0.00/0.00 % Leo-III: Strategy 1 (for '60') 132.20/30.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 132.20/30.71 % [INFO] Parsing done (233ms). 132.20/30.71 % [INFO] Running in sequential loop mode. 132.20/30.71 % [CONFIG] Using configuration: timeout(60) with strategy 132.20/30.71 % [INFO] eprover registered as external prover. 132.20/30.71 % [INFO] cvc4 registered as external prover. 132.20/30.71 % [INFO] Parsing finished. Scanning for conjecture ... 132.20/30.71 % [INFO] Found a conjecture and 361 axioms. Running axiom selection ... 132.20/30.71 % [INFO] Axiom selection finished. Selected 324 axioms (removed 37 axioms). 132.20/30.71 % [INFO] Problem is higher-order (TPTP THF). 132.20/30.71 % [INFO] Type checking passed. Searching for refutation ... 132.20/30.71 % External prover 'e' found a proof! 132.20/30.71 % [INFO] Killing All external provers ... 132.20/30.71 % Time passed: 24114ms (effective reasoning time: 23519ms) 132.20/30.71 % Solved by strategy 132.20/30.71 % Axioms used in derivation (324): fact_89_order_Otrans, fact_105_ord__le__eq__subst, fact_316_Collect__empty__eq__bot, fact_80_order__class_Oorder_Oeq__iff, fact_68_order__class_Oorder_Oantisym, fact_34_nres__order__simps_I20_J, fact_70_order__class_Oorder_Oantisym, fact_256_empty__Collect__eq, fact_104_ord__le__eq__subst, fact_155_Greatest__equality, fact_164_ord__eq__le__eq__trans, fact_117_Collect__mem__eq, fact_81_order__class_Oorder_Oeq__iff, fact_281_bot_Oextremum__unique, fact_346_nres__inequalities_I4_J, fact_216_pw__eqI, fact_331_pw__flat__ge__iff, fact_220_not__nofail__inres, fact_298_nofail__simps_I4_J, fact_195_subset__antisym, fact_157_GreatestI2__order, fact_310_bot__nres__def, fact_128_ord__eq__le__subst, fact_73_ord__le__eq__trans, fact_144_order__subst1, fact_122_ord__eq__le__subst, fact_84_antisym__conv, fact_349_eq__UNIV__iff, fact_21_the__RES_Osimps, fact_156_GreatestI2__order, fact_317_ComplI, fact_258_insert__iff, fact_25_le__funE, fact_48_dual__order_Oantisym, fact_203_pw__bind__le__iff, fact_52_dual__order_Oeq__iff, fact_96_antisym, fact_167_ord__eq__le__eq__trans, fact_19_order__mono__setup_Orefl, fact_237_set__eq__subset, fact_11_SPEC__cons__rule, fact_109_ord__le__eq__subst, help_If_2_1_If_001t__Set__Oset_Itf__a_J_T, fact_333_nofail__simps_I1_J, fact_64_order__trans, fact_182_nres__monad1, fact_202_pw__bind__le__iff, fact_218_pw__eq__iff, fact_320_ComplD, fact_77_ord__eq__le__trans, fact_13_nf__inres__RES, fact_306_nres__order__simps_I1_J, help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T, fact_32_nres__more__simps_I6_J, fact_75_ord__le__eq__trans, fact_72_ord__le__eq__trans, fact_49_dual__order_Oantisym, fact_5_RES__rule, fact_291_less__nres_Oinduct, fact_330_flat__ord__compat_I1_J, fact_16_order__mono__setup_Orefl, fact_69_order__class_Oorder_Oantisym, fact_259_singletonI, fact_255_Collect__empty__eq, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_131_order__subst2, fact_85_antisym__conv, fact_3_nres_Oinject, fact_264_insertE, fact_196_pw__bind__leI, fact_335_flat__ord__compat_I2_J, fact_300_bind__SUCCEED, fact_199_pw__bind__leI, fact_24_le__funD, fact_336_top__greatest, fact_240_Collect__mono, fact_273_insert__absorb, fact_189_pwD1, fact_249_less__eq__nres_Oelims_I2_J, fact_88_order_Otrans, fact_115_mem__Collect__eq, fact_123_ord__eq__le__subst, fact_213_pwD2, fact_158_GreatestI2__order, fact_308_nres__inequalities_I5_J, fact_53_dual__order_Oeq__iff, fact_62_dual__order_Orefl, fact_180_nres__monad2, fact_92_eq__refl, fact_139_order__subst2, fact_243_subset__iff, fact_148_order__subst1, fact_26_le__funI, fact_51_dual__order_Oantisym, fact_135_order__subst2, fact_107_ord__le__eq__subst, fact_304_nres__more__simps_I1_J, fact_222_pw__le__iff, fact_183_nres__monad1, fact_226_pw__leI, fact_348_UNIV__I, fact_247_subset__eq, fact_141_order__subst1, help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T, fact_27_Refine__Misc_Oif__mono, fact_292_less__eq__nres_Oinduct, fact_168_bind__cong, fact_71_order__class_Oorder_Oantisym, fact_45_order__mono__setup_Omono__if, fact_163_le__rel__bool__arg__iff, fact_94_eq__refl, fact_208_subsetD, fact_192_le__nofailI, fact_212_inres__simps_I3_J, fact_289_nres_Oexhaust, fact_334_inres__simps_I1_J, fact_58_dual__order_Otrans, fact_30_Refine__Misc_Oif__mono, fact_286_RETURN__def, fact_41_RETURN__to__SPEC__rule, fact_188_nofail__RES__conv, fact_257_insertCI, fact_46_order__mono__setup_Omono__if, fact_238_subset__trans, fact_171_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_305_bot__set__def, fact_344_nres__inequalities_I1_J, fact_166_ord__eq__le__eq__trans, fact_326_pw__flat__le__iff, fact_325_ASSUME__simps_I2_J, fact_293_less__eq__nres_Osimps_I1_J, fact_174_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_140_order__subst1, fact_232_inres__def, fact_63_dual__order_Orefl, fact_231_inres__def, fact_345_nres__cases, fact_57_dual__order_Otrans, fact_37_less__eq__nres_Osimps_I2_J, fact_227_pw__bind__nofail, fact_294_insert__subsetI, fact_314_subset__Compl__singleton, fact_28_Refine__Misc_Oif__mono, fact_54_dual__order_Oeq__iff, fact_87_antisym__conv, fact_302_nres__more__simps_I2_J, fact_161_le__rel__bool__arg__iff, fact_277_set__notEmptyE, fact_181_nres__monad1, fact_210_inres__simps_I2_J, fact_234_nf__inres__def, fact_269_ex__in__conv, fact_200_pw__bind__le__iff, fact_219_not__nofail__inres, fact_276_mk__disjoint__insert, fact_284_bot_Oextremum__uniqueI, fact_194_subsetI, fact_39_nres__order__simps_I5_J, fact_241_subset__refl, fact_283_bot_Oextremum__uniqueI, fact_272_insert__ident, fact_229_pw__bind__nofail, fact_260_insert__subset, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T, fact_280_bot_Oextremum, fact_172_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_176_nofail__simps_I2_J, fact_340_not__nofail__iff, fact_149_order__subst1, fact_23_nres__order__simps_I21_J, fact_78_ord__eq__le__trans, fact_119_Collect__cong, fact_120_ord__eq__le__subst, fact_278_memb__imp__not__empty, fact_288_nres_Oinduct, fact_134_order__subst2, fact_173_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_76_ord__eq__le__trans, fact_244_equalityD2, fact_137_order__subst2, fact_245_equalityD1, fact_33_nres__more__simps_I6_J, fact_93_eq__refl, fact_228_pw__bind__nofail, fact_18_order__mono__setup_Orefl, fact_295_subset__emptyI, fact_299_inres__simps_I4_J, fact_60_dual__order_Orefl, fact_313_is__singletonI_H, fact_266_equals0I, fact_191_le__nofailI, fact_100_eq__iff, fact_339_meta__le__everything__if__top, fact_318_Compl__iff, fact_7_SPEC__rule, fact_43_RETURN__rule, fact_153_Greatest__equality, fact_106_ord__le__eq__subst, fact_327_pw__ASSUME_I2_J, fact_290_sup__nres_Oinduct, fact_198_pw__bind__leI, fact_342_intro__nofail_I2_J, fact_111_ord__le__eq__subst, fact_82_order__class_Oorder_Oeq__iff, fact_225_pw__leI, fact_125_ord__eq__le__subst, fact_169_bind__cong, fact_206_in__mono, fact_185_subset__Collect__conv, fact_265_equals0D, fact_312_SUCCEED__rule, fact_236_Collect__mono__iff, fact_1_nres__more__simps_I4_J, fact_296_nres__order__simps_I2_J, fact_211_inres__simps_I3_J, fact_253_empty__iff, fact_79_ord__eq__le__trans, fact_67_order__trans, fact_9_SPEC__trans, fact_271_singletonD, conj_1, fact_254_all__not__in__conv, fact_274_insert__eq__iff, fact_101_eq__iff, fact_223_pw__leI_H, fact_324_bot__empty__eq, fact_233_nf__inres__def, fact_179_nres__monad2, fact_113_ord__le__eq__subst, fact_35_nres__order__simps_I20_J, fact_178_nofail__simps_I3_J, fact_251_nres__order__simps_I22_J, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T, fact_221_pw__le__iff, fact_159_GreatestI2__order, fact_108_ord__le__eq__subst, fact_142_order__subst1, fact_186_nofail__antimono__fun, fact_343_nres__order__simps_I3_J, fact_50_dual__order_Oantisym, fact_65_order__trans, fact_248_less__eq__nres_Oelims_I1_J, fact_263_emptyE, fact_136_order__subst2, fact_59_dual__order_Otrans, fact_15_nf__inres__SPEC, fact_297_nres__order__simps_I2_J, fact_145_order__subst1, fact_132_order__subst2, fact_147_order__subst1, fact_332_nres__order__simps_I4_J, fact_328_pw__ASSUME_I1_J, fact_252_less__eq__nres_Osimps_I3_J, fact_262_nres__more__simps_I3_J, fact_61_dual__order_Orefl, fact_224_pw__leI_H, fact_307_nres__order__simps_I1_J, fact_201_pw__bind__le__iff, fact_44_order__mono__setup_Omono__if, fact_86_antisym__conv, fact_319_ibind__strict_I1_J, fact_215_pw__eqI, fact_177_nofail__simps_I3_J, help_If_1_1_If_001t__Set__Oset_Itf__a_J_T, fact_74_ord__le__eq__trans, fact_250_less__eq__nres_Oelims_I3_J, fact_17_order__mono__setup_Orefl, fact_146_order__subst1, fact_341_nofail__def, fact_279_bot_Oextremum, fact_129_ord__eq__le__subst, fact_55_dual__order_Oeq__iff, fact_47_order__mono__setup_Omono__if, fact_99_antisym, fact_127_ord__eq__le__subst, fact_102_eq__iff, fact_112_ord__le__eq__subst, fact_121_ord__eq__le__subst, fact_275_singleton__iff, fact_270_Set_Oset__insert, fact_97_antisym, fact_124_ord__eq__le__subst, fact_267_insertI1, fact_337_top_Oextremum__unique, fact_152_Greatest__equality, fact_338_top_Oextremum__uniqueI, fact_83_order__class_Oorder_Oeq__iff, fact_29_Refine__Misc_Oif__mono, fact_31_le__fun__def, fact_90_order_Otrans, fact_56_dual__order_Otrans, fact_160_le__rel__bool__arg__iff, fact_162_le__rel__bool__arg__iff, help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T, fact_170_bind__cong, fact_217_pw__eq__iff, conj_0, fact_143_order__subst1, fact_285_subset__insert, fact_66_order__trans, fact_347_nres__inequalities_I2_J, fact_126_ord__eq__le__subst, fact_329_flat__ord__compat_I1_J, fact_133_order__subst2, fact_130_order__subst2, fact_268_insertI2, fact_287_nres_Odistinct_I1_J, fact_261_nres__more__simps_I5_J, fact_151_the__RES__inv, fact_110_ord__le__eq__subst, fact_214_pwD2, fact_282_bot_Oextremum__unique, fact_91_order_Otrans, fact_204_relprop__triggers_I6_J, fact_95_eq__refl, fact_138_order__subst2, fact_230_pw__bind__nofail, fact_190_pwD1, fact_154_Greatest__equality, fact_197_pw__bind__leI, fact_103_eq__iff, fact_98_antisym, fact_165_ord__eq__le__eq__trans 132.20/30.71 % No. of inferences in proof: 1291 132.20/30.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 24114 ms resp. 23519 ms w/o parsing 132.20/30.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 132.20/30.71 thf(refine787176636t_unit_type, type, refine787176636t_unit: $tType). 132.20/30.71 thf(refine424419629nres_a_type, type, refine424419629nres_a: $tType). 132.20/30.71 thf(set_Product_unit_type, type, set_Product_unit: $tType). 132.20/30.71 thf(product_unit_type, type, product_unit: $tType). 132.20/30.71 thf(set_a_type, type, set_a: $tType). 132.20/30.71 thf(a_type, type, a: $tType). 132.20/30.71 thf(uminus_uminus_set_a_type, type, uminus_uminus_set_a: (set_a > set_a)). 132.20/30.71 thf(if_o_R1705037948nres_a_type, type, if_o_R1705037948nres_a: ($o > (($o > refine424419629nres_a) > (($o > refine424419629nres_a) > ($o > refine424419629nres_a))))). 132.20/30.71 thf(if_Ref1369692790t_unit_type, type, if_Ref1369692790t_unit: ($o > (refine787176636t_unit > (refine787176636t_unit > refine787176636t_unit)))). 132.20/30.71 thf(if_Ref1724547303nres_a_type, type, if_Ref1724547303nres_a: ($o > (refine424419629nres_a > (refine424419629nres_a > refine424419629nres_a)))). 132.20/30.71 thf(if_set_a_type, type, if_set_a: ($o > (set_a > (set_a > set_a)))). 132.20/30.71 thf(bot_bot_a_o_type, type, bot_bot_a_o: (a > $o)). 132.20/30.71 thf(bot_bo658782032t_unit_type, type, bot_bo658782032t_unit: refine787176636t_unit). 132.20/30.71 thf(bot_bo529555393nres_a_type, type, bot_bo529555393nres_a: refine424419629nres_a). 132.20/30.71 thf(bot_bot_set_a_type, type, bot_bot_set_a: set_a). 132.20/30.71 thf(ord_le1960259811nres_a_type, type, ord_le1960259811nres_a: (($o > ($o > refine424419629nres_a)) > (($o > ($o > refine424419629nres_a)) > $o))). 132.20/30.71 thf(ord_le1633311077t_unit_type, type, ord_le1633311077t_unit: (($o > refine787176636t_unit) > (($o > refine787176636t_unit) > $o))). 132.20/30.71 thf(ord_le516598614nres_a_type, type, ord_le516598614nres_a: (($o > refine424419629nres_a) > (($o > refine424419629nres_a) > $o))). 132.20/30.71 thf(ord_less_eq_o_set_a_type, type, ord_less_eq_o_set_a: (($o > set_a) > (($o > set_a) > $o))). 132.20/30.71 thf(ord_le1051254044t_unit_type, type, ord_le1051254044t_unit: (refine787176636t_unit > (refine787176636t_unit > $o))). 132.20/30.71 thf(ord_le519537037nres_a_type, type, ord_le519537037nres_a: (refine424419629nres_a > (refine424419629nres_a > $o))). 132.20/30.71 thf(ord_less_eq_set_a_type, type, ord_less_eq_set_a: (set_a > (set_a > $o))). 132.20/30.71 thf(order_245837199nres_a_type, type, order_245837199nres_a: ((($o > refine424419629nres_a) > $o) > ($o > refine424419629nres_a))). 132.20/30.71 thf(order_453013155t_unit_type, type, order_453013155t_unit: ((refine787176636t_unit > $o) > refine787176636t_unit)). 132.20/30.71 thf(order_1714329108nres_a_type, type, order_1714329108nres_a: ((refine424419629nres_a > $o) > refine424419629nres_a)). 132.20/30.71 thf(order_Greatest_set_a_type, type, order_Greatest_set_a: ((set_a > $o) > set_a)). 132.20/30.71 thf(top_to177290092t_unit_type, type, top_to177290092t_unit: refine787176636t_unit). 132.20/30.71 thf(top_to231829469nres_a_type, type, top_to231829469nres_a: refine424419629nres_a). 132.20/30.71 thf(top_top_set_a_type, type, top_top_set_a: set_a). 132.20/30.71 thf(partia1658438072t_unit_type, type, partia1658438072t_unit: (refine787176636t_unit > (refine787176636t_unit > (refine787176636t_unit > $o)))). 132.20/30.71 thf(partia906949161nres_a_type, type, partia906949161nres_a: (refine424419629nres_a > (refine424419629nres_a > (refine424419629nres_a > $o)))). 132.20/30.71 thf(refine23983189ASSUME_type, type, refine23983189ASSUME: ($o > refine787176636t_unit)). 132.20/30.71 thf(refine1420258419t_unit_type, type, refine1420258419t_unit: (product_unit > refine787176636t_unit)). 132.20/30.71 thf(refine2063221604TURN_a_type, type, refine2063221604TURN_a: (a > refine424419629nres_a)). 132.20/30.71 thf(refine681446406t_unit_type, type, refine681446406t_unit: (refine787176636t_unit > ((product_unit > refine787176636t_unit) > refine787176636t_unit))). 132.20/30.71 thf(refine119808503unit_a_type, type, refine119808503unit_a: (refine787176636t_unit > ((product_unit > refine424419629nres_a) > refine424419629nres_a))). 132.20/30.71 thf(refine96995669t_unit_type, type, refine96995669t_unit: (refine424419629nres_a > ((a > refine787176636t_unit) > refine787176636t_unit))). 132.20/30.71 thf(refine436832838nd_a_a_type, type, refine436832838nd_a_a: (refine424419629nres_a > ((a > refine424419629nres_a) > refine424419629nres_a))). 132.20/30.71 thf(refine558004794t_unit_type, type, refine558004794t_unit: (refine787176636t_unit > (product_unit > $o))). 132.20/30.71 thf(refine1001002027nres_a_type, type, refine1001002027nres_a: (refine424419629nres_a > (a > $o))). 132.20/30.71 thf(refine983493746t_unit_type, type, refine983493746t_unit: (refine787176636t_unit > (product_unit > $o))). 132.20/30.71 thf(refine1312857699nres_a_type, type, refine1312857699nres_a: (refine424419629nres_a > (a > $o))). 132.20/30.71 thf(refine579265252t_unit_type, type, refine579265252t_unit: (refine787176636t_unit > $o)). 132.20/30.71 thf(refine412683989fail_a_type, type, refine412683989fail_a: (refine424419629nres_a > $o)). 132.20/30.71 thf(refine464223677AILi_a_type, type, refine464223677AILi_a: refine424419629nres_a). 132.20/30.71 thf(refine1198353288_RES_a_type, type, refine1198353288_RES_a: (set_a > refine424419629nres_a)). 132.20/30.71 thf(refine1822134885_RES_a_type, type, refine1822134885_RES_a: (refine424419629nres_a > set_a)). 132.20/30.71 thf(collect_a_type, type, collect_a: ((a > $o) > set_a)). 132.20/30.71 thf(insert_a_type, type, insert_a: (a > (set_a > set_a))). 132.20/30.71 thf(is_singleton_a_type, type, is_singleton_a: (set_a > $o)). 132.20/30.71 thf(member_a_type, type, member_a: (a > (set_a > $o))). 132.20/30.71 thf(s1_type, type, s1: refine424419629nres_a). 132.20/30.71 thf(s2_type, type, s2: refine424419629nres_a). 132.20/30.71 thf(phi_type, type, phi: (a > $o)). 132.20/30.71 thf(b_type, type, b: $o). 132.20/30.71 thf(sk1_type, type, sk1: ((product_unit > refine787176636t_unit) > (refine787176636t_unit > (refine787176636t_unit > product_unit)))). 132.20/30.71 thf(sk2_type, type, sk2: (set_a > (set_a > ((set_a > set_a) > (set_a > set_a))))). 132.20/30.71 thf(sk3_type, type, sk3: (set_a > (set_a > ((set_a > set_a) > (set_a > set_a))))). 132.20/30.71 thf(sk4_type, type, sk4: (refine787176636t_unit > ((refine787176636t_unit > refine787176636t_unit) > (refine787176636t_unit > (refine787176636t_unit > refine787176636t_unit))))). 132.20/30.71 thf(sk5_type, type, sk5: (refine787176636t_unit > ((refine787176636t_unit > refine787176636t_unit) > (refine787176636t_unit > (refine787176636t_unit > refine787176636t_unit))))). 132.20/30.71 thf(sk6_type, type, sk6: (refine787176636t_unit > (refine787176636t_unit > product_unit))). 132.20/30.71 thf(sk7_type, type, sk7: ((($o > refine424419629nres_a) > $o) > $o)). 132.20/30.71 thf(sk8_type, type, sk8: (($o > refine424419629nres_a) > ((($o > refine424419629nres_a) > $o) > ($o > refine424419629nres_a)))). 132.20/30.71 thf(sk9_type, type, sk9: ((($o > refine424419629nres_a) > $o) > (($o > refine424419629nres_a) > ((($o > refine424419629nres_a) > $o) > ($o > refine424419629nres_a))))). 132.20/30.71 thf(sk10_type, type, sk10: (set_a > (set_a > ((set_a > refine787176636t_unit) > (refine787176636t_unit > set_a))))). 132.20/30.71 thf(sk11_type, type, sk11: (set_a > (set_a > ((set_a > refine787176636t_unit) > (refine787176636t_unit > set_a))))). 132.20/30.71 thf(sk12_type, type, sk12: (refine787176636t_unit > (refine787176636t_unit > product_unit))). 132.20/30.71 thf(sk13_type, type, sk13: (set_a > a)). 132.20/30.71 thf(sk14_type, type, sk14: (set_a > (a > set_a))). 132.20/30.71 thf(sk15_type, type, sk15: (refine787176636t_unit > (refine787176636t_unit > ((refine787176636t_unit > set_a) > (set_a > refine787176636t_unit))))). 132.20/30.71 thf(sk16_type, type, sk16: (refine787176636t_unit > (refine787176636t_unit > ((refine787176636t_unit > set_a) > (set_a > refine787176636t_unit))))). 132.20/30.71 thf(sk17_type, type, sk17: (set_a > a)). 132.20/30.71 thf(sk18_type, type, sk18: (set_a > ((set_a > set_a) > (set_a > (set_a > set_a))))). 132.20/30.71 thf(sk19_type, type, sk19: (set_a > ((set_a > set_a) > (set_a > (set_a > set_a))))). 132.20/30.71 thf(sk20_type, type, sk20: (refine787176636t_unit > (refine787176636t_unit > ((refine787176636t_unit > refine787176636t_unit) > (refine787176636t_unit > refine787176636t_unit))))). 132.20/30.71 thf(sk21_type, type, sk21: (refine787176636t_unit > (refine787176636t_unit > ((refine787176636t_unit > refine787176636t_unit) > (refine787176636t_unit > refine787176636t_unit))))). 132.20/30.71 thf(sk183_type, type, sk183: (a > set_a)). 132.20/30.71 thf(sk185_type, type, sk185: (a > set_a)). 132.20/30.71 thf(sk186_type, type, sk186: (set_a > set_a)). 132.20/30.71 thf(sk187_type, type, sk187: (set_a > set_a)). 132.20/30.71 thf(sk188_type, type, sk188: set_a). 132.20/30.71 thf(sk189_type, type, sk189: set_a). 132.20/30.71 thf(sk232_type, type, sk232: a). 132.20/30.71 thf(sk235_type, type, sk235: a). 132.20/30.71 thf(sk236_type, type, sk236: a). 132.20/30.71 thf(sk237_type, type, sk237: a). 132.20/30.71 thf(sk238_type, type, sk238: a). 132.20/30.71 thf(sk239_type, type, sk239: a). 132.20/30.71 thf(sk241_type, type, sk241: a). 132.20/30.71 thf(sk249_type, type, sk249: a). 132.20/30.71 thf(91,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine787176636t_unit),D:(product_unit > refine787176636t_unit)]: ((((refine681446406t_unit @ A @ C) = (refine681446406t_unit @ B @ D)) <= (! [E:product_unit]: (((C @ E) = (D @ E)) <= (ord_le1051254044t_unit @ (refine1420258419t_unit @ E) @ B)))) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_bind__cong)). 132.20/30.71 thf(645,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine787176636t_unit),D:(product_unit > refine787176636t_unit)]: (((refine681446406t_unit @ A @ (C)) = (refine681446406t_unit @ B @ (D))) | ~ (! [E:product_unit]: (((C @ E) = (D @ E)) | ~ (ord_le1051254044t_unit @ (refine1420258419t_unit @ E) @ B))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 132.20/30.71 thf(273,axiom,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: (((! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))) => ((A @ B @ C) <= (! [D:set_a]: (A @ refine464223677AILi_a @ (refine1198353288_RES_a @ D))))) <= (! [D:refine424419629nres_a]: (A @ D @ refine464223677AILi_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_less__eq__nres_Oinduct)). 132.20/30.71 thf(1322,plain,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: (((! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))) => ((A @ B @ C) | ~ (! [D:set_a]: (A @ refine464223677AILi_a @ (refine1198353288_RES_a @ D))))) | ~ (! [D:refine424419629nres_a]: (A @ D @ refine464223677AILi_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 132.20/30.71 thf(319,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine787176636t_unit),D:refine787176636t_unit]: ((ord_le519537037nres_a @ A @ B) => (((C @ B) = D) => ((ord_le1051254044t_unit @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le1051254044t_unit @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_ord__le__eq__subst)). 132.20/30.71 thf(1501,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine787176636t_unit),D:refine787176636t_unit]: ((ord_le519537037nres_a @ A @ B) => (((C @ B) = D) => ((ord_le1051254044t_unit @ (C @ A) @ D) | ~ (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le1051254044t_unit @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 132.20/30.71 thf(85,axiom,((! [A:a,B:set_a]: (((insert_a @ A @ B) = B) <= (member_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_insert__absorb)). 132.20/30.71 thf(629,plain,((! [A:a,B:set_a]: (((insert_a @ A @ B) = B) | ~ (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 132.20/30.71 thf(309,axiom,((! [A:refine787176636t_unit,B:(refine424419629nres_a > refine787176636t_unit),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => (((ord_le1051254044t_unit @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) <= (ord_le519537037nres_a @ E @ F)))) <= (ord_le519537037nres_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_ord__eq__le__subst)). 132.20/30.71 thf(1469,plain,((! [A:refine787176636t_unit,B:(refine424419629nres_a > refine787176636t_unit),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => ((ord_le1051254044t_unit @ A @ (B @ D)) | ~ (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) | ~ (ord_le519537037nres_a @ E @ F))) | ~ (ord_le519537037nres_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 132.20/30.71 thf(124,axiom,((! [A:set_a,B:set_a]: ((! [C:a]: ((member_a @ C @ B) <= (member_a @ C @ A))) => (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_subsetI)). 132.20/30.71 thf(760,plain,((! [A:set_a,B:set_a]: ((! [C:a]: ((member_a @ C @ B) | ~ (member_a @ C @ A))) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 132.20/30.71 thf(101,axiom,((! [A:a]: (member_a @ A @ top_top_set_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_UNIV__I)). 132.20/30.71 thf(676,plain,((! [A:a]: (member_a @ A @ top_top_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 132.20/30.71 thf(677,plain,(! [A:a] : ((member_a @ A @ top_top_set_a))),inference(cnf,[status(esa)],[676])). 132.20/30.71 thf(37,axiom,((! [A:a,B:set_a,C:a]: ((member_a @ A @ (insert_a @ C @ B)) <= ((A = C) <= (~ (member_a @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_insertCI)). 132.20/30.71 thf(437,plain,((! [A:a,B:set_a,C:a]: ((member_a @ A @ (insert_a @ C @ B)) | ~ ((A = C) | (member_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 132.20/30.71 thf(439,plain,(! [C:a,B:set_a,A:a] : ((member_a @ A @ (insert_a @ C @ B)) | (~ (member_a @ A @ B)))),inference(cnf,[status(esa)],[437])). 132.20/30.71 thf(6149,plain,(! [D:a,C:set_a,B:a,A:a] : ((member_a @ B @ (insert_a @ D @ C)) | ((member_a @ A @ top_top_set_a) != (member_a @ B @ C)))),inference(paramod_ordered,[status(thm)],[677,439])). 132.20/30.71 thf(6150,plain,(! [B:a,A:a] : ((member_a @ A @ (insert_a @ B @ top_top_set_a)))),inference(pattern_uni,[status(thm)],[6149:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(top_top_set_a))]])). 132.20/30.71 thf(6171,plain,(! [B:a,A:a] : ((member_a @ A @ (insert_a @ B @ top_top_set_a)))),inference(simp,[status(thm)],[6150])). 132.20/30.71 thf(48,axiom,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_emptyE)). 132.20/30.71 thf(477,plain,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 132.20/30.71 thf(478,plain,((~ (? [A:a]: (member_a @ A @ bot_bot_set_a)))),inference(miniscope,[status(thm)],[477])). 132.20/30.71 thf(479,plain,(! [A:a] : ((~ (member_a @ A @ bot_bot_set_a)))),inference(cnf,[status(esa)],[478])). 132.20/30.71 thf(6207,plain,(! [C:a,B:a,A:a] : (((member_a @ A @ (insert_a @ B @ top_top_set_a)) != (member_a @ C @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[6171,479])). 132.20/30.71 thf(6226,plain,(! [C:a,B:a,A:a] : ((A != C) | ((insert_a @ B @ top_top_set_a) != bot_bot_set_a))),inference(simp,[status(thm)],[6207])). 132.20/30.71 thf(6231,plain,(! [A:a] : (((insert_a @ A @ top_top_set_a) != bot_bot_set_a))),inference(simp,[status(thm)],[6226])). 132.20/30.71 thf(282,axiom,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ bot_bo529555393nres_a) = (A = bot_bo529555393nres_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_nres__order__simps_I2_J)). 132.20/30.71 thf(1364,plain,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ bot_bo529555393nres_a) = (A = bot_bo529555393nres_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 132.20/30.71 thf(1365,plain,(! [A:refine424419629nres_a] : (((ord_le519537037nres_a @ A @ bot_bo529555393nres_a) = (A = bot_bo529555393nres_a)))),inference(cnf,[status(esa)],[1364])). 132.20/30.71 thf(1366,plain,(! [A:refine424419629nres_a] : (((ord_le519537037nres_a @ A @ bot_bo529555393nres_a) = (A = bot_bo529555393nres_a)))),inference(lifteq,[status(thm)],[1365])). 132.20/30.71 thf(237,axiom,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ top_to231829469nres_a @ A) = (A = top_to231829469nres_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_nres__order__simps_I4_J)). 132.20/30.71 thf(1175,plain,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ top_to231829469nres_a @ A) = (A = top_to231829469nres_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 132.20/30.71 thf(1176,plain,(! [A:refine424419629nres_a] : (((ord_le519537037nres_a @ top_to231829469nres_a @ A) = (A = top_to231829469nres_a)))),inference(cnf,[status(esa)],[1175])). 132.20/30.71 thf(1177,plain,(! [A:refine424419629nres_a] : (((ord_le519537037nres_a @ top_to231829469nres_a @ A) = (A = top_to231829469nres_a)))),inference(lifteq,[status(thm)],[1176])). 132.20/30.71 thf(5328,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : (((A = bot_bo529555393nres_a) = (B = top_to231829469nres_a)) | ((ord_le519537037nres_a @ A @ bot_bo529555393nres_a) != (ord_le519537037nres_a @ top_to231829469nres_a @ B)))),inference(paramod_ordered,[status(thm)],[1366,1177])). 132.20/30.71 thf(5329,plain,(((top_to231829469nres_a = bot_bo529555393nres_a) = (bot_bo529555393nres_a = top_to231829469nres_a))),inference(pattern_uni,[status(thm)],[5328:[bind(A, $thf(top_to231829469nres_a)),bind(B, $thf(bot_bo529555393nres_a))]])). 132.20/30.71 thf(165,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ A @ C) <= (ord_less_eq_set_a @ B @ C)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_subset__trans)). 132.20/30.71 thf(909,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ C) | ~ (ord_less_eq_set_a @ B @ C) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 132.20/30.71 thf(31,axiom,((! [A:$o,B:product_unit]: ((refine558004794t_unit @ (refine23983189ASSUME @ A) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_pw__ASSUME_I2_J)). 132.20/30.71 thf(406,plain,((! [A:$o,B:product_unit]: ((refine558004794t_unit @ (refine23983189ASSUME @ A) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 132.20/30.71 thf(407,plain,((! [A:product_unit]: ((refine558004794t_unit @ (refine23983189ASSUME @ $true) @ A) = $true))),inference(instance,[status(thm)],[406])). 132.20/30.71 thf(408,plain,((! [A:product_unit]: (refine558004794t_unit @ (refine23983189ASSUME @ $true) @ A))),inference(simp,[status(thm)],[407])). 132.20/30.71 thf(411,plain,(! [A:product_unit] : ((refine558004794t_unit @ (refine23983189ASSUME @ $true) @ A))),inference(cnf,[status(esa)],[408])). 132.20/30.71 thf(42,axiom,(((refine558004794t_unit @ bot_bo658782032t_unit) = (^ [A:product_unit]: ($false)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_inres__simps_I4_J)). 132.20/30.71 thf(456,plain,(((refine558004794t_unit @ bot_bo658782032t_unit) = (^ [A:product_unit]: ($false)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 132.20/30.71 thf(457,plain,(((refine558004794t_unit @ bot_bo658782032t_unit) = (^ [A:product_unit]: ($false)))),inference(lifteq,[status(thm)],[456])). 132.20/30.71 thf(1552,plain,(! [A:product_unit] : ((~ (refine558004794t_unit @ bot_bo658782032t_unit @ A)))),inference(func_ext,[status(esa)],[457])). 132.20/30.71 thf(1893,plain,(! [B:product_unit,A:product_unit] : (((refine558004794t_unit @ (refine23983189ASSUME @ $true) @ A) != (refine558004794t_unit @ bot_bo658782032t_unit @ B)))),inference(paramod_ordered,[status(thm)],[411,1552])). 132.20/30.71 thf(1896,plain,(! [B:product_unit,A:product_unit] : (((refine23983189ASSUME @ $true) != bot_bo658782032t_unit) | (A != B))),inference(simp,[status(thm)],[1893])). 132.20/30.71 thf(1899,plain,(((refine23983189ASSUME @ $true) != bot_bo658782032t_unit)),inference(simp,[status(thm)],[1896])). 132.20/30.71 thf(160,axiom,((! [A:refine424419629nres_a]: ((refine436832838nd_a_a @ A @ refine2063221604TURN_a) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_nres__monad2)). 132.20/30.71 thf(893,plain,((! [A:refine424419629nres_a]: ((refine436832838nd_a_a @ A @ (refine2063221604TURN_a)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 132.20/30.71 thf(59,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) => ((ord_le516598614nres_a @ A @ C) <= (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_ord__le__eq__trans)). 132.20/30.71 thf(518,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (A) @ (B)) => ((ord_le516598614nres_a @ (A) @ (C)) | ~ ((B) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 132.20/30.71 thf(182,axiom,((! [A:$o,B:set_a,C:set_a,D:set_a,E:set_a]: ((((ord_less_eq_set_a @ D @ E) <= (~ (A))) => (ord_less_eq_set_a @ (if_set_a @ A @ B @ D) @ (if_set_a @ A @ C @ E))) <= ((ord_less_eq_set_a @ B @ C) <= (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Refine__Misc_Oif__mono)). 132.20/30.71 thf(962,plain,((! [A:$o,B:set_a,C:set_a,D:set_a,E:set_a]: ((((ord_less_eq_set_a @ D @ E) | (A)) => (ord_less_eq_set_a @ (if_set_a @ A @ B @ D) @ (if_set_a @ A @ C @ E))) | ~ ((ord_less_eq_set_a @ B @ C) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 132.20/30.71 thf(65,axiom,((! [A:a,B:set_a,C:set_a]: ((~ (member_a @ A @ B)) => ((ord_less_eq_set_a @ B @ (insert_a @ A @ C)) = (ord_less_eq_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_subset__insert)). 132.20/30.71 thf(552,plain,((! [A:a,B:set_a,C:set_a]: ((~ (member_a @ A @ B)) => ((ord_less_eq_set_a @ B @ (insert_a @ A @ C)) = (ord_less_eq_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 132.20/30.71 thf(553,plain,((! [A:a,B:set_a]: ((~ (member_a @ A @ B)) => (! [C:set_a]: ((ord_less_eq_set_a @ B @ (insert_a @ A @ C)) = (ord_less_eq_set_a @ B @ C)))))),inference(miniscope,[status(thm)],[552])). 132.20/30.71 thf(554,plain,(! [C:set_a,B:set_a,A:a] : ((member_a @ A @ B) | ((ord_less_eq_set_a @ B @ (insert_a @ A @ C)) = (ord_less_eq_set_a @ B @ C)))),inference(cnf,[status(esa)],[553])). 132.20/30.71 thf(555,plain,(! [C:set_a,B:set_a,A:a] : (((ord_less_eq_set_a @ B @ (insert_a @ A @ C)) = (ord_less_eq_set_a @ B @ C)) | (member_a @ A @ B))),inference(lifteq,[status(thm)],[554])). 132.20/30.71 thf(24,axiom,((! [A:a]: (member_a @ A @ (insert_a @ A @ bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_singletonI)). 132.20/30.71 thf(383,plain,((! [A:a]: (member_a @ A @ (insert_a @ A @ bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 132.20/30.71 thf(384,plain,(! [A:a] : ((member_a @ A @ (insert_a @ A @ bot_bot_set_a)))),inference(cnf,[status(esa)],[383])). 132.20/30.71 thf(1954,plain,(! [B:a,A:a] : (((member_a @ A @ (insert_a @ A @ bot_bot_set_a)) != (member_a @ B @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[384,479])). 132.20/30.71 thf(1955,plain,(! [B:a,A:a] : ((A != B) | ((insert_a @ A @ bot_bot_set_a) != bot_bot_set_a))),inference(simp,[status(thm)],[1954])). 132.20/30.71 thf(1956,plain,(! [A:a] : (((insert_a @ A @ bot_bot_set_a) != bot_bot_set_a))),inference(simp,[status(thm)],[1955])). 132.20/30.71 thf(16,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((partia1658438072t_unit @ bot_bo658782032t_unit @ A @ B) => (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_flat__ord__compat_I1_J)). 132.20/30.71 thf(365,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((partia1658438072t_unit @ bot_bo658782032t_unit @ A @ B) => (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 132.20/30.71 thf(283,axiom,((! [A:set_a]: ((refine1822134885_RES_a @ (refine1198353288_RES_a @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_the__RES_Osimps)). 132.20/30.71 thf(1367,plain,((! [A:set_a]: ((refine1822134885_RES_a @ (refine1198353288_RES_a @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 132.20/30.71 thf(1368,plain,(! [A:set_a] : (((refine1822134885_RES_a @ (refine1198353288_RES_a @ A)) = A))),inference(cnf,[status(esa)],[1367])). 132.20/30.71 thf(1369,plain,(! [A:set_a] : (((refine1822134885_RES_a @ (refine1198353288_RES_a @ A)) = A))),inference(lifteq,[status(thm)],[1368])). 132.20/30.71 thf(241,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((if_Ref1724547303nres_a @ $false @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T)). 132.20/30.71 thf(1190,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((if_Ref1724547303nres_a @ $false @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 132.20/30.71 thf(218,axiom,((! [A:(a > $o)]: (((collect_a @ A) = bot_bot_set_a) = (! [B:a]: ~ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Collect__empty__eq)). 132.20/30.71 thf(1105,plain,((! [A:(a > $o)]: (((collect_a @ (A)) = bot_bot_set_a) = (! [B:a]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 132.20/30.71 thf(310,axiom,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Collect__mem__eq)). 132.20/30.71 thf(1477,plain,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 132.20/30.71 thf(1478,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(cnf,[status(esa)],[1477])). 132.20/30.71 thf(1479,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(lifteq,[status(thm)],[1478])). 132.20/30.71 thf(3310,plain,(! [B:set_a,A:set_a] : (((collect_a @ (^ [C:a]: (member_a @ C @ A))) = B) | (A != (refine1822134885_RES_a @ (refine1198353288_RES_a @ B))))),inference(paramod_ordered,[status(thm)],[1479,1369])). 132.20/30.71 thf(3311,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (refine1822134885_RES_a @ (refine1198353288_RES_a @ A))))) = A))),inference(pattern_uni,[status(thm)],[3310:[bind(A, $thf(refine1822134885_RES_a @ (refine1198353288_RES_a @ D))),bind(B, $thf(D))]])). 132.20/30.71 thf(3354,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (refine1822134885_RES_a @ (refine1198353288_RES_a @ A))))) = A))),inference(simp,[status(thm)],[3311])). 132.20/30.71 thf(13209,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(rewrite,[status(thm)],[3354,1369])). 132.20/30.71 thf(227,axiom,((! [A:set_a]: ((refine1001002027nres_a @ (refine1198353288_RES_a @ A)) = (^ [B:a]: (member_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_inres__simps_I2_J)). 132.20/30.71 thf(1148,plain,((! [A:set_a]: ((refine1001002027nres_a @ (refine1198353288_RES_a @ A)) = (^ [B:a]: (member_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 132.20/30.71 thf(1149,plain,(! [A:set_a] : (((refine1001002027nres_a @ (refine1198353288_RES_a @ A)) = (^ [B:a]: (member_a @ B @ A))))),inference(cnf,[status(esa)],[1148])). 132.20/30.71 thf(1150,plain,(! [A:set_a] : (((^ [B:a]: (member_a @ B @ A)) = (refine1001002027nres_a @ (refine1198353288_RES_a @ A))))),inference(lifteq,[status(thm)],[1149])). 132.20/30.71 thf(3471,plain,(! [A:set_a] : (((collect_a @ (refine1001002027nres_a @ (refine1198353288_RES_a @ A))) = A))),inference(rewrite,[status(thm)],[1479,1150])). 132.20/30.71 thf(287,axiom,((refine1001002027nres_a = (^ [A:refine424419629nres_a,B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_inres__def)). 132.20/30.71 thf(1386,plain,(((refine1001002027nres_a) = (^ [A:refine424419629nres_a,B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 132.20/30.71 thf(1387,plain,(((refine1001002027nres_a) = (^ [A:refine424419629nres_a,B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ A)))),inference(lifteq,[status(thm)],[1386])). 132.20/30.71 thf(1585,plain,(! [A:refine424419629nres_a] : (((refine1001002027nres_a @ A) = (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ A))))),inference(func_ext,[status(esa)],[1387])). 132.20/30.71 thf(4008,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ A)))) = A))),inference(rewrite,[status(thm)],[3471,1585])). 