))),inference(cnf,[status(esa)],[283])). 84.93/23.94 thf(285,plain,(! [B:(nat > $o),A:(nat > $o)] : (((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) = (! [C:nat]: ((B @ C) | ~ (A @ C)))))),inference(lifteq,[status(thm)],[284])). 84.93/23.94 thf(244,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((finite772653738at_nat @ A) => ((ord_le841296385at_nat @ B @ A) => (finite772653738at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_rev__finite__subset)). 84.93/23.94 thf(1106,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((finite772653738at_nat @ A) => ((ord_le841296385at_nat @ B @ A) => (finite772653738at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 84.93/23.94 thf(136,axiom,((! [A:nat]: (ord_less_eq_set_nat @ (adjacent_nodes_a @ c @ A) @ (v_a @ c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_adjacent__nodes__ss__V)). 84.93/23.94 thf(742,plain,((! [A:nat]: (ord_less_eq_set_nat @ (adjacent_nodes_a @ (c) @ A) @ (v_a @ (c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 84.93/23.94 thf(278,axiom,(((finite772653738at_nat @ (e_a @ c)) => (finite_Graph_a @ c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Finite__Graph__EI)). 84.93/23.94 thf(1234,plain,(((finite772653738at_nat @ (e_a @ (c))) => (finite_Graph_a @ (c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 84.93/23.94 thf(177,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ A) => ((ord_less_eq_nat @ (finite447719721at_nat @ A) @ (finite447719721at_nat @ B)) => (B = A))) <= (finite772653738at_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_card__seteq)). 84.93/23.94 thf(874,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ A) => ((ord_less_eq_nat @ (finite447719721at_nat @ A) @ (finite447719721at_nat @ B)) => (B = A))) | ~ (finite772653738at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 84.93/23.94 thf(94,axiom,((! [A:product_prod_nat_nat,B:list_P559422087at_nat,C:product_prod_nat_nat,D:list_P559422087at_nat]: (((cons_P66992567at_nat @ A @ B) = (cons_P66992567at_nat @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_list_Oinject)). 84.93/23.94 thf(615,plain,((! [A:product_prod_nat_nat,B:list_P559422087at_nat,C:product_prod_nat_nat,D:list_P559422087at_nat]: (((cons_P66992567at_nat @ A @ B) = (cons_P66992567at_nat @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 84.93/23.94 thf(249,axiom,((! [A:set_nat]: ((finite_finite_nat @ (v_a @ c)) => (finite772653738at_nat @ (incoming_a2 @ c @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_finite__incoming_H)). 84.93/23.94 thf(1121,plain,((! [A:set_nat]: ((finite_finite_nat @ (v_a @ (c))) => (finite772653738at_nat @ (incoming_a2 @ (c) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 84.93/23.94 thf(232,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((inf_in586391887at_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_inf_Oabsorb1)). 84.93/23.94 thf(1064,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((inf_in586391887at_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 84.93/23.94 thf(1233,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) | ~ (member701585322at_nat @ C @ A))))),inference(lifteq,[status(thm)],[1232])). 84.93/23.94 thf(1970,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) | ~ (member701585322at_nat @ C @ A))))),inference(rewrite,[status(thm)],[1233,793])). 84.93/23.94 thf(216,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((~ ((ord_le841296385at_nat @ A @ B) => (~ (ord_le841296385at_nat @ A @ C)))) <= (ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_inf_OboundedE)). 84.93/23.94 thf(1006,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (~ ((ord_le841296385at_nat @ A @ B) => (~ (ord_le841296385at_nat @ A @ C))) | ~ (ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 84.93/23.94 thf(248,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ A @ C) => (ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_inf_OboundedI)). 84.93/23.94 thf(1118,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ A @ C) => (ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 84.93/23.94 thf(1068,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B))))),inference(lifteq,[status(thm)],[1067])). 84.93/23.94 thf(1259,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B))))),inference(rewrite,[status(thm)],[1068,793])). 84.93/23.94 thf(14,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat,E:nat,F:nat]: (((member701585322at_nat @ (product_Pair_nat_nat @ E @ F) @ (set_Pr2131844118at_nat @ C)) => ((? [G:nat]: (member701585322at_nat @ (product_Pair_nat_nat @ F @ G) @ (set_Pr2131844118at_nat @ C))) <= (F != D))) <= (isPath_a @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_Graph_OisPath__ex__edge2)). 84.93/23.94 thf(317,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat,E:nat,F:nat]: (((member701585322at_nat @ (product_Pair_nat_nat @ E @ F) @ (set_Pr2131844118at_nat @ C)) => (? [G:nat]: (member701585322at_nat @ (product_Pair_nat_nat @ F @ G) @ (set_Pr2131844118at_nat @ C)) | (F = D))) | ~ (isPath_a @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 84.93/23.94 thf(1666,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) @ (sk47 @ s @ (v_a @ (c))))) | ((member_nat @ (size_s1990949619at_nat @ B) @ (v_a @ (c))) != (member_nat @ s @ (v_a @ (c)))))),inference(paramod_ordered,[status(thm)],[1076,1665])). 84.93/23.94 thf(1689,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) @ (sk47 @ s @ (v_a @ (c))))) | ((size_s1990949619at_nat @ B) != s) | ((v_a @ (c)) != (v_a @ (c))))),inference(simp,[status(thm)],[1666])). 84.93/23.94 thf(1700,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) @ (sk47 @ s @ (v_a @ (c))))) | ((size_s1990949619at_nat @ B) != s))),inference(simp,[status(thm)],[1689])). 84.93/23.94 thf(1721,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | ((size_s1990949619at_nat @ B) != s) | ((ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) @ (sk47 @ s @ (v_a @ (c)))) != (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | ~ ($true))),inference(eqfactor_ordered,[status(thm)],[1700])). 84.93/23.94 thf(1724,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | ((size_s1990949619at_nat @ B) != s) | ((size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) != (size_s1990949619at_nat @ B)) | ((sk47 @ s @ (v_a @ (c))) != (sk47 @ s @ (v_a @ (c)))))),inference(simp,[status(thm)],[1721])). 84.93/23.94 thf(1732,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | ((size_s1990949619at_nat @ B) != s) | ((size_s1990949619at_nat @ (cons_P66992567at_nat @ A @ B)) != (size_s1990949619at_nat @ B)))),inference(simp,[status(thm)],[1724])). 84.93/23.94 thf(1856,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : ((~ (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (sk47 @ s @ (v_a @ (c))))) | ((size_s1990949619at_nat @ B) != s) | ((cons_P66992567at_nat @ A @ B) != B))),inference(simp,[status(thm)],[1732])). 84.93/23.94 thf(132,axiom,((! [A:nat,B:nat,C:(nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((((ord_le841296385at_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le841296385at_nat @ (C @ E) @ (C @ F))))) <= ((C @ B) = D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_ord__le__eq__subst)). 84.93/23.94 thf(725,plain,((! [A:nat,B:nat,C:(nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le841296385at_nat @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 84.93/23.94 thf(257,axiom,((ord_le841296385at_nat @ (edmond475474835dges_a @ c @ s @ t) @ (e_a @ c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_spEdges__ss__E)). 84.93/23.94 thf(1160,plain,((ord_le841296385at_nat @ (edmond475474835dges_a @ (c) @ s @ t) @ (e_a @ (c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 84.93/23.94 thf(19,axiom,((edmond771116670s_uE_a = edmond771116670s_uE_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_ek__analysis__defs_OuE_Ocong)). 84.93/23.94 thf(339,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 84.93/23.94 thf(103,axiom,((! [A:set_nat,B:nat]: (((member_nat @ B @ A) => (? [C:nat]: ((member_nat @ C @ A) & (ord_less_eq_nat @ B @ C) & ! [D:nat]: (((C = D) <= (ord_less_eq_nat @ C @ D)) <= (member_nat @ D @ A))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_finite__has__maximal2)). 84.93/23.94 thf(637,plain,((! [A:set_nat,B:nat]: (((member_nat @ B @ A) => (? [C:nat]: ((member_nat @ C @ A) & (ord_less_eq_nat @ B @ C) & ! [D:nat]: ((C = D) | ~ (ord_less_eq_nat @ C @ D) | ~ (member_nat @ D @ A))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 84.93/23.94 thf(72,axiom,((! [A:list_nat]: (finite_finite_nat @ (set_nat2 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_List_Ofinite__set)). 84.93/23.94 thf(536,plain,((! [A:list_nat]: (finite_finite_nat @ (set_nat2 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 84.93/23.94 thf(537,plain,(! [A:list_nat] : ((finite_finite_nat @ (set_nat2 @ A)))),inference(cnf,[status(esa)],[536])). 84.93/23.94 thf(186,axiom,((! [A:(product_prod_nat_nat > $o),B:(product_prod_nat_nat > $o)]: ((ord_le841296385at_nat @ (collec7649004at_nat @ A) @ (collec7649004at_nat @ B)) = (! [C:product_prod_nat_nat]: ((A @ C) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_Collect__mono__iff)). 84.93/23.94 thf(901,plain,((! [A:(product_prod_nat_nat > $o),B:(product_prod_nat_nat > $o)]: ((ord_le841296385at_nat @ (collec7649004at_nat @ (A)) @ (collec7649004at_nat @ (B))) = (! [C:product_prod_nat_nat]: ((A @ C) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 84.93/23.94 thf(117,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_equalityD1)). 84.93/23.94 thf(686,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 84.93/23.94 thf(97,axiom,((! [A:product_prod_nat_nat,B:(product_prod_nat_nat > $o)]: ((member701585322at_nat @ A @ (collec7649004at_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_mem__Collect__eq)). 84.93/23.94 thf(622,plain,((! [A:product_prod_nat_nat,B:(product_prod_nat_nat > $o)]: ((member701585322at_nat @ A @ (collec7649004at_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 84.93/23.94 thf(207,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat,D:nat,E:nat]: ((((E != C) => (? [F:nat]: (member701585322at_nat @ (product_Pair_nat_nat @ E @ F) @ (set_Pr2131844118at_nat @ B)))) <= (member701585322at_nat @ (product_Pair_nat_nat @ D @ E) @ (set_Pr2131844118at_nat @ B))) <= (isPath_a @ c @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_isPath__ex__edge2)). 84.93/23.94 thf(985,plain,((! [A:nat,B:list_P559422087at_nat,C:nat,D:nat,E:nat]: (((~ (E = C)) => (? [F:nat]: (member701585322at_nat @ (product_Pair_nat_nat @ E @ F) @ (set_Pr2131844118at_nat @ B)))) | ~ (member701585322at_nat @ (product_Pair_nat_nat @ D @ E) @ (set_Pr2131844118at_nat @ B)) | ~ (isPath_a @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 84.93/23.94 thf(67,axiom,((reachableNodes_a = reachableNodes_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_Graph_OreachableNodes_Ocong)). 84.93/23.94 thf(515,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 84.93/23.94 thf(135,axiom,((! [A:set_Pr1986765409at_nat,B:(nat > set_Pr1986765409at_nat),C:nat,D:nat]: ((ord_le841296385at_nat @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le841296385at_nat @ (B @ E) @ (B @ F)))) => (ord_le841296385at_nat @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_order__subst1)). 84.93/23.94 thf(738,plain,((! [A:set_Pr1986765409at_nat,B:(nat > set_Pr1986765409at_nat),C:nat,D:nat]: ((ord_le841296385at_nat @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le841296385at_nat @ (B @ E) @ (B @ F)))) => (ord_le841296385at_nat @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 84.93/23.94 thf(270,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > set_nat),D:set_nat]: (((ord_less_eq_set_nat @ (C @ B) @ D) => ((ord_less_eq_set_nat @ (C @ A) @ D) <= (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ E @ F) => (ord_less_eq_set_nat @ (C @ E) @ (C @ F)))))) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_order__subst2)). 84.93/23.94 thf(1192,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > set_nat),D:set_nat]: (((ord_less_eq_set_nat @ (C @ B) @ D) => ((ord_less_eq_set_nat @ (C @ A) @ D) | ~ (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ E @ F) => (ord_less_eq_set_nat @ (C @ E) @ (C @ F)))))) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 84.93/23.94 thf(228,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_ord__le__eq__trans)). 84.93/23.94 thf(1050,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 84.93/23.94 thf(130,axiom,(((= @ set_Pr1986765409at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_dual__order_Oeq__iff)). 84.93/23.94 thf(720,plain,(((= @ set_Pr1986765409at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 84.93/23.94 thf(721,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) & (ord_le841296385at_nat @ B @ A))) = (= @ set_Pr1986765409at_nat))),inference(lifteq,[status(thm)],[720])). 84.93/23.94 thf(214,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ A @ C) <= (ord_le841296385at_nat @ B @ C)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_order__trans)). 84.93/23.94 thf(1002,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ C) | ~ (ord_le841296385at_nat @ B @ C) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 84.93/23.94 thf(461,plain,(((finite_Graph_a) = (^ [A:(product_prod_nat_nat > a)]: (finite_finite_nat @ (v_a @ A))))),inference(lifteq,[status(thm)],[460])). 84.93/23.94 thf(386,plain,(((finite_Graph_a) = (edmond1517640972ysis_a))),inference(lifteq,[status(thm)],[385])). 84.93/23.94 thf(1246,plain,(((^ [A:(product_prod_nat_nat > a)]: (finite_finite_nat @ (v_a @ A))) = (edmond1517640972ysis_a))),inference(rewrite,[status(thm)],[461,386])). 84.93/23.94 thf(26,axiom,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: ((((ord_less_eq_set_nat @ A @ (B @ D)) <= (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_nat @ E @ F)))) <= (ord_less_eq_set_nat @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_ord__eq__le__subst)). 84.93/23.94 thf(371,plain,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ A @ (B @ D)) | ~ (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) | ~ (ord_less_eq_set_nat @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 84.93/23.94 thf(105,axiom,((! [A:nat,B:(product_prod_nat_nat > a)]: ((ord_less_eq_set_nat @ (reachableNodes_a @ B @ A) @ (v_a @ B)) <= (member_nat @ A @ (v_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Graph_Oreachable__ss__V)). 84.93/23.94 thf(647,plain,((! [A:nat,B:(product_prod_nat_nat > a)]: ((ord_less_eq_set_nat @ (reachableNodes_a @ (B) @ A) @ (v_a @ (B))) | ~ (member_nat @ A @ (v_a @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 84.93/23.94 thf(1262,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A))) | ((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)) != (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)))),inference(paramod_ordered,[status(thm)],[1259,1255])). 84.93/23.94 thf(1263,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A)))),inference(pattern_uni,[status(thm)],[1262:[]])). 84.93/23.94 thf(212,axiom,((! [A:set_nat,B:(set_Pr1986765409at_nat > set_nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ A @ (B @ C)) => ((ord_le841296385at_nat @ C @ D) => ((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ E @ F) => (ord_less_eq_set_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_order__subst1)). 84.93/23.94 thf(997,plain,((! [A:set_nat,B:(set_Pr1986765409at_nat > set_nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ A @ (B @ C)) => ((ord_le841296385at_nat @ C @ D) => ((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ E @ F) => (ord_less_eq_set_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 84.93/23.94 thf(253,axiom,((ord_le841296385at_nat @ edges @ (set_Pr2131844118at_nat @ p))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_SP__EDGES)). 84.93/23.94 thf(1131,plain,((ord_le841296385at_nat @ edges @ (set_Pr2131844118at_nat @ p))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 84.93/23.94 thf(21,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ B @ C) => (ord_less_eq_set_nat @ A @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_order__trans)). 84.93/23.94 thf(343,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ B @ C) => (ord_less_eq_set_nat @ A @ C)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 84.93/23.94 thf(12,axiom,((! [A:set_nat,B:set_nat]: (((B = A) <= (ord_less_eq_set_nat @ B @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_dual__order_Oantisym)). 84.93/23.94 thf(311,plain,((! [A:set_nat,B:set_nat]: ((B = A) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 84.93/23.94 thf(143,axiom,((edmond1517640972ysis_a @ c)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_ek__analysis__axioms)). 84.93/23.94 thf(765,plain,((edmond1517640972ysis_a @ (c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 84.93/23.94 thf(235,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:product_prod_nat_nat]: ((ord_le841296385at_nat @ A @ B) => ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_subsetD)). 84.93/23.94 thf(1071,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:product_prod_nat_nat]: ((ord_le841296385at_nat @ A @ B) => ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 84.93/23.94 thf(70,axiom,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_set_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_order__subst1)). 84.93/23.94 thf(530,plain,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_set_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 84.93/23.94 thf(152,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ A @ B) => (((C @ B) = D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_le841296385at_nat @ (C @ E) @ (C @ F)))) => (ord_le841296385at_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_ord__le__eq__subst)). 84.93/23.94 thf(794,plain,((! [A:set_nat,B:set_nat,C:(set_nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ A @ B) => (((C @ B) = D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_le841296385at_nat @ (C @ E) @ (C @ F)))) => (ord_le841296385at_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 84.93/23.94 thf(83,axiom,((! [A:set_Pr1986765409at_nat]: ((collec7649004at_nat @ (^ [B:product_prod_nat_nat]: (member701585322at_nat @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Collect__mem__eq)). 84.93/23.94 thf(586,plain,((! [A:set_Pr1986765409at_nat]: ((collec7649004at_nat @ (^ [B:product_prod_nat_nat]: (member701585322at_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 84.93/23.94 thf(182,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) <= (ord_le841296385at_nat @ A @ C)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_le__infI)). 84.93/23.94 thf(888,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) | ~ (ord_le841296385at_nat @ A @ C) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 84.93/23.94 thf(934,plain,(! [D:$o,C:nat,B:list_P559422087at_nat,A:nat] : ((~ (D = (~ ((A = (sk91 @ D @ C @ B @ A)) & (isPath_a @ (c) @ (sk92 @ D @ C @ B @ A) @ (sk93 @ D @ C @ B @ A) @ C) & (member701585322at_nat @ (product_Pair_nat_nat @ (sk91 @ D @ C @ B @ A) @ (sk92 @ D @ C @ B @ A)) @ (e_a @ (c))))))) | (~ (D = (~ (A = C)))) | (~ ((isPath_a @ (c) @ A @ B @ C) = D)))),inference(cnf,[status(esa)],[930])). 84.93/23.94 thf(941,plain,(! [D:$o,C:nat,B:list_P559422087at_nat,A:nat] : (((~ ((A = (sk91 @ D @ C @ B @ A)) & (isPath_a @ (c) @ (sk92 @ D @ C @ B @ A) @ (sk93 @ D @ C @ B @ A) @ C) & (member701585322at_nat @ (product_Pair_nat_nat @ (sk91 @ D @ C @ B @ A) @ (sk92 @ D @ C @ B @ A)) @ (e_a @ (c))))) != D) | (D != (~ (A = C))) | ((isPath_a @ (c) @ A @ B @ C) != D))),inference(lifteq,[status(thm)],[934])). 84.93/23.94 thf(942,plain,(! [C:nat,B:list_P559422087at_nat,A:nat] : (((~ ((A = (sk91 @ (~ (A = C)) @ C @ B @ A)) & (isPath_a @ (c) @ (sk92 @ (~ (A = C)) @ C @ B @ A) @ (sk93 @ (~ (A = C)) @ C @ B @ A) @ C) & (member701585322at_nat @ (product_Pair_nat_nat @ (sk91 @ (~ (A = C)) @ C @ B @ A) @ (sk92 @ (~ (A = C)) @ C @ B @ A)) @ (e_a @ (c))))) != (~ (A = C))) | ((isPath_a @ (c) @ A @ B @ C) != (~ (A = C))))),inference(simp,[status(thm)],[941])). 