132.20/30.71 thf(13214,plain,(! [B:a,A:set_a] : (((collect_a @ (^ [C:a]: (member_a @ C @ A))) != bot_bot_set_a) | (A != (insert_a @ B @ top_top_set_a)))),inference(paramod_ordered,[status(thm)],[13209,6231])). 132.20/30.71 thf(13215,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ top_top_set_a)))) != bot_bot_set_a))),inference(pattern_uni,[status(thm)],[13214:[bind(A, $thf(insert_a @ C @ top_top_set_a)),bind(B, $thf(C))]])). 132.20/30.71 thf(13434,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ top_top_set_a)))) != bot_bot_set_a))),inference(simp,[status(thm)],[13215])). 132.20/30.71 thf(13983,plain,(((collect_a @ (^ [A:a]: ($true))) != bot_bot_set_a)),inference(rewrite,[status(thm)],[13434,6171])). 132.20/30.71 thf(13986,plain,(! [A:set_a] : ((A != bot_bot_set_a) | ((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ A)))) != (collect_a @ (^ [B:a]: ($true)))))),inference(paramod_ordered,[status(thm)],[4008,13983])). 132.20/30.71 thf(14006,plain,(((collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ bot_bot_set_a)))) != (collect_a @ (^ [A:a]: ($true))))),inference(simp,[status(thm)],[13986])). 132.20/30.71 thf(230,axiom,((bot_bo529555393nres_a = (refine1198353288_RES_a @ bot_bot_set_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_bot__nres__def)). 132.20/30.71 thf(1157,plain,((bot_bo529555393nres_a = (refine1198353288_RES_a @ bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 132.20/30.71 thf(1158,plain,(((refine1198353288_RES_a @ bot_bot_set_a) = bot_bo529555393nres_a)),inference(lifteq,[status(thm)],[1157])). 132.20/30.71 thf(15770,plain,(((collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a))) != (collect_a @ (^ [A:a]: ($true))))),inference(rewrite,[status(thm)],[14006,1158])). 132.20/30.71 thf(15772,plain,(! [A:set_a] : ((A != (collect_a @ (^ [B:a]: ($true)))) | ((collect_a @ (^ [B:a]: (member_a @ B @ A))) != (collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ bot_bo529555393nres_a)))))),inference(paramod_ordered,[status(thm)],[13209,15770])). 132.20/30.71 thf(15785,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true)))))) != (collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a))))),inference(simp,[status(thm)],[15772])). 132.20/30.71 thf(16576,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true)))))) != (collect_a @ (^ [A:a]: ((refine2063221604TURN_a @ A) = bot_bo529555393nres_a))))),inference(rewrite,[status(thm)],[15785,1366])). 132.20/30.71 thf(9,axiom,((! [A:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ bot_bo658782032t_unit) => (A = bot_bo658782032t_unit)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_bot_Oextremum__uniqueI)). 132.20/30.71 thf(347,plain,((! [A:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ bot_bo658782032t_unit) => (A = bot_bo658782032t_unit)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 132.20/30.71 thf(1727,plain,(! [B:a,A:a] : (((member_a @ A @ top_top_set_a) != (member_a @ B @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[677,479])). 132.20/30.71 thf(1728,plain,(! [B:a,A:a] : ((A != B) | (top_top_set_a != bot_bot_set_a))),inference(simp,[status(thm)],[1727])). 132.20/30.71 thf(1729,plain,((top_top_set_a != bot_bot_set_a)),inference(simp,[status(thm)],[1728])). 132.20/30.71 thf(97,axiom,((! [A:refine787176636t_unit,B:(product_unit > refine424419629nres_a)]: ((refine412683989fail_a @ (refine119808503unit_a @ A @ B)) = (! [C:product_unit]: ((refine412683989fail_a @ (B @ C)) <= (refine558004794t_unit @ A @ C)) & (refine579265252t_unit @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_pw__bind__nofail)). 132.20/30.71 thf(666,plain,((! [A:refine787176636t_unit,B:(product_unit > refine424419629nres_a)]: ((refine412683989fail_a @ (refine119808503unit_a @ A @ (B))) = (! [C:product_unit]: ((refine412683989fail_a @ (B @ C)) | ~ (refine558004794t_unit @ A @ C)) & (refine579265252t_unit @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 132.20/30.71 thf(266,axiom,((! [A:set_a,B:a]: (((refine1198353288_RES_a @ A) = (refine2063221604TURN_a @ B)) = (A = (insert_a @ B @ bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_nres__more__simps_I3_J)). 132.20/30.71 thf(1295,plain,((! [A:set_a,B:a]: (((refine1198353288_RES_a @ A) = (refine2063221604TURN_a @ B)) = (A = (insert_a @ B @ bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 132.20/30.71 thf(8,axiom,((! [A:product_unit,B:(product_unit > refine787176636t_unit)]: ((refine681446406t_unit @ (refine1420258419t_unit @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_nres__monad1)). 132.20/30.71 thf(344,plain,((! [A:product_unit,B:(product_unit > refine787176636t_unit)]: ((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 132.20/30.71 thf(345,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) = (B @ A)))),inference(cnf,[status(esa)],[344])). 132.20/30.71 thf(346,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) = (B @ A)))),inference(lifteq,[status(thm)],[345])). 132.20/30.71 thf(4,axiom,((! [A:product_unit]: (bot_bo658782032t_unit != (refine1420258419t_unit @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_nres__inequalities_I5_J)). 132.20/30.71 thf(331,plain,((! [A:product_unit]: ~ (bot_bo658782032t_unit = (refine1420258419t_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 132.20/30.71 thf(332,plain,((~ (? [A:product_unit]: (bot_bo658782032t_unit = (refine1420258419t_unit @ A))))),inference(miniscope,[status(thm)],[331])). 132.20/30.71 thf(333,plain,(! [A:product_unit] : ((~ (bot_bo658782032t_unit = (refine1420258419t_unit @ A))))),inference(cnf,[status(esa)],[332])). 132.20/30.71 thf(334,plain,(! [A:product_unit] : (((refine1420258419t_unit @ A) != bot_bo658782032t_unit))),inference(lifteq,[status(thm)],[333])). 132.20/30.71 thf(1647,plain,(! [C:product_unit,B:(product_unit > refine787176636t_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) != bot_bo658782032t_unit) | ((B @ A) != (refine1420258419t_unit @ C)))),inference(paramod_ordered,[status(thm)],[346,334])). 132.20/30.71 thf(1661,plain,(! [B:(product_unit > product_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (refine1420258419t_unit @ (B @ C)))) != bot_bo658782032t_unit))),inference(pre_uni,[status(thm)],[1647:[bind(A, $thf(A)),bind(B, $thf(^ [E:product_unit]: (refine1420258419t_unit @ (D @ E)))),bind(C, $thf(D @ A))]])). 132.20/30.71 thf(1686,plain,(! [B:(product_unit > product_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (refine1420258419t_unit @ (B @ C)))) != bot_bo658782032t_unit))),inference(simp,[status(thm)],[1661])). 132.20/30.71 thf(10,axiom,((top_to177290092t_unit != bot_bo658782032t_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_nres__inequalities_I2_J)). 132.20/30.71 thf(350,plain,((~ (top_to177290092t_unit = bot_bo658782032t_unit))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 132.20/30.71 thf(351,plain,((~ (top_to177290092t_unit = bot_bo658782032t_unit))),inference(polarity_switch,[status(thm)],[350])). 132.20/30.71 thf(352,plain,((top_to177290092t_unit != bot_bo658782032t_unit)),inference(lifteq,[status(thm)],[351])). 132.20/30.71 thf(44,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((refine579265252t_unit @ A) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) <= (refine558004794t_unit @ B @ C)) & (refine579265252t_unit @ B))) => (ord_le1051254044t_unit @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_pw__leI)). 132.20/30.71 thf(466,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((refine579265252t_unit @ A) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) | ~ (refine558004794t_unit @ B @ C)) & (refine579265252t_unit @ B))) => (ord_le1051254044t_unit @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 132.20/30.71 thf(467,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((refine579265252t_unit @ A) | (ord_le1051254044t_unit @ B @ A))),inference(cnf,[status(esa)],[466])). 132.20/30.71 thf(3,axiom,((! [A:refine787176636t_unit]: ((top_to177290092t_unit != A) = (refine579265252t_unit @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_intro__nofail_I2_J)). 132.20/30.71 thf(328,plain,((! [A:refine787176636t_unit]: ((~ (top_to177290092t_unit = A)) = (refine579265252t_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 132.20/30.71 thf(329,plain,(! [A:refine787176636t_unit] : (((~ (top_to177290092t_unit = A)) = (refine579265252t_unit @ A)))),inference(cnf,[status(esa)],[328])). 132.20/30.71 thf(330,plain,(! [A:refine787176636t_unit] : (((refine579265252t_unit @ A) = (~ (top_to177290092t_unit = A))))),inference(lifteq,[status(thm)],[329])). 132.20/30.71 thf(12498,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (top_to177290092t_unit = A)) | (ord_le1051254044t_unit @ B @ A))),inference(rewrite,[status(thm)],[467,330])). 132.20/30.71 thf(12499,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (top_to177290092t_unit = A)) | (ord_le1051254044t_unit @ B @ A))),inference(simp,[status(thm)],[12498])). 132.20/30.71 thf(12500,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((top_to177290092t_unit != A) | (ord_le1051254044t_unit @ B @ A))),inference(lifteq,[status(thm)],[12499])). 132.20/30.71 thf(6,axiom,((! [A:refine787176636t_unit]: ((~ (refine579265252t_unit @ A)) = (A = top_to177290092t_unit)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_not__nofail__iff)). 132.20/30.71 thf(338,plain,((! [A:refine787176636t_unit]: ((~ (refine579265252t_unit @ A)) = (A = top_to177290092t_unit)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 132.20/30.71 thf(339,plain,(! [A:refine787176636t_unit] : (((~ (refine579265252t_unit @ A)) = (A = top_to177290092t_unit)))),inference(cnf,[status(esa)],[338])). 132.20/30.71 thf(340,plain,(! [A:refine787176636t_unit] : (((~ (refine579265252t_unit @ A)) = (A = top_to177290092t_unit)))),inference(lifteq,[status(thm)],[339])). 132.20/30.71 thf(1595,plain,(! [A:refine787176636t_unit] : (((~ (~ (top_to177290092t_unit = A))) = (A = top_to177290092t_unit)))),inference(rewrite,[status(thm)],[340,330])). 132.20/30.71 thf(1596,plain,(! [A:refine787176636t_unit] : (((top_to177290092t_unit = A) = (A = top_to177290092t_unit)))),inference(simp,[status(thm)],[1595])). 132.20/30.71 thf(104,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ C @ B) <= (ord_less_eq_set_a @ C @ A)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_dual__order_Otrans)). 132.20/30.71 thf(683,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ C @ B) | ~ (ord_less_eq_set_a @ C @ A) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 132.20/30.71 thf(117,axiom,((! [A:(refine787176636t_unit > $o),B:refine787176636t_unit,C:(refine787176636t_unit > $o)]: ((A @ B) => ((! [D:refine787176636t_unit]: ((A @ D) => (ord_le1051254044t_unit @ D @ B))) => ((C @ (order_453013155t_unit @ A)) <= (! [D:refine787176636t_unit]: ((A @ D) => ((C @ D) <= (! [E:refine787176636t_unit]: ((ord_le1051254044t_unit @ E @ D) <= (A @ E))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_GreatestI2__order)). 132.20/30.71 thf(730,plain,((! [A:(refine787176636t_unit > $o),B:refine787176636t_unit,C:(refine787176636t_unit > $o)]: ((A @ B) => ((! [D:refine787176636t_unit]: ((A @ D) => (ord_le1051254044t_unit @ D @ B))) => ((C @ (order_453013155t_unit @ (A))) | ~ (! [D:refine787176636t_unit]: ((A @ D) => ((C @ D) | ~ (! [E:refine787176636t_unit]: ((ord_le1051254044t_unit @ E @ D) | ~ (A @ E))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 132.20/30.71 thf(323,axiom,((refine2063221604TURN_a = (^ [A:a]: (refine1198353288_RES_a @ (insert_a @ A @ bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_RETURN__def)). 132.20/30.71 thf(1522,plain,(((refine2063221604TURN_a) = (^ [A:a]: (refine1198353288_RES_a @ (insert_a @ A @ bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 132.20/30.71 thf(3307,plain,(! [B:a,A:set_a] : (((collect_a @ (^ [C:a]: (member_a @ C @ A))) != bot_bot_set_a) | (A != (insert_a @ B @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[1479,1956])). 132.20/30.71 thf(3308,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a)))) != bot_bot_set_a))),inference(pattern_uni,[status(thm)],[3307:[bind(A, $thf(insert_a @ C @ bot_bot_set_a)),bind(B, $thf(C))]])). 132.20/30.71 thf(3352,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a)))) != bot_bot_set_a))),inference(simp,[status(thm)],[3308])). 132.20/30.71 thf(3360,plain,(! [B:a,A:set_a] : (((collect_a @ (^ [C:a]: (member_a @ C @ (collect_a @ (^ [D:a]: (member_a @ D @ A)))))) != bot_bot_set_a) | (A != (insert_a @ B @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[1479,3352])). 132.20/30.71 thf(3361,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (collect_a @ (^ [C:a]: (member_a @ C @ (insert_a @ A @ bot_bot_set_a))))))) != bot_bot_set_a))),inference(pattern_uni,[status(thm)],[3360:[bind(A, $thf(insert_a @ C @ bot_bot_set_a)),bind(B, $thf(C))]])). 132.20/30.71 thf(3377,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (collect_a @ (^ [C:a]: (member_a @ C @ (insert_a @ A @ bot_bot_set_a))))))) != bot_bot_set_a))),inference(simp,[status(thm)],[3361])). 132.20/30.71 thf(292,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le1051254044t_unit @ A @ B) => (((C @ B) = D) => ((ord_le519537037nres_a @ (C @ A) @ D) <= (! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) <= (ord_le1051254044t_unit @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_ord__le__eq__subst)). 132.20/30.71 thf(1401,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le1051254044t_unit @ A @ B) => (((C @ B) = D) => ((ord_le519537037nres_a @ (C @ A) @ D) | ~ (! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) | ~ (ord_le1051254044t_unit @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 132.20/30.71 thf(296,axiom,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((((ord_le519537037nres_a @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F))))) <= (ord_le519537037nres_a @ C @ D)) <= (ord_le519537037nres_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_order__subst1)). 132.20/30.71 thf(1422,plain,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ (B @ D)) | ~ (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) | ~ (ord_le519537037nres_a @ C @ D) | ~ (ord_le519537037nres_a @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 132.20/30.71 thf(210,axiom,((ord_le519537037nres_a = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((refine412683989fail_a @ B) => ((refine412683989fail_a @ A) & ! [C:a]: ((refine1001002027nres_a @ A @ C) => (refine1001002027nres_a @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_pw__le__iff)). 132.20/30.71 thf(1072,plain,(((ord_le519537037nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((refine412683989fail_a @ B) => ((refine412683989fail_a @ A) & ! [C:a]: ((refine1001002027nres_a @ A @ C) => (refine1001002027nres_a @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 132.20/30.71 thf(1073,plain,(((ord_le519537037nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((refine412683989fail_a @ B) => ((refine412683989fail_a @ A) & ! [C:a]: ((refine1001002027nres_a @ A @ C) => (refine1001002027nres_a @ B @ C))))))),inference(lifteq,[status(thm)],[1072])). 132.20/30.71 thf(308,axiom,((bot_bot_set_a = (collect_a @ bot_bot_a_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_bot__set__def)). 132.20/30.71 thf(1467,plain,((bot_bot_set_a = (collect_a @ (bot_bot_a_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 132.20/30.71 thf(1468,plain,(((collect_a @ (bot_bot_a_o)) = bot_bot_set_a)),inference(lifteq,[status(thm)],[1467])). 132.20/30.71 thf(22,axiom,((bot_bot_a_o = (^ [A:a]: (member_a @ A @ bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_bot__empty__eq)). 132.20/30.71 thf(378,plain,(((bot_bot_a_o) = (^ [A:a]: (member_a @ A @ bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 132.20/30.71 thf(379,plain,(((^ [A:a]: (member_a @ A @ bot_bot_set_a)) = (bot_bot_a_o))),inference(lifteq,[status(thm)],[378])). 132.20/30.71 thf(1536,plain,(((bot_bot_a_o) = (^ [A:a]: ($false)))),inference(rewrite,[status(thm)],[379,479])). 132.20/30.71 thf(1537,plain,(! [A:a] : ((~ (bot_bot_a_o @ A)))),inference(func_ext,[status(esa)],[1536])). 132.20/30.71 thf(1589,plain,(((collect_a @ (^ [A:a]: ($false))) = bot_bot_set_a)),inference(rewrite,[status(thm)],[1468,1537])). 132.20/30.71 thf(4355,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (collect_a @ (^ [C:a]: (member_a @ C @ (insert_a @ A @ bot_bot_set_a))))))) != (collect_a @ (^ [B:a]: ($false)))))),inference(paramod_ordered,[status(thm)],[1589,3377])). 132.20/30.71 thf(4374,plain,(! [A:a] : (((^ [B:a]: (member_a @ B @ (collect_a @ (^ [C:a]: (member_a @ C @ (insert_a @ A @ bot_bot_set_a)))))) != (^ [B:a]: ($false))))),inference(simp,[status(thm)],[4355])). 132.20/30.71 thf(13311,plain,(! [B:a,A:set_a] : (((^ [C:a]: (member_a @ C @ A)) != (^ [C:a]: ($false))) | ((collect_a @ (^ [C:a]: (member_a @ C @ A))) != (collect_a @ (^ [C:a]: (member_a @ C @ (insert_a @ B @ bot_bot_set_a))))))),inference(paramod_ordered,[status(thm)],[13209,4374])). 132.20/30.71 thf(13312,plain,(! [A:a] : (((^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a))) != (^ [B:a]: ($false))))),inference(pattern_uni,[status(thm)],[13311:[bind(A, $thf(insert_a @ C @ bot_bot_set_a)),bind(B, $thf(C))]])). 132.20/30.71 thf(13424,plain,(! [A:a] : (((^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a))) != (^ [B:a]: ($false))))),inference(simp,[status(thm)],[13312])). 132.20/30.71 thf(41,axiom,((! [A:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a),C:(($o > refine424419629nres_a) > $o)]: ((A @ B) => ((! [D:($o > refine424419629nres_a)]: ((A @ D) => (ord_le516598614nres_a @ D @ B))) => ((! [D:($o > refine424419629nres_a)]: (((C @ D) <= (! [E:($o > refine424419629nres_a)]: ((A @ E) => (ord_le516598614nres_a @ E @ D)))) <= (A @ D))) => (C @ (order_245837199nres_a @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_GreatestI2__order)). 132.20/30.71 thf(449,plain,((! [A:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a),C:(($o > refine424419629nres_a) > $o)]: ((A @ (B)) => ((! [D:($o > refine424419629nres_a)]: ((A @ (D)) => (ord_le516598614nres_a @ (D) @ (B)))) => ((! [D:($o > refine424419629nres_a)]: ((C @ (D)) | ~ (! [E:($o > refine424419629nres_a)]: ((A @ (E)) => (ord_le516598614nres_a @ (E) @ (D)))) | ~ (A @ (D)))) => (C @ (order_245837199nres_a @ (A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 132.20/30.71 thf(155,axiom,((! [A:refine424419629nres_a,B:a]: ((~ (refine412683989fail_a @ A)) => (refine1001002027nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_not__nofail__inres)). 132.20/30.71 thf(878,plain,((! [A:refine424419629nres_a,B:a]: ((~ (refine412683989fail_a @ A)) => (refine1001002027nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 132.20/30.71 thf(297,axiom,(((b) => (ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ phi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)). 132.20/30.71 thf(1426,plain,(((b) => (ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ (phi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 132.20/30.71 thf(1427,plain,(~ (b) | (ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ (phi))))),inference(cnf,[status(esa)],[1426])). 132.20/30.71 thf(322,axiom,((! [A:set_a]: ~ (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_less__eq__nres_Osimps_I3_J)). 132.20/30.71 thf(1519,plain,((! [A:set_a]: ~ (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 132.20/30.71 thf(1520,plain,((~ (? [A:set_a]: (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ A))))),inference(miniscope,[status(thm)],[1519])). 132.20/30.71 thf(1521,plain,(! [A:set_a] : ((~ (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ A))))),inference(cnf,[status(esa)],[1520])). 132.20/30.71 thf(1723,plain,(! [A:set_a] : ((~ (ord_le519537037nres_a @ refine464223677AILi_a @ bot_bo529555393nres_a)) | ((refine1198353288_RES_a @ bot_bot_set_a) != (refine1198353288_RES_a @ A)))),inference(paramod_ordered,[status(thm)],[1158,1521])). 132.20/30.71 thf(1724,plain,((~ (ord_le519537037nres_a @ refine464223677AILi_a @ bot_bo529555393nres_a))),inference(pattern_uni,[status(thm)],[1723:[bind(A, $thf(bot_bot_set_a))]])). 132.20/30.71 thf(2891,plain,(~ (b) | ((ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ (phi)))) != (ord_le519537037nres_a @ refine464223677AILi_a @ bot_bo529555393nres_a))),inference(paramod_ordered,[status(thm)],[1427,1724])). 132.20/30.71 thf(2903,plain,(~ (b) | (s1 != refine464223677AILi_a) | ((refine1198353288_RES_a @ (collect_a @ (phi))) != bot_bo529555393nres_a)),inference(simp,[status(thm)],[2891])). 132.20/30.71 thf(3591,plain,(~ (b) | (s1 != refine464223677AILi_a) | ((refine1198353288_RES_a @ (collect_a @ (phi))) != (refine1198353288_RES_a @ bot_bot_set_a))),inference(paramod_ordered,[status(thm)],[1158,2903])). 132.20/30.71 thf(3597,plain,(~ (b) | (s1 != refine464223677AILi_a) | ((collect_a @ (phi)) != bot_bot_set_a)),inference(simp,[status(thm)],[3591])). 132.20/30.71 thf(267,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ refine464223677AILi_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_less__eq__nres_Osimps_I1_J)). 132.20/30.71 thf(1298,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ refine464223677AILi_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 132.20/30.71 thf(1299,plain,(! [A:refine424419629nres_a] : ((ord_le519537037nres_a @ A @ refine464223677AILi_a))),inference(cnf,[status(esa)],[1298])). 132.20/30.71 thf(4987,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((A = top_to231829469nres_a) | ((ord_le519537037nres_a @ top_to231829469nres_a @ A) != (ord_le519537037nres_a @ B @ refine464223677AILi_a)))),inference(paramod_ordered,[status(thm)],[1177,1299])). 132.20/30.71 thf(4988,plain,((refine464223677AILi_a = top_to231829469nres_a)),inference(pattern_uni,[status(thm)],[4987:[bind(A, $thf(refine464223677AILi_a)),bind(B, $thf(top_to231829469nres_a))]])). 132.20/30.71 thf(4994,plain,((refine464223677AILi_a = top_to231829469nres_a)),inference(lifteq,[status(thm)],[4988])). 132.20/30.71 thf(5279,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((collect_a @ (phi)) != bot_bot_set_a)),inference(rewrite,[status(thm)],[3597,4994])). 132.20/30.71 thf(13210,plain,(! [A:set_a] : (~ (b) | (s1 != top_to231829469nres_a) | (A != bot_bot_set_a) | ((collect_a @ (^ [B:a]: (member_a @ B @ A))) != (collect_a @ (phi))))),inference(paramod_ordered,[status(thm)],[13209,5279])). 132.20/30.71 thf(13403,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((collect_a @ (^ [A:a]: (member_a @ A @ bot_bot_set_a))) != (collect_a @ (phi)))),inference(simp,[status(thm)],[13210])). 132.20/30.71 thf(21802,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((collect_a @ (phi)) != (collect_a @ (^ [A:a]: ($false))))),inference(rewrite,[status(thm)],[13403,479])). 132.20/30.71 thf(21804,plain,(! [A:set_a] : (~ (b) | (s1 != top_to231829469nres_a) | (A != (collect_a @ (^ [B:a]: ($false)))) | ((collect_a @ (^ [B:a]: (member_a @ B @ A))) != (collect_a @ (phi))))),inference(paramod_ordered,[status(thm)],[13209,21802])). 132.20/30.71 thf(21827,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($false))))) != (phi))),inference(simp,[status(thm)],[21804])). 132.20/30.71 thf(21834,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((^ [A:a]: (member_a @ A @ bot_bot_set_a)) != (phi))),inference(rewrite,[status(thm)],[21827,1589])). 132.20/30.71 thf(199,axiom,((! [A:(a > $o)]: (((collect_a @ A) = bot_bot_set_a) = (A = bot_bot_a_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_Collect__empty__eq__bot)). 132.20/30.71 thf(1041,plain,((! [A:(a > $o)]: (((collect_a @ (A)) = bot_bot_set_a) = ((A) = (bot_bot_a_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 132.20/30.71 thf(313,axiom,((! [A:refine787176636t_unit,B:(refine424419629nres_a > refine787176636t_unit),C:refine424419629nres_a,D:refine424419629nres_a]: ((((ord_le1051254044t_unit @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) <= (ord_le519537037nres_a @ E @ F)))) <= (ord_le519537037nres_a @ C @ D)) <= (ord_le1051254044t_unit @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_order__subst1)). 132.20/30.71 thf(1486,plain,((! [A:refine787176636t_unit,B:(refine424419629nres_a > refine787176636t_unit),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_le1051254044t_unit @ A @ (B @ D)) | ~ (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) | ~ (ord_le519537037nres_a @ E @ F))) | ~ (ord_le519537037nres_a @ C @ D) | ~ (ord_le1051254044t_unit @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 132.20/30.71 thf(60,axiom,((! [A:set_a,B:(refine787176636t_unit > set_a),C:refine787176636t_unit,D:refine787176636t_unit]: (((ord_le1051254044t_unit @ C @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) <= (ord_le1051254044t_unit @ E @ F))) => (ord_less_eq_set_a @ A @ (B @ D)))) <= (ord_less_eq_set_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_order__subst1)). 132.20/30.71 thf(523,plain,((! [A:set_a,B:(refine787176636t_unit > set_a),C:refine787176636t_unit,D:refine787176636t_unit]: (((ord_le1051254044t_unit @ C @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) | ~ (ord_le1051254044t_unit @ E @ F))) => (ord_less_eq_set_a @ A @ (B @ D)))) | ~ (ord_less_eq_set_a @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 132.20/30.71 thf(13984,plain,(! [A:set_a] : ((A != bot_bot_set_a) | ((collect_a @ (^ [B:a]: (member_a @ B @ A))) != (collect_a @ (^ [B:a]: ($true)))))),inference(paramod_ordered,[status(thm)],[13209,13983])). 132.20/30.71 thf(14000,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ bot_bot_set_a))) != (collect_a @ (^ [A:a]: ($true))))),inference(simp,[status(thm)],[13984])). 132.20/30.71 thf(14016,plain,(((collect_a @ (^ [A:a]: ($false))) != (collect_a @ (^ [A:a]: ($true))))),inference(rewrite,[status(thm)],[14000,479])). 132.20/30.71 thf(14020,plain,(! [A:set_a] : ((A != (collect_a @ (^ [B:a]: ($true)))) | ((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ A)))) != (collect_a @ (^ [B:a]: ($false)))))),inference(paramod_ordered,[status(thm)],[4008,14016])). 132.20/30.71 thf(14036,plain,(((collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: ($true))))))) != (collect_a @ (^ [A:a]: ($false))))),inference(simp,[status(thm)],[14020])). 132.20/30.71 thf(15999,plain,(((collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: ($true))))))) != bot_bot_set_a)),inference(rewrite,[status(thm)],[14036,1589])). 132.20/30.71 thf(16002,plain,(! [A:set_a] : ((A != bot_bot_set_a) | ((collect_a @ (^ [B:a]: (member_a @ B @ A))) != (collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (collect_a @ (^ [C:a]: ($true)))))))))),inference(paramod_ordered,[status(thm)],[13209,15999])). 132.20/30.71 thf(16033,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ bot_bot_set_a))) != (collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: ($true))))))))),inference(simp,[status(thm)],[16002])). 132.20/30.71 thf(18172,plain,(((collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: ($true))))))) != (collect_a @ (^ [A:a]: ($false))))),inference(rewrite,[status(thm)],[16033,479])). 132.20/30.71 thf(18176,plain,(! [A:set_a] : ((A != (collect_a @ (^ [B:a]: ($false)))) | ((collect_a @ (^ [B:a]: (member_a @ B @ A))) != (collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (collect_a @ (^ [C:a]: ($true)))))))))),inference(paramod_ordered,[status(thm)],[13209,18172])). 132.20/30.71 thf(18208,plain,(((^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($false))))) != (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: ($true)))))))),inference(simp,[status(thm)],[18176])). 132.20/30.71 thf(18233,plain,(((^ [A:a]: (member_a @ A @ bot_bot_set_a)) != (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: ($true)))))))),inference(rewrite,[status(thm)],[18208,1589])). 132.20/30.71 thf(450,plain,((! [A:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a)]: ((A @ (B)) => ((! [C:($o > refine424419629nres_a)]: ((A @ (C)) => (ord_le516598614nres_a @ (C) @ (B)))) => (! [C:(($o > refine424419629nres_a) > $o)]: ((! [D:($o > refine424419629nres_a)]: ((C @ (D)) | ~ (! [E:($o > refine424419629nres_a)]: ((A @ (E)) => (ord_le516598614nres_a @ (E) @ (D)))) | ~ (A @ (D)))) => (C @ (order_245837199nres_a @ (A))))))))),inference(miniscope,[status(thm)],[449])). 132.20/30.71 thf(454,plain,(! [B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (A @ (sk8 @ B @ (A))) | (sk7 @ A))),inference(cnf,[status(esa)],[450])). 132.20/30.71 thf(216,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) => (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_eq__refl)). 132.20/30.71 thf(1097,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) => (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 132.20/30.71 thf(1098,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((~ (A = B)) | (ord_le519537037nres_a @ A @ B))),inference(cnf,[status(esa)],[1097])). 132.20/30.71 thf(1099,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((A != B) | (ord_le519537037nres_a @ A @ B))),inference(lifteq,[status(thm)],[1098])). 132.20/30.71 thf(1100,plain,(! [A:refine424419629nres_a] : ((ord_le519537037nres_a @ A @ A))),inference(simp,[status(thm)],[1099])). 132.20/30.71 thf(1,conjecture,((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)). 132.20/30.71 thf(2,negated_conjecture,((~ (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ phi))))),inference(neg_conjecture,[status(cth)],[1])). 132.20/30.71 thf(327,plain,((~ (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ (phi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 132.20/30.71 thf(2201,plain,(! [A:refine424419629nres_a] : (((ord_le519537037nres_a @ A @ A) != (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ (phi))))))),inference(paramod_ordered,[status(thm)],[1100,327])). 132.20/30.71 thf(2208,plain,(! [A:refine424419629nres_a] : ((A != (if_Ref1724547303nres_a @ b @ s1 @ s2)) | (A != (refine1198353288_RES_a @ (collect_a @ (phi)))))),inference(simp,[status(thm)],[2201])). 132.20/30.71 thf(2209,plain,(((if_Ref1724547303nres_a @ b @ s1 @ s2) != (refine1198353288_RES_a @ (collect_a @ (phi))))),inference(simp,[status(thm)],[2208])). 132.20/30.71 thf(9031,plain,(! [B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (sk7 @ (A)) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != (refine1198353288_RES_a @ (collect_a @ (phi)))) | ((A @ (sk8 @ B @ (A))) != b))),inference(paramod_ordered,[status(thm)],[454,2209])). 132.20/30.71 thf(9191,plain,(~ (b) | (sk7 @ (^ [A:($o > refine424419629nres_a)]: (b))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != (refine1198353288_RES_a @ (collect_a @ (phi))))),inference(pre_uni,[status(thm)],[9031:[bind(A, $thf(^ [C:($o > refine424419629nres_a)]: (b)))]])). 132.20/30.71 thf(225,axiom,((! [A:set_a]: (refine412683989fail_a @ (refine1198353288_RES_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_nofail__simps_I2_J)). 132.20/30.71 thf(1142,plain,((! [A:set_a]: (refine412683989fail_a @ (refine1198353288_RES_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 132.20/30.71 thf(260,axiom,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a]: (((A @ B) <= (! [C:set_a]: (A @ (refine1198353288_RES_a @ C)))) <= (A @ refine464223677AILi_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_nres_Oinduct)). 132.20/30.71 thf(1269,plain,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a]: ((A @ B) | ~ (! [C:set_a]: (A @ (refine1198353288_RES_a @ C))) | ~ (A @ refine464223677AILi_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 132.20/30.71 thf(82,axiom,((! [A:set_a]: ((A != bot_bot_set_a) => ((! [B:a,C:a]: (((B = C) <= (member_a @ C @ A)) <= (member_a @ B @ A))) => (is_singleton_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_is__singletonI_H)). 132.20/30.71 thf(614,plain,((! [A:set_a]: ((~ (A = bot_bot_set_a)) => ((! [B:a,C:a]: ((B = C) | ~ (member_a @ C @ A) | ~ (member_a @ B @ A))) => (is_singleton_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 132.20/30.71 thf(6508,plain,(! [D:(product_unit > product_unit),C:product_unit,B:(product_unit > refine787176636t_unit),A:product_unit] : (((B @ A) != bot_bo658782032t_unit) | ((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) != (refine681446406t_unit @ (refine1420258419t_unit @ C) @ (^ [E:product_unit]: (refine1420258419t_unit @ (D @ E))))))),inference(paramod_ordered,[status(thm)],[346,1686])). 132.20/30.71 thf(6509,plain,(! [B:(product_unit > product_unit),A:product_unit] : (((refine1420258419t_unit @ (B @ A)) != bot_bo658782032t_unit))),inference(pattern_uni,[status(thm)],[6508:[bind(A, $thf(A)),bind(B, $thf(^ [F:product_unit]: (refine1420258419t_unit @ (E @ F)))),bind(C, $thf(A)),bind(D, $thf(E))]])). 132.20/30.71 thf(6522,plain,(! [B:(product_unit > product_unit),A:product_unit] : (((refine1420258419t_unit @ (B @ A)) != bot_bo658782032t_unit))),inference(simp,[status(thm)],[6509])). 132.20/30.71 thf(25,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine787176636t_unit)]: (((refine579265252t_unit @ B) <= (refine579265252t_unit @ A)) => ((! [D:product_unit]: ((refine579265252t_unit @ B) => ((refine558004794t_unit @ B @ D) => (ord_le1051254044t_unit @ (C @ D) @ A)))) => (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_pw__bind__leI)). 132.20/30.71 thf(385,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine787176636t_unit)]: (((refine579265252t_unit @ B) | ~ (refine579265252t_unit @ A)) => ((! [D:product_unit]: ((refine579265252t_unit @ B) => ((refine558004794t_unit @ B @ D) => (ord_le1051254044t_unit @ (C @ D) @ A)))) => (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 132.20/30.71 thf(223,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_order__mono__setup_Orefl)). 132.20/30.71 thf(1137,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 132.20/30.71 thf(215,axiom,((refine412683989fail_a = (^ [A:refine424419629nres_a]: ? [B:set_a]: (A = (refine1198353288_RES_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_nofail__RES__conv)). 132.20/30.71 thf(1095,plain,(((refine412683989fail_a) = (^ [A:refine424419629nres_a]: ? [B:set_a]: (A = (refine1198353288_RES_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 132.20/30.71 thf(1096,plain,(((refine412683989fail_a) = (^ [A:refine424419629nres_a]: ? [B:set_a]: (A = (refine1198353288_RES_a @ B))))),inference(lifteq,[status(thm)],[1095])). 132.20/30.71 thf(1722,plain,(! [A:refine424419629nres_a] : (((refine412683989fail_a @ A) = (? [B:set_a]: (A = (refine1198353288_RES_a @ B)))))),inference(func_ext,[status(esa)],[1096])). 132.20/30.71 thf(1143,plain,(! [A:set_a] : ((refine412683989fail_a @ (refine1198353288_RES_a @ A)))),inference(cnf,[status(esa)],[1142])). 132.20/30.71 thf(1809,plain,(! [A:set_a] : ((refine412683989fail_a @ bot_bo529555393nres_a) | ((refine1198353288_RES_a @ bot_bot_set_a) != (refine1198353288_RES_a @ A)))),inference(paramod_ordered,[status(thm)],[1158,1143])). 132.20/30.71 thf(1810,plain,((refine412683989fail_a @ bot_bo529555393nres_a)),inference(pattern_uni,[status(thm)],[1809:[bind(A, $thf(bot_bot_set_a))]])). 132.20/30.71 thf(6535,plain,(! [A:refine424419629nres_a] : ((? [B:set_a]: (A = (refine1198353288_RES_a @ B))) | ((refine412683989fail_a @ A) != (refine412683989fail_a @ bot_bo529555393nres_a)))),inference(paramod_ordered,[status(thm)],[1722,1810])). 132.20/30.71 thf(6536,plain,((? [A:set_a]: (bot_bo529555393nres_a = (refine1198353288_RES_a @ A)))),inference(pattern_uni,[status(thm)],[6535:[bind(A, $thf(bot_bo529555393nres_a))]])). 132.20/30.71 thf(6564,plain,((bot_bo529555393nres_a = (refine1198353288_RES_a @ sk188))),inference(cnf,[status(esa)],[6536])). 132.20/30.71 thf(6565,plain,(((refine1198353288_RES_a @ sk188) = bot_bo529555393nres_a)),inference(lifteq,[status(thm)],[6564])). 132.20/30.71 thf(6861,plain,(! [A:set_a] : (((refine1822134885_RES_a @ bot_bo529555393nres_a) = A) | ((refine1198353288_RES_a @ sk188) != (refine1198353288_RES_a @ A)))),inference(paramod_ordered,[status(thm)],[6565,1369])). 132.20/30.71 thf(6862,plain,(((refine1822134885_RES_a @ bot_bo529555393nres_a) = sk188)),inference(pattern_uni,[status(thm)],[6861:[bind(A, $thf(sk188))]])). 132.20/30.71 thf(2691,plain,(! [A:set_a] : (((refine1822134885_RES_a @ bot_bo529555393nres_a) = A) | ((refine1198353288_RES_a @ bot_bot_set_a) != (refine1198353288_RES_a @ A)))),inference(paramod_ordered,[status(thm)],[1158,1369])). 132.20/30.71 thf(2692,plain,(((refine1822134885_RES_a @ bot_bo529555393nres_a) = bot_bot_set_a)),inference(pattern_uni,[status(thm)],[2691:[bind(A, $thf(bot_bot_set_a))]])). 132.20/30.71 thf(6939,plain,((sk188 = bot_bot_set_a)),inference(rewrite,[status(thm)],[6862,2692])). 132.20/30.71 thf(78,axiom,((! [A:a]: (refine412683989fail_a @ (refine2063221604TURN_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_nofail__simps_I3_J)). 132.20/30.71 thf(602,plain,((! [A:a]: (refine412683989fail_a @ (refine2063221604TURN_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 132.20/30.71 thf(603,plain,(! [A:a] : ((refine412683989fail_a @ (refine2063221604TURN_a @ A)))),inference(cnf,[status(esa)],[602])). 132.20/30.71 thf(6545,plain,(! [B:refine424419629nres_a,A:a] : ((? [C:set_a]: (B = (refine1198353288_RES_a @ C))) | ((refine412683989fail_a @ (refine2063221604TURN_a @ A)) != (refine412683989fail_a @ B)))),inference(paramod_ordered,[status(thm)],[603,1722])). 132.20/30.71 thf(6546,plain,(! [A:a] : ((? [B:set_a]: ((refine2063221604TURN_a @ A) = (refine1198353288_RES_a @ B))))),inference(pattern_uni,[status(thm)],[6545:[bind(A, $thf(C)),bind(B, $thf(refine2063221604TURN_a @ C))]])). 132.20/30.71 thf(6555,plain,(! [A:a] : (((refine2063221604TURN_a @ A) = (refine1198353288_RES_a @ (sk185 @ A))))),inference(cnf,[status(esa)],[6546])). 