84.93/23.94 thf(1278,plain,(! [C:nat,B:list_P559422087at_nat,A:nat] : ((((A = (sk91 @ (~ (A = C)) @ C @ B @ A)) & (isPath_a @ (c) @ (sk92 @ (~ (A = C)) @ C @ B @ A) @ (sk93 @ (~ (A = C)) @ C @ B @ A) @ C) & (member701585322at_nat @ (product_Pair_nat_nat @ (sk91 @ (~ (A = C)) @ C @ B @ A) @ (sk92 @ (~ (A = C)) @ C @ B @ A)) @ (e_a @ (c)))) != (A = C)) | ((isPath_a @ (c) @ A @ B @ C) != (~ (A = C))))),inference(simp,[status(thm)],[942])). 84.93/23.94 thf(95,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_subset__eq)). 84.93/23.94 thf(618,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 84.93/23.94 thf(44,axiom,((! [A:nat,B:list_nat]: ((member_nat @ A @ (set_nat2 @ B)) => ((~ (! [C:nat,D:list_nat]: ((B = (cons_nat @ C @ D)) => (~ (member_nat @ A @ (set_nat2 @ D)))))) <= (! [C:list_nat]: (B != (cons_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_list_Oset__cases)). 84.93/23.94 thf(425,plain,((! [A:nat,B:list_nat]: ((member_nat @ A @ (set_nat2 @ B)) => (~ (! [C:nat,D:list_nat]: ((B = (cons_nat @ C @ D)) => (~ (member_nat @ A @ (set_nat2 @ D))))) | ~ (! [C:list_nat]: ~ (B = (cons_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 84.93/23.94 thf(137,axiom,(((= @ set_Pr1986765409at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ B @ A) & (ord_le841296385at_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_set__eq__subset)). 84.93/23.94 thf(744,plain,(((= @ set_Pr1986765409at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ B @ A) & (ord_le841296385at_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 84.93/23.94 thf(745,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ B @ A) & (ord_le841296385at_nat @ A @ B))) = (= @ set_Pr1986765409at_nat))),inference(lifteq,[status(thm)],[744])). 84.93/23.94 thf(79,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: ((edmond1517640972ysis_a @ A) => (ord_less_eq_nat @ (finite447719721at_nat @ (edmond475474835dges_a @ A @ B @ C)) @ (finite447719721at_nat @ (edmond771116670s_uE_a @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_ek__analysis_Ocard__spEdges__le)). 84.93/23.94 thf(573,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: ((edmond1517640972ysis_a @ (A)) => (ord_less_eq_nat @ (finite447719721at_nat @ (edmond475474835dges_a @ (A) @ B @ C)) @ (finite447719721at_nat @ (edmond771116670s_uE_a @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 84.93/23.94 thf(8,axiom,((! [A:set_nat,B:set_nat]: ((A = B) => (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_eq__refl)). 84.93/23.94 thf(296,plain,((! [A:set_nat,B:set_nat]: ((A = B) => (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 84.93/23.94 thf(133,axiom,((e_a = e_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Graph_OE_Ocong)). 84.93/23.94 thf(733,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 84.93/23.94 thf(82,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_linear)). 84.93/23.94 thf(584,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)],[82])). 84.93/23.94 thf(187,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:product_prod_nat_nat]: ((ord_le841296385at_nat @ A @ B) => ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_in__mono)). 84.93/23.94 thf(904,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:product_prod_nat_nat]: ((ord_le841296385at_nat @ A @ B) => ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 84.93/23.94 thf(146,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_a @ c @ A @ B @ C) <= (isShortestPath_a @ c @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_shortestPath__is__path)). 84.93/23.94 thf(772,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isPath_a @ (c) @ A @ B @ C) | ~ (isShortestPath_a @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 84.93/23.94 thf(1928,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B)))) | ((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)) != (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)))),inference(paramod_ordered,[status(thm)],[1919,1259])). 84.93/23.94 thf(1929,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B))))),inference(pattern_uni,[status(thm)],[1928:[]])). 84.93/23.94 thf(250,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((finite772653738at_nat @ A) <= (finite772653738at_nat @ B)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_finite__subset)). 84.93/23.94 thf(1124,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((finite772653738at_nat @ A) | ~ (finite772653738at_nat @ B) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 84.93/23.94 thf(81,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_ord__le__eq__trans)). 84.93/23.94 thf(579,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)],[81])). 84.93/23.94 thf(290,plain,((! [A:nat,B:nat]: (! [C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(miniscope,[status(thm)],[289])). 84.93/23.94 thf(291,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ C) | (~ (ord_less_eq_nat @ B @ C)) | (~ (ord_less_eq_nat @ A @ B)))),inference(cnf,[status(esa)],[290])). 84.93/23.94 thf(276,axiom,((! [A:set_se1612935105at_nat,B:set_Pr1986765409at_nat]: ((finite1457549322at_nat @ A) => ((member298845450at_nat @ B @ A) => (? [C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ B @ C) & ! [D:set_Pr1986765409at_nat]: (((C = D) <= (ord_le841296385at_nat @ C @ D)) <= (member298845450at_nat @ D @ A)) & (member298845450at_nat @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_finite__has__maximal2)). 84.93/23.94 thf(1226,plain,((! [A:set_se1612935105at_nat,B:set_Pr1986765409at_nat]: ((finite1457549322at_nat @ A) => ((member298845450at_nat @ B @ A) => (? [C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ B @ C) & ! [D:set_Pr1986765409at_nat]: ((C = D) | ~ (ord_le841296385at_nat @ C @ D) | ~ (member298845450at_nat @ D @ A)) & (member298845450at_nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 84.93/23.94 thf(75,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((! [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)) <= ((C @ B) = D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ord__le__eq__subst)). 84.93/23.94 thf(545,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: (((! [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)) | ~ ((C @ B) = D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 84.93/23.94 thf(28,axiom,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C)) = ((member701585322at_nat @ A @ B) & (member701585322at_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Int__iff)). 84.93/23.94 thf(382,plain,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C)) = ((member701585322at_nat @ A @ B) & (member701585322at_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 84.93/23.94 thf(92,axiom,((isPath_a = isPath_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Graph_OisPath_Ocong)). 84.93/23.94 thf(611,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 84.93/23.94 thf(55,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_ord__eq__le__subst)). 84.93/23.94 thf(466,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 84.93/23.94 thf(124,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_antisym__conv)). 84.93/23.94 thf(704,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 84.93/23.94 thf(196,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ A) => (A = B)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_order__class_Oorder_Oantisym)). 84.93/23.94 thf(947,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ B @ A) => (A = B)) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 84.93/23.94 thf(2534,plain,(! [C:set_nat,B:set_nat,A:(nat > $o)] : (((finite_card_nat @ C) != (finite_card_nat @ B)) | (C = B) | (~ (finite_finite_nat @ B)) | ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (^ [D:nat]: ($true)))) != (ord_less_eq_set_nat @ C @ B)))),inference(paramod_ordered,[status(thm)],[1883,307])). 84.93/23.94 thf(2535,plain,(! [A:(nat > $o)] : (((finite_card_nat @ (collect_nat @ (A))) != (finite_card_nat @ (collect_nat @ (^ [B:nat]: ($true))))) | ((collect_nat @ (A)) = (collect_nat @ (^ [B:nat]: ($true)))) | (~ (finite_finite_nat @ (collect_nat @ (^ [B:nat]: ($true))))))),inference(pattern_uni,[status(thm)],[2534:[bind(A, $thf(D)),bind(B, $thf(collect_nat @ (^ [D:nat]: ($true)))),bind(C, $thf(collect_nat @ (D)))]])). 84.93/23.94 thf(2557,plain,(! [A:(nat > $o)] : (((finite_card_nat @ (collect_nat @ (A))) != (finite_card_nat @ (collect_nat @ (^ [B:nat]: ($true))))) | ((collect_nat @ (A)) = (collect_nat @ (^ [B:nat]: ($true)))) | (~ (finite_finite_nat @ (collect_nat @ (^ [B:nat]: ($true))))))),inference(simp,[status(thm)],[2535])). 84.93/23.94 thf(154,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(product_prod_nat_nat > $o),D:(product_prod_nat_nat > $o)]: (((! [E:product_prod_nat_nat]: (((D @ E) <= (C @ E)) <= (member701585322at_nat @ E @ A))) => (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ (collec7649004at_nat @ C)) @ (inf_in586391887at_nat @ B @ (collec7649004at_nat @ D)))) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Int__Collect__mono)). 84.93/23.94 thf(804,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(product_prod_nat_nat > $o),D:(product_prod_nat_nat > $o)]: (((! [E:product_prod_nat_nat]: ((D @ E) | ~ (C @ E) | ~ (member701585322at_nat @ E @ A))) => (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ (collec7649004at_nat @ (C))) @ (inf_in586391887at_nat @ B @ (collec7649004at_nat @ (D))))) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 84.93/23.94 thf(142,axiom,((finite772653738at_nat @ (e_a @ c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_finite__E)). 84.93/23.94 thf(764,plain,((finite772653738at_nat @ (e_a @ (c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 84.93/23.94 thf(272,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > nat),D:nat]: ((((C @ B) = D) => ((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_le841296385at_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D))) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_ord__le__eq__subst)). 