132.20/30.71 thf(6556,plain,(! [A:a] : (((refine1198353288_RES_a @ (sk185 @ A)) = (refine2063221604TURN_a @ A)))),inference(lifteq,[status(thm)],[6555])). 132.20/30.71 thf(6557,plain,(! [A:a] : (((refine1198353288_RES_a @ (sk185 @ A)) = (refine2063221604TURN_a @ A)))),inference(simp,[status(thm)],[6556])). 132.20/30.71 thf(7652,plain,(! [B:set_a,A:a] : (((refine1822134885_RES_a @ (refine2063221604TURN_a @ A)) = B) | ((refine1198353288_RES_a @ (sk185 @ A)) != (refine1198353288_RES_a @ B)))),inference(paramod_ordered,[status(thm)],[6557,1369])). 132.20/30.71 thf(7653,plain,(! [A:a] : (((sk185 @ A) = (refine1822134885_RES_a @ (refine2063221604TURN_a @ A))))),inference(pattern_uni,[status(thm)],[7652:[bind(A, $thf(C)),bind(B, $thf(sk185 @ C))]])). 132.20/30.71 thf(7697,plain,(! [A:a] : (((sk185 @ A) = (refine1822134885_RES_a @ (refine2063221604TURN_a @ A))))),inference(simp,[status(thm)],[7653])). 132.20/30.71 thf(252,axiom,((ord_le516598614nres_a = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_le__rel__bool__arg__iff)). 132.20/30.71 thf(1233,plain,(((ord_le516598614nres_a) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 132.20/30.71 thf(1234,plain,(((ord_le516598614nres_a) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))))),inference(lifteq,[status(thm)],[1233])). 132.20/30.71 thf(207,axiom,((ord_le516598614nres_a = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_le__fun__def)). 132.20/30.71 thf(1063,plain,(((ord_le516598614nres_a) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 132.20/30.71 thf(1064,plain,(((ord_le516598614nres_a) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C))))),inference(lifteq,[status(thm)],[1063])). 132.20/30.71 thf(1734,plain,(((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C)))) | ((ord_le516598614nres_a) != (ord_le516598614nres_a))),inference(paramod_ordered,[status(thm)],[1234,1064])). 132.20/30.71 thf(1735,plain,(((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C))))),inference(pattern_uni,[status(thm)],[1734:[]])). 132.20/30.71 thf(53,axiom,((! [A:a,B:set_a]: ((~ (! [C:set_a]: ((member_a @ A @ C) <= (B = (insert_a @ A @ C))))) <= (member_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_Set_Oset__insert)). 132.20/30.71 thf(499,plain,((! [A:a,B:set_a]: (~ (! [C:set_a]: ((member_a @ A @ C) | ~ (B = (insert_a @ A @ C)))) | ~ (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 132.20/30.71 thf(500,plain,(! [B:set_a,A:a] : ((~ (member_a @ A @ (sk14 @ B @ A))) | (~ (member_a @ A @ B)))),inference(cnf,[status(esa)],[499])). 132.20/30.71 thf(113,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit,E:$o]: (((ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ E @ A @ C) @ (if_Ref1369692790t_unit @ E @ B @ D)) <= (ord_le1051254044t_unit @ C @ D)) <= (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_order__mono__setup_Omono__if)). 132.20/30.71 thf(715,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit,E:$o]: ((ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ E @ A @ C) @ (if_Ref1369692790t_unit @ E @ B @ D)) | ~ (ord_le1051254044t_unit @ C @ D) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 132.20/30.71 thf(261,axiom,((! [A:(a > $o)]: ((bot_bot_set_a = (collect_a @ A)) = (! [B:a]: ~ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_empty__Collect__eq)). 132.20/30.71 thf(1275,plain,((! [A:(a > $o)]: ((bot_bot_set_a = (collect_a @ (A))) = (! [B:a]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 132.20/30.71 thf(46,axiom,((! [A:a,B:set_a]: (member_a @ A @ (insert_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_insertI1)). 132.20/30.71 thf(472,plain,((! [A:a,B:set_a]: (member_a @ A @ (insert_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 132.20/30.71 thf(109,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ A) = (B = A)) <= (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_antisym__conv)). 132.20/30.71 thf(698,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ A) = (B = A)) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 132.20/30.71 thf(453,plain,(! [C:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (~ (sk7 @ A)) | (A @ (sk9 @ (C) @ B @ (A))) | (C @ (order_245837199nres_a @ (A))))),inference(cnf,[status(esa)],[450])). 132.20/30.71 thf(204,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ bot_bo529555393nres_a @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_bot_Oextremum)). 132.20/30.71 thf(1056,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ bot_bo529555393nres_a @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 132.20/30.71 thf(1057,plain,(! [A:refine424419629nres_a] : ((ord_le519537037nres_a @ bot_bo529555393nres_a @ A))),inference(cnf,[status(esa)],[1056])). 132.20/30.71 thf(1792,plain,(! [A:refine424419629nres_a] : (((ord_le519537037nres_a @ bot_bo529555393nres_a @ A) != (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ (phi))))))),inference(paramod_ordered,[status(thm)],[1057,327])). 132.20/30.71 thf(1796,plain,(! [A:refine424419629nres_a] : (((if_Ref1724547303nres_a @ b @ s1 @ s2) != bot_bo529555393nres_a) | (A != (refine1198353288_RES_a @ (collect_a @ (phi)))))),inference(simp,[status(thm)],[1792])). 132.20/30.71 thf(1802,plain,(((if_Ref1724547303nres_a @ b @ s1 @ s2) != bot_bo529555393nres_a)),inference(simp,[status(thm)],[1796])). 132.20/30.71 thf(7933,plain,(! [C:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (~ (sk7 @ (A))) | (C @ (order_245837199nres_a @ (A))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != bot_bo529555393nres_a) | ((A @ (sk9 @ (C) @ B @ (A))) != b))),inference(paramod_ordered,[status(thm)],[453,1802])). 132.20/30.71 thf(8317,plain,(! [A:(($o > refine424419629nres_a) > $o)] : (~ (b) | (~ (sk7 @ (^ [B:($o > refine424419629nres_a)]: (b)))) | (A @ (order_245837199nres_a @ (^ [B:($o > refine424419629nres_a)]: (b)))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != bot_bo529555393nres_a))),inference(pre_uni,[status(thm)],[7933:[bind(A, $thf(^ [D:($o > refine424419629nres_a)]: (b)))]])). 132.20/30.71 thf(8571,plain,(! [A:(($o > refine424419629nres_a) > $o)] : (~ (b) | (~ (sk7 @ (^ [B:($o > refine424419629nres_a)]: (b)))) | (A @ (order_245837199nres_a @ (^ [B:($o > refine424419629nres_a)]: (b)))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != bot_bo529555393nres_a))),inference(simp,[status(thm)],[8317])). 132.20/30.71 thf(14051,plain,(! [B:a,A:(($o > refine424419629nres_a) > $o)] : (~ (b) | (~ (sk7 @ (^ [C:($o > refine424419629nres_a)]: (b)))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != bot_bo529555393nres_a) | ((A @ (order_245837199nres_a @ (^ [C:($o > refine424419629nres_a)]: (b)))) != (member_a @ B @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[8571,479])). 132.20/30.71 thf(14301,plain,(~ (b) | (~ (sk7 @ (^ [A:($o > refine424419629nres_a)]: (b)))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != bot_bo529555393nres_a)),inference(pre_uni,[status(thm)],[14051:[bind(A, $thf(^ [D:($o > refine424419629nres_a)]: (member_a @ (C @ D) @ bot_bot_set_a))),bind(B, $thf(C @ (order_245837199nres_a @ (^ [D:($o > refine424419629nres_a)]: (b)))))]])). 132.20/30.71 thf(249,axiom,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_order__subst1)). 132.20/30.71 thf(1222,plain,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 132.20/30.71 thf(233,axiom,(((= @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_eq__iff)). 132.20/30.71 thf(1164,plain,(((= @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 132.20/30.71 thf(132,axiom,((! [A:(set_a > $o),B:set_a]: ((A @ B) => ((! [C:set_a]: ((ord_less_eq_set_a @ C @ B) <= (A @ C))) => ((order_Greatest_set_a @ A) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_Greatest__equality)). 132.20/30.71 thf(797,plain,((! [A:(set_a > $o),B:set_a]: ((A @ B) => ((! [C:set_a]: ((ord_less_eq_set_a @ C @ B) | ~ (A @ C))) => ((order_Greatest_set_a @ (A)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 132.20/30.71 thf(14018,plain,(! [A:set_a] : ((A != (collect_a @ (^ [B:a]: ($true)))) | ((collect_a @ (^ [B:a]: (member_a @ B @ A))) != (collect_a @ (^ [B:a]: ($false)))))),inference(paramod_ordered,[status(thm)],[13209,14016])). 132.20/30.71 thf(14040,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true)))))) != (collect_a @ (^ [A:a]: ($false))))),inference(simp,[status(thm)],[14018])). 132.20/30.71 thf(15015,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true)))))) != bot_bot_set_a)),inference(rewrite,[status(thm)],[14040,1589])). 132.20/30.71 thf(15022,plain,(! [A:set_a] : ((A != bot_bot_set_a) | ((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ A)))) != (collect_a @ (^ [B:a]: (member_a @ B @ (collect_a @ (^ [C:a]: ($true))))))))),inference(paramod_ordered,[status(thm)],[4008,15015])). 132.20/30.71 thf(15045,plain,(((^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true))))) != (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ bot_bot_set_a))))),inference(simp,[status(thm)],[15022])). 132.20/30.71 thf(15791,plain,(((^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true))))) != (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a)))),inference(rewrite,[status(thm)],[15045,1158])). 132.20/30.71 thf(15792,plain,(((member_a @ sk241 @ (collect_a @ (^ [A:a]: ($true)))) != (ord_le519537037nres_a @ (refine2063221604TURN_a @ sk241) @ bot_bo529555393nres_a))),inference(func_ext,[status(esa)],[15791])). 132.20/30.71 thf(16630,plain,(((member_a @ sk241 @ (collect_a @ (^ [A:a]: ($true)))) != ((refine2063221604TURN_a @ sk241) = bot_bo529555393nres_a))),inference(rewrite,[status(thm)],[15792,1366])). 132.20/30.71 thf(243,axiom,((! [A:set_a,B:set_a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_less__eq__nres_Osimps_I2_J)). 132.20/30.71 thf(1196,plain,((! [A:set_a,B:set_a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 132.20/30.71 thf(193,axiom,((! [A:refine787176636t_unit,B:product_unit]: ((refine558004794t_unit @ A @ B) <= (~ (refine579265252t_unit @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_not__nofail__inres)). 132.20/30.71 thf(1001,plain,((! [A:refine787176636t_unit,B:product_unit]: ((refine558004794t_unit @ A @ B) | (refine579265252t_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 132.20/30.71 thf(184,axiom,((! [A:a,B:set_a,C:a]: ((member_a @ A @ B) => (member_a @ A @ (insert_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_insertI2)). 132.20/30.71 thf(973,plain,((! [A:a,B:set_a,C:a]: ((member_a @ A @ B) => (member_a @ A @ (insert_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 132.20/30.71 thf(30,axiom,((! [A:a,B:set_a]: ((~ (member_a @ A @ B)) <= (member_a @ A @ (uminus_uminus_set_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_ComplD)). 132.20/30.71 thf(404,plain,((! [A:a,B:set_a]: (~ (member_a @ A @ B) | ~ (member_a @ A @ (uminus_uminus_set_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 132.20/30.71 thf(129,axiom,((! [A:a,B:set_a]: ((member_a @ A @ B) => (? [C:set_a]: (~ (member_a @ A @ C) & (B = (insert_a @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_mk__disjoint__insert)). 132.20/30.71 thf(782,plain,((! [A:a,B:set_a]: ((member_a @ A @ B) => (? [C:set_a]: (~ (member_a @ A @ C) & (B = (insert_a @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 132.20/30.71 thf(1523,plain,(((^ [A:a]: (refine1198353288_RES_a @ (insert_a @ A @ bot_bot_set_a))) = (refine2063221604TURN_a))),inference(lifteq,[status(thm)],[1522])). 132.20/30.71 thf(1744,plain,(! [A:a] : (((refine1198353288_RES_a @ (insert_a @ A @ bot_bot_set_a)) = (refine2063221604TURN_a @ A)))),inference(func_ext,[status(esa)],[1523])). 132.20/30.71 thf(14041,plain,(((^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true))))) != (^ [A:a]: ($false)))),inference(simp,[status(thm)],[14018])). 132.20/30.71 thf(14545,plain,((member_a @ sk235 @ (collect_a @ (^ [A:a]: ($true))))),inference(func_ext,[status(esa)],[14041])). 132.20/30.71 thf(405,plain,(! [B:set_a,A:a] : ((~ (member_a @ A @ B)) | (~ (member_a @ A @ (uminus_uminus_set_a @ B))))),inference(cnf,[status(esa)],[404])). 132.20/30.71 thf(3510,plain,(! [C:set_a,B:a,A:a] : ((~ (member_a @ B @ (uminus_uminus_set_a @ C))) | ((member_a @ A @ top_top_set_a) != (member_a @ B @ C)))),inference(paramod_ordered,[status(thm)],[677,405])). 132.20/30.71 thf(3511,plain,(! [A:a] : ((~ (member_a @ A @ (uminus_uminus_set_a @ top_top_set_a))))),inference(pattern_uni,[status(thm)],[3510:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(top_top_set_a))]])). 132.20/30.71 thf(14596,plain,(! [A:a] : (((member_a @ sk235 @ (collect_a @ (^ [B:a]: ($true)))) != (member_a @ A @ (uminus_uminus_set_a @ top_top_set_a))))),inference(paramod_ordered,[status(thm)],[14545,3511])). 132.20/30.71 thf(14617,plain,(! [A:a] : ((sk235 != A) | ((collect_a @ (^ [B:a]: ($true))) != (uminus_uminus_set_a @ top_top_set_a)))),inference(simp,[status(thm)],[14596])). 132.20/30.71 thf(14633,plain,(((collect_a @ (^ [A:a]: ($true))) != (uminus_uminus_set_a @ top_top_set_a))),inference(simp,[status(thm)],[14617])). 132.20/30.71 thf(14638,plain,(! [A:set_a] : ((A != (uminus_uminus_set_a @ top_top_set_a)) | ((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ A)))) != (collect_a @ (^ [B:a]: ($true)))))),inference(paramod_ordered,[status(thm)],[4008,14633])). 132.20/30.71 thf(14655,plain,(((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (uminus_uminus_set_a @ top_top_set_a)))) != (^ [A:a]: ($true)))),inference(simp,[status(thm)],[14638])). 132.20/30.71 thf(15059,plain,((~ (ord_le519537037nres_a @ (refine2063221604TURN_a @ sk238) @ (refine1198353288_RES_a @ (uminus_uminus_set_a @ top_top_set_a))))),inference(func_ext,[status(esa)],[14655])). 132.20/30.71 thf(15369,plain,(! [A:refine424419629nres_a] : (((ord_le519537037nres_a @ A @ A) != (ord_le519537037nres_a @ (refine2063221604TURN_a @ sk238) @ (refine1198353288_RES_a @ (uminus_uminus_set_a @ top_top_set_a)))))),inference(paramod_ordered,[status(thm)],[1100,15059])). 132.20/30.71 thf(15401,plain,(! [A:refine424419629nres_a] : ((A != (refine2063221604TURN_a @ sk238)) | (A != (refine1198353288_RES_a @ (uminus_uminus_set_a @ top_top_set_a))))),inference(simp,[status(thm)],[15369])). 132.20/30.71 thf(15408,plain,(((refine1198353288_RES_a @ (uminus_uminus_set_a @ top_top_set_a)) != (refine2063221604TURN_a @ sk238))),inference(simp,[status(thm)],[15401])). 132.20/30.71 thf(15561,plain,(! [A:a] : (((refine2063221604TURN_a @ A) != (refine2063221604TURN_a @ sk238)) | ((refine1198353288_RES_a @ (insert_a @ A @ bot_bot_set_a)) != (refine1198353288_RES_a @ (uminus_uminus_set_a @ top_top_set_a))))),inference(paramod_ordered,[status(thm)],[1744,15408])). 132.20/30.71 thf(15573,plain,(! [A:a] : ((A != sk238) | ((insert_a @ A @ bot_bot_set_a) != (uminus_uminus_set_a @ top_top_set_a)))),inference(simp,[status(thm)],[15561])). 132.20/30.71 thf(15575,plain,(((insert_a @ sk238 @ bot_bot_set_a) != (uminus_uminus_set_a @ top_top_set_a))),inference(simp,[status(thm)],[15573])). 132.20/30.71 thf(62,axiom,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) => (A = bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_equals0I)). 132.20/30.71 thf(532,plain,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) => (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 132.20/30.71 thf(533,plain,((! [A:set_a]: ((~ (? [B:a]: (member_a @ B @ A))) => (A = bot_bot_set_a)))),inference(miniscope,[status(thm)],[532])). 132.20/30.71 thf(534,plain,(! [A:set_a] : ((member_a @ (sk17 @ A) @ A) | (A = bot_bot_set_a))),inference(cnf,[status(esa)],[533])). 132.20/30.71 thf(535,plain,(! [A:set_a] : ((A = bot_bot_set_a) | (member_a @ (sk17 @ A) @ A))),inference(lifteq,[status(thm)],[534])). 132.20/30.71 thf(18612,plain,(! [B:a,A:set_a] : ((A = bot_bot_set_a) | ((member_a @ (sk17 @ A) @ A) != (member_a @ B @ (uminus_uminus_set_a @ top_top_set_a))))),inference(paramod_ordered,[status(thm)],[535,3511])). 132.20/30.71 thf(18613,plain,(((uminus_uminus_set_a @ top_top_set_a) = bot_bot_set_a)),inference(pattern_uni,[status(thm)],[18612:[bind(A, $thf(uminus_uminus_set_a @ top_top_set_a)),bind(B, $thf(sk17 @ (uminus_uminus_set_a @ top_top_set_a)))]])). 132.20/30.71 thf(18834,plain,(((insert_a @ sk238 @ bot_bot_set_a) != bot_bot_set_a)),inference(rewrite,[status(thm)],[15575,18613])). 132.20/30.71 thf(301,axiom,((! [A:$o,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a,E:refine424419629nres_a]: (((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ A @ B @ D) @ (if_Ref1724547303nres_a @ A @ C @ E)) <= ((~ (A)) => (ord_le519537037nres_a @ D @ E))) <= ((ord_le519537037nres_a @ B @ C) <= (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Refine__Misc_Oif__mono)). 132.20/30.71 thf(1441,plain,((! [A:$o,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a,E:refine424419629nres_a]: ((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ A @ B @ D) @ (if_Ref1724547303nres_a @ A @ C @ E)) | ~ ((~ (A)) => (ord_le519537037nres_a @ D @ E)) | ~ ((ord_le519537037nres_a @ B @ C) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 132.20/30.71 thf(293,axiom,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ B) => (((C @ B) = D) => ((! [E:set_a,F:set_a]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_a @ E @ F))) => (ord_le519537037nres_a @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_ord__le__eq__subst)). 132.20/30.71 thf(1409,plain,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ B) => (((C @ B) = D) => ((! [E:set_a,F:set_a]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_a @ E @ F))) => (ord_le519537037nres_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 132.20/30.71 thf(438,plain,(! [C:a,B:set_a,A:a] : ((member_a @ A @ (insert_a @ C @ B)) | (~ (A = C)))),inference(cnf,[status(esa)],[437])). 132.20/30.71 thf(440,plain,(! [C:a,B:set_a,A:a] : ((A != C) | (member_a @ A @ (insert_a @ C @ B)))),inference(lifteq,[status(thm)],[438])). 132.20/30.71 thf(441,plain,(! [B:a,A:set_a] : ((member_a @ B @ (insert_a @ B @ A)))),inference(simp,[status(thm)],[440])). 132.20/30.71 thf(14593,plain,(! [B:set_a,A:a] : ((~ (member_a @ A @ (uminus_uminus_set_a @ B))) | ((member_a @ sk235 @ (collect_a @ (^ [C:a]: ($true)))) != (member_a @ A @ B)))),inference(paramod_ordered,[status(thm)],[14545,405])). 132.20/30.71 thf(14594,plain,((~ (member_a @ sk235 @ (uminus_uminus_set_a @ (collect_a @ (^ [A:a]: ($true))))))),inference(pattern_uni,[status(thm)],[14593:[bind(A, $thf(sk235)),bind(B, $thf(collect_a @ (^ [C:a]: ($true))))]])). 132.20/30.71 thf(14875,plain,(! [B:a,A:set_a] : (((member_a @ B @ (insert_a @ B @ A)) != (member_a @ sk235 @ (uminus_uminus_set_a @ (collect_a @ (^ [C:a]: ($true)))))))),inference(paramod_ordered,[status(thm)],[441,14594])). 132.20/30.71 thf(14893,plain,(! [B:a,A:set_a] : ((B != sk235) | ((insert_a @ B @ A) != (uminus_uminus_set_a @ (collect_a @ (^ [C:a]: ($true))))))),inference(simp,[status(thm)],[14875])). 132.20/30.71 thf(14909,plain,(! [A:set_a] : (((insert_a @ sk235 @ A) != (uminus_uminus_set_a @ (collect_a @ (^ [B:a]: ($true))))))),inference(simp,[status(thm)],[14893])). 132.20/30.71 thf(19,axiom,((! [A:refine787176636t_unit]: ((refine681446406t_unit @ A @ refine1420258419t_unit) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_nres__monad2)). 132.20/30.71 thf(372,plain,((! [A:refine787176636t_unit]: ((refine681446406t_unit @ A @ (refine1420258419t_unit)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 132.20/30.71 thf(258,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) <= (! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_le__funI)). 132.20/30.71 thf(1264,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (A) @ (B)) | ~ (! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 132.20/30.71 thf(304,axiom,((! [A:refine424419629nres_a,B:(a > $o),C:(a > $o)]: (((! [D:a]: ((C @ D) <= (B @ D))) => (ord_le519537037nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ C)))) <= (ord_le519537037nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_SPEC__cons__rule)). 132.20/30.71 thf(1455,plain,((! [A:refine424419629nres_a,B:(a > $o),C:(a > $o)]: (((! [D:a]: ((C @ D) | ~ (B @ D))) => (ord_le519537037nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ (C))))) | ~ (ord_le519537037nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 132.20/30.71 thf(173,axiom,(((= @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (ord_less_eq_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_set__eq__subset)). 132.20/30.71 thf(934,plain,(((= @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (ord_less_eq_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 132.20/30.71 thf(306,axiom,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ top_to231829469nres_a @ A) = (A = top_to231829469nres_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_top_Oextremum__unique)). 132.20/30.71 thf(1462,plain,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ top_to231829469nres_a @ A) = (A = top_to231829469nres_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 132.20/30.71 thf(133,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_order__trans)). 132.20/30.71 thf(802,plain,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 132.20/30.71 thf(4019,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ bot_bo529555393nres_a))) = A) | ((refine1198353288_RES_a @ bot_bot_set_a) != (refine1198353288_RES_a @ A)))),inference(paramod_ordered,[status(thm)],[1158,4008])). 132.20/30.71 thf(4020,plain,(((collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a))) = bot_bot_set_a)),inference(pattern_uni,[status(thm)],[4019:[bind(A, $thf(bot_bot_set_a))]])). 132.20/30.71 thf(5313,plain,(((collect_a @ (^ [A:a]: ((refine2063221604TURN_a @ A) = bot_bo529555393nres_a))) = bot_bot_set_a)),inference(rewrite,[status(thm)],[4020,1366])). 132.20/30.71 thf(13990,plain,(((collect_a @ (^ [A:a]: ((refine2063221604TURN_a @ A) = bot_bo529555393nres_a))) != (collect_a @ (^ [A:a]: ($true))))),inference(paramod_ordered,[status(thm)],[5313,13983])). 132.20/30.71 thf(14002,plain,(((^ [A:a]: ((refine2063221604TURN_a @ A) = bot_bo529555393nres_a)) != (^ [A:a]: ($true)))),inference(simp,[status(thm)],[13990])). 132.20/30.71 thf(88,axiom,(((= @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (ord_less_eq_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_dual__order_Oeq__iff)). 132.20/30.71 thf(637,plain,(((= @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (ord_less_eq_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 132.20/30.71 thf(638,plain,(((^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) & (ord_less_eq_set_a @ B @ A))) = (= @ set_a))),inference(lifteq,[status(thm)],[637])). 132.20/30.71 thf(171,axiom,(((refine558004794t_unit @ top_to177290092t_unit) = (^ [A:product_unit]: ($true)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_inres__simps_I1_J)). 132.20/30.71 thf(929,plain,(((refine558004794t_unit @ top_to177290092t_unit) = (^ [A:product_unit]: ($true)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 132.20/30.71 thf(930,plain,(((refine558004794t_unit @ top_to177290092t_unit) = (^ [A:product_unit]: ($true)))),inference(lifteq,[status(thm)],[929])). 132.20/30.71 thf(1566,plain,(! [A:product_unit] : ((refine558004794t_unit @ top_to177290092t_unit @ A))),inference(func_ext,[status(esa)],[930])). 132.20/30.71 thf(1888,plain,(! [C:product_unit,B:(product_unit > refine787176636t_unit),A:product_unit] : ((refine558004794t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) @ C) | ((B @ A) != top_to177290092t_unit))),inference(paramod_ordered,[status(thm)],[346,1566])). 132.20/30.71 thf(1890,plain,(! [B:product_unit,A:product_unit] : ((refine558004794t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (top_to177290092t_unit))) @ B))),inference(pre_uni,[status(thm)],[1888:[bind(A, $thf(A)),bind(B, $thf(^ [D:product_unit]: (top_to177290092t_unit)))]])). 132.20/30.71 thf(1892,plain,(! [B:product_unit,A:product_unit] : ((refine558004794t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (top_to177290092t_unit))) @ B))),inference(simp,[status(thm)],[1890])). 132.20/30.71 thf(272,axiom,((! [A:set_a,B:(a > $o)]: ((ord_less_eq_set_a @ A @ (collect_a @ B)) = (! [C:a]: ((B @ C) <= (member_a @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_subset__Collect__conv)). 132.20/30.71 thf(1319,plain,((! [A:set_a,B:(a > $o)]: ((ord_less_eq_set_a @ A @ (collect_a @ (B))) = (! [C:a]: ((B @ C) | ~ (member_a @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 132.20/30.71 thf(197,axiom,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((! [D:refine424419629nres_a]: (A @ refine464223677AILi_a @ D)) => ((! [D:set_a]: (A @ (refine1198353288_RES_a @ D) @ refine464223677AILi_a)) => ((A @ B @ C) <= (! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_less__nres_Oinduct)). 132.20/30.71 thf(1013,plain,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((! [D:refine424419629nres_a]: (A @ refine464223677AILi_a @ D)) => ((! [D:set_a]: (A @ (refine1198353288_RES_a @ D) @ refine464223677AILi_a)) => ((A @ B @ C) | ~ (! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 132.20/30.71 thf(156,axiom,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_order__mono__setup_Orefl)). 132.20/30.71 thf(881,plain,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 132.20/30.71 thf(15028,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true)))))) != (collect_a @ (^ [A:a]: ((refine2063221604TURN_a @ A) = bot_bo529555393nres_a))))),inference(paramod_ordered,[status(thm)],[5313,15015])). 132.20/30.71 thf(15041,plain,(((^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true))))) != (^ [A:a]: ((refine2063221604TURN_a @ A) = bot_bo529555393nres_a)))),inference(simp,[status(thm)],[15028])). 132.20/30.71 thf(15338,plain,(((member_a @ sk239 @ (collect_a @ (^ [A:a]: ($true)))) != ((refine2063221604TURN_a @ sk239) = bot_bo529555393nres_a))),inference(func_ext,[status(esa)],[15041])). 132.20/30.71 thf(4025,plain,(! [A:set_a] : (~ (b) | (s1 != refine464223677AILi_a) | (A != bot_bot_set_a) | ((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ A)))) != (collect_a @ (phi))))),inference(paramod_ordered,[status(thm)],[4008,3597])). 132.20/30.71 thf(4126,plain,(~ (b) | (s1 != refine464223677AILi_a) | ((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ bot_bot_set_a))) != (phi))),inference(simp,[status(thm)],[4025])). 132.20/30.71 thf(9768,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a)) != (phi))),inference(rewrite,[status(thm)],[4126,4994,1158])). 132.20/30.71 thf(316,axiom,(((ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ phi))) <= (~ (b)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)). 132.20/30.71 thf(1494,plain,(((ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ (phi)))) | (b))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 132.20/30.71 thf(1495,plain,((ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ (phi)))) | b),inference(cnf,[status(esa)],[1494])). 132.20/30.71 thf(1912,plain,(b | ((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ (phi)))) != (ord_le519537037nres_a @ s2 @ (refine1198353288_RES_a @ (collect_a @ (phi)))))),inference(paramod_ordered,[status(thm)],[1495,327])). 132.20/30.71 thf(1921,plain,(b | ((if_Ref1724547303nres_a @ b @ s1 @ s2) != s2) | ((refine1198353288_RES_a @ (collect_a @ (phi))) != (refine1198353288_RES_a @ (collect_a @ (phi))))),inference(simp,[status(thm)],[1912])). 132.20/30.71 thf(1922,plain,(b | ((if_Ref1724547303nres_a @ b @ s1 @ s2) != s2)),inference(simp,[status(thm)],[1921])). 132.20/30.71 thf(137,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ A @ C) <= (ord_less_eq_set_a @ B @ C)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_order_Otrans)). 132.20/30.71 thf(817,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ C) | ~ (ord_less_eq_set_a @ B @ C) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 132.20/30.71 thf(3473,plain,(! [A:a] : (((collect_a @ (refine1001002027nres_a @ (refine1198353288_RES_a @ (insert_a @ A @ bot_bot_set_a)))) != bot_bot_set_a))),inference(rewrite,[status(thm)],[3352,1150])). 132.20/30.71 thf(3854,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (insert_a @ A @ bot_bot_set_a))))) != bot_bot_set_a))),inference(rewrite,[status(thm)],[3473,1585])). 132.20/30.71 thf(11579,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine2063221604TURN_a @ A)))) != bot_bot_set_a))),inference(rewrite,[status(thm)],[3854,1744])). 132.20/30.71 thf(12437,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine2063221604TURN_a @ A)))) != (collect_a @ (^ [B:a]: ((refine2063221604TURN_a @ B) = bot_bo529555393nres_a)))))),inference(paramod_ordered,[status(thm)],[5313,11579])). 132.20/30.71 thf(12443,plain,(! [A:a] : (((^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine2063221604TURN_a @ A))) != (^ [B:a]: ((refine2063221604TURN_a @ B) = bot_bo529555393nres_a))))),inference(simp,[status(thm)],[12437])). 132.20/30.71 thf(279,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: (((ord_le519537037nres_a @ A @ C) <= (B = C)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ord__le__eq__trans)). 132.20/30.71 thf(1347,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ C) | ~ (B = C) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 132.20/30.71 thf(14583,plain,(! [C:a,B:set_a,A:a] : ((member_a @ A @ (insert_a @ C @ B)) | ((member_a @ sk235 @ (collect_a @ (^ [D:a]: ($true)))) != (member_a @ A @ B)))),inference(paramod_ordered,[status(thm)],[14545,439])). 132.20/30.71 thf(14584,plain,(! [A:a] : ((member_a @ sk235 @ (insert_a @ A @ (collect_a @ (^ [B:a]: ($true))))))),inference(pattern_uni,[status(thm)],[14583:[bind(A, $thf(sk235)),bind(B, $thf(collect_a @ (^ [D:a]: ($true)))),bind(C, $thf(C))]])). 132.20/30.71 thf(14631,plain,(! [A:a] : ((member_a @ sk235 @ (insert_a @ A @ (collect_a @ (^ [B:a]: ($true))))))),inference(simp,[status(thm)],[14584])). 132.20/30.71 thf(17127,plain,(! [A:a] : (((member_a @ sk235 @ (insert_a @ A @ (collect_a @ (^ [B:a]: ($true))))) != (member_a @ sk235 @ (uminus_uminus_set_a @ (collect_a @ (^ [B:a]: ($true)))))))),inference(paramod_ordered,[status(thm)],[14631,14594])). 132.20/30.71 thf(17164,plain,(! [A:a] : ((sk235 != sk235) | ((insert_a @ A @ (collect_a @ (^ [B:a]: ($true)))) != (uminus_uminus_set_a @ (collect_a @ (^ [B:a]: ($true))))))),inference(simp,[status(thm)],[17127])). 132.20/30.71 thf(17181,plain,(! [A:a] : (((insert_a @ A @ (collect_a @ (^ [B:a]: ($true)))) != (uminus_uminus_set_a @ (collect_a @ (^ [B:a]: ($true))))))),inference(simp,[status(thm)],[17164])). 132.20/30.71 thf(14876,plain,(((member_a @ sk235 @ (uminus_uminus_set_a @ (collect_a @ (^ [A:a]: ($true))))) != (member_a @ sk235 @ (collect_a @ (^ [A:a]: ($true)))))),inference(paramod_ordered,[status(thm)],[14545,14594])). 132.20/30.71 thf(14901,plain,((sk235 != sk235) | ((uminus_uminus_set_a @ (collect_a @ (^ [A:a]: ($true)))) != (collect_a @ (^ [A:a]: ($true))))),inference(simp,[status(thm)],[14876])). 132.20/30.71 thf(14913,plain,(((uminus_uminus_set_a @ (collect_a @ (^ [A:a]: ($true)))) != (collect_a @ (^ [A:a]: ($true))))),inference(simp,[status(thm)],[14901])). 132.20/30.71 thf(40,axiom,((! [A:set_a,B:set_a]: ((if_set_a @ $true @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Set__Oset_Itf__a_J_T)). 132.20/30.71 thf(446,plain,((! [A:set_a,B:set_a]: ((if_set_a @ $true @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 132.20/30.71 thf(447,plain,(! [B:set_a,A:set_a] : (((if_set_a @ $true @ A @ B) = A))),inference(cnf,[status(esa)],[446])). 132.20/30.71 thf(448,plain,(! [B:set_a,A:set_a] : (((if_set_a @ $true @ A @ B) = A))),inference(lifteq,[status(thm)],[447])). 132.20/30.71 thf(307,axiom,((! [A:(a > $o),B:a]: ((A @ B) => (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (collect_a @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_RETURN__rule)). 132.20/30.71 thf(1465,plain,((! [A:(a > $o),B:a]: ((A @ B) => (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (collect_a @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 132.20/30.71 thf(501,plain,(! [B:set_a,A:a] : ((B = (insert_a @ A @ (sk14 @ B @ A))) | (~ (member_a @ A @ B)))),inference(cnf,[status(esa)],[499])). 132.20/30.71 thf(502,plain,(! [B:set_a,A:a] : (((insert_a @ A @ (sk14 @ B @ A)) = B) | (~ (member_a @ A @ B)))),inference(lifteq,[status(thm)],[501])). 132.20/30.71 thf(16447,plain,(! [B:set_a,A:a] : (((insert_a @ A @ (sk14 @ B @ A)) = B) | ((member_a @ sk235 @ (collect_a @ (^ [C:a]: ($true)))) != (member_a @ A @ B)))),inference(paramod_ordered,[status(thm)],[14545,502])). 132.20/30.71 thf(16448,plain,(((insert_a @ sk235 @ (sk14 @ (collect_a @ (^ [A:a]: ($true))) @ sk235)) = (collect_a @ (^ [A:a]: ($true))))),inference(pattern_uni,[status(thm)],[16447:[bind(A, $thf(sk235)),bind(B, $thf(collect_a @ (^ [C:a]: ($true))))]])). 132.20/30.71 thf(142,axiom,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_subset__refl)). 132.20/30.71 thf(833,plain,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 132.20/30.71 thf(834,plain,(! [A:set_a] : ((ord_less_eq_set_a @ A @ A))),inference(cnf,[status(esa)],[833])). 132.20/30.71 thf(15374,plain,(! [A:refine424419629nres_a] : (((ord_le519537037nres_a @ bot_bo529555393nres_a @ A) != (ord_le519537037nres_a @ (refine2063221604TURN_a @ sk238) @ (refine1198353288_RES_a @ (uminus_uminus_set_a @ top_top_set_a)))))),inference(paramod_ordered,[status(thm)],[1057,15059])). 132.20/30.71 thf(15402,plain,(! [A:refine424419629nres_a] : (((refine2063221604TURN_a @ sk238) != bot_bo529555393nres_a) | (A != (refine1198353288_RES_a @ (uminus_uminus_set_a @ top_top_set_a))))),inference(simp,[status(thm)],[15374])). 132.20/30.71 thf(15409,plain,(((refine2063221604TURN_a @ sk238) != bot_bo529555393nres_a)),inference(simp,[status(thm)],[15402])). 132.20/30.71 thf(18938,plain,(! [A:set_a] : ((member_a @ (sk17 @ A) @ A) | (A != (insert_a @ sk238 @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[535,18834])). 132.20/30.71 thf(18939,plain,((member_a @ (sk17 @ (insert_a @ sk238 @ bot_bot_set_a)) @ (insert_a @ sk238 @ bot_bot_set_a))),inference(pattern_uni,[status(thm)],[18938:[bind(A, $thf(insert_a @ sk238 @ bot_bot_set_a))]])). 132.20/30.71 thf(20326,plain,(! [B:set_a,A:a] : ((~ (member_a @ A @ (uminus_uminus_set_a @ B))) | ((member_a @ (sk17 @ (insert_a @ sk238 @ bot_bot_set_a)) @ (insert_a @ sk238 @ bot_bot_set_a)) != (member_a @ A @ B)))),inference(paramod_ordered,[status(thm)],[18939,405])). 132.20/30.71 thf(20327,plain,((~ (member_a @ (sk17 @ (insert_a @ sk238 @ bot_bot_set_a)) @ (uminus_uminus_set_a @ (insert_a @ sk238 @ bot_bot_set_a))))),inference(pattern_uni,[status(thm)],[20326:[bind(A, $thf(sk17 @ (insert_a @ sk238 @ bot_bot_set_a))),bind(B, $thf(insert_a @ sk238 @ bot_bot_set_a))]])). 132.20/30.71 thf(20954,plain,(((member_a @ (sk17 @ (insert_a @ sk238 @ bot_bot_set_a)) @ (uminus_uminus_set_a @ (insert_a @ sk238 @ bot_bot_set_a))) != (member_a @ (sk17 @ (insert_a @ sk238 @ bot_bot_set_a)) @ (insert_a @ sk238 @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[18939,20327])). 132.20/30.71 thf(20959,plain,(((sk17 @ (insert_a @ sk238 @ bot_bot_set_a)) != (sk17 @ (insert_a @ sk238 @ bot_bot_set_a))) | ((uminus_uminus_set_a @ (insert_a @ sk238 @ bot_bot_set_a)) != (insert_a @ sk238 @ bot_bot_set_a))),inference(simp,[status(thm)],[20954])). 132.20/30.71 thf(20978,plain,(((uminus_uminus_set_a @ (insert_a @ sk238 @ bot_bot_set_a)) != (insert_a @ sk238 @ bot_bot_set_a))),inference(simp,[status(thm)],[20959])). 132.20/30.71 thf(239,axiom,((! [A:refine424419629nres_a]: ((~ (! [B:set_a]: (A != (refine1198353288_RES_a @ B)))) <= (A != refine464223677AILi_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_nres_Oexhaust)). 132.20/30.71 thf(1183,plain,((! [A:refine424419629nres_a]: (~ (! [B:set_a]: ~ (A = (refine1198353288_RES_a @ B))) | (A = refine464223677AILi_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 132.20/30.71 thf(49,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) => ((A = B) <= (ord_le516598614nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_antisym)). 132.20/30.71 thf(480,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (A) @ (B)) => (((A) = (B)) | ~ (ord_le516598614nres_a @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 132.20/30.71 thf(38,axiom,(((= @ refine787176636t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ B @ A) & (ord_le1051254044t_unit @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_order__class_Oorder_Oeq__iff)). 132.20/30.71 thf(442,plain,(((= @ refine787176636t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ B @ A) & (ord_le1051254044t_unit @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 132.20/30.71 thf(443,plain,(((^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ B @ A) & (ord_le1051254044t_unit @ A @ B))) = (= @ refine787176636t_unit))),inference(lifteq,[status(thm)],[442])). 132.20/30.71 thf(17098,plain,(! [B:a,A:a] : (((member_a @ sk235 @ (insert_a @ A @ (collect_a @ (^ [C:a]: ($true))))) != (member_a @ B @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[14631,479])). 132.20/30.71 thf(17153,plain,(! [B:a,A:a] : ((sk235 != B) | ((insert_a @ A @ (collect_a @ (^ [C:a]: ($true)))) != bot_bot_set_a))),inference(simp,[status(thm)],[17098])). 132.20/30.71 thf(17171,plain,(! [A:a] : (((insert_a @ A @ (collect_a @ (^ [B:a]: ($true)))) != bot_bot_set_a))),inference(simp,[status(thm)],[17153])). 132.20/30.71 thf(26,axiom,((! [A:set_a,B:set_a]: (((A = B) <= (ord_less_eq_set_a @ B @ A)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_order__class_Oorder_Oantisym)). 132.20/30.71 thf(393,plain,((! [A:set_a,B:set_a]: ((A = B) | ~ (ord_less_eq_set_a @ B @ A) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 132.20/30.71 thf(394,plain,(! [B:set_a,A:set_a] : ((A = B) | (~ (ord_less_eq_set_a @ B @ A)) | (~ (ord_less_eq_set_a @ A @ B)))),inference(cnf,[status(esa)],[393])). 132.20/30.71 thf(395,plain,(! [B:set_a,A:set_a] : ((A = B) | (~ (ord_less_eq_set_a @ B @ A)) | (~ (ord_less_eq_set_a @ A @ B)))),inference(lifteq,[status(thm)],[394])). 132.20/30.71 thf(2911,plain,(! [B:set_a,A:set_a] : ((~ (ord_less_eq_set_a @ B @ A)) | (~ (ord_less_eq_set_a @ A @ B)) | (B != bot_bot_set_a) | (A != top_top_set_a))),inference(paramod_ordered,[status(thm)],[395,1729])). 132.20/30.71 thf(2912,plain,(! [A:set_a] : ((~ (ord_less_eq_set_a @ A @ top_top_set_a)) | (~ (ord_less_eq_set_a @ top_top_set_a @ A)) | (A != bot_bot_set_a))),inference(pattern_uni,[status(thm)],[2911:[bind(A, $thf(top_top_set_a))]])). 132.20/30.71 thf(2996,plain,((~ (ord_less_eq_set_a @ bot_bot_set_a @ top_top_set_a)) | (~ (ord_less_eq_set_a @ top_top_set_a @ bot_bot_set_a))),inference(simp,[status(thm)],[2912])). 132.20/30.71 thf(16187,plain,(! [B:set_a,A:a] : ((~ (member_a @ A @ (sk14 @ B @ A))) | ((member_a @ sk235 @ (collect_a @ (^ [C:a]: ($true)))) != (member_a @ A @ B)))),inference(paramod_ordered,[status(thm)],[14545,500])). 132.20/30.71 thf(16188,plain,((~ (member_a @ sk235 @ (sk14 @ (collect_a @ (^ [A:a]: ($true))) @ sk235)))),inference(pattern_uni,[status(thm)],[16187:[bind(A, $thf(sk235)),bind(B, $thf(collect_a @ (^ [C:a]: ($true))))]])). 132.20/30.71 thf(16239,plain,(! [A:a] : (((member_a @ A @ top_top_set_a) != (member_a @ sk235 @ (sk14 @ (collect_a @ (^ [B:a]: ($true))) @ sk235))))),inference(paramod_ordered,[status(thm)],[677,16188])). 132.20/30.71 thf(16275,plain,(! [A:a] : ((A != sk235) | ((sk14 @ (collect_a @ (^ [B:a]: ($true))) @ sk235) != top_top_set_a))),inference(simp,[status(thm)],[16239])). 132.20/30.71 thf(16293,plain,(((sk14 @ (collect_a @ (^ [A:a]: ($true))) @ sk235) != top_top_set_a)),inference(simp,[status(thm)],[16275])). 132.20/30.71 thf(228,axiom,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((B @ C) <= (A @ C))) => (ord_less_eq_set_a @ (collect_a @ A) @ (collect_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Collect__mono)). 132.20/30.71 thf(1151,plain,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((B @ C) | ~ (A @ C))) => (ord_less_eq_set_a @ (collect_a @ (A)) @ (collect_a @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 132.20/30.71 thf(1581,plain,(! [A:($o > refine424419629nres_a)] : (((ord_le516598614nres_a @ A) = (^ [B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C)))))),inference(func_ext,[status(esa)],[1064])). 132.20/30.71 thf(11,axiom,(((refine23983189ASSUME @ $false) = bot_bo658782032t_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_ASSUME__simps_I2_J)). 132.20/30.71 thf(353,plain,(((refine23983189ASSUME @ $false) = bot_bo658782032t_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 132.20/30.71 thf(13,axiom,((! [A:refine787176636t_unit]: (ord_le1051254044t_unit @ bot_bo658782032t_unit @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_nres__order__simps_I1_J)). 132.20/30.71 thf(358,plain,((! [A:refine787176636t_unit]: (ord_le1051254044t_unit @ bot_bo658782032t_unit @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 132.20/30.71 thf(359,plain,(! [A:refine787176636t_unit] : ((ord_le1051254044t_unit @ bot_bo658782032t_unit @ A))),inference(cnf,[status(esa)],[358])). 132.20/30.71 thf(1652,plain,(! [C:refine787176636t_unit,B:(product_unit > refine787176636t_unit),A:product_unit] : ((ord_le1051254044t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) @ C) | ((B @ A) != bot_bo658782032t_unit))),inference(paramod_ordered,[status(thm)],[346,359])). 132.20/30.71 thf(1659,plain,(! [B:refine787176636t_unit,A:product_unit] : ((ord_le1051254044t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (bot_bo658782032t_unit))) @ B))),inference(pre_uni,[status(thm)],[1652:[bind(A, $thf(A)),bind(B, $thf(^ [D:product_unit]: (bot_bo658782032t_unit)))]])). 132.20/30.71 thf(1684,plain,(! [B:refine787176636t_unit,A:product_unit] : ((ord_le1051254044t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (bot_bo658782032t_unit))) @ B))),inference(simp,[status(thm)],[1659])). 132.20/30.71 thf(354,plain,(((refine23983189ASSUME @ $false) = bot_bo658782032t_unit)),inference(lifteq,[status(thm)],[353])). 132.20/30.71 thf(1655,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) = bot_bo658782032t_unit) | ((refine23983189ASSUME @ $false) != (B @ A)))),inference(paramod_ordered,[status(thm)],[354,346])). 132.20/30.71 thf(1665,plain,(! [A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [B:product_unit]: (refine23983189ASSUME @ $false))) = bot_bo658782032t_unit))),inference(pre_uni,[status(thm)],[1655:[bind(A, $thf(A)),bind(B, $thf(^ [C:product_unit]: (refine23983189ASSUME @ $false)))]])). 132.20/30.71 thf(2592,plain,(! [A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [B:product_unit]: (bot_bo658782032t_unit))) = bot_bo658782032t_unit))),inference(rewrite,[status(thm)],[1665,354])). 132.20/30.71 thf(6438,plain,(! [A:refine787176636t_unit] : ((ord_le1051254044t_unit @ bot_bo658782032t_unit @ A))),inference(rewrite,[status(thm)],[1684,2592])). 132.20/30.71 thf(248,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > refine424419629nres_a)]: (((refine412683989fail_a @ A) => (refine412683989fail_a @ B)) => ((! [D:a]: (((refine1001002027nres_a @ B @ D) => (ord_le519537037nres_a @ (C @ D) @ A)) <= (refine412683989fail_a @ B))) => (ord_le519537037nres_a @ (refine436832838nd_a_a @ B @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_pw__bind__leI)). 132.20/30.71 thf(1215,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > refine424419629nres_a)]: (((refine412683989fail_a @ A) => (refine412683989fail_a @ B)) => ((! [D:a]: (((refine1001002027nres_a @ B @ D) => (ord_le519537037nres_a @ (C @ D) @ A)) | ~ (refine412683989fail_a @ B))) => (ord_le519537037nres_a @ (refine436832838nd_a_a @ B @ (C)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 132.20/30.71 thf(18234,plain,(((member_a @ sk249 @ bot_bot_set_a) != (ord_le519537037nres_a @ (refine2063221604TURN_a @ sk249) @ (refine1198353288_RES_a @ (collect_a @ (^ [A:a]: ($true))))))),inference(func_ext,[status(esa)],[18233])). 132.20/30.71 thf(20368,plain,((ord_le519537037nres_a @ (refine2063221604TURN_a @ sk249) @ (refine1198353288_RES_a @ (collect_a @ (^ [A:a]: ($true)))))),inference(rewrite,[status(thm)],[18234,479])). 132.20/30.71 thf(150,axiom,(((= @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: (! [C:a]: ((refine1001002027nres_a @ A @ C) = (refine1001002027nres_a @ B @ C)) & ((refine412683989fail_a @ A) = (refine412683989fail_a @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_pw__eq__iff)). 132.20/30.71 thf(865,plain,(((= @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: (! [C:a]: ((refine1001002027nres_a @ A @ C) = (refine1001002027nres_a @ B @ C)) & ((refine412683989fail_a @ A) = (refine412683989fail_a @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 132.20/30.71 thf(866,plain,(((^ [A:refine424419629nres_a,B:refine424419629nres_a]: (! [C:a]: ((refine1001002027nres_a @ A @ C) = (refine1001002027nres_a @ B @ C)) & ((refine412683989fail_a @ A) = (refine412683989fail_a @ B)))) = (= @ refine424419629nres_a))),inference(lifteq,[status(thm)],[865])). 132.20/30.71 thf(192,axiom,((! [A:set_a,B:set_a,C:a]: (((member_a @ C @ A) => (member_a @ C @ B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_in__mono)). 132.20/30.71 thf(998,plain,((! [A:set_a,B:set_a,C:a]: (((member_a @ C @ A) => (member_a @ C @ B)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 132.20/30.71 thf(108,axiom,(((= @ refine787176636t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C)) & ((refine579265252t_unit @ A) = (refine579265252t_unit @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_pw__eq__iff)). 132.20/30.71 thf(696,plain,(((= @ refine787176636t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C)) & ((refine579265252t_unit @ A) = (refine579265252t_unit @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 132.20/30.71 thf(697,plain,(((^ [A:refine787176636t_unit,B:refine787176636t_unit]: (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C)) & ((refine579265252t_unit @ A) = (refine579265252t_unit @ B)))) = (= @ refine787176636t_unit))),inference(lifteq,[status(thm)],[696])). 132.20/30.71 thf(1943,plain,(((^ [A:refine787176636t_unit,B:refine787176636t_unit]: (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C)) & ((~ (top_to177290092t_unit = A)) = (~ (top_to177290092t_unit = B))))) = (= @ refine787176636t_unit))),inference(rewrite,[status(thm)],[697,330])). 132.20/30.71 thf(254,axiom,((! [A:refine787176636t_unit,B:(product_unit > refine424419629nres_a),C:refine424419629nres_a]: ((ord_le519537037nres_a @ (refine119808503unit_a @ A @ B) @ C) = (! [D:product_unit]: ((ord_le519537037nres_a @ (B @ D) @ C) <= ((refine579265252t_unit @ A) & (refine558004794t_unit @ A @ D))) & ((refine579265252t_unit @ A) <= (refine412683989fail_a @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_pw__bind__le__iff)). 132.20/30.71 thf(1242,plain,((! [A:refine787176636t_unit,B:(product_unit > refine424419629nres_a),C:refine424419629nres_a]: ((ord_le519537037nres_a @ (refine119808503unit_a @ A @ (B)) @ C) = (! [D:product_unit]: ((ord_le519537037nres_a @ (B @ D) @ C) | ~ ((refine579265252t_unit @ A) & (refine558004794t_unit @ A @ D))) & ((refine579265252t_unit @ A) | ~ (refine412683989fail_a @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 132.20/30.71 thf(61,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: (((ord_le1051254044t_unit @ A @ C) <= (ord_le1051254044t_unit @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_ord__eq__le__trans)). 132.20/30.71 thf(527,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ C) | ~ (ord_le1051254044t_unit @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 132.20/30.71 thf(187,axiom,((! [A:a,B:a,C:set_a]: ((member_a @ A @ (insert_a @ B @ C)) = ((A = B) | (member_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_insert__iff)). 132.20/30.71 thf(981,plain,((! [A:a,B:a,C:set_a]: ((member_a @ A @ (insert_a @ B @ C)) = ((A = B) | (member_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 132.20/30.71 thf(235,axiom,((! [A:set_a,B:a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine2063221604TURN_a @ B)) = (ord_less_eq_set_a @ A @ (insert_a @ B @ bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_nres__order__simps_I22_J)). 132.20/30.71 thf(1169,plain,((! [A:set_a,B:a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine2063221604TURN_a @ B)) = (ord_less_eq_set_a @ A @ (insert_a @ B @ bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 132.20/30.71 thf(27,axiom,((! [A:refine787176636t_unit]: (ord_le1051254044t_unit @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_order__mono__setup_Orefl)). 132.20/30.71 thf(396,plain,((! [A:refine787176636t_unit]: (ord_le1051254044t_unit @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 132.20/30.71 thf(397,plain,(! [A:refine787176636t_unit] : ((ord_le1051254044t_unit @ A @ A))),inference(cnf,[status(esa)],[396])). 132.20/30.71 thf(154,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_relprop__triggers_I6_J)). 132.20/30.71 thf(877,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 132.20/30.71 thf(107,axiom,((! [A:set_a]: ((A != bot_bot_set_a) => (~ (! [B:a]: ~ (member_a @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_set__notEmptyE)). 132.20/30.71 thf(692,plain,((! [A:set_a]: ((~ (A = bot_bot_set_a)) => (~ (! [B:a]: ~ (member_a @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 132.20/30.71 thf(290,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((A = B) => ((ord_le519537037nres_a @ B @ C) => (ord_le519537037nres_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ord__eq__le__trans)). 132.20/30.71 thf(1394,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((A = B) => ((ord_le519537037nres_a @ B @ C) => (ord_le519537037nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 132.20/30.71 thf(6543,plain,(! [B:a,A:refine424419629nres_a] : ((? [C:set_a]: (A = (refine1198353288_RES_a @ C))) | ((refine412683989fail_a @ A) != (refine412683989fail_a @ (refine2063221604TURN_a @ B))))),inference(paramod_ordered,[status(thm)],[1722,603])). 132.20/30.71 thf(6544,plain,(! [A:a] : ((? [B:set_a]: ((refine2063221604TURN_a @ A) = (refine1198353288_RES_a @ B))))),inference(pattern_uni,[status(thm)],[6543:[bind(A, $thf(refine2063221604TURN_a @ C)),bind(B, $thf(C))]])). 132.20/30.71 thf(6547,plain,(! [A:a] : (((refine2063221604TURN_a @ A) = (refine1198353288_RES_a @ (sk183 @ A))))),inference(cnf,[status(esa)],[6544])). 132.20/30.71 thf(6548,plain,(! [A:a] : (((refine1198353288_RES_a @ (sk183 @ A)) = (refine2063221604TURN_a @ A)))),inference(lifteq,[status(thm)],[6547])). 132.20/30.71 thf(6549,plain,(! [A:a] : (((refine1198353288_RES_a @ (sk183 @ A)) = (refine2063221604TURN_a @ A)))),inference(simp,[status(thm)],[6548])). 132.20/30.71 thf(7602,plain,(! [B:set_a,A:a] : (((refine1822134885_RES_a @ (refine2063221604TURN_a @ A)) = B) | ((refine1198353288_RES_a @ (sk183 @ A)) != (refine1198353288_RES_a @ B)))),inference(paramod_ordered,[status(thm)],[6549,1369])). 132.20/30.71 thf(7603,plain,(! [A:a] : (((sk183 @ A) = (refine1822134885_RES_a @ (refine2063221604TURN_a @ A))))),inference(pattern_uni,[status(thm)],[7602:[bind(A, $thf(C)),bind(B, $thf(sk183 @ C))]])). 132.20/30.71 thf(7645,plain,(! [A:a] : (((sk183 @ A) = (refine1822134885_RES_a @ (refine2063221604TURN_a @ A))))),inference(simp,[status(thm)],[7603])). 132.20/30.71 thf(325,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > refine787176636t_unit),D:(a > refine787176636t_unit)]: (((! [E:a]: ((ord_le1051254044t_unit @ (C @ E) @ (D @ E)) <= (ord_le519537037nres_a @ (refine2063221604TURN_a @ E) @ A))) => (ord_le1051254044t_unit @ (refine96995669t_unit @ A @ C) @ (refine96995669t_unit @ B @ D))) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J)). 132.20/30.71 thf(1526,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > refine787176636t_unit),D:(a > refine787176636t_unit)]: (((! [E:a]: ((ord_le1051254044t_unit @ (C @ E) @ (D @ E)) | ~ (ord_le519537037nres_a @ (refine2063221604TURN_a @ E) @ A))) => (ord_le1051254044t_unit @ (refine96995669t_unit @ A @ (C)) @ (refine96995669t_unit @ B @ (D)))) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 132.20/30.71 thf(17131,plain,(! [C:set_a,B:a,A:a] : ((~ (member_a @ B @ (uminus_uminus_set_a @ C))) | ((member_a @ sk235 @ (insert_a @ A @ (collect_a @ (^ [D:a]: ($true))))) != (member_a @ B @ C)))),inference(paramod_ordered,[status(thm)],[14631,405])). 132.20/30.71 thf(17132,plain,(! [A:a] : ((~ (member_a @ sk235 @ (uminus_uminus_set_a @ (insert_a @ A @ (collect_a @ (^ [B:a]: ($true))))))))),inference(pattern_uni,[status(thm)],[17131:[bind(A, $thf(D)),bind(B, $thf(sk235)),bind(C, $thf(insert_a @ D @ (collect_a @ (^ [E:a]: ($true)))))]])). 132.20/30.71 thf(17189,plain,(! [A:a] : ((~ (member_a @ sk235 @ (uminus_uminus_set_a @ (insert_a @ A @ (collect_a @ (^ [B:a]: ($true))))))))),inference(simp,[status(thm)],[17132])). 132.20/30.71 thf(211,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((B != refine464223677AILi_a) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => (~ (ord_less_eq_set_a @ C @ D))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_less__eq__nres_Oelims_I2_J)). 132.20/30.71 thf(1074,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((~ (B = refine464223677AILi_a)) => (~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((B = (refine1198353288_RES_a @ D)) => (~ (ord_less_eq_set_a @ C @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 132.20/30.71 thf(6531,plain,(! [B:set_a,A:refine424419629nres_a] : ((? [C:set_a]: (A = (refine1198353288_RES_a @ C))) | ((refine412683989fail_a @ A) != (refine412683989fail_a @ (refine1198353288_RES_a @ B))))),inference(paramod_ordered,[status(thm)],[1722,1143])). 132.20/30.71 thf(6532,plain,(! [A:set_a] : ((? [B:set_a]: ((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B))))),inference(pattern_uni,[status(thm)],[6531:[bind(A, $thf(refine1198353288_RES_a @ C)),bind(B, $thf(C))]])). 132.20/30.71 thf(6558,plain,(! [A:set_a] : (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ (sk186 @ A))))),inference(cnf,[status(esa)],[6532])). 132.20/30.71 thf(6559,plain,(! [A:set_a] : (((refine1198353288_RES_a @ (sk186 @ A)) = (refine1198353288_RES_a @ A)))),inference(lifteq,[status(thm)],[6558])). 132.20/30.71 thf(6560,plain,(! [A:set_a] : (((refine1198353288_RES_a @ (sk186 @ A)) = (refine1198353288_RES_a @ A)))),inference(simp,[status(thm)],[6559])). 132.20/30.71 thf(8830,plain,(! [B:set_a,A:set_a] : (((refine1822134885_RES_a @ (refine1198353288_RES_a @ A)) = B) | ((refine1198353288_RES_a @ (sk186 @ A)) != (refine1198353288_RES_a @ B)))),inference(paramod_ordered,[status(thm)],[6560,1369])). 132.20/30.71 thf(8831,plain,(! [A:set_a] : (((sk186 @ A) = (refine1822134885_RES_a @ (refine1198353288_RES_a @ A))))),inference(pattern_uni,[status(thm)],[8830:[bind(A, $thf(C)),bind(B, $thf(sk186 @ C))]])). 132.20/30.71 thf(8885,plain,(! [A:set_a] : (((sk186 @ A) = (refine1822134885_RES_a @ (refine1198353288_RES_a @ A))))),inference(simp,[status(thm)],[8831])). 132.20/30.71 thf(9720,plain,(! [A:set_a] : (((sk186 @ A) = A))),inference(rewrite,[status(thm)],[8885,1369])). 132.20/30.71 thf(23,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: (((ord_le516598614nres_a @ C @ B) <= (ord_le516598614nres_a @ C @ A)) <= (ord_le516598614nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_dual__order_Otrans)). 132.20/30.71 thf(380,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (C) @ (B)) | ~ (ord_le516598614nres_a @ (C) @ (A)) | ~ (ord_le516598614nres_a @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 132.20/30.71 thf(102,axiom,((! [A:refine787176636t_unit]: (ord_le1051254044t_unit @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_dual__order_Orefl)). 132.20/30.71 thf(678,plain,((! [A:refine787176636t_unit]: (ord_le1051254044t_unit @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 132.20/30.71 thf(95,axiom,(((= @ refine787176636t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ B @ A) & (ord_le1051254044t_unit @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_eq__iff)). 132.20/30.71 thf(661,plain,(((= @ refine787176636t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ B @ A) & (ord_le1051254044t_unit @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 132.20/30.71 thf(244,axiom,((! [A:refine424419629nres_a,B:(refine787176636t_unit > refine424419629nres_a),C:refine787176636t_unit,D:refine787176636t_unit]: ((ord_le519537037nres_a @ A @ (B @ C)) => ((ord_le1051254044t_unit @ C @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_order__subst1)). 132.20/30.71 thf(1199,plain,((! [A:refine424419629nres_a,B:(refine787176636t_unit > refine424419629nres_a),C:refine787176636t_unit,D:refine787176636t_unit]: ((ord_le519537037nres_a @ A @ (B @ C)) => ((ord_le1051254044t_unit @ C @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 132.20/30.71 thf(366,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (partia1658438072t_unit @ bot_bo658782032t_unit @ A @ B)) | (ord_le1051254044t_unit @ A @ B))),inference(cnf,[status(esa)],[365])). 132.20/30.71 thf(3844,plain,(~ (b) | (s1 != refine464223677AILi_a) | ((collect_a @ (phi)) != (collect_a @ (^ [A:a]: ($false))))),inference(paramod_ordered,[status(thm)],[1589,3597])). 132.20/30.71 thf(3849,plain,(~ (b) | (s1 != refine464223677AILi_a) | ((phi) != (^ [A:a]: ($false)))),inference(simp,[status(thm)],[3844])). 132.20/30.71 thf(5281,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((phi) != (^ [A:a]: ($false)))),inference(rewrite,[status(thm)],[3849,4994])). 132.20/30.71 thf(12434,plain,(! [B:a,A:set_a] : ((A != bot_bot_set_a) | ((collect_a @ (^ [C:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ C) @ (refine1198353288_RES_a @ A)))) != (collect_a @ (^ [C:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ C) @ (refine2063221604TURN_a @ B))))))),inference(paramod_ordered,[status(thm)],[4008,11579])). 132.20/30.71 thf(12446,plain,(! [A:a] : (((^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ bot_bot_set_a))) != (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine2063221604TURN_a @ A)))))),inference(simp,[status(thm)],[12434])). 132.20/30.71 thf(12451,plain,(! [A:a] : (((^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ bot_bot_set_a))) != (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine2063221604TURN_a @ A)))))),inference(simp,[status(thm)],[12446])). 132.20/30.71 thf(12673,plain,(! [A:a] : (((^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine2063221604TURN_a @ A))) != (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ bot_bo529555393nres_a))))),inference(rewrite,[status(thm)],[12451,1158])). 132.20/30.71 thf(245,axiom,((! [A:set_a]: (top_to231829469nres_a != (refine1198353288_RES_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_nres__inequalities_I1_J)). 132.20/30.71 thf(1203,plain,((! [A:set_a]: ~ (top_to231829469nres_a = (refine1198353288_RES_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 132.20/30.71 thf(1204,plain,((~ (? [A:set_a]: (top_to231829469nres_a = (refine1198353288_RES_a @ A))))),inference(miniscope,[status(thm)],[1203])). 132.20/30.71 thf(1205,plain,(! [A:set_a] : ((~ (top_to231829469nres_a = (refine1198353288_RES_a @ A))))),inference(cnf,[status(esa)],[1204])). 132.20/30.71 thf(1206,plain,(! [A:set_a] : (((refine1198353288_RES_a @ A) != top_to231829469nres_a))),inference(lifteq,[status(thm)],[1205])). 132.20/30.71 thf(452,plain,(! [C:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (~ (sk7 @ A)) | (~ (C @ (sk9 @ (C) @ B @ (A)))) | (C @ (order_245837199nres_a @ (A))))),inference(cnf,[status(esa)],[450])). 132.20/30.71 thf(56,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ C) => (ord_le1051254044t_unit @ A @ C)) <= (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_order__trans)). 132.20/30.71 thf(510,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ C) => (ord_le1051254044t_unit @ A @ C)) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 132.20/30.71 thf(511,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (! [C:refine787176636t_unit]: ((ord_le1051254044t_unit @ B @ C) => (ord_le1051254044t_unit @ A @ C)) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(miniscope,[status(thm)],[510])). 132.20/30.71 thf(512,plain,(! [C:refine787176636t_unit,B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (ord_le1051254044t_unit @ B @ C)) | (ord_le1051254044t_unit @ A @ C) | (~ (ord_le1051254044t_unit @ A @ B)))),inference(cnf,[status(esa)],[511])). 132.20/30.71 thf(16257,plain,(! [B:a,A:set_a] : (((member_a @ B @ (insert_a @ B @ A)) != (member_a @ sk235 @ (sk14 @ (collect_a @ (^ [C:a]: ($true))) @ sk235))))),inference(paramod_ordered,[status(thm)],[441,16188])). 132.20/30.71 thf(16283,plain,(! [B:a,A:set_a] : ((B != sk235) | ((insert_a @ B @ A) != (sk14 @ (collect_a @ (^ [C:a]: ($true))) @ sk235)))),inference(simp,[status(thm)],[16257])). 132.20/30.71 thf(16297,plain,(! [A:set_a] : (((insert_a @ sk235 @ A) != (sk14 @ (collect_a @ (^ [B:a]: ($true))) @ sk235)))),inference(simp,[status(thm)],[16283])). 132.20/30.71 thf(16258,plain,(((member_a @ sk235 @ (sk14 @ (collect_a @ (^ [A:a]: ($true))) @ sk235)) != (member_a @ sk235 @ (collect_a @ (^ [A:a]: ($true)))))),inference(paramod_ordered,[status(thm)],[14545,16188])). 132.20/30.71 thf(16272,plain,((sk235 != sk235) | ((sk14 @ (collect_a @ (^ [A:a]: ($true))) @ sk235) != (collect_a @ (^ [A:a]: ($true))))),inference(simp,[status(thm)],[16258])). 132.20/30.71 thf(16292,plain,(((sk14 @ (collect_a @ (^ [A:a]: ($true))) @ sk235) != (collect_a @ (^ [A:a]: ($true))))),inference(simp,[status(thm)],[16272])). 132.20/30.71 thf(201,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ C @ A) => (ord_le519537037nres_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_dual__order_Otrans)). 132.20/30.71 thf(1047,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ C @ A) => (ord_le519537037nres_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 132.20/30.71 thf(180,axiom,((ord_le1960259811nres_a = (^ [A:($o > ($o > refine424419629nres_a)),B:($o > ($o > refine424419629nres_a))]: ((ord_le516598614nres_a @ (A @ $true) @ (B @ $true)) & (ord_le516598614nres_a @ (A @ $false) @ (B @ $false)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_le__rel__bool__arg__iff)). 132.20/30.71 thf(957,plain,(((ord_le1960259811nres_a) = (^ [A:($o > ($o > refine424419629nres_a)),B:($o > ($o > refine424419629nres_a))]: ((ord_le516598614nres_a @ (A @ $true) @ (B @ $true)) & (ord_le516598614nres_a @ (A @ $false) @ (B @ $false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 132.20/30.71 thf(178,axiom,((! [A:a]: ((refine1001002027nres_a @ (refine2063221604TURN_a @ A)) = (= @ a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_inres__simps_I3_J)). 132.20/30.71 thf(952,plain,((! [A:a]: ((refine1001002027nres_a @ (refine2063221604TURN_a @ A)) = (= @ a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 132.20/30.71 thf(222,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (ord_le519537037nres_a @ A @ B)) => ((~ ((A = refine464223677AILi_a) => (! [C:set_a]: (B != (refine1198353288_RES_a @ C))))) <= (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((ord_less_eq_set_a @ C @ D) <= (B = (refine1198353288_RES_a @ D)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_less__eq__nres_Oelims_I3_J)). 132.20/30.71 thf(1123,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((~ (ord_le519537037nres_a @ A @ B)) => (~ ((A = refine464223677AILi_a) => (! [C:set_a]: ~ (B = (refine1198353288_RES_a @ C)))) | ~ (! [C:set_a]: ((A = (refine1198353288_RES_a @ C)) => (! [D:set_a]: ((ord_less_eq_set_a @ C @ D) | ~ (B = (refine1198353288_RES_a @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 132.20/30.71 thf(138,axiom,((! [A:a,B:set_a]: ((member_a @ A @ B) => (B != bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_memb__imp__not__empty)). 132.20/30.71 thf(820,plain,((! [A:a,B:set_a]: ((member_a @ A @ B) => (~ (B = bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 132.20/30.71 thf(66,axiom,((! [A:set_a,B:set_a,C:(set_a > refine787176636t_unit),D:refine787176636t_unit]: ((ord_less_eq_set_a @ A @ B) => (((! [E:set_a,F:set_a]: ((ord_le1051254044t_unit @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_a @ E @ F))) => (ord_le1051254044t_unit @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_ord__le__eq__subst)). 132.20/30.71 thf(556,plain,((! [A:set_a,B:set_a,C:(set_a > refine787176636t_unit),D:refine787176636t_unit]: ((ord_less_eq_set_a @ A @ B) => (((! [E:set_a,F:set_a]: ((ord_le1051254044t_unit @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_a @ E @ F))) => (ord_le1051254044t_unit @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 132.20/30.71 thf(557,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => (! [C:(set_a > refine787176636t_unit),D:refine787176636t_unit]: (((! [E:set_a,F:set_a]: ((ord_le1051254044t_unit @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_a @ E @ F))) => (ord_le1051254044t_unit @ (C @ A) @ D)) | ~ ((C @ B) = D)))))),inference(miniscope,[status(thm)],[556])). 132.20/30.71 thf(558,plain,(! [D:refine787176636t_unit,C:(set_a > refine787176636t_unit),B:set_a,A:set_a] : ((~ (ord_less_eq_set_a @ A @ B)) | (~ (ord_le1051254044t_unit @ (C @ (sk22 @ D @ (C) @ B @ A)) @ (C @ (sk23 @ D @ (C) @ B @ A)))) | (ord_le1051254044t_unit @ (C @ A) @ D) | (~ ((C @ B) = D)))),inference(cnf,[status(esa)],[557])). 132.20/30.71 thf(560,plain,(! [D:refine787176636t_unit,C:(set_a > refine787176636t_unit),B:set_a,A:set_a] : (((C @ B) != D) | (~ (ord_less_eq_set_a @ A @ B)) | (~ (ord_le1051254044t_unit @ (C @ (sk22 @ D @ (C) @ B @ A)) @ (C @ (sk23 @ D @ (C) @ B @ A)))) | (ord_le1051254044t_unit @ (C @ A) @ D))),inference(lifteq,[status(thm)],[558])). 132.20/30.71 thf(561,plain,(! [C:(set_a > refine787176636t_unit),B:set_a,A:set_a] : ((~ (ord_less_eq_set_a @ A @ B)) | (~ (ord_le1051254044t_unit @ (C @ (sk22 @ (C @ B) @ (C) @ B @ A)) @ (C @ (sk23 @ (C @ B) @ (C) @ B @ A)))) | (ord_le1051254044t_unit @ (C @ A) @ (C @ B)))),inference(simp,[status(thm)],[560])). 132.20/30.71 thf(284,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) <= (A = top_to231829469nres_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_meta__le__everything__if__top)). 132.20/30.71 thf(1370,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) | ~ (A = top_to231829469nres_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 132.20/30.71 thf(278,axiom,((! [A:refine424419629nres_a]: ((A != top_to231829469nres_a) => (~ (! [B:set_a]: (A != (refine1198353288_RES_a @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_nres__cases)). 132.20/30.71 thf(1343,plain,((! [A:refine424419629nres_a]: ((~ (A = top_to231829469nres_a)) => (~ (! [B:set_a]: ~ (A = (refine1198353288_RES_a @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 132.20/30.71 thf(4165,plain,(~ (b) | (s1 != refine464223677AILi_a) | ((collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a))) != (collect_a @ (phi)))),inference(paramod_ordered,[status(thm)],[4020,3597])). 132.20/30.71 thf(4210,plain,(~ (b) | (s1 != refine464223677AILi_a) | ((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a)) != (phi))),inference(simp,[status(thm)],[4165])). 132.20/30.71 thf(5284,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a)) != (phi))),inference(rewrite,[status(thm)],[4210,4994])). 132.20/30.71 thf(6328,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((phi) != (^ [A:a]: ((refine2063221604TURN_a @ A) = bot_bo529555393nres_a)))),inference(rewrite,[status(thm)],[5284,1366])). 132.20/30.71 thf(373,plain,(! [A:refine787176636t_unit] : (((refine681446406t_unit @ A @ (refine1420258419t_unit)) = A))),inference(cnf,[status(esa)],[372])). 132.20/30.71 thf(374,plain,(! [A:refine787176636t_unit] : (((refine681446406t_unit @ A @ (refine1420258419t_unit)) = A))),inference(lifteq,[status(thm)],[373])). 132.20/30.71 thf(1567,plain,(((refine558004794t_unit @ top_to177290092t_unit) != (refine558004794t_unit @ bot_bo658782032t_unit))),inference(paramod_ordered,[status(thm)],[930,457])). 132.20/30.71 thf(1569,plain,(((^ [A:product_unit]: (top_to177290092t_unit)) != (^ [A:product_unit]: (bot_bo658782032t_unit))) | ((^ [A:product_unit]: (A)) != (^ [A:product_unit]: (A)))),inference(simp,[status(thm)],[1567])). 132.20/30.71 thf(1571,plain,(((^ [A:product_unit]: (top_to177290092t_unit)) != (^ [A:product_unit]: (bot_bo658782032t_unit)))),inference(simp,[status(thm)],[1569])). 132.20/30.71 thf(1651,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((^ [C:product_unit]: (refine681446406t_unit @ (refine1420258419t_unit @ A) @ B)) != (^ [C:product_unit]: (bot_bo658782032t_unit))) | ((B @ A) != top_to177290092t_unit))),inference(paramod_ordered,[status(thm)],[346,1571])). 132.20/30.71 thf(1669,plain,(! [A:product_unit] : (((^ [B:product_unit]: (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (top_to177290092t_unit)))) != (^ [B:product_unit]: (bot_bo658782032t_unit))))),inference(pre_uni,[status(thm)],[1651:[bind(A, $thf(A)),bind(B, $thf(^ [C:product_unit]: (top_to177290092t_unit)))]])). 132.20/30.71 thf(1866,plain,(! [B:product_unit,A:refine787176636t_unit] : (((^ [C:product_unit]: (A)) != (^ [C:product_unit]: (bot_bo658782032t_unit))) | ((refine681446406t_unit @ A @ (refine1420258419t_unit)) != (refine681446406t_unit @ (refine1420258419t_unit @ B) @ (^ [C:product_unit]: (top_to177290092t_unit)))))),inference(paramod_ordered,[status(thm)],[374,1669])). 132.20/30.71 thf(1878,plain,(! [B:product_unit,A:refine787176636t_unit] : (((^ [C:product_unit]: (A)) != (^ [C:product_unit]: (bot_bo658782032t_unit))) | (A != (refine1420258419t_unit @ B)) | ((refine1420258419t_unit) != (^ [C:product_unit]: (top_to177290092t_unit))))),inference(simp,[status(thm)],[1866])). 132.20/30.71 thf(1883,plain,(! [A:product_unit] : (((^ [B:product_unit]: (refine1420258419t_unit @ A)) != (^ [B:product_unit]: (bot_bo658782032t_unit))) | ((refine1420258419t_unit) != (^ [B:product_unit]: (top_to177290092t_unit))))),inference(simp,[status(thm)],[1878])). 132.20/30.71 thf(93,axiom,((! [A:$o]: (refine579265252t_unit @ (refine23983189ASSUME @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_pw__ASSUME_I1_J)). 132.20/30.71 thf(656,plain,((! [A:$o]: (refine579265252t_unit @ (refine23983189ASSUME @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 132.20/30.71 thf(658,plain,((refine579265252t_unit @ (refine23983189ASSUME @ $false))),inference(instance,[status(thm)],[656])). 132.20/30.71 thf(1558,plain,((~ (top_to177290092t_unit = (refine23983189ASSUME @ $false)))),inference(rewrite,[status(thm)],[658,330])). 132.20/30.71 thf(1559,plain,((~ (top_to177290092t_unit = (refine23983189ASSUME @ $false)))),inference(simp,[status(thm)],[1558])). 132.20/30.71 thf(1560,plain,(((refine23983189ASSUME @ $false) != top_to177290092t_unit)),inference(lifteq,[status(thm)],[1559])). 132.20/30.71 thf(84,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > refine787176636t_unit),D:refine787176636t_unit]: (((ord_le1051254044t_unit @ (C @ B) @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ (C @ E) @ (C @ F)) <= (ord_le1051254044t_unit @ E @ F))) => (ord_le1051254044t_unit @ (C @ A) @ D))) <= (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order__subst2)). 132.20/30.71 thf(625,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > refine787176636t_unit),D:refine787176636t_unit]: (((ord_le1051254044t_unit @ (C @ B) @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ (C @ E) @ (C @ F)) | ~ (ord_le1051254044t_unit @ E @ F))) => (ord_le1051254044t_unit @ (C @ A) @ D))) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 132.20/30.71 thf(238,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: ((A = B) => (((C = D) => (ord_le519537037nres_a @ A @ D)) <= (ord_le519537037nres_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_ord__eq__le__eq__trans)). 132.20/30.71 thf(1178,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a]: ((A = B) => (((C = D) => (ord_le519537037nres_a @ A @ D)) | ~ (ord_le519537037nres_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 132.20/30.71 thf(231,axiom,((! [A:(a > $o)]: (ord_le519537037nres_a @ bot_bo529555393nres_a @ (refine1198353288_RES_a @ (collect_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_SUCCEED__rule)). 132.20/30.71 thf(1159,plain,((! [A:(a > $o)]: (ord_le519537037nres_a @ bot_bo529555393nres_a @ (refine1198353288_RES_a @ (collect_a @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 132.20/30.71 thf(64,axiom,((! [A:refine787176636t_unit,B:(refine787176636t_unit > refine787176636t_unit),C:refine787176636t_unit,D:refine787176636t_unit]: ((((ord_le1051254044t_unit @ A @ (B @ D)) <= (! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) <= (ord_le1051254044t_unit @ E @ F)))) <= (ord_le1051254044t_unit @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ord__eq__le__subst)). 132.20/30.71 thf(544,plain,((! [A:refine787176636t_unit,B:(refine787176636t_unit > refine787176636t_unit),C:refine787176636t_unit,D:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ (B @ D)) | ~ (! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) | ~ (ord_le1051254044t_unit @ E @ F))) | ~ (ord_le1051254044t_unit @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 132.20/30.71 thf(545,plain,((! [A:refine787176636t_unit,B:(refine787176636t_unit > refine787176636t_unit),C:refine787176636t_unit]: (! [D:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ (B @ D)) | ~ (! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) | ~ (ord_le1051254044t_unit @ E @ F))) | ~ (ord_le1051254044t_unit @ C @ D)) | ~ (A = (B @ C))))),inference(miniscope,[status(thm)],[544])). 132.20/30.71 thf(547,plain,(! [D:refine787176636t_unit,C:refine787176636t_unit,B:(refine787176636t_unit > refine787176636t_unit),A:refine787176636t_unit] : ((ord_le1051254044t_unit @ A @ (B @ D)) | (ord_le1051254044t_unit @ (sk20 @ D @ C @ (B) @ A) @ (sk21 @ D @ C @ (B) @ A)) | (~ (ord_le1051254044t_unit @ C @ D)) | (~ (A = (B @ C))))),inference(cnf,[status(esa)],[545])). 132.20/30.71 thf(550,plain,(! [D:refine787176636t_unit,C:refine787176636t_unit,B:(refine787176636t_unit > refine787176636t_unit),A:refine787176636t_unit] : ((A != (B @ C)) | (ord_le1051254044t_unit @ A @ (B @ D)) | (ord_le1051254044t_unit @ (sk20 @ D @ C @ (B) @ A) @ (sk21 @ D @ C @ (B) @ A)) | (~ (ord_le1051254044t_unit @ C @ D)))),inference(lifteq,[status(thm)],[547])). 132.20/30.71 thf(551,plain,(! [C:refine787176636t_unit,B:refine787176636t_unit,A:(refine787176636t_unit > refine787176636t_unit)] : ((ord_le1051254044t_unit @ (A @ B) @ (A @ C)) | (ord_le1051254044t_unit @ (sk20 @ C @ B @ (A) @ (A @ B)) @ (sk21 @ C @ B @ (A) @ (A @ B))) | (~ (ord_le1051254044t_unit @ B @ C)))),inference(simp,[status(thm)],[550])). 132.20/30.71 thf(263,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:a]: (((refine1001002027nres_a @ B @ C) <= (refine1001002027nres_a @ A @ C)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_pwD2)). 132.20/30.71 thf(1281,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:a]: ((refine1001002027nres_a @ B @ C) | ~ (refine1001002027nres_a @ A @ C) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 132.20/30.71 thf(289,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((refine412683989fail_a @ A) <= (refine412683989fail_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_pwD1)). 