84.93/23.94 thf(1209,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > nat),D:nat]: ((((C @ B) = D) => ((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_le841296385at_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D))) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 84.93/23.94 thf(165,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => (ord_le841296385at_nat @ (inf_in586391887at_nat @ C @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_inf_OcoboundedI2)). 84.93/23.94 thf(831,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => (ord_le841296385at_nat @ (inf_in586391887at_nat @ C @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 84.93/23.94 thf(209,axiom,((! [A:nat]: ((finite_finite_nat @ (v_a @ c)) => (finite772653738at_nat @ (incoming_a @ c @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_finite__incoming)). 84.93/23.94 thf(990,plain,((! [A:nat]: ((finite_finite_nat @ (v_a @ (c))) => (finite772653738at_nat @ (incoming_a @ (c) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 84.93/23.94 thf(303,plain,(! [D:set_nat,C:(nat > set_nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_set_nat @ (C @ B) @ D)) | (ord_less_eq_set_nat @ (C @ A) @ D) | (ord_less_eq_nat @ (sk2 @ D @ (C) @ B @ A) @ (sk3 @ D @ (C) @ B @ A)))),inference(cnf,[status(esa)],[301])). 84.93/23.94 thf(174,axiom,((! [A:(product_prod_nat_nat > $o),B:(product_prod_nat_nat > $o)]: ((! [C:product_prod_nat_nat]: ((A @ C) => (B @ C))) => (ord_le841296385at_nat @ (collec7649004at_nat @ A) @ (collec7649004at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Collect__mono)). 84.93/23.94 thf(863,plain,((! [A:(product_prod_nat_nat > $o),B:(product_prod_nat_nat > $o)]: ((! [C:product_prod_nat_nat]: ((A @ C) => (B @ C))) => (ord_le841296385at_nat @ (collec7649004at_nat @ (A)) @ (collec7649004at_nat @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 84.93/23.94 thf(179,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((inf_in586391887at_nat @ A @ B) = A) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_inf__absorb1)). 84.93/23.94 thf(880,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((inf_in586391887at_nat @ A @ B) = A) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 84.93/23.94 thf(106,axiom,((! [A:set_nat,B:set_nat]: (((~ (finite_finite_nat @ A)) => (~ (finite_finite_nat @ B))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_infinite__super)). 84.93/23.94 thf(649,plain,((! [A:set_nat,B:set_nat]: (((~ (finite_finite_nat @ A)) => (~ (finite_finite_nat @ B))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 84.93/23.94 thf(225,axiom,((! [A:(product_prod_nat_nat > a),B:set_nat]: (ord_le841296385at_nat @ (outgoing_a2 @ A @ B) @ (e_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Graph_Ooutgoing_H__edges)). 84.93/23.94 thf(1043,plain,((! [A:(product_prod_nat_nat > a),B:set_nat]: (ord_le841296385at_nat @ (outgoing_a2 @ (A) @ B) @ (e_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 84.93/23.94 thf(46,axiom,((finite_finite_nat = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_finite__nat__set__iff__bounded__le)). 84.93/23.94 thf(433,plain,(((finite_finite_nat) = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 84.93/23.94 thf(434,plain,(((finite_finite_nat) = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),inference(lifteq,[status(thm)],[433])). 84.93/23.94 thf(101,axiom,((! [A:set_nat,B:set_nat]: (((ord_less_eq_nat @ (finite_card_nat @ B) @ (finite_card_nat @ A)) <= (ord_less_eq_set_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_card__mono)). 84.93/23.94 thf(631,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_nat @ (finite_card_nat @ B) @ (finite_card_nat @ A)) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 84.93/23.94 thf(140,axiom,((! [A:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_subset__refl)). 84.93/23.94 thf(758,plain,((! [A:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 84.93/23.94 thf(172,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat,D:product_prod_nat_nat]: (((member701585322at_nat @ D @ (e_a @ c)) <= (member701585322at_nat @ D @ (set_Pr2131844118at_nat @ B))) <= (isPath_a @ c @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_isPath__edgeset)). 84.93/23.94 thf(858,plain,((! [A:nat,B:list_P559422087at_nat,C:nat,D:product_prod_nat_nat]: ((member701585322at_nat @ D @ (e_a @ (c))) | ~ (member701585322at_nat @ D @ (set_Pr2131844118at_nat @ B)) | ~ (isPath_a @ (c) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 84.93/23.94 thf(86,axiom,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C)) => (member701585322at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_IntD1)). 84.93/23.94 thf(594,plain,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C)) => (member701585322at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 84.93/23.94 thf(122,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ A) => (ord_less_eq_set_nat @ C @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_dual__order_Otrans)). 84.93/23.94 thf(700,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ A) => (ord_less_eq_set_nat @ C @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 84.93/23.94 thf(184,axiom,((! [A:list_P559422087at_nat,B:(product_prod_nat_nat > a),C:nat,D:nat]: ((ord_le841296385at_nat @ (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ A) @ (e_a @ c)) @ (e_a @ B)) => ((isPath_a @ c @ C @ A @ D) => (isPath_a @ B @ C @ A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_transfer__path)). 84.93/23.94 thf(895,plain,((! [A:list_P559422087at_nat,B:(product_prod_nat_nat > a),C:nat,D:nat]: ((ord_le841296385at_nat @ (inf_in586391887at_nat @ (set_Pr2131844118at_nat @ A) @ (e_a @ (c))) @ (e_a @ (B))) => ((isPath_a @ (c) @ C @ A @ D) => (isPath_a @ (B) @ C @ A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 84.93/23.94 thf(255,axiom,((! [A:nat,B:(set_Pr1986765409at_nat > nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ C @ D) => ((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_le841296385at_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_ord__eq__le__subst)). 84.93/23.94 thf(1149,plain,((! [A:nat,B:(set_Pr1986765409at_nat > nat),C:set_Pr1986765409at_nat,D:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ C @ D) => ((! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_le841296385at_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 84.93/23.94 thf(191,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((~ ((ord_le841296385at_nat @ A @ B) => (~ (ord_le841296385at_nat @ B @ A)))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_equalityE)). 84.93/23.94 thf(915,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (~ ((ord_le841296385at_nat @ A @ B) => (~ (ord_le841296385at_nat @ B @ A))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 84.93/23.94 thf(145,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ c @ A @ B @ C) = ((isPath_a @ c @ A @ B @ C) & ! [D:list_P559422087at_nat]: ((isPath_a @ c @ A @ D @ C) => (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (size_s1990949619at_nat @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_isShortestPath__def)). 84.93/23.94 thf(769,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((isShortestPath_a @ (c) @ A @ B @ C) = ((isPath_a @ (c) @ A @ B @ C) & ! [D:list_P559422087at_nat]: ((isPath_a @ (c) @ A @ D @ C) => (ord_less_eq_nat @ (size_s1990949619at_nat @ B) @ (size_s1990949619at_nat @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 84.93/23.94 thf(194,axiom,((! [A:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_order__refl)). 84.93/23.94 thf(943,plain,((! [A:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 84.93/23.94 thf(2276,plain,(((ord_le841296385at_nat @ (edmond475474835dges_a @ (c) @ s @ t) @ (e_a @ (c))) != (ord_le841296385at_nat @ edges @ (e_a @ (c))))),inference(paramod_ordered,[status(thm)],[1160,282])). 84.93/23.94 thf(2277,plain,(((edmond475474835dges_a @ (c) @ s @ t) != edges) | ((e_a @ (c)) != (e_a @ (c)))),inference(simp,[status(thm)],[2276])). 84.93/23.94 thf(2278,plain,(((edmond475474835dges_a @ (c) @ s @ t) != edges)),inference(simp,[status(thm)],[2277])). 84.93/23.94 thf(263,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Int__lower2)). 84.93/23.94 thf(1177,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 84.93/23.94 thf(54,axiom,((! [A:(nat > (list_P559422087at_nat > (nat > $o))),B:nat,C:list_P559422087at_nat,D:nat]: ((! [E:nat,F:nat]: (A @ E @ nil_Pr1308055047at_nat @ F)) => ((A @ B @ C @ D) <= (! [E:nat,F:nat,G:nat,H:list_P559422087at_nat,I:nat]: ((A @ G @ H @ I) => (A @ E @ (cons_P66992567at_nat @ (product_Pair_nat_nat @ F @ G) @ H) @ I))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_Graph_OisPath_Oinduct)). 84.93/23.94 thf(462,plain,((! [A:(nat > (list_P559422087at_nat > (nat > $o))),B:nat,C:list_P559422087at_nat,D:nat]: ((! [E:nat,F:nat]: (A @ E @ nil_Pr1308055047at_nat @ F)) => ((A @ B @ C @ D) | ~ (! [E:nat,F:nat,G:nat,H:list_P559422087at_nat,I:nat]: ((A @ G @ H @ I) => (A @ E @ (cons_P66992567at_nat @ (product_Pair_nat_nat @ F @ G) @ H) @ I))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 84.93/23.94 thf(246,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((A = B) <= (ord_le841296385at_nat @ B @ A)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_subset__antisym)). 84.93/23.94 thf(1112,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((A = B) | ~ (ord_le841296385at_nat @ B @ A) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 84.93/23.94 thf(156,axiom,((! [A:(product_prod_nat_nat > a)]: ((finite_Graph_a @ A) => (finite772653738at_nat @ (e_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Finite__Graph_Ofinite__E)). 84.93/23.94 thf(811,plain,((! [A:(product_prod_nat_nat > a)]: ((finite_Graph_a @ (A)) => (finite772653738at_nat @ (e_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 84.93/23.94 thf(30,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_order__class_Oorder_Oantisym)). 