132.20/30.71 thf(1392,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((refine412683989fail_a @ A) | ~ (refine412683989fail_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 132.20/30.71 thf(12501,plain,(! [A:refine787176636t_unit] : ((ord_le1051254044t_unit @ A @ top_to177290092t_unit))),inference(simp,[status(thm)],[12500])). 132.20/30.71 thf(12571,plain,(! [A:refine787176636t_unit] : ((ord_le1051254044t_unit @ A @ top_to177290092t_unit))),inference(simp,[status(thm)],[12501])). 132.20/30.71 thf(167,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit]: ((A = B) => ((ord_le1051254044t_unit @ B @ C) => ((C = D) => (ord_le1051254044t_unit @ A @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_ord__eq__le__eq__trans)). 132.20/30.71 thf(916,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit]: ((A = B) => ((ord_le1051254044t_unit @ B @ C) => ((C = D) => (ord_le1051254044t_unit @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 132.20/30.71 thf(469,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (refine558004794t_unit @ A @ (sk12 @ B @ A))) | (~ (refine579265252t_unit @ B)) | (ord_le1051254044t_unit @ B @ A))),inference(cnf,[status(esa)],[466])). 132.20/30.71 thf(13549,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (refine558004794t_unit @ A @ (sk12 @ B @ A))) | (~ (~ (top_to177290092t_unit = B))) | (ord_le1051254044t_unit @ B @ A))),inference(rewrite,[status(thm)],[469,330])). 132.20/30.71 thf(13550,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (refine558004794t_unit @ A @ (sk12 @ B @ A))) | (top_to177290092t_unit = B) | (ord_le1051254044t_unit @ B @ A))),inference(simp,[status(thm)],[13549])). 132.20/30.71 thf(13551,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((top_to177290092t_unit = B) | (~ (refine558004794t_unit @ A @ (sk12 @ B @ A))) | (ord_le1051254044t_unit @ B @ A))),inference(lifteq,[status(thm)],[13550])). 132.20/30.71 thf(147,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:$o]: ((ord_le516598614nres_a @ A @ B) => ((refine412683989fail_a @ (B @ C)) => (refine412683989fail_a @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_nofail__antimono__fun)). 132.20/30.71 thf(852,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:$o]: ((ord_le516598614nres_a @ (A) @ (B)) => ((refine412683989fail_a @ (B @ C)) => (refine412683989fail_a @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 132.20/30.71 thf(657,plain,((refine579265252t_unit @ (refine23983189ASSUME @ $true))),inference(instance,[status(thm)],[656])). 132.20/30.71 thf(1553,plain,((~ (top_to177290092t_unit = (refine23983189ASSUME @ $true)))),inference(rewrite,[status(thm)],[657,330])). 132.20/30.71 thf(1554,plain,((~ (top_to177290092t_unit = (refine23983189ASSUME @ $true)))),inference(simp,[status(thm)],[1553])). 132.20/30.71 thf(1555,plain,(((refine23983189ASSUME @ $true) != top_to177290092t_unit)),inference(lifteq,[status(thm)],[1554])). 132.20/30.71 thf(74,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ A @ C) <= (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_ord__le__eq__trans)). 132.20/30.71 thf(583,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 132.20/30.71 thf(141,axiom,((! [A:product_unit]: ((refine558004794t_unit @ (refine1420258419t_unit @ A)) = (= @ product_unit @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_inres__simps_I3_J)). 132.20/30.71 thf(830,plain,((! [A:product_unit]: ((refine558004794t_unit @ (refine1420258419t_unit @ A)) = (= @ product_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 132.20/30.71 thf(145,axiom,(((= @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_eq__iff)). 132.20/30.71 thf(842,plain,(((= @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 132.20/30.71 thf(72,axiom,((! [A:set_a,B:set_a]: (((ord_less_eq_set_a @ B @ A) => (B = A)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_dual__order_Oantisym)). 132.20/30.71 thf(578,plain,((! [A:set_a,B:set_a]: (((ord_less_eq_set_a @ B @ A) => (B = A)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 132.20/30.71 thf(176,axiom,((refine558004794t_unit = (^ [A:refine787176636t_unit,B:product_unit]: (ord_le1051254044t_unit @ (refine1420258419t_unit @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_inres__def)). 132.20/30.71 thf(948,plain,(((refine558004794t_unit) = (^ [A:refine787176636t_unit,B:product_unit]: (ord_le1051254044t_unit @ (refine1420258419t_unit @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 132.20/30.71 thf(275,axiom,((! [A:set_a]: (refine464223677AILi_a != (refine1198353288_RES_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_nres_Odistinct_I1_J)). 132.20/30.71 thf(1328,plain,((! [A:set_a]: ~ (refine464223677AILi_a = (refine1198353288_RES_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 132.20/30.71 thf(285,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((A = B) <= (ord_le519537037nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_order__class_Oorder_Oantisym)). 132.20/30.71 thf(1375,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((A = B) | ~ (ord_le519537037nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 132.20/30.71 thf(116,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: (((ord_le516598614nres_a @ A @ C) <= (ord_le516598614nres_a @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_ord__eq__le__trans)). 132.20/30.71 thf(725,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (A) @ (C)) | ~ (ord_le516598614nres_a @ (B) @ (C)) | ~ ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 132.20/30.71 thf(81,axiom,((! [A:a,B:set_a,C:set_a]: (((~ (member_a @ A @ C)) => (((insert_a @ A @ B) = (insert_a @ A @ C)) = (B = C))) <= (~ (member_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_insert__ident)). 132.20/30.71 thf(610,plain,((! [A:a,B:set_a,C:set_a]: (((~ (member_a @ A @ C)) => (((insert_a @ A @ B) = (insert_a @ A @ C)) = (B = C))) | (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 132.20/30.71 thf(33,axiom,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((A = (B @ C)) => (((ord_less_eq_set_a @ A @ (B @ D)) <= (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_a @ E @ F)))) <= (ord_less_eq_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_ord__eq__le__subst)). 132.20/30.71 thf(415,plain,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((A = (B @ C)) => ((ord_less_eq_set_a @ A @ (B @ D)) | ~ (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_a @ E @ F))) | ~ (ord_less_eq_set_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 132.20/30.71 thf(416,plain,((! [A:set_a,B:(set_a > set_a),C:set_a]: ((A = (B @ C)) => (! [D:set_a]: ((ord_less_eq_set_a @ A @ (B @ D)) | ~ (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_a @ E @ F))) | ~ (ord_less_eq_set_a @ C @ D)))))),inference(miniscope,[status(thm)],[415])). 132.20/30.71 thf(417,plain,(! [D:set_a,C:set_a,B:(set_a > set_a),A:set_a] : ((~ (A = (B @ C))) | (ord_less_eq_set_a @ A @ (B @ D)) | (~ (ord_less_eq_set_a @ (B @ (sk2 @ D @ C @ (B) @ A)) @ (B @ (sk3 @ D @ C @ (B) @ A)))) | (~ (ord_less_eq_set_a @ C @ D)))),inference(cnf,[status(esa)],[416])). 132.20/30.71 thf(419,plain,(! [D:set_a,C:set_a,B:(set_a > set_a),A:set_a] : ((A != (B @ C)) | (ord_less_eq_set_a @ A @ (B @ D)) | (~ (ord_less_eq_set_a @ (B @ (sk2 @ D @ C @ (B) @ A)) @ (B @ (sk3 @ D @ C @ (B) @ A)))) | (~ (ord_less_eq_set_a @ C @ D)))),inference(lifteq,[status(thm)],[417])). 132.20/30.71 thf(420,plain,(! [C:set_a,B:set_a,A:(set_a > set_a)] : ((ord_less_eq_set_a @ (A @ B) @ (A @ C)) | (~ (ord_less_eq_set_a @ (A @ (sk2 @ C @ B @ (A) @ (A @ B))) @ (A @ (sk3 @ C @ B @ (A) @ (A @ B))))) | (~ (ord_less_eq_set_a @ B @ C)))),inference(simp,[status(thm)],[419])). 132.20/30.71 thf(2896,plain,(~ (b) | ((ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ (phi)))) != (ord_le519537037nres_a @ s1 @ (refine1198353288_RES_a @ (collect_a @ (phi)))))),inference(paramod_ordered,[status(thm)],[1427,327])). 132.20/30.71 thf(2904,plain,(~ (b) | ((if_Ref1724547303nres_a @ b @ s1 @ s2) != s1) | ((refine1198353288_RES_a @ (collect_a @ (phi))) != (refine1198353288_RES_a @ (collect_a @ (phi))))),inference(simp,[status(thm)],[2896])). 132.20/30.71 thf(2906,plain,(~ (b) | ((if_Ref1724547303nres_a @ b @ s1 @ s2) != s1)),inference(simp,[status(thm)],[2904])). 132.20/30.71 thf(7860,plain,(! [C:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (~ (sk7 @ (A))) | (C @ (order_245837199nres_a @ (A))) | ~ (b) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != s1) | ((A @ (sk9 @ (C) @ B @ (A))) != b))),inference(paramod_ordered,[status(thm)],[453,2906])). 132.20/30.71 thf(8287,plain,(! [A:(($o > refine424419629nres_a) > $o)] : (~ (b) | (~ (sk7 @ (^ [B:($o > refine424419629nres_a)]: (b)))) | (A @ (order_245837199nres_a @ (^ [B:($o > refine424419629nres_a)]: (b)))) | ~ (b) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != s1))),inference(pre_uni,[status(thm)],[7860:[bind(A, $thf(^ [D:($o > refine424419629nres_a)]: (b)))]])). 132.20/30.71 thf(8548,plain,(! [A:(($o > refine424419629nres_a) > $o)] : (~ (b) | (~ (sk7 @ (^ [B:($o > refine424419629nres_a)]: (b)))) | (A @ (order_245837199nres_a @ (^ [B:($o > refine424419629nres_a)]: (b)))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != s1))),inference(simp,[status(thm)],[8287])). 132.20/30.71 thf(11834,plain,(! [B:a,A:(($o > refine424419629nres_a) > $o)] : (~ (b) | (~ (sk7 @ (^ [C:($o > refine424419629nres_a)]: (b)))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != s1) | ((A @ (order_245837199nres_a @ (^ [C:($o > refine424419629nres_a)]: (b)))) != (bot_bot_a_o @ B)))),inference(paramod_ordered,[status(thm)],[8548,1537])). 132.20/30.71 thf(11923,plain,(~ (b) | (~ (sk7 @ (^ [A:($o > refine424419629nres_a)]: (b)))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != s1)),inference(pre_uni,[status(thm)],[11834:[bind(A, $thf(^ [D:($o > refine424419629nres_a)]: (bot_bot_a_o @ (C @ D)))),bind(B, $thf(C @ (order_245837199nres_a @ (^ [D:($o > refine424419629nres_a)]: (b)))))]])). 132.20/30.71 thf(318,axiom,((! [A:set_a,B:set_a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_nres__order__simps_I5_J)). 132.20/30.71 thf(1498,plain,((! [A:set_a,B:set_a]: ((ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ B)) = (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 132.20/30.71 thf(14858,plain,(! [A:a] : (((member_a @ A @ top_top_set_a) != (member_a @ sk235 @ (uminus_uminus_set_a @ (collect_a @ (^ [B:a]: ($true)))))))),inference(paramod_ordered,[status(thm)],[677,14594])). 132.20/30.71 thf(14903,plain,(! [A:a] : ((A != sk235) | ((uminus_uminus_set_a @ (collect_a @ (^ [B:a]: ($true)))) != top_top_set_a))),inference(simp,[status(thm)],[14858])). 132.20/30.71 thf(14914,plain,(((uminus_uminus_set_a @ (collect_a @ (^ [A:a]: ($true)))) != top_top_set_a)),inference(simp,[status(thm)],[14903])). 132.20/30.71 thf(51,axiom,((! [A:set_a]: ((ord_less_eq_set_a @ A @ bot_bot_set_a) <= (! [B:a]: ~ (member_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_subset__emptyI)). 132.20/30.71 thf(488,plain,((! [A:set_a]: ((ord_less_eq_set_a @ A @ bot_bot_set_a) | ~ (! [B:a]: ~ (member_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 132.20/30.71 thf(265,axiom,((! [A:a,B:set_a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ B)) = (member_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_nres__order__simps_I21_J)). 132.20/30.71 thf(1292,plain,((! [A:a,B:set_a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ B)) = (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 132.20/30.71 thf(98,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((if_Ref1369692790t_unit @ $false @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T)). 132.20/30.71 thf(669,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((if_Ref1369692790t_unit @ $false @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 132.20/30.71 thf(90,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((if_o_R1705037948nres_a @ $true @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T)). 132.20/30.71 thf(642,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((if_o_R1705037948nres_a @ $true @ A @ B) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 132.20/30.71 thf(524,plain,((! [A:set_a,B:(refine787176636t_unit > set_a),C:refine787176636t_unit]: (! [D:refine787176636t_unit]: ((ord_le1051254044t_unit @ C @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) | ~ (ord_le1051254044t_unit @ E @ F))) => (ord_less_eq_set_a @ A @ (B @ D)))) | ~ (ord_less_eq_set_a @ A @ (B @ C))))),inference(miniscope,[status(thm)],[523])). 132.20/30.71 thf(526,plain,(! [D:refine787176636t_unit,C:refine787176636t_unit,B:(refine787176636t_unit > set_a),A:set_a] : ((~ (ord_le1051254044t_unit @ C @ D)) | (ord_le1051254044t_unit @ (sk15 @ D @ C @ (B) @ A) @ (sk16 @ D @ C @ (B) @ A)) | (ord_less_eq_set_a @ A @ (B @ D)) | (~ (ord_less_eq_set_a @ A @ (B @ C))))),inference(cnf,[status(esa)],[524])). 132.20/30.71 thf(183,axiom,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) = (A = bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_all__not__in__conv)). 132.20/30.71 thf(970,plain,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) = (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 132.20/30.71 thf(112,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((! [C:product_unit]: ((refine579265252t_unit @ A) => ((refine558004794t_unit @ A @ C) <= (refine558004794t_unit @ B @ C)))) => (ord_le1051254044t_unit @ B @ A)) <= ((refine579265252t_unit @ B) <= (refine579265252t_unit @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_pw__leI_H)). 132.20/30.71 thf(706,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((! [C:product_unit]: ((refine579265252t_unit @ A) => ((refine558004794t_unit @ A @ C) | ~ (refine558004794t_unit @ B @ C)))) => (ord_le1051254044t_unit @ B @ A)) | ~ ((refine579265252t_unit @ B) | ~ (refine579265252t_unit @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 132.20/30.71 thf(295,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:$o]: ((ord_le516598614nres_a @ A @ B) => (ord_le519537037nres_a @ (A @ C) @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_le__funE)). 132.20/30.71 thf(1419,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:$o]: ((ord_le516598614nres_a @ (A) @ (B)) => (ord_le519537037nres_a @ (A @ C) @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 132.20/30.71 thf(45,axiom,(((= @ ($o > refine424419629nres_a)) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) & (ord_le516598614nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_order__class_Oorder_Oeq__iff)). 132.20/30.71 thf(470,plain,(((= @ ($o > refine424419629nres_a)) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) & (ord_le516598614nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 132.20/30.71 thf(471,plain,(((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) & (ord_le516598614nres_a @ B @ A))) = (= @ ($o > refine424419629nres_a)))),inference(lifteq,[status(thm)],[470])). 132.20/30.71 thf(105,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) => ((ord_le516598614nres_a @ B @ C) => (ord_le516598614nres_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_order_Otrans)). 132.20/30.71 thf(686,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (A) @ (B)) => ((ord_le516598614nres_a @ (B) @ (C)) => (ord_le516598614nres_a @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 132.20/30.71 thf(47,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a),D:($o > refine424419629nres_a),E:$o]: (((ord_le516598614nres_a @ C @ D) => (ord_le516598614nres_a @ (if_o_R1705037948nres_a @ E @ A @ C) @ (if_o_R1705037948nres_a @ E @ B @ D))) <= (ord_le516598614nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_order__mono__setup_Omono__if)). 132.20/30.71 thf(474,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a),D:($o > refine424419629nres_a),E:$o]: (((ord_le516598614nres_a @ (C) @ (D)) => (ord_le516598614nres_a @ (if_o_R1705037948nres_a @ E @ A @ C) @ (if_o_R1705037948nres_a @ E @ B @ D))) | ~ (ord_le516598614nres_a @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 132.20/30.71 thf(475,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: (! [C:($o > refine424419629nres_a),D:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (C) @ (D)) => (! [E:$o]: (ord_le516598614nres_a @ (if_o_R1705037948nres_a @ E @ A @ C) @ (if_o_R1705037948nres_a @ E @ B @ D)))) | ~ (ord_le516598614nres_a @ (A) @ (B))))),inference(miniscope,[status(thm)],[474])). 132.20/30.71 thf(476,plain,(! [E:$o,D:($o > refine424419629nres_a),C:($o > refine424419629nres_a),B:($o > refine424419629nres_a),A:($o > refine424419629nres_a)] : ((~ (ord_le516598614nres_a @ (C) @ (D))) | (ord_le516598614nres_a @ (if_o_R1705037948nres_a @ E @ A @ C) @ (if_o_R1705037948nres_a @ E @ B @ D)) | (~ (ord_le516598614nres_a @ (A) @ (B))))),inference(cnf,[status(esa)],[475])). 132.20/30.71 thf(198,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((ord_le519537037nres_a @ A @ B) = C) => (((~ ((A = refine464223677AILi_a) => ((? [D:set_a]: (B = (refine1198353288_RES_a @ D))) => (C)))) <= (! [D:set_a]: ((! [E:set_a]: ((C = (~ (ord_less_eq_set_a @ D @ E))) <= (B = (refine1198353288_RES_a @ E)))) <= (A = (refine1198353288_RES_a @ D))))) <= ((~ (C)) <= (B = refine464223677AILi_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_less__eq__nres_Oelims_I1_J)). 132.20/30.71 thf(1016,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:$o]: (((ord_le519537037nres_a @ A @ B) = C) => (~ ((A = refine464223677AILi_a) => ((? [D:set_a]: (B = (refine1198353288_RES_a @ D))) => (C))) | ~ (! [D:set_a]: (! [E:set_a]: ((C = (~ (ord_less_eq_set_a @ D @ E))) | ~ (B = (refine1198353288_RES_a @ E))) | ~ (A = (refine1198353288_RES_a @ D)))) | ~ (~ (C) | ~ (B = refine464223677AILi_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 132.20/30.71 thf(246,axiom,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a]: (((! [C:refine424419629nres_a]: ((ord_le519537037nres_a @ C @ B) <= (A @ C))) => ((order_1714329108nres_a @ A) = B)) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Greatest__equality)). 132.20/30.71 thf(1207,plain,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a]: (((! [C:refine424419629nres_a]: ((ord_le519537037nres_a @ C @ B) | ~ (A @ C))) => ((order_1714329108nres_a @ (A)) = B)) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 132.20/30.71 thf(83,axiom,((! [A:a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (insert_a @ A @ B) @ C) = ((ord_less_eq_set_a @ B @ C) & (member_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_insert__subset)). 132.20/30.71 thf(622,plain,((! [A:a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (insert_a @ A @ B) @ C) = ((ord_less_eq_set_a @ B @ C) & (member_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 132.20/30.71 thf(58,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ A) <= (refine579265252t_unit @ A)) => (ord_le1051254044t_unit @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_le__nofailI)). 132.20/30.71 thf(515,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ A) | ~ (refine579265252t_unit @ A)) => (ord_le1051254044t_unit @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 132.20/30.71 thf(303,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > refine424419629nres_a),D:(a > refine424419629nres_a)]: (((! [E:a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ E) @ A) => (ord_le519537037nres_a @ (C @ E) @ (D @ E)))) => (ord_le519537037nres_a @ (refine436832838nd_a_a @ A @ C) @ (refine436832838nd_a_a @ B @ D))) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J)). 132.20/30.71 thf(1451,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > refine424419629nres_a),D:(a > refine424419629nres_a)]: (((! [E:a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ E) @ A) => (ord_le519537037nres_a @ (C @ E) @ (D @ E)))) => (ord_le519537037nres_a @ (refine436832838nd_a_a @ A @ (C)) @ (refine436832838nd_a_a @ B @ (D)))) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 132.20/30.71 thf(326,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))) => (ord_le519537037nres_a @ (C @ A) @ D)) <= (ord_le519537037nres_a @ (C @ B) @ D)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_order__subst2)). 132.20/30.71 thf(1530,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: (((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))) => (ord_le519537037nres_a @ (C @ A) @ D)) | ~ (ord_le519537037nres_a @ (C @ B) @ D) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 132.20/30.71 thf(259,axiom,((! [A:set_a,B:a]: ((refine1312857699nres_a @ (refine1198353288_RES_a @ A) @ B) = (member_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_nf__inres__RES)). 132.20/30.71 thf(1266,plain,((! [A:set_a,B:a]: ((refine1312857699nres_a @ (refine1198353288_RES_a @ A) @ B) = (member_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 132.20/30.71 thf(386,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((refine579265252t_unit @ B) | ~ (refine579265252t_unit @ A)) => (! [C:(product_unit > refine787176636t_unit)]: (((refine579265252t_unit @ B) => (! [D:product_unit]: ((refine558004794t_unit @ B @ D) => (ord_le1051254044t_unit @ (C @ D) @ A)))) => (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A)))))),inference(miniscope,[status(thm)],[385])). 132.20/30.71 thf(391,plain,(! [C:(product_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (refine579265252t_unit @ B)) | (refine558004794t_unit @ B @ (sk1 @ (C) @ B @ A)) | (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A))),inference(cnf,[status(esa)],[386])). 132.20/30.71 thf(2353,plain,(! [C:(product_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (~ (top_to177290092t_unit = B))) | (refine558004794t_unit @ B @ (sk1 @ (C) @ B @ A)) | (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A))),inference(rewrite,[status(thm)],[391,330])). 132.20/30.71 thf(2354,plain,(! [C:(product_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((top_to177290092t_unit = B) | (refine558004794t_unit @ B @ (sk1 @ (C) @ B @ A)) | (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A))),inference(simp,[status(thm)],[2353])). 132.20/30.71 thf(2355,plain,(! [C:(product_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((top_to177290092t_unit = B) | (refine558004794t_unit @ B @ (sk1 @ (C) @ B @ A)) | (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A))),inference(lifteq,[status(thm)],[2354])). 132.20/30.71 thf(202,axiom,((! [A:set_a,B:set_a]: (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_nres_Oinject)). 132.20/30.71 thf(1050,plain,((! [A:set_a,B:set_a]: (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 132.20/30.71 thf(69,axiom,((! [A:refine787176636t_unit,B:(refine787176636t_unit > refine787176636t_unit),C:refine787176636t_unit,D:refine787176636t_unit]: (((ord_le1051254044t_unit @ C @ D) => ((ord_le1051254044t_unit @ A @ (B @ D)) <= (! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) <= (ord_le1051254044t_unit @ E @ F))))) <= (ord_le1051254044t_unit @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_order__subst1)). 132.20/30.71 thf(569,plain,((! [A:refine787176636t_unit,B:(refine787176636t_unit > refine787176636t_unit),C:refine787176636t_unit,D:refine787176636t_unit]: (((ord_le1051254044t_unit @ C @ D) => ((ord_le1051254044t_unit @ A @ (B @ D)) | ~ (! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) | ~ (ord_le1051254044t_unit @ E @ F))))) | ~ (ord_le1051254044t_unit @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 132.20/30.71 thf(6537,plain,(! [A:refine424419629nres_a] : ((? [B:set_a]: (A = (refine1198353288_RES_a @ B))) | ((refine412683989fail_a @ bot_bo529555393nres_a) != (refine412683989fail_a @ A)))),inference(paramod_ordered,[status(thm)],[1810,1722])). 132.20/30.71 thf(6538,plain,((? [A:set_a]: (bot_bo529555393nres_a = (refine1198353288_RES_a @ A)))),inference(pattern_uni,[status(thm)],[6537:[bind(A, $thf(bot_bo529555393nres_a))]])). 132.20/30.71 thf(6566,plain,((bot_bo529555393nres_a = (refine1198353288_RES_a @ sk189))),inference(cnf,[status(esa)],[6538])). 132.20/30.71 thf(6567,plain,(((refine1198353288_RES_a @ sk189) = bot_bo529555393nres_a)),inference(lifteq,[status(thm)],[6566])). 132.20/30.71 thf(6899,plain,(! [A:set_a] : (((refine1822134885_RES_a @ bot_bo529555393nres_a) = A) | ((refine1198353288_RES_a @ sk189) != (refine1198353288_RES_a @ A)))),inference(paramod_ordered,[status(thm)],[6567,1369])). 132.20/30.71 thf(6900,plain,(((refine1822134885_RES_a @ bot_bo529555393nres_a) = sk189)),inference(pattern_uni,[status(thm)],[6899:[bind(A, $thf(sk189))]])). 132.20/30.71 thf(6988,plain,((sk189 = bot_bot_set_a)),inference(rewrite,[status(thm)],[6900,2692])). 132.20/30.71 thf(54,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((B = C) => (ord_le1051254044t_unit @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ord__le__eq__trans)). 132.20/30.71 thf(503,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((B = C) => (ord_le1051254044t_unit @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 132.20/30.71 thf(110,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((ord_le1051254044t_unit @ C @ A) => (ord_le1051254044t_unit @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_dual__order_Otrans)). 132.20/30.71 thf(701,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((ord_le1051254044t_unit @ C @ A) => (ord_le1051254044t_unit @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 132.20/30.71 thf(8945,plain,(! [B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (sk7 @ (A)) | ((^ [C:($o > refine424419629nres_a),D:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (C @ $false) @ (D @ $false)) & (ord_le519537037nres_a @ (C @ $true) @ (D @ $true)))) = (ord_le516598614nres_a)) | (~ (A @ (sk8 @ B @ (A)))))),inference(paramod_ordered,[status(thm)],[454,1234])). 132.20/30.71 thf(9230,plain,(~ ($true) | (sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))) = (ord_le516598614nres_a))),inference(pre_uni,[status(thm)],[8945:[bind(A, $thf(^ [C:($o > refine424419629nres_a)]: ($true)))]])). 132.20/30.71 thf(9348,plain,((sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))) = (ord_le516598614nres_a))),inference(simp,[status(thm)],[9230])). 132.20/30.71 thf(188,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: (((ord_le516598614nres_a @ A @ C) <= (ord_le516598614nres_a @ B @ C)) <= (ord_le516598614nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_order__trans)). 132.20/30.71 thf(984,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (A) @ (C)) | ~ (ord_le516598614nres_a @ (B) @ (C)) | ~ (ord_le516598614nres_a @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 132.20/30.71 thf(14007,plain,(((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ bot_bot_set_a))) != (^ [A:a]: ($true)))),inference(simp,[status(thm)],[13986])). 132.20/30.71 thf(14667,plain,(((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a)) != (^ [A:a]: ($true)))),inference(rewrite,[status(thm)],[14007,1158])). 132.20/30.71 thf(14668,plain,((~ (ord_le519537037nres_a @ (refine2063221604TURN_a @ sk236) @ bot_bo529555393nres_a))),inference(func_ext,[status(esa)],[14667])). 132.20/30.71 thf(14669,plain,((~ ((refine2063221604TURN_a @ sk236) = bot_bo529555393nres_a))),inference(rewrite,[status(thm)],[14668,1366])). 132.20/30.71 thf(14670,plain,(((refine2063221604TURN_a @ sk236) != bot_bo529555393nres_a)),inference(lifteq,[status(thm)],[14669])). 132.20/30.71 thf(7,axiom,((! [A:(product_unit > refine787176636t_unit)]: ((refine681446406t_unit @ bot_bo658782032t_unit @ A) = bot_bo658782032t_unit))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_ibind__strict_I1_J)). 132.20/30.71 thf(341,plain,((! [A:(product_unit > refine787176636t_unit)]: ((refine681446406t_unit @ bot_bo658782032t_unit @ (A)) = bot_bo658782032t_unit))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 132.20/30.71 thf(342,plain,(! [A:(product_unit > refine787176636t_unit)] : (((refine681446406t_unit @ bot_bo658782032t_unit @ (A)) = bot_bo658782032t_unit))),inference(cnf,[status(esa)],[341])). 132.20/30.71 thf(343,plain,(! [A:(product_unit > refine787176636t_unit)] : (((refine681446406t_unit @ bot_bo658782032t_unit @ (A)) = bot_bo658782032t_unit))),inference(lifteq,[status(thm)],[342])). 132.20/30.71 thf(13221,plain,(! [B:a,A:set_a] : (((collect_a @ (^ [C:a]: (member_a @ C @ A))) != bot_bot_set_a) | (A != (insert_a @ B @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[13209,1956])). 132.20/30.71 thf(13222,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a)))) != bot_bot_set_a))),inference(pattern_uni,[status(thm)],[13221:[bind(A, $thf(insert_a @ C @ bot_bot_set_a)),bind(B, $thf(C))]])). 132.20/30.71 thf(13436,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a)))) != bot_bot_set_a))),inference(simp,[status(thm)],[13222])). 132.20/30.71 thf(14,axiom,((! [A:refine787176636t_unit]: (ord_le1051254044t_unit @ bot_bo658782032t_unit @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_bot_Oextremum)). 132.20/30.71 thf(360,plain,((! [A:refine787176636t_unit]: (ord_le1051254044t_unit @ bot_bo658782032t_unit @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 132.20/30.71 thf(134,axiom,((! [A:set_a,B:set_a]: ((if_set_a @ $false @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Set__Oset_Itf__a_J_T)). 132.20/30.71 thf(805,plain,((! [A:set_a,B:set_a]: ((if_set_a @ $false @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 132.20/30.71 thf(55,axiom,((! [A:product_unit]: (refine579265252t_unit @ (refine1420258419t_unit @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_nofail__simps_I3_J)). 132.20/30.71 thf(508,plain,((! [A:product_unit]: (refine579265252t_unit @ (refine1420258419t_unit @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 132.20/30.71 thf(13993,plain,(! [B:set_a,A:set_a] : ((~ (ord_less_eq_set_a @ B @ A)) | (~ (ord_less_eq_set_a @ A @ B)) | (B != bot_bot_set_a) | (A != (collect_a @ (^ [C:a]: ($true)))))),inference(paramod_ordered,[status(thm)],[395,13983])). 132.20/30.71 thf(13994,plain,(! [A:set_a] : ((~ (ord_less_eq_set_a @ A @ (collect_a @ (^ [B:a]: ($true))))) | (~ (ord_less_eq_set_a @ (collect_a @ (^ [B:a]: ($true))) @ A)) | (A != bot_bot_set_a))),inference(pattern_uni,[status(thm)],[13993:[bind(A, $thf(collect_a @ (^ [C:a]: ($true)))),bind(B, $thf(B))]])). 132.20/30.71 thf(14008,plain,((~ (ord_less_eq_set_a @ bot_bot_set_a @ (collect_a @ (^ [A:a]: ($true))))) | (~ (ord_less_eq_set_a @ (collect_a @ (^ [A:a]: ($true))) @ bot_bot_set_a))),inference(simp,[status(thm)],[13994])). 132.20/30.71 thf(168,axiom,((! [A:a,B:set_a]: ((member_a @ A @ (uminus_uminus_set_a @ B)) <= (~ (member_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_ComplI)). 132.20/30.71 thf(921,plain,((! [A:a,B:set_a]: ((member_a @ A @ (uminus_uminus_set_a @ B)) | (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 132.20/30.71 thf(63,axiom,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ A @ B) => (((ord_less_eq_set_a @ (C @ A) @ D) <= (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F))))) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_ord__le__eq__subst)). 132.20/30.71 thf(536,plain,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ (C @ A) @ D) | ~ (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 132.20/30.71 thf(537,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => (! [C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ (C @ A) @ D) | ~ (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D)))))),inference(miniscope,[status(thm)],[536])). 132.20/30.71 thf(538,plain,(! [D:set_a,C:(set_a > set_a),B:set_a,A:set_a] : ((~ (ord_less_eq_set_a @ A @ B)) | (ord_less_eq_set_a @ (C @ A) @ D) | (ord_less_eq_set_a @ (sk18 @ D @ (C) @ B @ A) @ (sk19 @ D @ (C) @ B @ A)) | (~ ((C @ B) = D)))),inference(cnf,[status(esa)],[537])). 132.20/30.71 thf(540,plain,(! [D:set_a,C:(set_a > set_a),B:set_a,A:set_a] : (((C @ B) != D) | (~ (ord_less_eq_set_a @ A @ B)) | (ord_less_eq_set_a @ (C @ A) @ D) | (ord_less_eq_set_a @ (sk18 @ D @ (C) @ B @ A) @ (sk19 @ D @ (C) @ B @ A)))),inference(lifteq,[status(thm)],[538])). 132.20/30.71 thf(541,plain,(! [C:(set_a > set_a),B:set_a,A:set_a] : ((~ (ord_less_eq_set_a @ A @ B)) | (ord_less_eq_set_a @ (C @ A) @ (C @ B)) | (ord_less_eq_set_a @ (sk18 @ (C @ B) @ (C) @ B @ A) @ (sk19 @ (C @ B) @ (C) @ B @ A)))),inference(simp,[status(thm)],[540])). 132.20/30.71 thf(28,axiom,((! [A:refine424419629nres_a,B:(a > refine787176636t_unit),C:refine787176636t_unit]: ((ord_le1051254044t_unit @ (refine96995669t_unit @ A @ B) @ C) = (((refine412683989fail_a @ A) <= (refine579265252t_unit @ C)) & ! [D:a]: (((refine412683989fail_a @ A) & (refine1001002027nres_a @ A @ D)) => (ord_le1051254044t_unit @ (B @ D) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_pw__bind__le__iff)). 132.20/30.71 thf(398,plain,((! [A:refine424419629nres_a,B:(a > refine787176636t_unit),C:refine787176636t_unit]: ((ord_le1051254044t_unit @ (refine96995669t_unit @ A @ (B)) @ C) = (((refine412683989fail_a @ A) | ~ (refine579265252t_unit @ C)) & ! [D:a]: (((refine412683989fail_a @ A) & (refine1001002027nres_a @ A @ D)) => (ord_le1051254044t_unit @ (B @ D) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 132.20/30.71 thf(16252,plain,(! [B:a,A:a] : (((member_a @ A @ (insert_a @ B @ top_top_set_a)) != (member_a @ sk235 @ (sk14 @ (collect_a @ (^ [C:a]: ($true))) @ sk235))))),inference(paramod_ordered,[status(thm)],[6171,16188])). 132.20/30.71 thf(16282,plain,(! [B:a,A:a] : ((A != sk235) | ((insert_a @ B @ top_top_set_a) != (sk14 @ (collect_a @ (^ [C:a]: ($true))) @ sk235)))),inference(simp,[status(thm)],[16252])). 132.20/30.71 thf(16296,plain,(! [A:a] : (((insert_a @ A @ top_top_set_a) != (sk14 @ (collect_a @ (^ [B:a]: ($true))) @ sk235)))),inference(simp,[status(thm)],[16282])). 132.20/30.71 thf(131,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((if_Ref1369692790t_unit @ $true @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T)). 132.20/30.71 thf(794,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((if_Ref1369692790t_unit @ $true @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 132.20/30.71 thf(114,axiom,((! [A:refine787176636t_unit,B:(set_a > refine787176636t_unit),C:set_a,D:set_a]: ((((! [E:set_a,F:set_a]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_a @ E @ F))) => (ord_le1051254044t_unit @ A @ (B @ D))) <= (ord_less_eq_set_a @ C @ D)) <= (ord_le1051254044t_unit @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_order__subst1)). 132.20/30.71 thf(718,plain,((! [A:refine787176636t_unit,B:(set_a > refine787176636t_unit),C:set_a,D:set_a]: (((! [E:set_a,F:set_a]: ((ord_le1051254044t_unit @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_a @ E @ F))) => (ord_le1051254044t_unit @ A @ (B @ D))) | ~ (ord_less_eq_set_a @ C @ D) | ~ (ord_le1051254044t_unit @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 132.20/30.71 thf(240,axiom,((! [A:set_a]: (((refine1198353288_RES_a @ A) = bot_bo529555393nres_a) = (A = bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_nres__more__simps_I2_J)). 132.20/30.71 thf(1187,plain,((! [A:set_a]: (((refine1198353288_RES_a @ A) = bot_bo529555393nres_a) = (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 132.20/30.71 thf(100,axiom,((refine1312857699nres_a = (^ [A:refine424419629nres_a,B:a]: ((refine1001002027nres_a @ A @ B) & (refine412683989fail_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_nf__inres__def)). 132.20/30.71 thf(674,plain,(((refine1312857699nres_a) = (^ [A:refine424419629nres_a,B:a]: ((refine1001002027nres_a @ A @ B) & (refine412683989fail_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 132.20/30.71 thf(12674,plain,(! [A:a] : (((refine2063221604TURN_a) != (refine2063221604TURN_a)) | ((^ [B:a]: (refine2063221604TURN_a @ A)) != (^ [B:a]: (bot_bo529555393nres_a))))),inference(simp,[status(thm)],[12673])). 132.20/30.71 thf(12676,plain,(! [A:a] : (((^ [B:a]: (refine2063221604TURN_a @ A)) != (^ [B:a]: (bot_bo529555393nres_a))))),inference(simp,[status(thm)],[12674])). 132.20/30.71 thf(12677,plain,(! [A:a] : (((refine2063221604TURN_a @ A) != bot_bo529555393nres_a))),inference(func_ext,[status(esa)],[12676])). 132.20/30.71 thf(170,axiom,((! [A:product_unit,B:product_unit]: ((ord_le1051254044t_unit @ (refine1420258419t_unit @ A) @ (refine1420258419t_unit @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_nres__order__simps_I20_J)). 132.20/30.71 thf(926,plain,((! [A:product_unit,B:product_unit]: ((ord_le1051254044t_unit @ (refine1420258419t_unit @ A) @ (refine1420258419t_unit @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 132.20/30.71 thf(164,axiom,((! [A:refine424419629nres_a,B:(a > refine424419629nres_a)]: ((refine412683989fail_a @ (refine436832838nd_a_a @ A @ B)) = (! [C:a]: ((refine1001002027nres_a @ A @ C) => (refine412683989fail_a @ (B @ C))) & (refine412683989fail_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_pw__bind__nofail)). 132.20/30.71 thf(906,plain,((! [A:refine424419629nres_a,B:(a > refine424419629nres_a)]: ((refine412683989fail_a @ (refine436832838nd_a_a @ A @ (B))) = (! [C:a]: ((refine1001002027nres_a @ A @ C) => (refine412683989fail_a @ (B @ C))) & (refine412683989fail_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 132.20/30.71 thf(34,axiom,((! [A:set_a,B:set_a,C:set_a,D:set_a,E:$o]: (((ord_less_eq_set_a @ (if_set_a @ E @ A @ C) @ (if_set_a @ E @ B @ D)) <= (ord_less_eq_set_a @ C @ D)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_order__mono__setup_Omono__if)). 