84.93/23.94 thf(387,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 84.93/23.94 thf(35,axiom,((adjacent_nodes_a = adjacent_nodes_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Graph_Oadjacent__nodes_Ocong)). 84.93/23.94 thf(399,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 84.93/23.94 thf(199,axiom,((isShortestPath_a @ c @ s @ p @ t)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_SP)). 84.93/23.94 thf(959,plain,((isShortestPath_a @ (c) @ s @ p @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 84.93/23.94 thf(163,axiom,((! [A:nat]: (finite_finite_nat @ (adjacent_nodes_a @ c @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_adjacent__nodes__finite)). 84.93/23.94 thf(827,plain,((! [A:nat]: (finite_finite_nat @ (adjacent_nodes_a @ (c) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 84.93/23.94 thf(120,axiom,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ B) => ((member_nat @ C @ A) => (member_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_in__mono)). 84.93/23.94 thf(695,plain,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ B) => ((member_nat @ C @ A) => (member_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 84.93/23.94 thf(149,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((~ (isPath_a @ c @ A @ B @ C)) => ((~ (! [D:nat,E:nat,F:list_P559422087at_nat]: (((A = D) & (member701585322at_nat @ (product_Pair_nat_nat @ D @ E) @ (e_a @ c)) & (isPath_a @ c @ E @ F @ C)) <= (B = (cons_P66992567at_nat @ (product_Pair_nat_nat @ D @ E) @ F))))) <= ((A = C) <= (B = nil_Pr1308055047at_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_isPath_Oelims_I3_J)). 84.93/23.94 thf(780,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: ((~ (isPath_a @ (c) @ A @ B @ C)) => (~ (! [D:nat,E:nat,F:list_P559422087at_nat]: (((A = D) & (member701585322at_nat @ (product_Pair_nat_nat @ D @ E) @ (e_a @ (c))) & (isPath_a @ (c) @ E @ F @ C)) | ~ (B = (cons_P66992567at_nat @ (product_Pair_nat_nat @ D @ E) @ F)))) | ~ ((A = C) | ~ (B = nil_Pr1308055047at_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 84.93/23.94 thf(180,axiom,((! [A:nat,B:nat]: ((isPath_a @ c @ A @ nil_Pr1308055047at_nat @ B) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_isPath_Osimps_I1_J)). 84.93/23.94 thf(883,plain,((! [A:nat,B:nat]: ((isPath_a @ (c) @ A @ nil_Pr1308055047at_nat @ B) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 84.93/23.94 thf(91,axiom,((! [A:(product_prod_nat_nat > a),B:nat]: ((finite_finite_nat @ (adjacent_nodes_a @ A @ B)) <= (finite_Graph_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Finite__Graph_Oadjacent__nodes__finite)). 84.93/23.94 thf(608,plain,((! [A:(product_prod_nat_nat > a),B:nat]: ((finite_finite_nat @ (adjacent_nodes_a @ (A) @ B)) | ~ (finite_Graph_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 84.93/23.94 thf(297,plain,(! [B:set_nat,A:set_nat] : ((~ (A = B)) | (ord_less_eq_set_nat @ A @ B))),inference(cnf,[status(esa)],[296])). 84.93/23.94 thf(298,plain,(! [B:set_nat,A:set_nat] : ((A != B) | (ord_less_eq_set_nat @ A @ B))),inference(lifteq,[status(thm)],[297])). 84.93/23.94 thf(299,plain,(! [A:set_nat] : ((ord_less_eq_set_nat @ A @ A))),inference(simp,[status(thm)],[298])). 84.93/23.94 thf(243,axiom,((! [A:nat,B:nat,C:(nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_le841296385at_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_le841296385at_nat @ (C @ A) @ D)) <= (ord_le841296385at_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_order__subst2)). 84.93/23.94 thf(1102,plain,((! [A:nat,B:nat,C:(nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_le841296385at_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_le841296385at_nat @ (C @ A) @ D)) | ~ (ord_le841296385at_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 84.93/23.94 thf(45,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_dual__order_Orefl)). 84.93/23.94 thf(431,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 84.93/23.94 thf(192,axiom,((! [A:set_Pr1986765409at_nat,B:(nat > set_Pr1986765409at_nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_le841296385at_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_ord__eq__le__subst)). 84.93/23.94 thf(922,plain,((! [A:set_Pr1986765409at_nat,B:(nat > set_Pr1986765409at_nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_le841296385at_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_le841296385at_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 84.93/23.94 thf(116,axiom,((incoming_a = incoming_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Graph_Oincoming_Ocong)). 84.93/23.94 thf(685,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 84.93/23.94 thf(261,axiom,((! [A:nat,B:(product_prod_nat_nat > a),C:nat,D:nat]: ((member_nat @ A @ (reachableNodes_a @ B @ C)) => ((member_nat @ D @ (reachableNodes_a @ B @ C)) <= (member701585322at_nat @ (product_Pair_nat_nat @ A @ D) @ (e_a @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Graph_OreachableNodes__append__edge)). 84.93/23.94 thf(1171,plain,((! [A:nat,B:(product_prod_nat_nat > a),C:nat,D:nat]: ((member_nat @ A @ (reachableNodes_a @ (B) @ C)) => ((member_nat @ D @ (reachableNodes_a @ (B) @ C)) | ~ (member701585322at_nat @ (product_Pair_nat_nat @ A @ D) @ (e_a @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 84.93/23.94 thf(131,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) <= (A = (inf_in586391887at_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_inf_OorderI)). 84.93/23.94 thf(722,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) | ~ (A = (inf_in586391887at_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 84.93/23.94 thf(223,axiom,((! [A:set_se1612935105at_nat,B:set_Pr1986765409at_nat]: (((? [C:set_Pr1986765409at_nat]: ((member298845450at_nat @ C @ A) & (ord_le841296385at_nat @ C @ B) & ! [D:set_Pr1986765409at_nat]: (((C = D) <= (ord_le841296385at_nat @ D @ C)) <= (member298845450at_nat @ D @ A)))) <= (member298845450at_nat @ B @ A)) <= (finite1457549322at_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_finite__has__minimal2)). 84.93/23.94 thf(1034,plain,((! [A:set_se1612935105at_nat,B:set_Pr1986765409at_nat]: (? [C:set_Pr1986765409at_nat]: ((member298845450at_nat @ C @ A) & (ord_le841296385at_nat @ C @ B) & ! [D:set_Pr1986765409at_nat]: ((C = D) | ~ (ord_le841296385at_nat @ D @ C) | ~ (member298845450at_nat @ D @ A))) | ~ (member298845450at_nat @ B @ A) | ~ (finite1457549322at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 84.93/23.94 thf(114,axiom,((! [A:list_P559422087at_nat]: (finite772653738at_nat @ (set_Pr2131844118at_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_List_Ofinite__set)). 84.93/23.94 thf(675,plain,((! [A:list_P559422087at_nat]: (finite772653738at_nat @ (set_Pr2131844118at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 84.93/23.94 thf(84,axiom,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => ((finite_finite_nat @ B) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_rev__finite__subset)). 84.93/23.94 thf(589,plain,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => ((finite_finite_nat @ B) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 84.93/23.94 thf(68,axiom,((! [A:set_nat,B:nat]: ((! [C:set_nat]: (((finite_finite_nat @ C) => (ord_less_eq_nat @ (finite_card_nat @ C) @ B)) <= (ord_less_eq_set_nat @ C @ A))) => ((ord_less_eq_nat @ (finite_card_nat @ A) @ B) & (finite_finite_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_finite__if__finite__subsets__card__bdd)). 84.93/23.94 thf(516,plain,((! [A:set_nat,B:nat]: ((! [C:set_nat]: (((finite_finite_nat @ C) => (ord_less_eq_nat @ (finite_card_nat @ C) @ B)) | ~ (ord_less_eq_set_nat @ C @ A))) => ((ord_less_eq_nat @ (finite_card_nat @ A) @ B) & (finite_finite_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 84.93/23.94 thf(139,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_eq__refl)). 84.93/23.94 thf(754,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 84.93/23.94 thf(76,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_order__refl)). 84.93/23.94 thf(553,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 84.93/23.94 thf(265,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ C @ A) => (ord_le841296385at_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_dual__order_Otrans)). 84.93/23.94 thf(1181,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ C @ A) => (ord_le841296385at_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 84.93/23.94 thf(161,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((finite772653738at_nat @ A) => ((ord_less_eq_nat @ (finite447719721at_nat @ B) @ (finite447719721at_nat @ A)) <= (ord_le841296385at_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_card__mono)). 84.93/23.94 thf(823,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((finite772653738at_nat @ A) => ((ord_less_eq_nat @ (finite447719721at_nat @ B) @ (finite447719721at_nat @ A)) | ~ (ord_le841296385at_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 84.93/23.94 thf(127,axiom,((! [A:nat,B:nat]: (((B = A) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_dual__order_Oantisym)). 84.93/23.94 thf(712,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)],[127])). 84.93/23.94 thf(171,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((A = (inf_in586391887at_nat @ A @ B)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_inf_OorderE)). 84.93/23.94 thf(855,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((A = (inf_in586391887at_nat @ A @ B)) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 84.93/23.94 thf(118,axiom,((! [A:(product_prod_nat_nat > a),B:nat]: (ord_less_eq_set_nat @ (adjacent_nodes_a @ A @ B) @ (v_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Graph_Oadjacent__nodes__ss__V)). 84.93/23.94 thf(690,plain,((! [A:(product_prod_nat_nat > a),B:nat]: (ord_less_eq_set_nat @ (adjacent_nodes_a @ (A) @ B) @ (v_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 84.93/23.94 thf(125,axiom,(((= @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_order__class_Oorder_Oeq__iff)). 84.93/23.94 thf(707,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)],[125])). 