132.20/30.71 thf(423,plain,((! [A:set_a,B:set_a,C:set_a,D:set_a,E:$o]: ((ord_less_eq_set_a @ (if_set_a @ E @ A @ C) @ (if_set_a @ E @ B @ D)) | ~ (ord_less_eq_set_a @ C @ D) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 132.20/30.71 thf(424,plain,((! [A:set_a,B:set_a]: (! [C:set_a,D:set_a]: (! [E:$o]: (ord_less_eq_set_a @ (if_set_a @ E @ A @ C) @ (if_set_a @ E @ B @ D)) | ~ (ord_less_eq_set_a @ C @ D)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(miniscope,[status(thm)],[423])). 132.20/30.71 thf(425,plain,(! [E:$o,D:set_a,C:set_a,B:set_a,A:set_a] : ((ord_less_eq_set_a @ (if_set_a @ E @ A @ C) @ (if_set_a @ E @ B @ D)) | (~ (ord_less_eq_set_a @ C @ D)) | (~ (ord_less_eq_set_a @ A @ B)))),inference(cnf,[status(esa)],[424])). 132.20/30.71 thf(57,axiom,(((= @ ($o > refine424419629nres_a)) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) & (ord_le516598614nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_eq__iff)). 132.20/30.71 thf(513,plain,(((= @ ($o > refine424419629nres_a)) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) & (ord_le516598614nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 132.20/30.71 thf(139,axiom,((! [A:product_unit,B:product_unit]: (((refine1420258419t_unit @ A) = (refine1420258419t_unit @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_nres__more__simps_I6_J)). 132.20/30.71 thf(824,plain,((! [A:product_unit,B:product_unit]: (((refine1420258419t_unit @ A) = (refine1420258419t_unit @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 132.20/30.71 thf(3363,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a)))) != (collect_a @ (^ [B:a]: ($false)))))),inference(paramod_ordered,[status(thm)],[1589,3352])). 132.20/30.71 thf(3376,plain,(! [A:a] : (((^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a))) != (^ [B:a]: ($false))))),inference(simp,[status(thm)],[3363])). 132.20/30.71 thf(3387,plain,(! [B:a,A:set_a] : (((^ [C:a]: (member_a @ C @ (collect_a @ (^ [D:a]: (member_a @ D @ A))))) != (^ [C:a]: ($false))) | (A != (insert_a @ B @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[1479,3376])). 132.20/30.71 thf(3388,plain,(! [A:a] : (((^ [B:a]: (member_a @ B @ (collect_a @ (^ [C:a]: (member_a @ C @ (insert_a @ A @ bot_bot_set_a)))))) != (^ [B:a]: ($false))))),inference(pattern_uni,[status(thm)],[3387:[bind(A, $thf(insert_a @ C @ bot_bot_set_a)),bind(B, $thf(C))]])). 132.20/30.71 thf(3401,plain,(! [A:a] : (((^ [B:a]: (member_a @ B @ (collect_a @ (^ [C:a]: (member_a @ C @ (insert_a @ A @ bot_bot_set_a)))))) != (^ [B:a]: ($false))))),inference(simp,[status(thm)],[3388])). 132.20/30.71 thf(3475,plain,(! [A:a] : (((refine1001002027nres_a @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a)))))) != (^ [B:a]: ($false))))),inference(rewrite,[status(thm)],[3401,1150])). 132.20/30.71 thf(4874,plain,(! [A:a] : (((^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (collect_a @ (^ [C:a]: (member_a @ C @ (insert_a @ A @ bot_bot_set_a))))))) != (^ [B:a]: ($false))))),inference(rewrite,[status(thm)],[3475,1585])). 132.20/30.71 thf(312,axiom,((! [A:set_a,B:set_a]: (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nres__more__simps_I4_J)). 132.20/30.71 thf(1483,plain,((! [A:set_a,B:set_a]: (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 132.20/30.71 thf(3077,plain,((~ (ord_less_eq_set_a @ bot_bot_set_a @ top_top_set_a)) | ((ord_less_eq_set_a @ top_top_set_a @ bot_bot_set_a) != (ord_less_eq_set_a @ bot_bot_set_a @ top_top_set_a)) | ~ ($true)),inference(eqfactor_ordered,[status(thm)],[2996])). 132.20/30.71 thf(3079,plain,((~ (ord_less_eq_set_a @ bot_bot_set_a @ top_top_set_a)) | ((ord_less_eq_set_a @ top_top_set_a @ bot_bot_set_a) != (ord_less_eq_set_a @ bot_bot_set_a @ top_top_set_a))),inference(simp,[status(thm)],[3077])). 132.20/30.71 thf(15044,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true)))))) != (collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ bot_bot_set_a)))))),inference(simp,[status(thm)],[15022])). 132.20/30.71 thf(17695,plain,(((collect_a @ (^ [A:a]: (member_a @ A @ (collect_a @ (^ [B:a]: ($true)))))) != (collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a))))),inference(rewrite,[status(thm)],[15044,1158])). 132.20/30.71 thf(119,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: (((A = B) <= (ord_le516598614nres_a @ B @ A)) <= (ord_le516598614nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_order__class_Oorder_Oantisym)). 132.20/30.71 thf(745,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: (((A) = (B)) | ~ (ord_le516598614nres_a @ (B) @ (A)) | ~ (ord_le516598614nres_a @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 132.20/30.71 thf(70,axiom,(((= @ ($o > refine424419629nres_a)) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) & (ord_le516598614nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_dual__order_Oeq__iff)). 132.20/30.71 thf(573,plain,(((= @ ($o > refine424419629nres_a)) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) & (ord_le516598614nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 132.20/30.71 thf(106,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_antisym)). 132.20/30.71 thf(689,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 132.20/30.71 thf(39,axiom,((! [A:($o > refine424419629nres_a)]: (ord_le516598614nres_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_dual__order_Orefl)). 132.20/30.71 thf(444,plain,((! [A:($o > refine424419629nres_a)]: (ord_le516598614nres_a @ (A) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 132.20/30.71 thf(1371,plain,((! [A:refine424419629nres_a]: (! [B:refine424419629nres_a]: (ord_le519537037nres_a @ B @ A) | ~ (A = top_to231829469nres_a)))),inference(miniscope,[status(thm)],[1370])). 132.20/30.71 thf(1372,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((ord_le519537037nres_a @ B @ A) | (~ (A = top_to231829469nres_a)))),inference(cnf,[status(esa)],[1371])). 132.20/30.71 thf(1373,plain,(! [B:refine424419629nres_a,A:refine424419629nres_a] : ((A != top_to231829469nres_a) | (ord_le519537037nres_a @ B @ A))),inference(lifteq,[status(thm)],[1372])). 132.20/30.71 thf(1374,plain,(! [A:refine424419629nres_a] : ((ord_le519537037nres_a @ A @ top_to231829469nres_a))),inference(simp,[status(thm)],[1373])). 132.20/30.71 thf(20,axiom,((refine579265252t_unit = (^ [A:refine787176636t_unit]: (A != top_to177290092t_unit)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_nofail__def)). 132.20/30.71 thf(375,plain,(((refine579265252t_unit) = (^ [A:refine787176636t_unit]: ~ (A = top_to177290092t_unit)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 132.20/30.71 thf(262,axiom,((! [A:set_a,B:(a > $o)]: ((! [C:a]: ((B @ C) <= (member_a @ C @ A))) => (ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ (collect_a @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_RES__rule)). 132.20/30.71 thf(1278,plain,((! [A:set_a,B:(a > $o)]: ((! [C:a]: ((B @ C) | ~ (member_a @ C @ A))) => (ord_le519537037nres_a @ (refine1198353288_RES_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 132.20/30.71 thf(3474,plain,(! [A:a] : (((refine1001002027nres_a @ (refine1198353288_RES_a @ (insert_a @ A @ bot_bot_set_a))) != (^ [B:a]: ($false))))),inference(rewrite,[status(thm)],[3376,1150])). 132.20/30.71 thf(3859,plain,(! [A:a] : (((^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (insert_a @ A @ bot_bot_set_a)))) != (^ [B:a]: ($false))))),inference(rewrite,[status(thm)],[3474,1585])). 132.20/30.71 thf(11578,plain,(! [A:a] : (((^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine2063221604TURN_a @ A))) != (^ [B:a]: ($false))))),inference(rewrite,[status(thm)],[3859,1744])). 132.20/30.71 thf(229,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((B = A) <= (ord_le519537037nres_a @ B @ A)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_dual__order_Oantisym)). 132.20/30.71 thf(1154,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((B = A) | ~ (ord_le519537037nres_a @ B @ A) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 132.20/30.71 thf(195,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ A) = (refine412683989fail_a @ B)) => ((! [C:a]: ((refine1001002027nres_a @ A @ C) = (refine1001002027nres_a @ B @ C))) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_pw__eqI)). 132.20/30.71 thf(1007,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ A) = (refine412683989fail_a @ B)) => ((! [C:a]: ((refine1001002027nres_a @ A @ C) = (refine1001002027nres_a @ B @ C))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 132.20/30.71 thf(843,plain,(((^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))) = (= @ set_a))),inference(lifteq,[status(thm)],[842])). 132.20/30.71 thf(127,axiom,((! [A:a,B:a]: ((A = B) <= (member_a @ A @ (insert_a @ B @ bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_singletonD)). 132.20/30.71 thf(772,plain,((! [A:a,B:a]: ((A = B) | ~ (member_a @ A @ (insert_a @ B @ bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 132.20/30.71 thf(288,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) <= ((! [C:a]: ((refine1001002027nres_a @ A @ C) <= (refine1001002027nres_a @ B @ C)) & (refine412683989fail_a @ B)) <= (refine412683989fail_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_pw__leI)). 132.20/30.71 thf(1388,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) | ~ ((! [C:a]: ((refine1001002027nres_a @ A @ C) | ~ (refine1001002027nres_a @ B @ C)) & (refine412683989fail_a @ B)) | ~ (refine412683989fail_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 132.20/30.71 thf(153,axiom,((ord_le1051254044t_unit = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((refine579265252t_unit @ B) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) => (refine558004794t_unit @ B @ C)) & (refine579265252t_unit @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_pw__le__iff)). 132.20/30.71 thf(875,plain,(((ord_le1051254044t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((refine579265252t_unit @ B) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) => (refine558004794t_unit @ B @ C)) & (refine579265252t_unit @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 132.20/30.71 thf(958,plain,(((ord_le1960259811nres_a) = (^ [A:($o > ($o > refine424419629nres_a)),B:($o > ($o > refine424419629nres_a))]: ((ord_le516598614nres_a @ (A @ $true) @ (B @ $true)) & (ord_le516598614nres_a @ (A @ $false) @ (B @ $false)))))),inference(lifteq,[status(thm)],[957])). 132.20/30.71 thf(257,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > ($o > refine424419629nres_a)),D:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ A @ B) => (((ord_le516598614nres_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le516598614nres_a @ (C @ E) @ (C @ F)) <= (ord_le519537037nres_a @ E @ F)))) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_ord__le__eq__subst)). 132.20/30.71 thf(1256,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > ($o > refine424419629nres_a)),D:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ A @ B) => ((ord_le516598614nres_a @ (C @ A) @ (D)) | ~ (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le516598614nres_a @ (C @ E) @ (C @ F)) | ~ (ord_le519537037nres_a @ E @ F))) | ~ ((C @ B) = (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 132.20/30.71 thf(250,axiom,((! [A:a,B:set_a]: (((refine2063221604TURN_a @ A) = (refine1198353288_RES_a @ B)) = ((insert_a @ A @ bot_bot_set_a) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_nres__more__simps_I5_J)). 132.20/30.71 thf(1226,plain,((! [A:a,B:set_a]: (((refine2063221604TURN_a @ A) = (refine1198353288_RES_a @ B)) = ((insert_a @ A @ bot_bot_set_a) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 132.20/30.71 thf(298,axiom,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((! [D:refine424419629nres_a]: (A @ D @ refine464223677AILi_a)) => (((A @ B @ C) <= (! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E)))) <= (! [D:set_a]: (A @ refine464223677AILi_a @ (refine1198353288_RES_a @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_sup__nres_Oinduct)). 132.20/30.71 thf(1428,plain,((! [A:(refine424419629nres_a > (refine424419629nres_a > $o)),B:refine424419629nres_a,C:refine424419629nres_a]: ((! [D:refine424419629nres_a]: (A @ D @ refine464223677AILi_a)) => ((A @ B @ C) | ~ (! [D:set_a,E:set_a]: (A @ (refine1198353288_RES_a @ D) @ (refine1198353288_RES_a @ E))) | ~ (! [D:set_a]: (A @ refine464223677AILi_a @ (refine1198353288_RES_a @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 132.20/30.71 thf(381,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: (! [C:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (C) @ (B)) | ~ (ord_le516598614nres_a @ (C) @ (A))) | ~ (ord_le516598614nres_a @ (A) @ (B))))),inference(miniscope,[status(thm)],[380])). 132.20/30.71 thf(382,plain,(! [C:($o > refine424419629nres_a),B:($o > refine424419629nres_a),A:($o > refine424419629nres_a)] : ((ord_le516598614nres_a @ (C) @ (B)) | (~ (ord_le516598614nres_a @ (C) @ (A))) | (~ (ord_le516598614nres_a @ (A) @ (B))))),inference(cnf,[status(esa)],[381])). 132.20/30.71 thf(205,axiom,((! [A:refine424419629nres_a,B:(a > refine424419629nres_a),C:refine424419629nres_a]: ((ord_le519537037nres_a @ (refine436832838nd_a_a @ A @ B) @ C) = (((refine412683989fail_a @ A) <= (refine412683989fail_a @ C)) & ! [D:a]: ((ord_le519537037nres_a @ (B @ D) @ C) <= ((refine1001002027nres_a @ A @ D) & (refine412683989fail_a @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_pw__bind__le__iff)). 132.20/30.71 thf(1058,plain,((! [A:refine424419629nres_a,B:(a > refine424419629nres_a),C:refine424419629nres_a]: ((ord_le519537037nres_a @ (refine436832838nd_a_a @ A @ (B)) @ C) = (((refine412683989fail_a @ A) | ~ (refine412683989fail_a @ C)) & ! [D:a]: ((ord_le519537037nres_a @ (B @ D) @ C) | ~ ((refine1001002027nres_a @ A @ D) & (refine412683989fail_a @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 132.20/30.71 thf(276,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ C) => (ord_le519537037nres_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_order_Otrans)). 132.20/30.71 thf(1332,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ C) => (ord_le519537037nres_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 132.20/30.71 thf(5,axiom,((! [A:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ bot_bo658782032t_unit) = (A = bot_bo658782032t_unit)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_bot_Oextremum__unique)). 132.20/30.71 thf(335,plain,((! [A:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ bot_bo658782032t_unit) = (A = bot_bo658782032t_unit)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 132.20/30.71 thf(399,plain,(! [C:refine787176636t_unit,B:(a > refine787176636t_unit),A:refine424419629nres_a] : (((ord_le1051254044t_unit @ (refine96995669t_unit @ A @ (B)) @ C) = (((refine412683989fail_a @ A) | ~ (refine579265252t_unit @ C)) & ! [D:a]: (((refine412683989fail_a @ A) & (refine1001002027nres_a @ A @ D)) => (ord_le1051254044t_unit @ (B @ D) @ C)))))),inference(cnf,[status(esa)],[398])). 132.20/30.71 thf(400,plain,(! [C:refine787176636t_unit,B:(a > refine787176636t_unit),A:refine424419629nres_a] : (((ord_le1051254044t_unit @ (refine96995669t_unit @ A @ (B)) @ C) = (((refine412683989fail_a @ A) | ~ (refine579265252t_unit @ C)) & ! [D:a]: (((refine412683989fail_a @ A) & (refine1001002027nres_a @ A @ D)) => (ord_le1051254044t_unit @ (B @ D) @ C)))))),inference(lifteq,[status(thm)],[399])). 132.20/30.71 thf(3090,plain,(! [C:refine787176636t_unit,B:(a > refine787176636t_unit),A:refine424419629nres_a] : (((ord_le1051254044t_unit @ (refine96995669t_unit @ A @ (B)) @ C) = (((refine412683989fail_a @ A) | ~ (~ (top_to177290092t_unit = C))) & ! [D:a]: (((refine412683989fail_a @ A) & (refine1001002027nres_a @ A @ D)) => (ord_le1051254044t_unit @ (B @ D) @ C)))))),inference(rewrite,[status(thm)],[400,330])). 132.20/30.71 thf(3091,plain,(! [C:refine787176636t_unit,B:(a > refine787176636t_unit),A:refine424419629nres_a] : (((ord_le1051254044t_unit @ (refine96995669t_unit @ A @ (B)) @ C) = (((refine412683989fail_a @ A) | (top_to177290092t_unit = C)) & ! [D:a]: (((refine412683989fail_a @ A) & (refine1001002027nres_a @ A @ D)) => (ord_le1051254044t_unit @ (B @ D) @ C)))))),inference(simp,[status(thm)],[3090])). 132.20/30.71 thf(281,axiom,((! [A:refine424419629nres_a,B:(refine787176636t_unit > refine424419629nres_a),C:refine787176636t_unit,D:refine787176636t_unit]: ((A = (B @ C)) => ((ord_le1051254044t_unit @ C @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le519537037nres_a @ (B @ E) @ (B @ F)) <= (ord_le1051254044t_unit @ E @ F))) => (ord_le519537037nres_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_ord__eq__le__subst)). 132.20/30.71 thf(1356,plain,((! [A:refine424419629nres_a,B:(refine787176636t_unit > refine424419629nres_a),C:refine787176636t_unit,D:refine787176636t_unit]: ((A = (B @ C)) => ((ord_le1051254044t_unit @ C @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le519537037nres_a @ (B @ E) @ (B @ F)) | ~ (ord_le1051254044t_unit @ E @ F))) => (ord_le519537037nres_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 132.20/30.71 thf(99,axiom,((ord_less_eq_o_set_a = (^ [A:($o > set_a),B:($o > set_a)]: ((ord_less_eq_set_a @ (A @ $true) @ (B @ $true)) & (ord_less_eq_set_a @ (A @ $false) @ (B @ $false)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_le__rel__bool__arg__iff)). 132.20/30.71 thf(672,plain,(((ord_less_eq_o_set_a) = (^ [A:($o > set_a),B:($o > set_a)]: ((ord_less_eq_set_a @ (A @ $true) @ (B @ $true)) & (ord_less_eq_set_a @ (A @ $false) @ (B @ $false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 132.20/30.71 thf(224,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a,E:$o]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ C @ D) => (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ E @ A @ C) @ (if_Ref1724547303nres_a @ E @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_order__mono__setup_Omono__if)). 132.20/30.71 thf(1139,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a,D:refine424419629nres_a,E:$o]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ C @ D) => (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ E @ A @ C) @ (if_Ref1724547303nres_a @ E @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 132.20/30.71 thf(445,plain,(! [A:($o > refine424419629nres_a)] : ((ord_le516598614nres_a @ (A) @ (A)))),inference(cnf,[status(esa)],[444])). 132.20/30.71 thf(22195,plain,(! [B:a,A:a] : (((member_a @ A @ top_top_set_a) != (member_a @ sk235 @ (uminus_uminus_set_a @ (insert_a @ B @ (collect_a @ (^ [C:a]: ($true))))))))),inference(paramod_ordered,[status(thm)],[677,17189])). 132.20/30.71 thf(22266,plain,(! [B:a,A:a] : ((A != sk235) | ((uminus_uminus_set_a @ (insert_a @ B @ (collect_a @ (^ [C:a]: ($true))))) != top_top_set_a))),inference(simp,[status(thm)],[22195])). 132.20/30.71 thf(22298,plain,(! [A:a] : (((uminus_uminus_set_a @ (insert_a @ A @ (collect_a @ (^ [B:a]: ($true))))) != top_top_set_a))),inference(simp,[status(thm)],[22266])). 132.20/30.71 thf(174,axiom,((! [A:a,B:set_a,C:a,D:set_a]: ((~ (member_a @ A @ B)) => ((((insert_a @ A @ B) = (insert_a @ C @ D)) = (((? [E:set_a]: ((B = (insert_a @ C @ E)) & ~ (member_a @ A @ E) & (D = (insert_a @ A @ E)) & ~ (member_a @ C @ E))) <= (A != C)) & ((B = D) <= (A = C)))) <= (~ (member_a @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_insert__eq__iff)). 132.20/30.71 thf(936,plain,((! [A:a,B:set_a,C:a,D:set_a]: ((~ (member_a @ A @ B)) => ((((insert_a @ A @ B) = (insert_a @ C @ D)) = ((? [E:set_a]: ((B = (insert_a @ C @ E)) & ~ (member_a @ A @ E) & (D = (insert_a @ A @ E)) & ~ (member_a @ C @ E)) | (A = C)) & ((B = D) | ~ (A = C)))) | (member_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 132.20/30.71 thf(5282,plain,(~ (b) | (s1 != top_to231829469nres_a) | ((refine1198353288_RES_a @ (collect_a @ (phi))) != bot_bo529555393nres_a)),inference(rewrite,[status(thm)],[2903,4994])). 132.20/30.71 thf(52,axiom,((! [A:$o,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit,E:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ C) <= (A)) => ((ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ A @ B @ D) @ (if_Ref1369692790t_unit @ A @ C @ E)) <= ((ord_le1051254044t_unit @ D @ E) <= (~ (A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Refine__Misc_Oif__mono)). 132.20/30.71 thf(491,plain,((! [A:$o,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit,E:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ C) | ~ (A)) => ((ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ A @ B @ D) @ (if_Ref1369692790t_unit @ A @ C @ E)) | ~ ((ord_le1051254044t_unit @ D @ E) | (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 132.20/30.71 thf(494,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit]: (((ord_le1051254044t_unit @ A @ B) | ~ ($false)) => ((ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ $false @ A @ C) @ (if_Ref1369692790t_unit @ $false @ B @ D)) | ~ ((ord_le1051254044t_unit @ C @ D) | ($false)))))),inference(instance,[status(thm)],[491])). 132.20/30.71 thf(495,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit]: ((ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ $false @ A @ C) @ (if_Ref1369692790t_unit @ $false @ B @ D)) | ~ (ord_le1051254044t_unit @ C @ D)))),inference(simp,[status(thm)],[494])). 132.20/30.71 thf(498,plain,(! [D:refine787176636t_unit,C:refine787176636t_unit,B:refine787176636t_unit,A:refine787176636t_unit] : ((ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ $false @ A @ C) @ (if_Ref1369692790t_unit @ $false @ B @ D)) | (~ (ord_le1051254044t_unit @ C @ D)))),inference(cnf,[status(esa)],[495])). 132.20/30.71 thf(214,axiom,((! [A:refine424419629nres_a]: (((refine1198353288_RES_a @ (refine1822134885_RES_a @ A)) = A) <= (refine412683989fail_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_the__RES__inv)). 132.20/30.71 thf(1092,plain,((! [A:refine424419629nres_a]: (((refine1198353288_RES_a @ (refine1822134885_RES_a @ A)) = A) | ~ (refine412683989fail_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 132.20/30.71 thf(111,axiom,(((= @ refine787176636t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) & (ord_le1051254044t_unit @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dual__order_Oeq__iff)). 132.20/30.71 thf(704,plain,(((= @ refine787176636t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) & (ord_le1051254044t_unit @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 132.20/30.71 thf(6240,plain,(! [C:a,B:a,A:set_a] : (((member_a @ B @ (insert_a @ B @ A)) != (member_a @ C @ bot_bot_set_a)))),inference(paramod_ordered,[status(thm)],[441,479])). 132.20/30.71 thf(6253,plain,(! [C:a,B:a,A:set_a] : ((B != C) | ((insert_a @ B @ A) != bot_bot_set_a))),inference(simp,[status(thm)],[6240])). 132.20/30.71 thf(6261,plain,(! [B:a,A:set_a] : (((insert_a @ B @ A) != bot_bot_set_a))),inference(simp,[status(thm)],[6253])). 132.20/30.71 thf(8961,plain,(! [B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (sk7 @ (A)) | ((^ [C:($o > ($o > refine424419629nres_a)),D:($o > ($o > refine424419629nres_a))]: ((ord_le516598614nres_a @ (C @ $true) @ (D @ $true)) & (ord_le516598614nres_a @ (C @ $false) @ (D @ $false)))) = (ord_le1960259811nres_a)) | (~ (A @ (sk8 @ B @ (A)))))),inference(paramod_ordered,[status(thm)],[454,958])). 132.20/30.71 thf(9331,plain,(~ ($true) | (sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > ($o > refine424419629nres_a)),B:($o > ($o > refine424419629nres_a))]: ((ord_le516598614nres_a @ (A @ $true) @ (B @ $true)) & (ord_le516598614nres_a @ (A @ $false) @ (B @ $false)))) = (ord_le1960259811nres_a))),inference(pre_uni,[status(thm)],[8961:[bind(A, $thf(^ [C:($o > refine424419629nres_a)]: ($true)))]])). 132.20/30.71 thf(9439,plain,((sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > ($o > refine424419629nres_a)),B:($o > ($o > refine424419629nres_a))]: ((ord_le516598614nres_a @ (A @ $true) @ (B @ $true)) & (ord_le516598614nres_a @ (A @ $false) @ (B @ $false)))) = (ord_le1960259811nres_a))),inference(simp,[status(thm)],[9331])). 132.20/30.71 thf(79,axiom,((! [A:a,B:a,C:set_a]: ((member_a @ A @ (insert_a @ B @ C)) => ((member_a @ A @ C) <= (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_insertE)). 132.20/30.71 thf(604,plain,((! [A:a,B:a,C:set_a]: ((member_a @ A @ (insert_a @ B @ C)) => ((member_a @ A @ C) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 132.20/30.71 thf(1841,plain,(! [A:refine424419629nres_a] : (((ord_le519537037nres_a @ A @ top_to231829469nres_a) != (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ (collect_a @ (phi))))))),inference(paramod_ordered,[status(thm)],[1374,327])). 132.20/30.71 thf(1847,plain,(! [A:refine424419629nres_a] : ((A != (if_Ref1724547303nres_a @ b @ s1 @ s2)) | ((refine1198353288_RES_a @ (collect_a @ (phi))) != top_to231829469nres_a))),inference(simp,[status(thm)],[1841])). 132.20/30.71 thf(1853,plain,(((refine1198353288_RES_a @ (collect_a @ (phi))) != top_to231829469nres_a)),inference(simp,[status(thm)],[1847])). 132.20/30.71 thf(324,axiom,((! [A:refine424419629nres_a,B:a]: ((ord_le519537037nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ (= @ a @ B)))) => (ord_le519537037nres_a @ A @ (refine2063221604TURN_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_RETURN__to__SPEC__rule)). 132.20/30.71 thf(1524,plain,((! [A:refine424419629nres_a,B:a]: ((ord_le519537037nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ (= @ a @ B)))) => (ord_le519537037nres_a @ A @ (refine2063221604TURN_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 132.20/30.71 thf(118,axiom,((! [A:set_a,B:(refine787176636t_unit > set_a),C:refine787176636t_unit,D:refine787176636t_unit]: ((((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) <= (ord_le1051254044t_unit @ E @ F))) => (ord_less_eq_set_a @ A @ (B @ D))) <= (ord_le1051254044t_unit @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ord__eq__le__subst)). 132.20/30.71 thf(737,plain,((! [A:set_a,B:(refine787176636t_unit > set_a),C:refine787176636t_unit,D:refine787176636t_unit]: (((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) | ~ (ord_le1051254044t_unit @ E @ F))) => (ord_less_eq_set_a @ A @ (B @ D))) | ~ (ord_le1051254044t_unit @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 132.20/30.71 thf(36,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((refine579265252t_unit @ A) = (refine579265252t_unit @ B)) => ((A = B) <= (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_pw__eqI)). 132.20/30.71 thf(434,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((refine579265252t_unit @ A) = (refine579265252t_unit @ B)) => ((A = B) | ~ (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 132.20/30.71 thf(21,axiom,((refine579265252t_unit @ bot_bo658782032t_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_nofail__simps_I4_J)). 132.20/30.71 thf(377,plain,((refine579265252t_unit @ bot_bo658782032t_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 132.20/30.71 thf(315,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_dual__order_Orefl)). 132.20/30.71 thf(1492,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 132.20/30.71 thf(376,plain,(((refine579265252t_unit) = (^ [A:refine787176636t_unit]: ~ (A = top_to177290092t_unit)))),inference(lifteq,[status(thm)],[375])). 132.20/30.71 thf(1603,plain,(((^ [A:refine787176636t_unit]: ~ (top_to177290092t_unit = A)) = (^ [A:refine787176636t_unit]: ~ (A = top_to177290092t_unit)))),inference(rewrite,[status(thm)],[376,330])). 132.20/30.71 thf(15,axiom,((! [A:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ bot_bo658782032t_unit) = (A = bot_bo658782032t_unit)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_nres__order__simps_I2_J)). 132.20/30.71 thf(362,plain,((! [A:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ bot_bo658782032t_unit) = (A = bot_bo658782032t_unit)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 132.20/30.71 thf(451,plain,(! [B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (~ (ord_le516598614nres_a @ (sk8 @ B @ (A)) @ (B))) | (sk7 @ A))),inference(cnf,[status(esa)],[450])). 132.20/30.71 thf(68,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ B) <= (member_a @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_subset__iff)). 132.20/30.71 thf(567,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ B) | ~ (member_a @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 132.20/30.71 thf(226,axiom,((! [A:refine424419629nres_a,B:(($o > refine424419629nres_a) > refine424419629nres_a),C:($o > refine424419629nres_a),D:($o > refine424419629nres_a)]: (((ord_le516598614nres_a @ C @ D) => ((! [E:($o > refine424419629nres_a),F:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D)))) <= (ord_le519537037nres_a @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_order__subst1)). 132.20/30.71 thf(1144,plain,((! [A:refine424419629nres_a,B:(($o > refine424419629nres_a) > refine424419629nres_a),C:($o > refine424419629nres_a),D:($o > refine424419629nres_a)]: (((ord_le516598614nres_a @ (C) @ (D)) => ((! [E:($o > refine424419629nres_a),F:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (E) @ (F)) => (ord_le519537037nres_a @ (B @ (E)) @ (B @ (F))))) => (ord_le519537037nres_a @ A @ (B @ (D))))) | ~ (ord_le519537037nres_a @ A @ (B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 132.20/30.71 thf(77,axiom,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => ((member_a @ C @ B) <= (member_a @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_subsetD)). 132.20/30.71 thf(599,plain,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => ((member_a @ C @ B) | ~ (member_a @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 132.20/30.71 thf(300,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((partia906949161nres_a @ bot_bo529555393nres_a @ A @ B) => (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_flat__ord__compat_I1_J)). 132.20/30.71 thf(1439,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((partia906949161nres_a @ bot_bo529555393nres_a @ A @ B) => (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 132.20/30.71 thf(123,axiom,((ord_le1633311077t_unit = (^ [A:($o > refine787176636t_unit),B:($o > refine787176636t_unit)]: ((ord_le1051254044t_unit @ (A @ $true) @ (B @ $true)) & (ord_le1051254044t_unit @ (A @ $false) @ (B @ $false)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_le__rel__bool__arg__iff)). 132.20/30.71 thf(758,plain,(((ord_le1633311077t_unit) = (^ [A:($o > refine787176636t_unit),B:($o > refine787176636t_unit)]: ((ord_le1051254044t_unit @ (A @ $true) @ (B @ $true)) & (ord_le1051254044t_unit @ (A @ $false) @ (B @ $false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 132.20/30.71 thf(50,axiom,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((A = B) => (((C = D) => (ord_less_eq_set_a @ A @ D)) <= (ord_less_eq_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_ord__eq__le__eq__trans)). 132.20/30.71 thf(483,plain,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((A = B) => (((C = D) => (ord_less_eq_set_a @ A @ D)) | ~ (ord_less_eq_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 132.20/30.71 thf(274,axiom,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ top_to231829469nres_a @ A) => (A = top_to231829469nres_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_top_Oextremum__uniqueI)). 132.20/30.71 thf(1325,plain,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ top_to231829469nres_a @ A) => (A = top_to231829469nres_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 132.20/30.71 thf(894,plain,(! [A:refine424419629nres_a] : (((refine436832838nd_a_a @ A @ (refine2063221604TURN_a)) = A))),inference(cnf,[status(esa)],[893])). 132.20/30.71 thf(895,plain,(! [A:refine424419629nres_a] : (((refine436832838nd_a_a @ A @ (refine2063221604TURN_a)) = A))),inference(lifteq,[status(thm)],[894])). 132.20/30.71 thf(206,axiom,(((= @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_dual__order_Oeq__iff)). 132.20/30.71 thf(1061,plain,(((= @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 132.20/30.71 thf(220,axiom,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((((ord_le519537037nres_a @ A @ (B @ D)) <= (! [E:set_a,F:set_a]: ((ord_le519537037nres_a @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_a @ E @ F)))) <= (ord_less_eq_set_a @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_ord__eq__le__subst)). 132.20/30.71 thf(1112,plain,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le519537037nres_a @ A @ (B @ D)) | ~ (! [E:set_a,F:set_a]: ((ord_le519537037nres_a @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_a @ E @ F))) | ~ (ord_less_eq_set_a @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 132.20/30.71 thf(159,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((partia1658438072t_unit @ bot_bo658782032t_unit @ A @ B) = ((? [C:product_unit]: (refine558004794t_unit @ A @ C)) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C)) & ((refine579265252t_unit @ A) = (refine579265252t_unit @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_pw__flat__le__iff)). 132.20/30.71 thf(890,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((partia1658438072t_unit @ bot_bo658782032t_unit @ A @ B) = ((? [C:product_unit]: (refine558004794t_unit @ A @ C)) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C)) & ((refine579265252t_unit @ A) = (refine579265252t_unit @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 132.20/30.71 thf(1650,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((^ [C:refine787176636t_unit]: ~ (C = (refine681446406t_unit @ (refine1420258419t_unit @ A) @ B))) = (^ [C:refine787176636t_unit]: ~ (top_to177290092t_unit = C))) | ((B @ A) != top_to177290092t_unit))),inference(paramod_ordered,[status(thm)],[346,1603])). 132.20/30.71 thf(1667,plain,(! [A:product_unit] : (((^ [B:refine787176636t_unit]: ~ (B = (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (top_to177290092t_unit))))) = (^ [B:refine787176636t_unit]: ~ (top_to177290092t_unit = B))))),inference(pre_uni,[status(thm)],[1650:[bind(A, $thf(A)),bind(B, $thf(^ [C:product_unit]: (top_to177290092t_unit)))]])). 132.20/30.71 thf(17,axiom,((! [A:(product_unit > refine787176636t_unit)]: ((refine681446406t_unit @ bot_bo658782032t_unit @ A) = bot_bo658782032t_unit))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_bind__SUCCEED)). 132.20/30.71 thf(367,plain,((! [A:(product_unit > refine787176636t_unit)]: ((refine681446406t_unit @ bot_bo658782032t_unit @ (A)) = bot_bo658782032t_unit))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 132.20/30.71 thf(4177,plain,((~ (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ bot_bot_set_a))) | ((collect_a @ (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a))) != (collect_a @ (phi)))),inference(paramod_ordered,[status(thm)],[4020,327])). 132.20/30.71 thf(4195,plain,((~ (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ (refine1198353288_RES_a @ bot_bot_set_a))) | ((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a)) != (phi))),inference(simp,[status(thm)],[4177])). 132.20/30.71 thf(19737,plain,((~ (ord_le519537037nres_a @ (if_Ref1724547303nres_a @ b @ s1 @ s2) @ bot_bo529555393nres_a)) | ((phi) != (^ [A:a]: ((refine2063221604TURN_a @ A) = bot_bo529555393nres_a)))),inference(rewrite,[status(thm)],[4195,1158,1366])). 132.20/30.71 thf(166,axiom,((! [A:set_a,B:set_a]: ((A = B) => (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_eq__refl)). 132.20/30.71 thf(912,plain,((! [A:set_a,B:set_a]: ((A = B) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 132.20/30.71 thf(181,axiom,((! [A:a,B:a]: ((member_a @ A @ (insert_a @ B @ bot_bot_set_a)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_singleton__iff)). 132.20/30.71 thf(959,plain,((! [A:a,B:a]: ((member_a @ A @ (insert_a @ B @ bot_bot_set_a)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 132.20/30.71 thf(140,axiom,((! [A:refine787176636t_unit,B:(product_unit > refine787176636t_unit),C:refine787176636t_unit]: ((ord_le1051254044t_unit @ (refine681446406t_unit @ A @ B) @ C) = (((refine579265252t_unit @ C) => (refine579265252t_unit @ A)) & ! [D:product_unit]: ((ord_le1051254044t_unit @ (B @ D) @ C) <= ((refine579265252t_unit @ A) & (refine558004794t_unit @ A @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_pw__bind__le__iff)). 132.20/30.71 thf(827,plain,((! [A:refine787176636t_unit,B:(product_unit > refine787176636t_unit),C:refine787176636t_unit]: ((ord_le1051254044t_unit @ (refine681446406t_unit @ A @ (B)) @ C) = (((refine579265252t_unit @ C) => (refine579265252t_unit @ A)) & ! [D:product_unit]: ((ord_le1051254044t_unit @ (B @ D) @ C) | ~ ((refine579265252t_unit @ A) & (refine558004794t_unit @ A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 132.20/30.71 thf(1702,plain,(! [C:product_unit,B:(product_unit > refine787176636t_unit),A:product_unit] : ((~ (refine558004794t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) @ C)) | ((B @ A) != bot_bo658782032t_unit))),inference(paramod_ordered,[status(thm)],[346,1552])). 132.20/30.71 thf(1703,plain,(! [B:product_unit,A:product_unit] : ((~ (refine558004794t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (bot_bo658782032t_unit))) @ B)))),inference(pre_uni,[status(thm)],[1702:[bind(A, $thf(A)),bind(B, $thf(^ [D:product_unit]: (bot_bo658782032t_unit)))]])). 132.20/30.71 thf(1704,plain,(! [B:product_unit,A:product_unit] : ((~ (refine558004794t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (bot_bo658782032t_unit))) @ B)))),inference(simp,[status(thm)],[1703])). 132.20/30.71 thf(10925,plain,(! [A:product_unit] : ((~ (refine558004794t_unit @ bot_bo658782032t_unit @ A)))),inference(rewrite,[status(thm)],[1704,2592])). 