84.93/23.94 thf(204,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) <= (member701585322at_nat @ C @ A))) => (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_subsetI)). 84.93/23.94 thf(971,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) | ~ (member701585322at_nat @ C @ A))) => (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 84.93/23.94 thf(309,plain,((! [A:product_prod_nat_nat,B:set_Pr1986765409at_nat]: (! [C:set_Pr1986765409at_nat]: ((member701585322at_nat @ A @ C) => (member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C))) | ~ (member701585322at_nat @ A @ B)))),inference(miniscope,[status(thm)],[308])). 84.93/23.94 thf(310,plain,(! [C:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,A:product_prod_nat_nat] : ((~ (member701585322at_nat @ A @ C)) | (member701585322at_nat @ A @ (inf_in586391887at_nat @ B @ C)) | (~ (member701585322at_nat @ A @ B)))),inference(cnf,[status(esa)],[309])). 84.93/23.94 thf(210,axiom,(((finite772653738at_nat @ (e_a @ c)) => (finite_finite_nat @ (v_a @ c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_Efin__imp__Vfin)). 84.93/23.94 thf(993,plain,(((finite772653738at_nat @ (e_a @ (c))) => (finite_finite_nat @ (v_a @ (c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 84.93/23.94 thf(220,axiom,((ord_le841296385at_nat = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_inf_Oabsorb__iff1)). 84.93/23.94 thf(1025,plain,(((ord_le841296385at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 84.93/23.94 thf(7,axiom,((! [A:(product_prod_nat_nat > a)]: ((finite_Graph_a @ A) => (finite_finite_nat @ (v_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Finite__Graph_Ofinite__V)). 84.93/23.94 thf(294,plain,((! [A:(product_prod_nat_nat > a)]: ((finite_Graph_a @ (A)) => (finite_finite_nat @ (v_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 84.93/23.94 thf(295,plain,(! [A:(product_prod_nat_nat > a)] : ((~ (finite_Graph_a @ (A))) | (finite_finite_nat @ (v_a @ (A))))),inference(cnf,[status(esa)],[294])). 84.93/23.94 thf(150,axiom,((finite772653738at_nat @ (edmond771116670s_uE_a @ c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_finite__uE)). 84.93/23.94 thf(791,plain,((finite772653738at_nat @ (edmond771116670s_uE_a @ (c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 84.93/23.94 thf(1764,plain,(! [E:product_prod_nat_nat,D:list_P559422087at_nat,C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ B @ C)) | (~ (ord_less_eq_nat @ A @ B)) | ((ord_less_eq_nat @ A @ C) != (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ E @ D)) @ (size_s1990949619at_nat @ D))))),inference(paramod_ordered,[status(thm)],[291,356])). 84.93/23.94 thf(1765,plain,(! [C:list_P559422087at_nat,B:product_prod_nat_nat,A:nat] : ((~ (ord_less_eq_nat @ A @ (size_s1990949619at_nat @ C))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ B @ C)) @ A)))),inference(pattern_uni,[status(thm)],[1764:[bind(A, $thf(size_s1990949619at_nat @ (cons_P66992567at_nat @ G @ I))),bind(B, $thf(B)),bind(C, $thf(size_s1990949619at_nat @ I)),bind(D, $thf(I)),bind(E, $thf(G))]])). 84.93/23.94 thf(1785,plain,(! [C:list_P559422087at_nat,B:product_prod_nat_nat,A:nat] : ((~ (ord_less_eq_nat @ A @ (size_s1990949619at_nat @ C))) | (~ (ord_less_eq_nat @ (size_s1990949619at_nat @ (cons_P66992567at_nat @ B @ C)) @ A)))),inference(simp,[status(thm)],[1765])). 84.93/23.94 thf(1979,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) | ~ (member701585322at_nat @ C @ A))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A))) | ((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)) != (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)))),inference(paramod_ordered,[status(thm)],[1970,1255])). 84.93/23.94 thf(1980,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) | ~ (member701585322at_nat @ C @ A))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A)))),inference(pattern_uni,[status(thm)],[1979:[]])). 84.93/23.94 thf(1734,plain,(((ord_le841296385at_nat @ edges @ (set_Pr2131844118at_nat @ p)) != (ord_le841296385at_nat @ edges @ (e_a @ (c))))),inference(paramod_ordered,[status(thm)],[1131,282])). 84.93/23.94 thf(1736,plain,((edges != edges) | ((set_Pr2131844118at_nat @ p) != (e_a @ (c)))),inference(simp,[status(thm)],[1734])). 84.93/23.94 thf(1738,plain,(((set_Pr2131844118at_nat @ p) != (e_a @ (c)))),inference(simp,[status(thm)],[1736])). 84.93/23.94 thf(104,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_eq__refl)). 84.93/23.94 thf(643,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 84.93/23.94 thf(274,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((inf_in586391887at_nat @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Int__absorb1)). 84.93/23.94 thf(1220,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((inf_in586391887at_nat @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 84.93/23.94 thf(188,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_antisym)). 84.93/23.94 thf(907,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 84.93/23.94 thf(268,axiom,((! [A:(product_prod_nat_nat > a),B:set_nat]: (ord_le841296385at_nat @ (incoming_a2 @ A @ B) @ (e_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Graph_Oincoming_H__edges)). 84.93/23.94 thf(1188,plain,((! [A:(product_prod_nat_nat > a),B:set_nat]: (ord_le841296385at_nat @ (incoming_a2 @ (A) @ B) @ (e_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 84.93/23.94 thf(267,axiom,((! [A:(product_prod_nat_nat > a),B:nat]: (ord_le841296385at_nat @ (outgoing_a @ A @ B) @ (e_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Graph_Ooutgoing__edges)). 84.93/23.94 thf(1186,plain,((! [A:(product_prod_nat_nat > a),B:nat]: (ord_le841296385at_nat @ (outgoing_a @ (A) @ B) @ (e_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 84.93/23.94 thf(240,axiom,((! [A:(set_Pr1986765409at_nat > (set_Pr1986765409at_nat > set_Pr1986765409at_nat)),B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((! [D:set_Pr1986765409at_nat,E:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (A @ D @ E) @ D)) => (((! [D:set_Pr1986765409at_nat,E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ D @ F) => (ord_le841296385at_nat @ D @ (A @ E @ F))) <= (ord_le841296385at_nat @ D @ E))) => ((inf_in586391887at_nat @ B @ C) = (A @ B @ C))) <= (! [D:set_Pr1986765409at_nat,E:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (A @ D @ E) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_inf__unique)). 84.93/23.94 thf(1085,plain,((! [A:(set_Pr1986765409at_nat > (set_Pr1986765409at_nat > set_Pr1986765409at_nat)),B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((! [D:set_Pr1986765409at_nat,E:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (A @ D @ E) @ D)) => (((! [D:set_Pr1986765409at_nat,E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ D @ F) => (ord_le841296385at_nat @ D @ (A @ E @ F))) | ~ (ord_le841296385at_nat @ D @ E))) => ((inf_in586391887at_nat @ B @ C) = (A @ B @ C))) | ~ (! [D:set_Pr1986765409at_nat,E:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (A @ D @ E) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 84.93/23.94 thf(80,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((A = B) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_order__class_Oorder_Oantisym)). 84.93/23.94 thf(576,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 84.93/23.94 thf(109,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) <= (B = C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_ord__le__eq__trans)). 84.93/23.94 thf(656,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (B = C) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 84.93/23.94 thf(88,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) <= (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_dual__order_Otrans)). 84.93/23.94 thf(600,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 84.93/23.94 thf(13,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_subsetI)). 84.93/23.94 thf(314,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 84.93/23.94 thf(93,axiom,((! [A:(product_prod_nat_nat > a),B:set_nat]: ((finite772653738at_nat @ (incoming_a2 @ A @ B)) <= (finite_finite_nat @ (v_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Graph_Ofinite__incoming_H)). 84.93/23.94 thf(612,plain,((! [A:(product_prod_nat_nat > a),B:set_nat]: ((finite772653738at_nat @ (incoming_a2 @ (A) @ B)) | ~ (finite_finite_nat @ (v_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 84.93/23.94 thf(2536,plain,(! [C:set_nat,B:set_nat,A:(nat > $o)] : (((finite_card_nat @ C) != (finite_card_nat @ B)) | (C = B) | (~ (finite_finite_nat @ B)) | ((ord_less_eq_set_nat @ (collect_nat @ (^ [D:nat]: ($false))) @ (collect_nat @ (A))) != (ord_less_eq_set_nat @ C @ B)))),inference(paramod_ordered,[status(thm)],[1739,307])). 84.93/23.94 thf(2537,plain,(! [A:(nat > $o)] : (((finite_card_nat @ (collect_nat @ (^ [B:nat]: ($false)))) != (finite_card_nat @ (collect_nat @ (A)))) | ((collect_nat @ (^ [B:nat]: ($false))) = (collect_nat @ (A))) | (~ (finite_finite_nat @ (collect_nat @ (A)))))),inference(pattern_uni,[status(thm)],[2536:[bind(A, $thf(E)),bind(B, $thf(collect_nat @ (E))),bind(C, $thf(collect_nat @ (^ [D:nat]: ($false))))]])). 84.93/23.94 thf(2558,plain,(! [A:(nat > $o)] : (((finite_card_nat @ (collect_nat @ (^ [B:nat]: ($false)))) != (finite_card_nat @ (collect_nat @ (A)))) | ((collect_nat @ (^ [B:nat]: ($false))) = (collect_nat @ (A))) | (~ (finite_finite_nat @ (collect_nat @ (A)))))),inference(simp,[status(thm)],[2537])). 84.93/23.94 thf(123,axiom,((incoming_a2 = incoming_a2)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Graph_Oincoming_H_Ocong)). 84.93/23.94 thf(703,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 84.93/23.94 thf(99,axiom,((! [A:set_nat,B:set_nat]: (((finite_finite_nat @ B) => (finite_finite_nat @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_finite__subset)). 84.93/23.94 thf(627,plain,((! [A:set_nat,B:set_nat]: (((finite_finite_nat @ B) => (finite_finite_nat @ A)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 84.93/23.94 thf(51,axiom,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D)))) <= (ord_less_eq_set_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_order__subst1)). 84.93/23.94 thf(450,plain,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D)))) | ~ (ord_less_eq_set_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 84.93/23.94 thf(25,axiom,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_set_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_nat @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ord__le__eq__subst)). 84.93/23.94 thf(363,plain,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_set_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_nat @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 84.93/23.94 thf(59,axiom,((! [A:set_nat,B:set_nat]: (((A = B) <= (ord_less_eq_set_nat @ B @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_subset__antisym)). 84.93/23.94 thf(482,plain,((! [A:set_nat,B:set_nat]: ((A = B) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 84.93/23.94 thf(256,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: (((ord_le841296385at_nat @ A @ C) <= (ord_le841296385at_nat @ B @ C)) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_subset__trans)). 84.93/23.94 thf(1157,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ C) | ~ (ord_le841296385at_nat @ B @ C) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 84.93/23.94 thf(2163,plain,(! [C:list_P559422087at_nat,B:product_prod_nat_nat,A:nat] : (((size_s1990949619at_nat @ C) != s) | ((size_s1990949619at_nat @ (cons_P66992567at_nat @ B @ C)) != (size_s1990949619at_nat @ C)) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ (size_s1990949619at_nat @ C) @ (sk47 @ s @ (v_a @ (c))))))),inference(paramod_ordered,[status(thm)],[394,1732])). 84.93/23.94 thf(2178,plain,(! [C:list_P559422087at_nat,B:product_prod_nat_nat,A:nat] : (((size_s1990949619at_nat @ C) != s) | ((cons_P66992567at_nat @ B @ C) != C) | (A != (size_s1990949619at_nat @ C)) | (A != (sk47 @ s @ (v_a @ (c)))))),inference(simp,[status(thm)],[2163])). 84.93/23.94 thf(2194,plain,(! [B:list_P559422087at_nat,A:product_prod_nat_nat] : (((size_s1990949619at_nat @ B) != s) | ((cons_P66992567at_nat @ A @ B) != B) | ((size_s1990949619at_nat @ B) != (sk47 @ s @ (v_a @ (c)))))),inference(simp,[status(thm)],[2178])). 84.93/23.94 thf(183,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((A = B) => (ord_le841296385at_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_equalityD2)). 84.93/23.94 thf(891,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((A = B) => (ord_le841296385at_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 84.93/23.94 thf(157,axiom,((! [A:nat]: (ord_le841296385at_nat @ (incoming_a @ c @ A) @ (e_a @ c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_incoming__edges)). 84.93/23.94 thf(813,plain,((! [A:nat]: (ord_le841296385at_nat @ (incoming_a @ (c) @ A) @ (e_a @ (c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 84.93/23.94 thf(201,axiom,((! [A:nat,B:list_P559422087at_nat,C:nat]: (((isPath_a @ c @ A @ B @ C) => (ord_less_eq_set_nat @ (set_nat2 @ (pathVertices @ A @ B)) @ (v_a @ c))) <= (member_nat @ A @ (v_a @ c))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_pathVertices__edgeset)). 84.93/23.94 thf(963,plain,((! [A:nat,B:list_P559422087at_nat,C:nat]: (((isPath_a @ (c) @ A @ B @ C) => (ord_less_eq_set_nat @ (set_nat2 @ (pathVertices @ A @ B)) @ (v_a @ (c)))) | ~ (member_nat @ A @ (v_a @ (c)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 84.93/23.94 thf(231,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((~ (finite772653738at_nat @ B)) <= (~ (finite772653738at_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_infinite__super)). 84.93/23.94 thf(1062,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => (~ (finite772653738at_nat @ B) | (finite772653738at_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 84.93/23.94 thf(242,axiom,((finite_Graph_a @ c)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Finite__Graph__axioms)). 84.93/23.94 thf(1101,plain,((finite_Graph_a @ (c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 84.93/23.94 thf(31,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_subset__refl)). 84.93/23.94 thf(390,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 84.93/23.94 thf(37,axiom,((! [A:list_nat,B:set_nat]: ((ord_less_eq_set_nat @ (set_nat2 @ A) @ B) = (! [C:nat]: ((member_nat @ C @ B) <= (member_nat @ C @ (set_nat2 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_subset__code_I1_J)). 84.93/23.94 thf(401,plain,((! [A:list_nat,B:set_nat]: ((ord_less_eq_set_nat @ (set_nat2 @ A) @ B) = (! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ (set_nat2 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 84.93/23.94 thf(42,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_subset__trans)). 84.93/23.94 thf(418,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 84.93/23.94 thf(211,axiom,(((= @ set_Pr1986765409at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ B @ A) & (ord_le841296385at_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_eq__iff)). 84.93/23.94 thf(995,plain,(((= @ set_Pr1986765409at_nat) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ B @ A) & (ord_le841296385at_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 84.93/23.94 thf(22,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((A @ D @ E) <= (A @ E @ D))) => (A @ B @ C)) <= (! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_linorder__wlog)). 84.93/23.94 thf(346,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((A @ D @ E) | ~ (A @ E @ D))) => (A @ B @ C)) | ~ (! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 84.93/23.94 thf(226,axiom,((! [A:(product_prod_nat_nat > a),B:nat]: (ord_le841296385at_nat @ (incoming_a @ A @ B) @ (e_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Graph_Oincoming__edges)). 84.93/23.94 thf(1045,plain,((! [A:(product_prod_nat_nat > a),B:nat]: (ord_le841296385at_nat @ (incoming_a @ (A) @ B) @ (e_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 84.93/23.94 thf(238,axiom,((! [A:set_Pr1986765409at_nat,B:nat]: ((~ (finite772653738at_nat @ A)) => (? [C:set_Pr1986765409at_nat]: ((finite772653738at_nat @ C) & ((finite447719721at_nat @ C) = B) & (ord_le841296385at_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_infinite__arbitrarily__large)). 84.93/23.94 thf(1077,plain,((! [A:set_Pr1986765409at_nat,B:nat]: ((~ (finite772653738at_nat @ A)) => (? [C:set_Pr1986765409at_nat]: ((finite772653738at_nat @ C) & ((finite447719721at_nat @ C) = B) & (ord_le841296385at_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 84.93/23.94 thf(57,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((A = B) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_antisym)). 84.93/23.94 thf(478,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 84.93/23.94 thf(258,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_equalityD1)). 84.93/23.94 thf(1161,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 84.93/23.94 thf(96,axiom,((! [A:(product_prod_nat_nat > a)]: ((finite_Graph_a @ A) => (edmond1517640972ysis_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_ek__analysis_Ointro)). 84.93/23.94 thf(620,plain,((! [A:(product_prod_nat_nat > a)]: ((finite_Graph_a @ (A)) => (edmond1517640972ysis_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 84.93/23.94 thf(197,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((inf_in586391887at_nat @ A @ B) = A) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Int__absorb2)). 84.93/23.94 thf(950,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((inf_in586391887at_nat @ A @ B) = A) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 84.93/23.94 thf(159,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: ((edmond1517640972ysis_a @ A) => (ord_le841296385at_nat @ (edmond475474835dges_a @ A @ B @ C) @ (e_a @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_ek__analysis_OspEdges__ss__E)). 84.93/23.94 thf(818,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:nat]: ((edmond1517640972ysis_a @ (A)) => (ord_le841296385at_nat @ (edmond475474835dges_a @ (A) @ B @ C) @ (e_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 84.93/23.94 thf(1985,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) | ~ (member701585322at_nat @ C @ A))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B)))) | ((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)) != (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)))),inference(paramod_ordered,[status(thm)],[1970,1259])). 84.93/23.94 thf(1986,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ B) | ~ (member701585322at_nat @ C @ A))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (A = (inf_in586391887at_nat @ A @ B))))),inference(pattern_uni,[status(thm)],[1985:[]])). 84.93/23.94 thf(89,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_order__subst2)). 84.93/23.94 thf(603,plain,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 84.93/23.94 thf(48,axiom,((! [A:set_nat]: ((? [B:list_nat]: ((set_nat2 @ B) = A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_finite__list)). 84.93/23.94 thf(437,plain,((! [A:set_nat]: (? [B:list_nat]: ((set_nat2 @ B) = A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 84.93/23.94 thf(56,axiom,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat,E:nat,F:nat]: (((member701585322at_nat @ (product_Pair_nat_nat @ E @ F) @ (set_Pr2131844118at_nat @ C)) => ((? [G:nat]: (member701585322at_nat @ (product_Pair_nat_nat @ G @ E) @ (set_Pr2131844118at_nat @ C))) <= (E != B))) <= (isPath_a @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_Graph_OisPath__ex__edge1)). 84.93/23.94 thf(474,plain,((! [A:(product_prod_nat_nat > a),B:nat,C:list_P559422087at_nat,D:nat,E:nat,F:nat]: (((member701585322at_nat @ (product_Pair_nat_nat @ E @ F) @ (set_Pr2131844118at_nat @ C)) => (? [G:nat]: (member701585322at_nat @ (product_Pair_nat_nat @ G @ E) @ (set_Pr2131844118at_nat @ C)) | (E = B))) | ~ (isPath_a @ (A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 84.93/23.94 thf(111,axiom,(((= @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_order__class_Oorder_Oeq__iff)). 