132.20/30.71 thf(317,axiom,(((= @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_order__class_Oorder_Oeq__iff)). 132.20/30.71 thf(1496,plain,(((= @ refine424419629nres_a) = (^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 132.20/30.71 thf(4971,plain,(! [B:set_a,A:refine424419629nres_a] : ((~ (A = top_to231829469nres_a)) | ((ord_le519537037nres_a @ top_to231829469nres_a @ A) != (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ B))))),inference(paramod_ordered,[status(thm)],[1177,1521])). 132.20/30.71 thf(5003,plain,(! [B:set_a,A:refine424419629nres_a] : ((A != top_to231829469nres_a) | ((ord_le519537037nres_a @ top_to231829469nres_a @ A) != (ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ B))))),inference(lifteq,[status(thm)],[4971])). 132.20/30.71 thf(5017,plain,(! [A:set_a] : (((ord_le519537037nres_a @ refine464223677AILi_a @ (refine1198353288_RES_a @ A)) != (ord_le519537037nres_a @ top_to231829469nres_a @ top_to231829469nres_a)))),inference(simp,[status(thm)],[5003])). 132.20/30.71 thf(6180,plain,(! [A:set_a] : ((~ (ord_le519537037nres_a @ top_to231829469nres_a @ (refine1198353288_RES_a @ A))))),inference(rewrite,[status(thm)],[5017,4994,1100])). 132.20/30.71 thf(35,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > refine787176636t_unit),D:refine787176636t_unit]: ((((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ E @ F) => (ord_le1051254044t_unit @ (C @ E) @ (C @ F)))) => (ord_le1051254044t_unit @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_ord__le__eq__subst)). 132.20/30.71 thf(426,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > refine787176636t_unit),D:refine787176636t_unit]: (((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ E @ F) => (ord_le1051254044t_unit @ (C @ E) @ (C @ F)))) => (ord_le1051254044t_unit @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 132.20/30.71 thf(427,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (! [C:(refine787176636t_unit > refine787176636t_unit),D:refine787176636t_unit]: (((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ E @ F) => (ord_le1051254044t_unit @ (C @ E) @ (C @ F)))) => (ord_le1051254044t_unit @ (C @ A) @ D)) | ~ ((C @ B) = D)) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(miniscope,[status(thm)],[426])). 132.20/30.71 thf(428,plain,(! [D:refine787176636t_unit,C:(refine787176636t_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((ord_le1051254044t_unit @ (sk4 @ D @ (C) @ B @ A) @ (sk5 @ D @ (C) @ B @ A)) | (ord_le1051254044t_unit @ (C @ A) @ D) | (~ ((C @ B) = D)) | (~ (ord_le1051254044t_unit @ A @ B)))),inference(cnf,[status(esa)],[427])). 132.20/30.71 thf(430,plain,(! [D:refine787176636t_unit,C:(refine787176636t_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : (((C @ B) != D) | (ord_le1051254044t_unit @ (sk4 @ D @ (C) @ B @ A) @ (sk5 @ D @ (C) @ B @ A)) | (ord_le1051254044t_unit @ (C @ A) @ D) | (~ (ord_le1051254044t_unit @ A @ B)))),inference(lifteq,[status(thm)],[428])). 132.20/30.71 thf(431,plain,(! [C:(refine787176636t_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((ord_le1051254044t_unit @ (sk4 @ (C @ B) @ (C) @ B @ A) @ (sk5 @ (C @ B) @ (C) @ B @ A)) | (ord_le1051254044t_unit @ (C @ A) @ (C @ B)) | (~ (ord_le1051254044t_unit @ A @ B)))),inference(simp,[status(thm)],[430])). 132.20/30.71 thf(92,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((partia1658438072t_unit @ top_to177290092t_unit @ A @ B) = ((refine579265252t_unit @ A) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C)) & (refine579265252t_unit @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_pw__flat__ge__iff)). 132.20/30.71 thf(653,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((partia1658438072t_unit @ top_to177290092t_unit @ A @ B) = ((refine579265252t_unit @ A) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) = (refine558004794t_unit @ B @ C)) & (refine579265252t_unit @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 132.20/30.71 thf(200,axiom,((! [A:set_a]: ((bot_bo529555393nres_a = (refine1198353288_RES_a @ A)) = (A = bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_nres__more__simps_I1_J)). 132.20/30.71 thf(1044,plain,((! [A:set_a]: ((bot_bo529555393nres_a = (refine1198353288_RES_a @ A)) = (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 132.20/30.71 thf(255,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((if_Ref1724547303nres_a @ $true @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T)). 132.20/30.71 thf(1245,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((if_Ref1724547303nres_a @ $true @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 132.20/30.71 thf(455,plain,(! [D:($o > refine424419629nres_a),C:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (~ (sk7 @ A)) | (~ (A @ (D))) | (ord_le516598614nres_a @ (D) @ (sk9 @ (C) @ B @ (A))) | (C @ (order_245837199nres_a @ (A))))),inference(cnf,[status(esa)],[450])). 132.20/30.71 thf(157,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > set_a),D:set_a]: (((ord_less_eq_set_a @ (C @ B) @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) <= (ord_le1051254044t_unit @ E @ F))) => (ord_less_eq_set_a @ (C @ A) @ D))) <= (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_order__subst2)). 132.20/30.71 thf(883,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > set_a),D:set_a]: (((ord_less_eq_set_a @ (C @ B) @ D) => ((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) | ~ (ord_le1051254044t_unit @ E @ F))) => (ord_less_eq_set_a @ (C @ A) @ D))) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 132.20/30.71 thf(115,axiom,((! [A:product_unit,B:(product_unit > refine424419629nres_a)]: ((refine119808503unit_a @ (refine1420258419t_unit @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_nres__monad1)). 132.20/30.71 thf(722,plain,((! [A:product_unit,B:(product_unit > refine424419629nres_a)]: ((refine119808503unit_a @ (refine1420258419t_unit @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 132.20/30.71 thf(269,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine787176636t_unit),D:refine787176636t_unit]: ((((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1051254044t_unit @ (C @ E) @ (C @ F)) <= (ord_le519537037nres_a @ E @ F))) => (ord_le1051254044t_unit @ (C @ A) @ D)) <= (ord_le1051254044t_unit @ (C @ B) @ D)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_order__subst2)). 132.20/30.71 thf(1304,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine787176636t_unit),D:refine787176636t_unit]: (((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le1051254044t_unit @ (C @ E) @ (C @ F)) | ~ (ord_le519537037nres_a @ E @ F))) => (ord_le1051254044t_unit @ (C @ A) @ D)) | ~ (ord_le1051254044t_unit @ (C @ B) @ D) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 132.20/30.71 thf(96,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((ord_le1051254044t_unit @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_antisym)). 132.20/30.71 thf(663,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((ord_le1051254044t_unit @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 132.20/30.71 thf(212,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:$o]: ((ord_le519537037nres_a @ (A @ C) @ (B @ C)) <= (ord_le516598614nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_le__funD)). 132.20/30.71 thf(1081,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:$o]: ((ord_le519537037nres_a @ (A @ C) @ (B @ C)) | ~ (ord_le516598614nres_a @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 132.20/30.71 thf(17201,plain,(! [B:a,A:set_a] : (((collect_a @ (^ [C:a]: (member_a @ C @ A))) != bot_bot_set_a) | (A != (insert_a @ B @ (collect_a @ (^ [C:a]: ($true))))))),inference(paramod_ordered,[status(thm)],[13209,17171])). 132.20/30.71 thf(17202,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ (collect_a @ (^ [C:a]: ($true))))))) != bot_bot_set_a))),inference(pattern_uni,[status(thm)],[17201:[bind(A, $thf(insert_a @ C @ (collect_a @ (^ [D:a]: ($true))))),bind(B, $thf(C))]])). 132.20/30.71 thf(17244,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ (collect_a @ (^ [C:a]: ($true))))))) != bot_bot_set_a))),inference(simp,[status(thm)],[17202])). 132.20/30.71 thf(12,axiom,((bot_bo658782032t_unit != top_to177290092t_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_nres__inequalities_I4_J)). 132.20/30.71 thf(355,plain,((~ (bot_bo658782032t_unit = top_to177290092t_unit))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 132.20/30.71 thf(121,axiom,((! [A:set_a]: ((A = top_top_set_a) = (! [B:a]: (member_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_eq__UNIV__iff)). 132.20/30.71 thf(752,plain,((! [A:set_a]: ((A = top_top_set_a) = (! [B:a]: (member_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 132.20/30.71 thf(753,plain,(! [A:set_a] : (((A = top_top_set_a) = (! [B:a]: (member_a @ B @ A))))),inference(cnf,[status(esa)],[752])). 132.20/30.71 thf(754,plain,(! [A:set_a] : (((A = top_top_set_a) = (! [B:a]: (member_a @ B @ A))))),inference(lifteq,[status(thm)],[753])). 132.20/30.71 thf(489,plain,((! [A:set_a]: ((ord_less_eq_set_a @ A @ bot_bot_set_a) | ~ (~ (? [B:a]: (member_a @ B @ A)))))),inference(miniscope,[status(thm)],[488])). 132.20/30.71 thf(490,plain,(! [A:set_a] : ((ord_less_eq_set_a @ A @ bot_bot_set_a) | (member_a @ (sk13 @ A) @ A))),inference(cnf,[status(esa)],[489])). 132.20/30.71 thf(675,plain,(((refine1312857699nres_a) = (^ [A:refine424419629nres_a,B:a]: ((refine1001002027nres_a @ A @ B) & (refine412683989fail_a @ A))))),inference(lifteq,[status(thm)],[674])). 132.20/30.71 thf(234,axiom,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ B)) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_mem__Collect__eq)). 132.20/30.71 thf(1166,plain,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 132.20/30.71 thf(103,axiom,((! [A:a,B:a]: (((refine2063221604TURN_a @ A) = (refine2063221604TURN_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_nres__more__simps_I6_J)). 132.20/30.71 thf(680,plain,((! [A:a,B:a]: (((refine2063221604TURN_a @ A) = (refine2063221604TURN_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 132.20/30.71 thf(8981,plain,(! [B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (sk7 @ (A)) | ~ (b) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != s1) | ((A @ (sk8 @ B @ (A))) != b))),inference(paramod_ordered,[status(thm)],[454,2906])). 132.20/30.71 thf(9148,plain,(~ (b) | (sk7 @ (^ [A:($o > refine424419629nres_a)]: (b))) | ~ (b) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != s1)),inference(pre_uni,[status(thm)],[8981:[bind(A, $thf(^ [C:($o > refine424419629nres_a)]: (b)))]])). 132.20/30.71 thf(9514,plain,(~ (b) | (sk7 @ (^ [A:($o > refine424419629nres_a)]: (b))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != s1)),inference(simp,[status(thm)],[9148])). 132.20/30.71 thf(136,axiom,((! [A:set_a,B:a]: ((A = bot_bot_set_a) => (~ (member_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_equals0D)). 132.20/30.71 thf(812,plain,((! [A:set_a,B:a]: ((A = bot_bot_set_a) => (~ (member_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 132.20/30.71 thf(320,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((ord_le519537037nres_a @ B @ A) <= (! [C:a]: (((refine1001002027nres_a @ A @ C) <= (refine1001002027nres_a @ B @ C)) <= (refine412683989fail_a @ A)))) <= ((refine412683989fail_a @ A) => (refine412683989fail_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_pw__leI_H)). 132.20/30.71 thf(1509,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ B @ A) | ~ (! [C:a]: ((refine1001002027nres_a @ A @ C) | ~ (refine1001002027nres_a @ B @ C) | ~ (refine412683989fail_a @ A))) | ~ ((refine412683989fail_a @ A) => (refine412683989fail_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 132.20/30.71 thf(435,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((~ ((refine579265252t_unit @ A) = (refine579265252t_unit @ B))) | (A = B) | (~ ((refine558004794t_unit @ A @ (sk6 @ B @ A)) = (refine558004794t_unit @ B @ (sk6 @ B @ A)))))),inference(cnf,[status(esa)],[434])). 132.20/30.71 thf(436,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : (((refine579265252t_unit @ A) != (refine579265252t_unit @ B)) | (A = B) | ((refine558004794t_unit @ A @ (sk6 @ B @ A)) != (refine558004794t_unit @ B @ (sk6 @ B @ A))))),inference(lifteq,[status(thm)],[435])). 132.20/30.71 thf(5357,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : (((~ (top_to177290092t_unit = A)) != (~ (top_to177290092t_unit = B))) | (A = B) | ((refine558004794t_unit @ A @ (sk6 @ B @ A)) != (refine558004794t_unit @ B @ (sk6 @ B @ A))))),inference(rewrite,[status(thm)],[436,330])). 132.20/30.71 thf(5358,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : (((top_to177290092t_unit = A) != (top_to177290092t_unit = B)) | (A = B) | ((refine558004794t_unit @ A @ (sk6 @ B @ A)) != (refine558004794t_unit @ B @ (sk6 @ B @ A))))),inference(simp,[status(thm)],[5357])). 132.20/30.71 thf(43,axiom,((! [A:refine787176636t_unit,B:(set_a > refine787176636t_unit),C:set_a,D:set_a]: ((A = (B @ C)) => (((ord_le1051254044t_unit @ A @ (B @ D)) <= (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le1051254044t_unit @ (B @ E) @ (B @ F))))) <= (ord_less_eq_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_ord__eq__le__subst)). 132.20/30.71 thf(458,plain,((! [A:refine787176636t_unit,B:(set_a > refine787176636t_unit),C:set_a,D:set_a]: ((A = (B @ C)) => ((ord_le1051254044t_unit @ A @ (B @ D)) | ~ (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le1051254044t_unit @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_set_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 132.20/30.71 thf(525,plain,(! [D:refine787176636t_unit,C:refine787176636t_unit,B:(refine787176636t_unit > set_a),A:set_a] : ((~ (ord_le1051254044t_unit @ C @ D)) | (~ (ord_less_eq_set_a @ (B @ (sk15 @ D @ C @ (B) @ A)) @ (B @ (sk16 @ D @ C @ (B) @ A)))) | (ord_less_eq_set_a @ A @ (B @ D)) | (~ (ord_less_eq_set_a @ A @ (B @ C))))),inference(cnf,[status(esa)],[524])). 132.20/30.71 thf(148,axiom,((! [A:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a)]: (((! [C:($o > refine424419629nres_a)]: ((A @ C) => (ord_le516598614nres_a @ C @ B))) => ((order_245837199nres_a @ A) = B)) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Greatest__equality)). 132.20/30.71 thf(855,plain,((! [A:(($o > refine424419629nres_a) > $o),B:($o > refine424419629nres_a)]: (((! [C:($o > refine424419629nres_a)]: ((A @ (C)) => (ord_le516598614nres_a @ (C) @ (B)))) => ((order_245837199nres_a @ (A)) = (B))) | ~ (A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 132.20/30.71 thf(321,axiom,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ bot_bo529555393nres_a) => (A = bot_bo529555393nres_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_bot_Oextremum__uniqueI)). 132.20/30.71 thf(1516,plain,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ bot_bo529555393nres_a) => (A = bot_bo529555393nres_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 132.20/30.71 thf(152,axiom,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_empty__iff)). 132.20/30.71 thf(872,plain,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 132.20/30.71 thf(158,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((A = B) <= (ord_le1051254044t_unit @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_order__class_Oorder_Oantisym)). 132.20/30.71 thf(887,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((A = B) | ~ (ord_le1051254044t_unit @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 132.20/30.71 thf(32,axiom,((! [A:$o]: ((A = $true) | (A = $false)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T)). 132.20/30.71 thf(414,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 132.20/30.71 thf(705,plain,(((^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) & (ord_le1051254044t_unit @ B @ A))) = (= @ refine787176636t_unit))),inference(lifteq,[status(thm)],[704])). 132.20/30.71 thf(1610,plain,(! [A:set_a] : ((top_to231829469nres_a != bot_bo529555393nres_a) | ((refine1198353288_RES_a @ bot_bot_set_a) != (refine1198353288_RES_a @ A)))),inference(paramod_ordered,[status(thm)],[1158,1206])). 132.20/30.71 thf(1611,plain,((top_to231829469nres_a != bot_bo529555393nres_a)),inference(pattern_uni,[status(thm)],[1610:[bind(A, $thf(bot_bot_set_a))]])). 132.20/30.71 thf(203,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ A @ C) <= (ord_le519537037nres_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_order__trans)). 132.20/30.71 thf(1053,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ A @ C) | ~ (ord_le519537037nres_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 132.20/30.71 thf(673,plain,(((ord_less_eq_o_set_a) = (^ [A:($o > set_a),B:($o > set_a)]: ((ord_less_eq_set_a @ (A @ $true) @ (B @ $true)) & (ord_less_eq_set_a @ (A @ $false) @ (B @ $false)))))),inference(lifteq,[status(thm)],[672])). 132.20/30.71 thf(387,plain,(! [C:(product_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (refine579265252t_unit @ B)) | (~ (ord_le1051254044t_unit @ (C @ (sk1 @ (C) @ B @ A)) @ A)) | (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A))),inference(cnf,[status(esa)],[386])). 132.20/30.71 thf(1985,plain,(! [C:(product_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (~ (top_to177290092t_unit = B))) | (~ (ord_le1051254044t_unit @ (C @ (sk1 @ (C) @ B @ A)) @ A)) | (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A))),inference(rewrite,[status(thm)],[387,330])). 132.20/30.71 thf(1986,plain,(! [C:(product_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((top_to177290092t_unit = B) | (~ (ord_le1051254044t_unit @ (C @ (sk1 @ (C) @ B @ A)) @ A)) | (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A))),inference(simp,[status(thm)],[1985])). 132.20/30.71 thf(1987,plain,(! [C:(product_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((top_to177290092t_unit = B) | (~ (ord_le1051254044t_unit @ (C @ (sk1 @ (C) @ B @ A)) @ A)) | (ord_le1051254044t_unit @ (refine681446406t_unit @ B @ (C)) @ A))),inference(lifteq,[status(thm)],[1986])). 132.20/30.71 thf(268,axiom,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le519537037nres_a @ A @ (B @ C)) => (((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))) <= (ord_less_eq_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_order__subst1)). 132.20/30.71 thf(1300,plain,((! [A:refine424419629nres_a,B:(set_a > refine424419629nres_a),C:set_a,D:set_a]: ((ord_le519537037nres_a @ A @ (B @ C)) => (((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le519537037nres_a @ (B @ E) @ (B @ F)))) => (ord_le519537037nres_a @ A @ (B @ D))) | ~ (ord_less_eq_set_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 132.20/30.71 thf(18,axiom,((~ (refine579265252t_unit @ top_to177290092t_unit))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_nofail__simps_I1_J)). 132.20/30.71 thf(370,plain,((~ (refine579265252t_unit @ top_to177290092t_unit))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 132.20/30.71 thf(253,axiom,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a,C:(refine424419629nres_a > $o)]: ((((! [D:refine424419629nres_a]: ((A @ D) => ((C @ D) <= (! [E:refine424419629nres_a]: ((A @ E) => (ord_le519537037nres_a @ E @ D)))))) => (C @ (order_1714329108nres_a @ A))) <= (! [D:refine424419629nres_a]: ((ord_le519537037nres_a @ D @ B) <= (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_GreatestI2__order)). 132.20/30.71 thf(1235,plain,((! [A:(refine424419629nres_a > $o),B:refine424419629nres_a,C:(refine424419629nres_a > $o)]: (((! [D:refine424419629nres_a]: ((A @ D) => ((C @ D) | ~ (! [E:refine424419629nres_a]: ((A @ E) => (ord_le519537037nres_a @ E @ D)))))) => (C @ (order_1714329108nres_a @ (A)))) | ~ (! [D:refine424419629nres_a]: ((ord_le519537037nres_a @ D @ B) | ~ (A @ D))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 132.20/30.71 thf(459,plain,((! [A:refine787176636t_unit,B:(set_a > refine787176636t_unit),C:set_a]: ((A = (B @ C)) => (! [D:set_a]: ((ord_le1051254044t_unit @ A @ (B @ D)) | ~ (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le1051254044t_unit @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_set_a @ C @ D)))))),inference(miniscope,[status(thm)],[458])). 132.20/30.71 thf(460,plain,(! [D:set_a,C:set_a,B:(set_a > refine787176636t_unit),A:refine787176636t_unit] : ((~ (A = (B @ C))) | (ord_le1051254044t_unit @ A @ (B @ D)) | (ord_less_eq_set_a @ (sk10 @ D @ C @ (B) @ A) @ (sk11 @ D @ C @ (B) @ A)) | (~ (ord_less_eq_set_a @ C @ D)))),inference(cnf,[status(esa)],[459])). 132.20/30.71 thf(462,plain,(! [D:set_a,C:set_a,B:(set_a > refine787176636t_unit),A:refine787176636t_unit] : ((A != (B @ C)) | (ord_le1051254044t_unit @ A @ (B @ D)) | (ord_less_eq_set_a @ (sk10 @ D @ C @ (B) @ A) @ (sk11 @ D @ C @ (B) @ A)) | (~ (ord_less_eq_set_a @ C @ D)))),inference(lifteq,[status(thm)],[460])). 132.20/30.71 thf(463,plain,(! [C:set_a,B:set_a,A:(set_a > refine787176636t_unit)] : ((ord_le1051254044t_unit @ (A @ B) @ (A @ C)) | (ord_less_eq_set_a @ (sk10 @ C @ B @ (A) @ (A @ B)) @ (sk11 @ C @ B @ (A) @ (A @ B))) | (~ (ord_less_eq_set_a @ B @ C)))),inference(simp,[status(thm)],[462])). 132.20/30.71 thf(135,axiom,((! [A:set_a,B:set_a,C:(set_a > refine787176636t_unit),D:refine787176636t_unit]: ((ord_less_eq_set_a @ A @ B) => ((ord_le1051254044t_unit @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le1051254044t_unit @ (C @ E) @ (C @ F)))) => (ord_le1051254044t_unit @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_order__subst2)). 132.20/30.71 thf(808,plain,((! [A:set_a,B:set_a,C:(set_a > refine787176636t_unit),D:refine787176636t_unit]: ((ord_less_eq_set_a @ A @ B) => ((ord_le1051254044t_unit @ (C @ B) @ D) => ((! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_le1051254044t_unit @ (C @ E) @ (C @ F)))) => (ord_le1051254044t_unit @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 132.20/30.71 thf(18839,plain,((~ (ord_le519537037nres_a @ (refine2063221604TURN_a @ sk238) @ (refine1198353288_RES_a @ bot_bot_set_a)))),inference(rewrite,[status(thm)],[15059,18613])). 132.20/30.71 thf(19628,plain,((~ (ord_le519537037nres_a @ (refine2063221604TURN_a @ sk238) @ bot_bo529555393nres_a))),inference(rewrite,[status(thm)],[18839,1158])). 132.20/30.71 thf(949,plain,(((refine558004794t_unit) = (^ [A:refine787176636t_unit,B:product_unit]: (ord_le1051254044t_unit @ (refine1420258419t_unit @ B) @ A)))),inference(lifteq,[status(thm)],[948])). 132.20/30.71 thf(1579,plain,(! [A:refine787176636t_unit] : (((refine558004794t_unit @ A) = (^ [B:product_unit]: (ord_le1051254044t_unit @ (refine1420258419t_unit @ B) @ A))))),inference(func_ext,[status(esa)],[949])). 132.20/30.71 thf(1636,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) != top_to177290092t_unit) | ((B @ A) != (refine23983189ASSUME @ $true)))),inference(paramod_ordered,[status(thm)],[346,1555])). 132.20/30.71 thf(1670,plain,(! [A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [B:product_unit]: (refine23983189ASSUME @ $true))) != top_to177290092t_unit))),inference(pre_uni,[status(thm)],[1636:[bind(A, $thf(A)),bind(B, $thf(^ [C:product_unit]: (refine23983189ASSUME @ $true)))]])). 132.20/30.71 thf(11635,plain,((sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C))) = (ord_le516598614nres_a)) | ((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))) != (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))))),inference(paramod_ordered,[status(thm)],[1735,9348])). 132.20/30.71 thf(11636,plain,((sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C))) = (ord_le516598614nres_a))),inference(pattern_uni,[status(thm)],[11635:[]])). 132.20/30.71 thf(492,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit]: (((ord_le1051254044t_unit @ A @ B) | ~ ($true)) => ((ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ $true @ A @ C) @ (if_Ref1369692790t_unit @ $true @ B @ D)) | ~ ((ord_le1051254044t_unit @ C @ D) | ($true)))))),inference(instance,[status(thm)],[491])). 132.20/30.71 thf(493,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit,D:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => (ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ $true @ A @ C) @ (if_Ref1369692790t_unit @ $true @ B @ D))))),inference(simp,[status(thm)],[492])). 132.20/30.71 thf(496,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => (! [C:refine787176636t_unit,D:refine787176636t_unit]: (ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ $true @ A @ C) @ (if_Ref1369692790t_unit @ $true @ B @ D)))))),inference(miniscope,[status(thm)],[493])). 132.20/30.71 thf(497,plain,(! [D:refine787176636t_unit,C:refine787176636t_unit,B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (ord_le1051254044t_unit @ A @ B)) | (ord_le1051254044t_unit @ (if_Ref1369692790t_unit @ $true @ A @ C) @ (if_Ref1369692790t_unit @ $true @ B @ D)))),inference(cnf,[status(esa)],[496])). 132.20/30.71 thf(14871,plain,(! [B:a,A:a] : (((member_a @ A @ (insert_a @ B @ top_top_set_a)) != (member_a @ sk235 @ (uminus_uminus_set_a @ (collect_a @ (^ [C:a]: ($true)))))))),inference(paramod_ordered,[status(thm)],[6171,14594])). 132.20/30.71 thf(14888,plain,(! [B:a,A:a] : ((A != sk235) | ((insert_a @ B @ top_top_set_a) != (uminus_uminus_set_a @ (collect_a @ (^ [C:a]: ($true))))))),inference(simp,[status(thm)],[14871])). 132.20/30.71 thf(14906,plain,(! [A:a] : (((insert_a @ A @ top_top_set_a) != (uminus_uminus_set_a @ (collect_a @ (^ [B:a]: ($true))))))),inference(simp,[status(thm)],[14888])). 132.20/30.71 thf(18554,plain,(! [A:set_a] : ((member_a @ (sk17 @ A) @ A) | (A != (collect_a @ (^ [B:a]: ($true)))))),inference(paramod_ordered,[status(thm)],[535,13983])). 132.20/30.71 thf(18555,plain,((member_a @ (sk17 @ (collect_a @ (^ [A:a]: ($true)))) @ (collect_a @ (^ [A:a]: ($true))))),inference(pattern_uni,[status(thm)],[18554:[bind(A, $thf(collect_a @ (^ [B:a]: ($true))))]])). 132.20/30.71 thf(19000,plain,(! [B:set_a,A:a] : ((~ (member_a @ A @ (uminus_uminus_set_a @ B))) | ((member_a @ (sk17 @ (collect_a @ (^ [C:a]: ($true)))) @ (collect_a @ (^ [C:a]: ($true)))) != (member_a @ A @ B)))),inference(paramod_ordered,[status(thm)],[18555,405])). 132.20/30.71 thf(19001,plain,((~ (member_a @ (sk17 @ (collect_a @ (^ [A:a]: ($true)))) @ (uminus_uminus_set_a @ (collect_a @ (^ [A:a]: ($true))))))),inference(pattern_uni,[status(thm)],[19000:[bind(A, $thf(sk17 @ (collect_a @ (^ [C:a]: ($true))))),bind(B, $thf(collect_a @ (^ [C:a]: ($true))))]])). 132.20/30.71 thf(264,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > refine424419629nres_a),D:(a > refine424419629nres_a)]: (((! [E:a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ E) @ B) => ((C @ E) = (D @ E)))) => ((refine436832838nd_a_a @ A @ C) = (refine436832838nd_a_a @ B @ D))) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_bind__cong)). 132.20/30.71 thf(1284,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > refine424419629nres_a),D:(a > refine424419629nres_a)]: (((! [E:a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ E) @ B) => ((C @ E) = (D @ E)))) => ((refine436832838nd_a_a @ A @ (C)) = (refine436832838nd_a_a @ B @ (D)))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 132.20/30.71 thf(186,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) => ((ord_le516598614nres_a @ B @ A) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_antisym__conv)). 132.20/30.71 thf(978,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (A) @ (B)) => ((ord_le516598614nres_a @ (B) @ (A)) = ((B) = (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 132.20/30.71 thf(190,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine787176636t_unit),D:(product_unit > refine787176636t_unit)]: ((ord_le1051254044t_unit @ A @ B) => ((! [E:product_unit]: ((ord_le1051254044t_unit @ (refine1420258419t_unit @ E) @ A) => (ord_le1051254044t_unit @ (C @ E) @ (D @ E)))) => (ord_le1051254044t_unit @ (refine681446406t_unit @ A @ C) @ (refine681446406t_unit @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J)). 132.20/30.71 thf(991,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine787176636t_unit),D:(product_unit > refine787176636t_unit)]: ((ord_le1051254044t_unit @ A @ B) => ((! [E:product_unit]: ((ord_le1051254044t_unit @ (refine1420258419t_unit @ E) @ A) => (ord_le1051254044t_unit @ (C @ E) @ (D @ E)))) => (ord_le1051254044t_unit @ (refine681446406t_unit @ A @ (C)) @ (refine681446406t_unit @ B @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 132.20/30.71 thf(73,axiom,((refine983493746t_unit = (^ [A:refine787176636t_unit,B:product_unit]: ((refine558004794t_unit @ A @ B) & (refine579265252t_unit @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_nf__inres__def)). 132.20/30.71 thf(581,plain,(((refine983493746t_unit) = (^ [A:refine787176636t_unit,B:product_unit]: ((refine558004794t_unit @ A @ B) & (refine579265252t_unit @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 132.20/30.71 thf(582,plain,(((refine983493746t_unit) = (^ [A:refine787176636t_unit,B:product_unit]: ((refine558004794t_unit @ A @ B) & (refine579265252t_unit @ A))))),inference(lifteq,[status(thm)],[581])). 132.20/30.71 thf(1617,plain,(((refine983493746t_unit) = (^ [A:refine787176636t_unit,B:product_unit]: ((refine558004794t_unit @ A @ B) & ~ (top_to177290092t_unit = A))))),inference(rewrite,[status(thm)],[582,330])). 132.20/30.71 thf(461,plain,(! [D:set_a,C:set_a,B:(set_a > refine787176636t_unit),A:refine787176636t_unit] : ((~ (A = (B @ C))) | (ord_le1051254044t_unit @ A @ (B @ D)) | (~ (ord_le1051254044t_unit @ (B @ (sk10 @ D @ C @ (B) @ A)) @ (B @ (sk11 @ D @ C @ (B) @ A)))) | (~ (ord_less_eq_set_a @ C @ D)))),inference(cnf,[status(esa)],[459])). 132.20/30.71 thf(464,plain,(! [D:set_a,C:set_a,B:(set_a > refine787176636t_unit),A:refine787176636t_unit] : ((A != (B @ C)) | (ord_le1051254044t_unit @ A @ (B @ D)) | (~ (ord_le1051254044t_unit @ (B @ (sk10 @ D @ C @ (B) @ A)) @ (B @ (sk11 @ D @ C @ (B) @ A)))) | (~ (ord_less_eq_set_a @ C @ D)))),inference(lifteq,[status(thm)],[461])). 132.20/30.71 thf(465,plain,(! [C:set_a,B:set_a,A:(set_a > refine787176636t_unit)] : ((ord_le1051254044t_unit @ (A @ B) @ (A @ C)) | (~ (ord_le1051254044t_unit @ (A @ (sk10 @ C @ B @ (A) @ (A @ B))) @ (A @ (sk11 @ C @ B @ (A) @ (A @ B))))) | (~ (ord_less_eq_set_a @ B @ C)))),inference(simp,[status(thm)],[464])). 132.20/30.71 thf(305,axiom,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ bot_bo529555393nres_a) = (A = bot_bo529555393nres_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_bot_Oextremum__unique)). 132.20/30.71 thf(1459,plain,((! [A:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ bot_bo529555393nres_a) = (A = bot_bo529555393nres_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 132.20/30.71 thf(172,axiom,((! [A:a,B:set_a]: ((member_a @ A @ (uminus_uminus_set_a @ B)) = (~ (member_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_Compl__iff)). 132.20/30.71 thf(931,plain,((! [A:a,B:set_a]: ((member_a @ A @ (uminus_uminus_set_a @ B)) = (~ (member_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 132.20/30.71 thf(481,plain,(! [B:($o > refine424419629nres_a),A:($o > refine424419629nres_a)] : ((~ (ord_le516598614nres_a @ (A) @ (B))) | ((A) = (B)) | (~ (ord_le516598614nres_a @ (B) @ (A))))),inference(cnf,[status(esa)],[480])). 132.20/30.71 thf(482,plain,(! [B:($o > refine424419629nres_a),A:($o > refine424419629nres_a)] : (((A) = (B)) | (~ (ord_le516598614nres_a @ (A) @ (B))) | (~ (ord_le516598614nres_a @ (B) @ (A))))),inference(lifteq,[status(thm)],[481])). 132.20/30.71 thf(759,plain,(((ord_le1633311077t_unit) = (^ [A:($o > refine787176636t_unit),B:($o > refine787176636t_unit)]: ((ord_le1051254044t_unit @ (A @ $true) @ (B @ $true)) & (ord_le1051254044t_unit @ (A @ $false) @ (B @ $false)))))),inference(lifteq,[status(thm)],[758])). 132.20/30.71 thf(146,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine424419629nres_a),D:(product_unit > refine424419629nres_a)]: ((((refine119808503unit_a @ A @ C) = (refine119808503unit_a @ B @ D)) <= (! [E:product_unit]: ((ord_le1051254044t_unit @ (refine1420258419t_unit @ E) @ B) => ((C @ E) = (D @ E))))) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_bind__cong)). 132.20/30.71 thf(844,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine424419629nres_a),D:(product_unit > refine424419629nres_a)]: (((refine119808503unit_a @ A @ (C)) = (refine119808503unit_a @ B @ (D))) | ~ (! [E:product_unit]: ((ord_le1051254044t_unit @ (refine1420258419t_unit @ E) @ B) => ((C @ E) = (D @ E)))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 132.20/30.71 thf(219,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le1051254044t_unit @ A @ B) => (((ord_le519537037nres_a @ (C @ A) @ D) <= (! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) <= (ord_le1051254044t_unit @ E @ F)))) <= (ord_le519537037nres_a @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_order__subst2)). 132.20/30.71 thf(1108,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > refine424419629nres_a),D:refine424419629nres_a]: ((ord_le1051254044t_unit @ A @ B) => ((ord_le519537037nres_a @ (C @ A) @ D) | ~ (! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) | ~ (ord_le1051254044t_unit @ E @ F))) | ~ (ord_le519537037nres_a @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 132.20/30.71 thf(271,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ A) => (ord_le519537037nres_a @ B @ A)) => (ord_le519537037nres_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_le__nofailI)). 132.20/30.71 thf(1316,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((refine412683989fail_a @ A) => (ord_le519537037nres_a @ B @ A)) => (ord_le519537037nres_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 132.20/30.71 thf(213,axiom,((! [A:refine424419629nres_a,B:refine787176636t_unit,C:(product_unit > refine424419629nres_a)]: (((refine579265252t_unit @ B) <= (refine412683989fail_a @ A)) => ((ord_le519537037nres_a @ (refine119808503unit_a @ B @ C) @ A) <= (! [D:product_unit]: ((refine579265252t_unit @ B) => ((ord_le519537037nres_a @ (C @ D) @ A) <= (refine558004794t_unit @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_pw__bind__leI)). 132.20/30.71 thf(1084,plain,((! [A:refine424419629nres_a,B:refine787176636t_unit,C:(product_unit > refine424419629nres_a)]: (((refine579265252t_unit @ B) | ~ (refine412683989fail_a @ A)) => ((ord_le519537037nres_a @ (refine119808503unit_a @ B @ (C)) @ A) | ~ (! [D:product_unit]: ((refine579265252t_unit @ B) => ((ord_le519537037nres_a @ (C @ D) @ A) | ~ (refine558004794t_unit @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 132.20/30.71 thf(6264,plain,(! [B:a,A:set_a] : (((collect_a @ (^ [C:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ C) @ (refine1198353288_RES_a @ A)))) != bot_bot_set_a) | (A != (insert_a @ B @ top_top_set_a)))),inference(paramod_ordered,[status(thm)],[4008,6231])). 132.20/30.71 thf(6265,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (insert_a @ A @ top_top_set_a))))) != bot_bot_set_a))),inference(pattern_uni,[status(thm)],[6264:[bind(A, $thf(insert_a @ C @ top_top_set_a)),bind(B, $thf(C))]])). 132.20/30.71 thf(6277,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (insert_a @ A @ top_top_set_a))))) != bot_bot_set_a))),inference(simp,[status(thm)],[6265])). 132.20/30.71 thf(6394,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (insert_a @ A @ top_top_set_a))))) != (collect_a @ (^ [B:a]: ($false)))))),inference(paramod_ordered,[status(thm)],[1589,6277])). 132.20/30.71 thf(6408,plain,(! [A:a] : (((^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ (insert_a @ A @ top_top_set_a)))) != (^ [B:a]: ($false))))),inference(simp,[status(thm)],[6394])). 132.20/30.71 thf(185,axiom,(((= @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_order__class_Oorder_Oeq__iff)). 132.20/30.71 thf(976,plain,(((= @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 132.20/30.71 thf(14037,plain,(((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: ($true)))))) != (^ [A:a]: ($false)))),inference(simp,[status(thm)],[14020])). 132.20/30.71 thf(163,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:product_unit]: ((ord_le1051254044t_unit @ A @ B) => ((refine558004794t_unit @ B @ C) <= (refine558004794t_unit @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_pwD2)). 132.20/30.71 thf(903,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:product_unit]: ((ord_le1051254044t_unit @ A @ B) => ((refine558004794t_unit @ B @ C) | ~ (refine558004794t_unit @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 132.20/30.71 thf(196,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: (((A = B) <= (ord_le519537037nres_a @ B @ A)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_antisym)). 132.20/30.71 thf(1010,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((A = B) | ~ (ord_le519537037nres_a @ B @ A) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 132.20/30.71 thf(14014,plain,((~ ((refine2063221604TURN_a @ sk232) = bot_bo529555393nres_a))),inference(func_ext,[status(esa)],[14002])). 132.20/30.71 thf(14015,plain,(((refine2063221604TURN_a @ sk232) != bot_bo529555393nres_a)),inference(lifteq,[status(thm)],[14014])). 132.20/30.71 thf(75,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_eq__refl)). 132.20/30.71 thf(588,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 132.20/30.71 thf(1901,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) != bot_bo658782032t_unit) | ((B @ A) != (refine23983189ASSUME @ $true)))),inference(paramod_ordered,[status(thm)],[346,1899])). 