84.93/23.94 thf(664,plain,(((= @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 84.93/23.94 thf(36,axiom,((outgoing_a2 = outgoing_a2)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_Graph_Ooutgoing_H_Ocong)). 84.93/23.94 thf(400,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 84.93/23.94 thf(828,plain,(! [A:nat] : ((finite_finite_nat @ (adjacent_nodes_a @ (c) @ A)))),inference(cnf,[status(esa)],[827])). 84.93/23.94 thf(200,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) => (~ ((~ (ord_le841296385at_nat @ A @ C)) <= (ord_le841296385at_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_le__infE)). 84.93/23.94 thf(960,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ (inf_in586391887at_nat @ B @ C)) => (~ (~ (ord_le841296385at_nat @ A @ C) | ~ (ord_le841296385at_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 84.93/23.94 thf(259,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((inf_in586391887at_nat @ B @ A) = A) <= (ord_le841296385at_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_inf_Oabsorb2)). 84.93/23.94 thf(1165,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (((inf_in586391887at_nat @ B @ A) = A) | ~ (ord_le841296385at_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 84.93/23.94 thf(41,axiom,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Collect__mem__eq)). 84.93/23.94 thf(415,plain,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 84.93/23.94 thf(279,axiom,((! [A:set_nat]: (ord_le841296385at_nat @ (outgoing_a2 @ c @ A) @ (e_a @ c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_outgoing_H__edges)). 84.93/23.94 thf(1236,plain,((! [A:set_nat]: (ord_le841296385at_nat @ (outgoing_a2 @ (c) @ A) @ (e_a @ (c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 84.93/23.94 thf(1922,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A))) | ((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)) != (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ B @ A) = A)))),inference(paramod_ordered,[status(thm)],[1919,1255])). 84.93/23.94 thf(1923,plain,(((^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ! [C:product_prod_nat_nat]: ((member701585322at_nat @ C @ A) => (member701585322at_nat @ C @ B))) = (^ [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: ((inf_in586391887at_nat @ A @ B) = A)))),inference(pattern_uni,[status(thm)],[1922:[]])). 84.93/23.94 thf(169,axiom,((! [A:nat]: ((finite_finite_nat @ (v_a @ c)) => (finite772653738at_nat @ (outgoing_a @ c @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_finite__outgoing)). 84.93/23.94 thf(850,plain,((! [A:nat]: ((finite_finite_nat @ (v_a @ (c))) => (finite772653738at_nat @ (outgoing_a @ (c) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 84.93/23.94 thf(50,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (((C @ B) = D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_set_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ord__le__eq__subst)). 84.93/23.94 thf(442,plain,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (((C @ B) = D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_set_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 84.93/23.94 thf(90,axiom,((isShortestPath_a = isShortestPath_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Graph_OisShortestPath_Ocong)). 84.93/23.94 thf(607,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 84.93/23.94 thf(241,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => (((ord_le841296385at_nat @ (C @ A) @ D) <= (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (C @ E) @ (C @ F)) <= (ord_le841296385at_nat @ E @ F)))) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ord__le__eq__subst)). 84.93/23.94 thf(1093,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat,C:(set_Pr1986765409at_nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ A @ B) => ((ord_le841296385at_nat @ (C @ A) @ D) | ~ (! [E:set_Pr1986765409at_nat,F:set_Pr1986765409at_nat]: ((ord_le841296385at_nat @ (C @ E) @ (C @ F)) | ~ (ord_le841296385at_nat @ E @ F))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 84.93/23.94 thf(34,axiom,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D)))) <= (ord_less_eq_set_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_order__subst1)). 84.93/23.94 thf(395,plain,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D)))) | ~ (ord_less_eq_set_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 84.93/23.94 thf(61,axiom,((! [A:set_nat,B:set_nat]: ((~ ((~ (ord_less_eq_set_nat @ B @ A)) <= (ord_less_eq_set_nat @ A @ B))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_equalityE)). 84.93/23.94 thf(486,plain,((! [A:set_nat,B:set_nat]: (~ (~ (ord_less_eq_set_nat @ B @ A) | ~ (ord_less_eq_set_nat @ A @ B)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 84.93/23.94 thf(18,axiom,(((= @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_eq__iff)). 84.93/23.94 thf(337,plain,(((= @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 84.93/23.94 thf(217,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ A @ B) => (((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_le841296385at_nat @ (C @ E) @ (C @ F)))) => (ord_le841296385at_nat @ (C @ A) @ D)) <= (ord_le841296385at_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_order__subst2)). 84.93/23.94 thf(1009,plain,((! [A:set_nat,B:set_nat,C:(set_nat > set_Pr1986765409at_nat),D:set_Pr1986765409at_nat]: ((ord_less_eq_set_nat @ A @ B) => (((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_le841296385at_nat @ (C @ E) @ (C @ F)))) => (ord_le841296385at_nat @ (C @ A) @ D)) | ~ (ord_le841296385at_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 84.93/23.94 thf(266,axiom,((! [A:(product_prod_nat_nat > a)]: ((finite772653738at_nat @ (e_a @ A)) => (finite_Graph_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_Graph_OFinite__Graph__EI)). 84.93/23.94 thf(1184,plain,((! [A:(product_prod_nat_nat > a)]: ((finite772653738at_nat @ (e_a @ (A))) => (finite_Graph_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 84.93/23.94 thf(74,axiom,((! [A:(product_prod_nat_nat > a)]: ((finite772653738at_nat @ (edmond771116670s_uE_a @ A)) <= (edmond1517640972ysis_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_ek__analysis_Ofinite__uE)). 84.93/23.94 thf(543,plain,((! [A:(product_prod_nat_nat > a)]: ((finite772653738at_nat @ (edmond771116670s_uE_a @ (A))) | ~ (edmond1517640972ysis_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 84.93/23.94 thf(676,plain,(! [A:list_P559422087at_nat] : ((finite772653738at_nat @ (set_Pr2131844118at_nat @ A)))),inference(cnf,[status(esa)],[675])). 84.93/23.94 thf(85,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_le__cases)). 84.93/23.94 thf(592,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)],[85])). 84.93/23.94 thf(63,axiom,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: ((A = (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_ord__eq__le__subst)). 84.93/23.94 thf(496,plain,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: ((A = (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 84.93/23.94 thf(52,axiom,((! [A:product_prod_nat_nat,B:list_P559422087at_nat]: ((member701585322at_nat @ A @ (set_Pr2131844118at_nat @ B)) => ((! [C:list_P559422087at_nat]: (B != (cons_P66992567at_nat @ A @ C))) => (~ (! [C:product_prod_nat_nat,D:list_P559422087at_nat]: ((~ (member701585322at_nat @ A @ (set_Pr2131844118at_nat @ D))) <= (B = (cons_P66992567at_nat @ C @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_list_Oset__cases)). 84.93/23.94 thf(454,plain,((! [A:product_prod_nat_nat,B:list_P559422087at_nat]: ((member701585322at_nat @ A @ (set_Pr2131844118at_nat @ B)) => ((! [C:list_P559422087at_nat]: ~ (B = (cons_P66992567at_nat @ A @ C))) => (~ (! [C:product_prod_nat_nat,D:list_P559422087at_nat]: (~ (member701585322at_nat @ A @ (set_Pr2131844118at_nat @ D)) | ~ (B = (cons_P66992567at_nat @ C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 84.93/23.94 thf(234,axiom,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Int__lower1)). 84.93/23.94 thf(1069,plain,((! [A:set_Pr1986765409at_nat,B:set_Pr1986765409at_nat]: (ord_le841296385at_nat @ (inf_in586391887at_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 84.93/23.94 thf(10772,plain,($false),inference(e,[status(thm)],[1665,2630,809,629,1190,1031,1083,1179,666,1168,760,777,555,481,352,977,1005,308,379,677,597,861,878,440,655,511,2195,385,715,698,1919,913,945,340,538,930,670,1196,898,1001,1914,1243,709,288,436,651,829,404,1055,719,504,802,357,460,1059,1132,559,853,969,1013,1115,289,1232,421,870,966,821,1040,1109,321,485,834,766,2281,634,692,734,293,866,774,411,1433,307,1074,292,512,661,793,534,1067,1047,334,910,1223,746,1021,1174,1217,392,407,815,1238,1883,1255,302,847,625,435,329,522,493,1027,1128,842,974,285,1106,742,1234,874,615,1121,1064,1970,1006,356,1118,989,1259,317,1856,725,1160,339,637,1700,1739,537,901,686,622,393,985,515,738,1192,1050,721,1002,1246,371,647,1263,997,1131,654,343,792,311,765,1071,530,953,794,586,718,888,1278,618,425,745,573,296,733,584,904,772,286,1929,826,958,1124,579,291,1226,545,382,611,466,704,947,2557,804,764,1209,831,990,303,863,509,880,649,1043,434,631,758,858,594,700,895,1149,915,769,943,2278,1177,462,1112,811,387,399,959,827,695,780,883,608,394,299,1102,431,922,685,1171,1076,722,1034,675,589,516,754,553,1181,823,712,855,690,282,707,971,310,993,1025,295,791,1785,1980,1738,643,1220,907,1188,1186,1085,576,744,656,600,386,314,612,2558,703,627,450,363,482,1157,2194,891,1126,813,963,304,1062,1101,390,401,418,995,346,536,1045,433,510,1077,478,1161,287,300,620,950,818,1986,603,294,437,474,664,400,828,960,283,720,1165,886,415,1236,1923,850,442,607,1093,395,486,337,1009,2206,1184,543,676,592,496,454,1069])). 84.93/23.94 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 84.93/23.94 % [INFO] Killing All external provers ... 84.93/23.94 WARNING: TreeLimitedRun lost 3.58s, total lost is 3.58s 84.93/23.94 FINAL WATCH: 79.6 CPU 21.8 WC 84.93/23.94 Killed 1 orphans 84.93/23.94 Killed 1 orphans 84.93/23.94 EOF