132.20/30.71 thf(1903,plain,(! [A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [B:product_unit]: (refine23983189ASSUME @ $true))) != bot_bo658782032t_unit))),inference(pre_uni,[status(thm)],[1901:[bind(A, $thf(A)),bind(B, $thf(^ [C:product_unit]: (refine23983189ASSUME @ $true)))]])). 132.20/30.71 thf(1062,plain,(((^ [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) & (ord_le519537037nres_a @ B @ A))) = (= @ refine424419629nres_a))),inference(lifteq,[status(thm)],[1061])). 132.20/30.71 thf(217,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > ($o > refine424419629nres_a)),D:($o > refine424419629nres_a)]: ((((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le516598614nres_a @ (C @ E) @ (C @ F)) <= (ord_le519537037nres_a @ E @ F))) => (ord_le516598614nres_a @ (C @ A) @ D)) <= (ord_le516598614nres_a @ (C @ B) @ D)) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_order__subst2)). 132.20/30.71 thf(1101,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > ($o > refine424419629nres_a)),D:($o > refine424419629nres_a)]: (((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le516598614nres_a @ (C @ E) @ (C @ F)) | ~ (ord_le519537037nres_a @ E @ F))) => (ord_le516598614nres_a @ (C @ A) @ (D))) | ~ (ord_le516598614nres_a @ (C @ B) @ (D)) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 132.20/30.71 thf(86,axiom,((! [A:a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ (insert_a @ A @ C) @ B) <= (ord_less_eq_set_a @ C @ B)) <= (member_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_insert__subsetI)). 132.20/30.71 thf(632,plain,((! [A:a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (insert_a @ A @ C) @ B) | ~ (ord_less_eq_set_a @ C @ B) | ~ (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 132.20/30.71 thf(29,axiom,((! [A:set_a]: ((? [B:a]: (member_a @ B @ A)) = (A != bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_ex__in__conv)). 132.20/30.71 thf(401,plain,((! [A:set_a]: ((? [B:a]: (member_a @ B @ A)) = (~ (A = bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 132.20/30.71 thf(130,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > set_a),D:set_a]: ((ord_le1051254044t_unit @ A @ B) => (((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_a @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ord__le__eq__subst)). 132.20/30.71 thf(786,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(refine787176636t_unit > set_a),D:set_a]: ((ord_le1051254044t_unit @ A @ B) => (((! [E:refine787176636t_unit,F:refine787176636t_unit]: ((ord_le1051254044t_unit @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))) => (ord_less_eq_set_a @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 132.20/30.71 thf(191,axiom,((! [A:refine787176636t_unit,B:(product_unit > refine787176636t_unit)]: ((refine579265252t_unit @ (refine681446406t_unit @ A @ B)) = ((refine579265252t_unit @ A) & ! [C:product_unit]: ((refine579265252t_unit @ (B @ C)) <= (refine558004794t_unit @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_pw__bind__nofail)). 132.20/30.71 thf(995,plain,((! [A:refine787176636t_unit,B:(product_unit > refine787176636t_unit)]: ((refine579265252t_unit @ (refine681446406t_unit @ A @ (B))) = ((refine579265252t_unit @ A) & ! [C:product_unit]: ((refine579265252t_unit @ (B @ C)) | ~ (refine558004794t_unit @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 132.20/30.71 thf(161,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((if_o_R1705037948nres_a @ $false @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T)). 132.20/30.71 thf(896,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((if_o_R1705037948nres_a @ $false @ A @ B) = (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 132.20/30.71 thf(120,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_eq__refl)). 132.20/30.71 thf(748,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (A) @ (B)) | ~ ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 132.20/30.71 thf(568,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ B) | ~ (member_a @ C @ A))))),inference(lifteq,[status(thm)],[567])). 132.20/30.71 thf(270,axiom,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => (((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ (B @ E) @ (B @ F)) <= (ord_le519537037nres_a @ E @ F))) => (ord_le519537037nres_a @ A @ (B @ D))) <= (ord_le519537037nres_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_ord__eq__le__subst)). 132.20/30.71 thf(1308,plain,((! [A:refine424419629nres_a,B:(refine424419629nres_a > refine424419629nres_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => (((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ (B @ E) @ (B @ F)) | ~ (ord_le519537037nres_a @ E @ F))) => (ord_le519537037nres_a @ A @ (B @ D))) | ~ (ord_le519537037nres_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 132.20/30.71 thf(242,axiom,((! [A:(a > $o),B:(a > $o)]: ((ord_less_eq_set_a @ (collect_a @ A) @ (collect_a @ B)) = (! [C:a]: ((B @ C) <= (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Collect__mono__iff)). 132.20/30.71 thf(1193,plain,((! [A:(a > $o),B:(a > $o)]: ((ord_less_eq_set_a @ (collect_a @ (A)) @ (collect_a @ (B))) = (! [C:a]: ((B @ C) | ~ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 132.20/30.71 thf(247,axiom,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) => (B @ C))) => (ord_le519537037nres_a @ (refine1198353288_RES_a @ (collect_a @ A)) @ (refine1198353288_RES_a @ (collect_a @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_SPEC__rule)). 132.20/30.71 thf(1212,plain,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) => (B @ C))) => (ord_le519537037nres_a @ (refine1198353288_RES_a @ (collect_a @ (A))) @ (refine1198353288_RES_a @ (collect_a @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 132.20/30.71 thf(125,axiom,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => (((ord_less_eq_set_a @ A @ (B @ D)) <= (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F))))) <= (ord_less_eq_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_order__subst1)). 132.20/30.71 thf(763,plain,((! [A:set_a,B:(set_a > set_a),C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ (B @ C)) => ((ord_less_eq_set_a @ A @ (B @ D)) | ~ (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ E @ F) => (ord_less_eq_set_a @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_set_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 132.20/30.71 thf(162,axiom,((! [A:set_a,B:set_a]: ((A = B) => (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_equalityD1)). 132.20/30.71 thf(899,plain,((! [A:set_a,B:set_a]: ((A = B) => (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 132.20/30.71 thf(546,plain,(! [D:refine787176636t_unit,C:refine787176636t_unit,B:(refine787176636t_unit > refine787176636t_unit),A:refine787176636t_unit] : ((ord_le1051254044t_unit @ A @ (B @ D)) | (~ (ord_le1051254044t_unit @ (B @ (sk20 @ D @ C @ (B) @ A)) @ (B @ (sk21 @ D @ C @ (B) @ A)))) | (~ (ord_le1051254044t_unit @ C @ D)) | (~ (A = (B @ C))))),inference(cnf,[status(esa)],[545])). 132.20/30.71 thf(548,plain,(! [D:refine787176636t_unit,C:refine787176636t_unit,B:(refine787176636t_unit > refine787176636t_unit),A:refine787176636t_unit] : ((A != (B @ C)) | (ord_le1051254044t_unit @ A @ (B @ D)) | (~ (ord_le1051254044t_unit @ (B @ (sk20 @ D @ C @ (B) @ A)) @ (B @ (sk21 @ D @ C @ (B) @ A)))) | (~ (ord_le1051254044t_unit @ C @ D)))),inference(lifteq,[status(thm)],[546])). 132.20/30.71 thf(549,plain,(! [C:refine787176636t_unit,B:refine787176636t_unit,A:(refine787176636t_unit > refine787176636t_unit)] : ((ord_le1051254044t_unit @ (A @ B) @ (A @ C)) | (~ (ord_le1051254044t_unit @ (A @ (sk20 @ C @ B @ (A) @ (A @ B))) @ (A @ (sk21 @ C @ B @ (A) @ (A @ B))))) | (~ (ord_le1051254044t_unit @ B @ C)))),inference(simp,[status(thm)],[548])). 132.20/30.71 thf(9023,plain,(! [B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (sk7 @ (A)) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != bot_bo529555393nres_a) | ((A @ (sk8 @ B @ (A))) != b))),inference(paramod_ordered,[status(thm)],[454,1802])). 132.20/30.71 thf(9321,plain,(~ (b) | (sk7 @ (^ [A:($o > refine424419629nres_a)]: (b))) | ((if_Ref1724547303nres_a @ $true @ s1 @ s2) != bot_bo529555393nres_a)),inference(pre_uni,[status(thm)],[9023:[bind(A, $thf(^ [C:($o > refine424419629nres_a)]: (b)))]])). 132.20/30.71 thf(232,axiom,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) = (B @ C))) => ((collect_a @ A) = (collect_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Collect__cong)). 132.20/30.71 thf(1161,plain,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) = (B @ C))) => ((collect_a @ (A)) = (collect_a @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 132.20/30.71 thf(429,plain,(! [D:refine787176636t_unit,C:(refine787176636t_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (ord_le1051254044t_unit @ (C @ (sk4 @ D @ (C) @ B @ A)) @ (C @ (sk5 @ D @ (C) @ B @ A)))) | (ord_le1051254044t_unit @ (C @ A) @ D) | (~ ((C @ B) = D)) | (~ (ord_le1051254044t_unit @ A @ B)))),inference(cnf,[status(esa)],[427])). 132.20/30.71 thf(432,plain,(! [D:refine787176636t_unit,C:(refine787176636t_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : (((C @ B) != D) | (~ (ord_le1051254044t_unit @ (C @ (sk4 @ D @ (C) @ B @ A)) @ (C @ (sk5 @ D @ (C) @ B @ A)))) | (ord_le1051254044t_unit @ (C @ A) @ D) | (~ (ord_le1051254044t_unit @ A @ B)))),inference(lifteq,[status(thm)],[429])). 132.20/30.71 thf(433,plain,(! [C:(refine787176636t_unit > refine787176636t_unit),B:refine787176636t_unit,A:refine787176636t_unit] : ((~ (ord_le1051254044t_unit @ (C @ (sk4 @ (C @ B) @ (C) @ B @ A)) @ (C @ (sk5 @ (C @ B) @ (C) @ B @ A)))) | (ord_le1051254044t_unit @ (C @ A) @ (C @ B)) | (~ (ord_le1051254044t_unit @ A @ B)))),inference(simp,[status(thm)],[432])). 132.20/30.71 thf(876,plain,(((ord_le1051254044t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((refine579265252t_unit @ B) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) => (refine558004794t_unit @ B @ C)) & (refine579265252t_unit @ A)))))),inference(lifteq,[status(thm)],[875])). 132.20/30.71 thf(2142,plain,(((ord_le1051254044t_unit) = (^ [A:refine787176636t_unit,B:refine787176636t_unit]: ((~ (top_to177290092t_unit = B)) => (! [C:product_unit]: ((refine558004794t_unit @ A @ C) => (refine558004794t_unit @ B @ C)) & ~ (top_to177290092t_unit = A)))))),inference(rewrite,[status(thm)],[876,330])). 132.20/30.71 thf(468,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((refine558004794t_unit @ B @ (sk12 @ B @ A)) | (~ (refine579265252t_unit @ B)) | (ord_le1051254044t_unit @ B @ A))),inference(cnf,[status(esa)],[466])). 132.20/30.71 thf(12700,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((refine558004794t_unit @ B @ (sk12 @ B @ A)) | (~ (~ (top_to177290092t_unit = B))) | (ord_le1051254044t_unit @ B @ A))),inference(rewrite,[status(thm)],[468,330])). 132.20/30.71 thf(12701,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((refine558004794t_unit @ B @ (sk12 @ B @ A)) | (top_to177290092t_unit = B) | (ord_le1051254044t_unit @ B @ A))),inference(simp,[status(thm)],[12700])). 132.20/30.71 thf(12702,plain,(! [B:refine787176636t_unit,A:refine787176636t_unit] : ((top_to177290092t_unit = B) | (refine558004794t_unit @ B @ (sk12 @ B @ A)) | (ord_le1051254044t_unit @ B @ A))),inference(lifteq,[status(thm)],[12701])). 132.20/30.71 thf(14984,plain,((ord_le519537037nres_a @ (refine2063221604TURN_a @ sk237) @ (refine1198353288_RES_a @ (collect_a @ (^ [A:a]: ($true)))))),inference(func_ext,[status(esa)],[14037])). 132.20/30.71 thf(151,axiom,((! [A:set_a,B:set_a,C:set_a]: ((A = B) => ((ord_less_eq_set_a @ A @ C) <= (ord_less_eq_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_ord__eq__le__trans)). 132.20/30.71 thf(867,plain,((! [A:set_a,B:set_a,C:set_a]: ((A = B) => ((ord_less_eq_set_a @ A @ C) | ~ (ord_less_eq_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 132.20/30.71 thf(177,axiom,((! [A:($o > refine424419629nres_a)]: (ord_le516598614nres_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_order__mono__setup_Orefl)). 132.20/30.71 thf(950,plain,((! [A:($o > refine424419629nres_a)]: (ord_le516598614nres_a @ (A) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 132.20/30.71 thf(143,axiom,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ (C @ B) @ D) => ((ord_less_eq_set_a @ (C @ A) @ D) <= (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_a @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_order__subst2)). 132.20/30.71 thf(835,plain,((! [A:set_a,B:set_a,C:(set_a > set_a),D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ (C @ B) @ D) => ((ord_less_eq_set_a @ (C @ A) @ D) | ~ (! [E:set_a,F:set_a]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_a @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 132.20/30.71 thf(251,axiom,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ B) => (((ord_le519537037nres_a @ (C @ A) @ D) <= (! [E:set_a,F:set_a]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_a @ E @ F)))) <= (ord_le519537037nres_a @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_order__subst2)). 132.20/30.71 thf(1229,plain,((! [A:set_a,B:set_a,C:(set_a > refine424419629nres_a),D:refine424419629nres_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_le519537037nres_a @ (C @ A) @ D) | ~ (! [E:set_a,F:set_a]: ((ord_le519537037nres_a @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_a @ E @ F))) | ~ (ord_le519537037nres_a @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 132.20/30.71 thf(1649,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((^ [C:refine787176636t_unit]: ~ ((refine681446406t_unit @ (refine1420258419t_unit @ A) @ B) = C)) = (^ [C:refine787176636t_unit]: ~ (C = top_to177290092t_unit))) | ((B @ A) != top_to177290092t_unit))),inference(paramod_ordered,[status(thm)],[346,1603])). 132.20/30.71 thf(1673,plain,(! [A:product_unit] : (((^ [B:refine787176636t_unit]: ~ ((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (top_to177290092t_unit))) = B)) = (^ [B:refine787176636t_unit]: ~ (B = top_to177290092t_unit))))),inference(pre_uni,[status(thm)],[1649:[bind(A, $thf(A)),bind(B, $thf(^ [C:product_unit]: (top_to177290092t_unit)))]])). 132.20/30.71 thf(418,plain,(! [D:set_a,C:set_a,B:(set_a > set_a),A:set_a] : ((~ (A = (B @ C))) | (ord_less_eq_set_a @ A @ (B @ D)) | (ord_less_eq_set_a @ (sk2 @ D @ C @ (B) @ A) @ (sk3 @ D @ C @ (B) @ A)) | (~ (ord_less_eq_set_a @ C @ D)))),inference(cnf,[status(esa)],[416])). 132.20/30.71 thf(421,plain,(! [D:set_a,C:set_a,B:(set_a > set_a),A:set_a] : ((A != (B @ C)) | (ord_less_eq_set_a @ A @ (B @ D)) | (ord_less_eq_set_a @ (sk2 @ D @ C @ (B) @ A) @ (sk3 @ D @ C @ (B) @ A)) | (~ (ord_less_eq_set_a @ C @ D)))),inference(lifteq,[status(thm)],[418])). 132.20/30.71 thf(422,plain,(! [C:set_a,B:set_a,A:(set_a > set_a)] : ((ord_less_eq_set_a @ (A @ B) @ (A @ C)) | (ord_less_eq_set_a @ (sk2 @ C @ B @ (A) @ (A @ B)) @ (sk3 @ C @ B @ (A) @ (A @ B))) | (~ (ord_less_eq_set_a @ B @ C)))),inference(simp,[status(thm)],[421])). 132.20/30.71 thf(256,axiom,((! [A:($o > refine424419629nres_a),B:(refine424419629nres_a > ($o > refine424419629nres_a)),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((ord_le516598614nres_a @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le516598614nres_a @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_ord__eq__le__subst)). 132.20/30.71 thf(1248,plain,((! [A:($o > refine424419629nres_a),B:(refine424419629nres_a > ($o > refine424419629nres_a)),C:refine424419629nres_a,D:refine424419629nres_a]: (((A) = (B @ C)) => ((ord_le519537037nres_a @ C @ D) => ((ord_le516598614nres_a @ (A) @ (B @ D)) | ~ (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le516598614nres_a @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 132.20/30.71 thf(311,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ A) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_antisym__conv)). 132.20/30.71 thf(1480,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((ord_le519537037nres_a @ A @ B) => ((ord_le519537037nres_a @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 132.20/30.71 thf(67,axiom,((! [A:set_a,B:a]: ((ord_less_eq_set_a @ A @ (uminus_uminus_set_a @ (insert_a @ B @ bot_bot_set_a))) = (~ (member_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_subset__Compl__singleton)). 132.20/30.71 thf(564,plain,((! [A:set_a,B:a]: ((ord_less_eq_set_a @ A @ (uminus_uminus_set_a @ (insert_a @ B @ bot_bot_set_a))) = (~ (member_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 132.20/30.71 thf(509,plain,(! [A:product_unit] : ((refine579265252t_unit @ (refine1420258419t_unit @ A)))),inference(cnf,[status(esa)],[508])). 132.20/30.71 thf(1708,plain,(! [A:product_unit] : ((~ (top_to177290092t_unit = (refine1420258419t_unit @ A))))),inference(rewrite,[status(thm)],[509,330])). 132.20/30.71 thf(1709,plain,(! [A:product_unit] : ((~ (top_to177290092t_unit = (refine1420258419t_unit @ A))))),inference(simp,[status(thm)],[1708])). 132.20/30.71 thf(1710,plain,(! [A:product_unit] : (((refine1420258419t_unit @ A) != top_to177290092t_unit))),inference(lifteq,[status(thm)],[1709])). 132.20/30.71 thf(87,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((refine579265252t_unit @ A) <= (refine579265252t_unit @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_pwD1)). 132.20/30.71 thf(635,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((ord_le1051254044t_unit @ A @ B) => ((refine579265252t_unit @ A) | ~ (refine579265252t_unit @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 132.20/30.71 thf(179,axiom,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_dual__order_Orefl)). 132.20/30.71 thf(955,plain,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 132.20/30.71 thf(7610,plain,(! [B:set_a,A:a] : (((refine2063221604TURN_a @ A) != top_to231829469nres_a) | ((refine1198353288_RES_a @ (sk183 @ A)) != (refine1198353288_RES_a @ B)))),inference(paramod_ordered,[status(thm)],[6549,1206])). 132.20/30.71 thf(7611,plain,(! [A:a] : (((refine2063221604TURN_a @ A) != top_to231829469nres_a))),inference(pattern_uni,[status(thm)],[7610:[bind(A, $thf(C)),bind(B, $thf(sk183 @ C))]])). 132.20/30.71 thf(7648,plain,(! [A:a] : (((refine2063221604TURN_a @ A) != top_to231829469nres_a))),inference(simp,[status(thm)],[7611])). 132.20/30.71 thf(1644,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) != bot_bo658782032t_unit) | ((B @ A) != top_to177290092t_unit))),inference(paramod_ordered,[status(thm)],[346,352])). 132.20/30.71 thf(1657,plain,(! [A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [B:product_unit]: (top_to177290092t_unit))) != bot_bo658782032t_unit))),inference(pre_uni,[status(thm)],[1644:[bind(A, $thf(A)),bind(B, $thf(^ [C:product_unit]: (top_to177290092t_unit)))]])). 132.20/30.71 thf(1711,plain,(! [C:product_unit,B:(product_unit > refine787176636t_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) != top_to177290092t_unit) | ((B @ A) != (refine1420258419t_unit @ C)))),inference(paramod_ordered,[status(thm)],[346,1710])). 132.20/30.71 thf(1712,plain,(! [B:(product_unit > product_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (refine1420258419t_unit @ (B @ C)))) != top_to177290092t_unit))),inference(pre_uni,[status(thm)],[1711:[bind(A, $thf(A)),bind(B, $thf(^ [E:product_unit]: (refine1420258419t_unit @ (D @ E)))),bind(C, $thf(D @ A))]])). 132.20/30.71 thf(1713,plain,(! [B:(product_unit > product_unit),A:product_unit] : (((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (refine1420258419t_unit @ (B @ C)))) != top_to177290092t_unit))),inference(simp,[status(thm)],[1712])). 132.20/30.71 thf(11540,plain,(! [D:(product_unit > product_unit),C:product_unit,B:(product_unit > refine787176636t_unit),A:product_unit] : (((B @ A) != top_to177290092t_unit) | ((refine681446406t_unit @ (refine1420258419t_unit @ A) @ (B)) != (refine681446406t_unit @ (refine1420258419t_unit @ C) @ (^ [E:product_unit]: (refine1420258419t_unit @ (D @ E))))))),inference(paramod_ordered,[status(thm)],[346,1713])). 132.20/30.71 thf(11541,plain,(! [B:(product_unit > product_unit),A:product_unit] : (((refine1420258419t_unit @ (B @ A)) != top_to177290092t_unit))),inference(pattern_uni,[status(thm)],[11540:[bind(A, $thf(A)),bind(B, $thf(^ [F:product_unit]: (refine1420258419t_unit @ (E @ F)))),bind(C, $thf(A)),bind(D, $thf(E))]])). 132.20/30.71 thf(11557,plain,(! [B:(product_unit > product_unit),A:product_unit] : (((refine1420258419t_unit @ (B @ A)) != top_to177290092t_unit))),inference(simp,[status(thm)],[11541])). 132.20/30.71 thf(277,axiom,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => (((ord_less_eq_set_a @ A @ (B @ D)) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) <= (ord_le519537037nres_a @ E @ F)))) <= (ord_le519537037nres_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_ord__eq__le__subst)). 132.20/30.71 thf(1335,plain,((! [A:set_a,B:(refine424419629nres_a > set_a),C:refine424419629nres_a,D:refine424419629nres_a]: ((A = (B @ C)) => ((ord_less_eq_set_a @ A @ (B @ D)) | ~ (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_less_eq_set_a @ (B @ E) @ (B @ F)) | ~ (ord_le519537037nres_a @ E @ F))) | ~ (ord_le519537037nres_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 132.20/30.71 thf(236,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > $o)]: (((ord_le519537037nres_a @ B @ (refine1198353288_RES_a @ (collect_a @ C))) => (ord_le519537037nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ C)))) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_SPEC__trans)). 132.20/30.71 thf(1172,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(a > $o)]: (((ord_le519537037nres_a @ B @ (refine1198353288_RES_a @ (collect_a @ (C)))) => (ord_le519537037nres_a @ A @ (refine1198353288_RES_a @ (collect_a @ (C))))) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 132.20/30.71 thf(1635,plain,(! [B:(product_unit > refine787176636t_unit),A:product_unit] : (((refine558004794t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ B)) = (^ [C:product_unit]: ($true))) | ((B @ A) != top_to177290092t_unit))),inference(paramod_ordered,[status(thm)],[346,930])). 132.20/30.71 thf(1671,plain,(! [A:product_unit] : (((refine558004794t_unit @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [B:product_unit]: (top_to177290092t_unit)))) = (^ [B:product_unit]: ($true))))),inference(pre_uni,[status(thm)],[1635:[bind(A, $thf(A)),bind(B, $thf(^ [C:product_unit]: (top_to177290092t_unit)))]])). 132.20/30.71 thf(3479,plain,(! [A:product_unit] : (((^ [B:product_unit]: (ord_le1051254044t_unit @ (refine1420258419t_unit @ B) @ (refine681446406t_unit @ (refine1420258419t_unit @ A) @ (^ [C:product_unit]: (top_to177290092t_unit))))) = (^ [B:product_unit]: ($true))))),inference(rewrite,[status(thm)],[1671,1579])). 132.20/30.71 thf(126,axiom,((! [A:(refine787176636t_unit > $o),B:refine787176636t_unit]: ((A @ B) => (((order_453013155t_unit @ A) = B) <= (! [C:refine787176636t_unit]: ((ord_le1051254044t_unit @ C @ B) <= (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Greatest__equality)). 132.20/30.71 thf(767,plain,((! [A:(refine787176636t_unit > $o),B:refine787176636t_unit]: ((A @ B) => (((order_453013155t_unit @ (A)) = B) | ~ (! [C:refine787176636t_unit]: ((ord_le1051254044t_unit @ C @ B) | ~ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 132.20/30.71 thf(208,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le519537037nres_a @ A @ B) => (((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) <= (ord_le519537037nres_a @ E @ F))) => (ord_less_eq_set_a @ (C @ A) @ D)) <= (ord_less_eq_set_a @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_order__subst2)). 132.20/30.71 thf(1065,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((ord_le519537037nres_a @ A @ B) => (((! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_less_eq_set_a @ (C @ E) @ (C @ F)) | ~ (ord_le519537037nres_a @ E @ F))) => (ord_less_eq_set_a @ (C @ A) @ D)) | ~ (ord_less_eq_set_a @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 132.20/30.71 thf(189,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_equalityD2)). 132.20/30.71 thf(987,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 132.20/30.71 thf(280,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine424419629nres_a),D:(product_unit > refine424419629nres_a)]: (((! [E:product_unit]: ((ord_le1051254044t_unit @ (refine1420258419t_unit @ E) @ A) => (ord_le519537037nres_a @ (C @ E) @ (D @ E)))) => (ord_le519537037nres_a @ (refine119808503unit_a @ A @ C) @ (refine119808503unit_a @ B @ D))) <= (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J)). 132.20/30.71 thf(1352,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:(product_unit > refine424419629nres_a),D:(product_unit > refine424419629nres_a)]: (((! [E:product_unit]: ((ord_le1051254044t_unit @ (refine1420258419t_unit @ E) @ A) => (ord_le519537037nres_a @ (C @ E) @ (D @ E)))) => (ord_le519537037nres_a @ (refine119808503unit_a @ A @ (C)) @ (refine119808503unit_a @ B @ (D)))) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 132.20/30.71 thf(71,axiom,((! [A:a,B:(a > refine424419629nres_a)]: ((refine436832838nd_a_a @ (refine2063221604TURN_a @ A) @ B) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_nres__monad1)). 132.20/30.71 thf(575,plain,((! [A:a,B:(a > refine424419629nres_a)]: ((refine436832838nd_a_a @ (refine2063221604TURN_a @ A) @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 132.20/30.71 thf(149,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a),D:($o > refine424419629nres_a)]: ((A = B) => ((ord_le516598614nres_a @ B @ C) => ((C = D) => (ord_le516598614nres_a @ A @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_ord__eq__le__eq__trans)). 132.20/30.71 thf(860,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a),C:($o > refine424419629nres_a),D:($o > refine424419629nres_a)]: (((A) = (B)) => ((ord_le516598614nres_a @ (B) @ (C)) => (((C) = (D)) => (ord_le516598614nres_a @ (A) @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 132.20/30.71 thf(286,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((((C @ B) = D) => ((ord_le519537037nres_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))))) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_ord__le__eq__subst)). 132.20/30.71 thf(1378,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > refine424419629nres_a),D:refine424419629nres_a]: ((((C @ B) = D) => ((ord_le519537037nres_a @ (C @ A) @ D) | ~ (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_le519537037nres_a @ (C @ E) @ (C @ F)))))) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 132.20/30.71 thf(6533,plain,(! [B:refine424419629nres_a,A:set_a] : ((? [C:set_a]: (B = (refine1198353288_RES_a @ C))) | ((refine412683989fail_a @ (refine1198353288_RES_a @ A)) != (refine412683989fail_a @ B)))),inference(paramod_ordered,[status(thm)],[1143,1722])). 132.20/30.71 thf(6534,plain,(! [A:set_a] : ((? [B:set_a]: ((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ B))))),inference(pattern_uni,[status(thm)],[6533:[bind(A, $thf(C)),bind(B, $thf(refine1198353288_RES_a @ C))]])). 132.20/30.71 thf(6561,plain,(! [A:set_a] : (((refine1198353288_RES_a @ A) = (refine1198353288_RES_a @ (sk187 @ A))))),inference(cnf,[status(esa)],[6534])). 132.20/30.71 thf(6562,plain,(! [A:set_a] : (((refine1198353288_RES_a @ (sk187 @ A)) = (refine1198353288_RES_a @ A)))),inference(lifteq,[status(thm)],[6561])). 132.20/30.71 thf(6563,plain,(! [A:set_a] : (((refine1198353288_RES_a @ (sk187 @ A)) = (refine1198353288_RES_a @ A)))),inference(simp,[status(thm)],[6562])). 132.20/30.71 thf(9568,plain,(! [B:set_a,A:set_a] : (((refine1822134885_RES_a @ (refine1198353288_RES_a @ A)) = B) | ((refine1198353288_RES_a @ (sk187 @ A)) != (refine1198353288_RES_a @ B)))),inference(paramod_ordered,[status(thm)],[6563,1369])). 132.20/30.71 thf(9569,plain,(! [A:set_a] : (((sk187 @ A) = (refine1822134885_RES_a @ (refine1198353288_RES_a @ A))))),inference(pattern_uni,[status(thm)],[9568:[bind(A, $thf(C)),bind(B, $thf(sk187 @ C))]])). 132.20/30.71 thf(9621,plain,(! [A:set_a] : (((sk187 @ A) = (refine1822134885_RES_a @ (refine1198353288_RES_a @ A))))),inference(simp,[status(thm)],[9569])). 132.20/30.71 thf(10877,plain,(! [A:set_a] : (((sk187 @ A) = A))),inference(rewrite,[status(thm)],[9621,1369])). 132.20/30.71 thf(291,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ top_to231829469nres_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_top__greatest)). 132.20/30.71 thf(1399,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ top_to231829469nres_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 132.20/30.71 thf(80,axiom,((! [A:refine424419629nres_a,B:(a > refine787176636t_unit)]: ((refine579265252t_unit @ (refine96995669t_unit @ A @ B)) = ((refine412683989fail_a @ A) & ! [C:a]: ((refine579265252t_unit @ (B @ C)) <= (refine1001002027nres_a @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_pw__bind__nofail)). 132.20/30.71 thf(607,plain,((! [A:refine424419629nres_a,B:(a > refine787176636t_unit)]: ((refine579265252t_unit @ (refine96995669t_unit @ A @ (B))) = ((refine412683989fail_a @ A) & ! [C:a]: ((refine579265252t_unit @ (B @ C)) | ~ (refine1001002027nres_a @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 132.20/30.71 thf(144,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit]: (((B = A) <= (ord_le1051254044t_unit @ B @ A)) <= (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_dual__order_Oantisym)). 132.20/30.71 thf(839,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit]: ((B = A) | ~ (ord_le1051254044t_unit @ B @ A) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 132.20/30.71 thf(299,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((((C @ B) = D) => ((ord_less_eq_set_a @ (C @ A) @ D) <= (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))))) <= (ord_le519537037nres_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_ord__le__eq__subst)). 132.20/30.71 thf(1431,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a,C:(refine424419629nres_a > set_a),D:set_a]: ((((C @ B) = D) => ((ord_less_eq_set_a @ (C @ A) @ D) | ~ (! [E:refine424419629nres_a,F:refine424419629nres_a]: ((ord_le519537037nres_a @ E @ F) => (ord_less_eq_set_a @ (C @ E) @ (C @ F)))))) | ~ (ord_le519537037nres_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 132.20/30.71 thf(194,axiom,((! [A:set_a,B:set_a]: (((ord_less_eq_set_a @ B @ A) = (B = A)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_antisym__conv)). 132.20/30.71 thf(1004,plain,((! [A:set_a,B:set_a]: (((ord_less_eq_set_a @ B @ A) = (B = A)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 132.20/30.71 thf(9017,plain,(! [B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (sk7 @ (A)) | ((^ [C:($o > set_a),D:($o > set_a)]: ((ord_less_eq_set_a @ (C @ $true) @ (D @ $true)) & (ord_less_eq_set_a @ (C @ $false) @ (D @ $false)))) = (ord_less_eq_o_set_a)) | (~ (A @ (sk8 @ B @ (A)))))),inference(paramod_ordered,[status(thm)],[454,673])). 132.20/30.71 thf(9217,plain,(~ ($true) | (sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > set_a),B:($o > set_a)]: ((ord_less_eq_set_a @ (A @ $true) @ (B @ $true)) & (ord_less_eq_set_a @ (A @ $false) @ (B @ $false)))) = (ord_less_eq_o_set_a))),inference(pre_uni,[status(thm)],[9017:[bind(A, $thf(^ [C:($o > refine424419629nres_a)]: ($true)))]])). 132.20/30.71 thf(9335,plain,((sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > set_a),B:($o > set_a)]: ((ord_less_eq_set_a @ (A @ $true) @ (B @ $true)) & (ord_less_eq_set_a @ (A @ $false) @ (B @ $false)))) = (ord_less_eq_o_set_a))),inference(simp,[status(thm)],[9217])). 132.20/30.71 thf(9030,plain,(! [B:($o > refine424419629nres_a),A:(($o > refine424419629nres_a) > $o)] : ((~ (A @ (B))) | (sk7 @ (A)) | ((^ [C:($o > refine787176636t_unit),D:($o > refine787176636t_unit)]: ((ord_le1051254044t_unit @ (C @ $true) @ (D @ $true)) & (ord_le1051254044t_unit @ (C @ $false) @ (D @ $false)))) = (ord_le1633311077t_unit)) | (~ (A @ (sk8 @ B @ (A)))))),inference(paramod_ordered,[status(thm)],[454,759])). 132.20/30.71 thf(9256,plain,(~ ($true) | (sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > refine787176636t_unit),B:($o > refine787176636t_unit)]: ((ord_le1051254044t_unit @ (A @ $true) @ (B @ $true)) & (ord_le1051254044t_unit @ (A @ $false) @ (B @ $false)))) = (ord_le1633311077t_unit))),inference(pre_uni,[status(thm)],[9030:[bind(A, $thf(^ [C:($o > refine424419629nres_a)]: ($true)))]])). 132.20/30.71 thf(9370,plain,((sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > refine787176636t_unit),B:($o > refine787176636t_unit)]: ((ord_le1051254044t_unit @ (A @ $true) @ (B @ $true)) & (ord_le1051254044t_unit @ (A @ $false) @ (B @ $false)))) = (ord_le1633311077t_unit))),inference(simp,[status(thm)],[9256])). 132.20/30.71 thf(221,axiom,((! [A:a,B:a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine2063221604TURN_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_nres__order__simps_I20_J)). 132.20/30.71 thf(1120,plain,((! [A:a,B:a]: ((ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine2063221604TURN_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 132.20/30.71 thf(15774,plain,(! [A:set_a] : ((A != (collect_a @ (^ [B:a]: ($true)))) | ((collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ (refine1198353288_RES_a @ A)))) != (collect_a @ (^ [B:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ B) @ bot_bo529555393nres_a)))))),inference(paramod_ordered,[status(thm)],[4008,15770])). 132.20/30.71 thf(15784,plain,(((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: ($true)))))) != (^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ bot_bo529555393nres_a)))),inference(simp,[status(thm)],[15774])). 132.20/30.71 thf(16368,plain,(((^ [A:a]: (ord_le519537037nres_a @ (refine2063221604TURN_a @ A) @ (refine1198353288_RES_a @ (collect_a @ (^ [B:a]: ($true)))))) != (^ [A:a]: ((refine2063221604TURN_a @ A) = bot_bo529555393nres_a)))),inference(rewrite,[status(thm)],[15784,1366])). 132.20/30.71 thf(20893,plain,(! [A:a] : (((member_a @ A @ top_top_set_a) != (member_a @ (sk17 @ (insert_a @ sk238 @ bot_bot_set_a)) @ (uminus_uminus_set_a @ (insert_a @ sk238 @ bot_bot_set_a)))))),inference(paramod_ordered,[status(thm)],[677,20327])). 132.20/30.71 thf(20957,plain,(! [A:a] : ((A != (sk17 @ (insert_a @ sk238 @ bot_bot_set_a))) | ((uminus_uminus_set_a @ (insert_a @ sk238 @ bot_bot_set_a)) != top_top_set_a))),inference(simp,[status(thm)],[20893])). 132.20/30.71 thf(20977,plain,(((uminus_uminus_set_a @ (insert_a @ sk238 @ bot_bot_set_a)) != top_top_set_a)),inference(simp,[status(thm)],[20957])). 132.20/30.71 thf(336,plain,(! [A:refine787176636t_unit] : (((ord_le1051254044t_unit @ A @ bot_bo658782032t_unit) = (A = bot_bo658782032t_unit)))),inference(cnf,[status(esa)],[335])). 132.20/30.71 thf(337,plain,(! [A:refine787176636t_unit] : (((ord_le1051254044t_unit @ A @ bot_bo658782032t_unit) = (A = bot_bo658782032t_unit)))),inference(lifteq,[status(thm)],[336])). 132.20/30.71 thf(169,axiom,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ C) => (ord_le1051254044t_unit @ A @ C)) <= (ord_le1051254044t_unit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_order_Otrans)). 132.20/30.71 thf(923,plain,((! [A:refine787176636t_unit,B:refine787176636t_unit,C:refine787176636t_unit]: (((ord_le1051254044t_unit @ B @ C) => (ord_le1051254044t_unit @ A @ C)) | ~ (ord_le1051254044t_unit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 132.20/30.71 thf(94,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ B) <= (member_a @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_subset__eq)). 132.20/30.71 thf(659,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ B) | ~ (member_a @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 132.20/30.71 thf(539,plain,(! [D:set_a,C:(set_a > set_a),B:set_a,A:set_a] : ((~ (ord_less_eq_set_a @ A @ B)) | (ord_less_eq_set_a @ (C @ A) @ D) | (~ (ord_less_eq_set_a @ (C @ (sk18 @ D @ (C) @ B @ A)) @ (C @ (sk19 @ D @ (C) @ B @ A)))) | (~ ((C @ B) = D)))),inference(cnf,[status(esa)],[537])). 132.20/30.71 thf(542,plain,(! [D:set_a,C:(set_a > set_a),B:set_a,A:set_a] : (((C @ B) != D) | (~ (ord_less_eq_set_a @ A @ B)) | (ord_less_eq_set_a @ (C @ A) @ D) | (~ (ord_less_eq_set_a @ (C @ (sk18 @ D @ (C) @ B @ A)) @ (C @ (sk19 @ D @ (C) @ B @ A)))))),inference(lifteq,[status(thm)],[539])). 132.20/30.71 thf(543,plain,(! [C:(set_a > set_a),B:set_a,A:set_a] : ((~ (ord_less_eq_set_a @ A @ B)) | (ord_less_eq_set_a @ (C @ A) @ (C @ B)) | (~ (ord_less_eq_set_a @ (C @ (sk18 @ (C @ B) @ (C) @ B @ A)) @ (C @ (sk19 @ (C @ B) @ (C) @ B @ A)))))),inference(simp,[status(thm)],[542])). 132.20/30.71 thf(17056,plain,(! [A:a] : (((collect_a @ (^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a)))) != (collect_a @ (^ [B:a]: ((refine2063221604TURN_a @ B) = bot_bo529555393nres_a)))))),inference(paramod_ordered,[status(thm)],[5313,13436])). 132.20/30.71 thf(17076,plain,(! [A:a] : (((^ [B:a]: (member_a @ B @ (insert_a @ A @ bot_bot_set_a))) != (^ [B:a]: ((refine2063221604TURN_a @ B) = bot_bo529555393nres_a))))),inference(simp,[status(thm)],[17056])). 132.20/30.71 thf(89,axiom,((! [A:set_a,B:set_a]: (((ord_less_eq_set_a @ B @ A) => (A = B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_subset__antisym)). 132.20/30.71 thf(639,plain,((! [A:set_a,B:set_a]: (((ord_less_eq_set_a @ B @ A) => (A = B)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 132.20/30.71 thf(302,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ bot_bo529555393nres_a @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_nres__order__simps_I1_J)). 132.20/30.71 thf(1449,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ bot_bo529555393nres_a @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 132.20/30.71 thf(76,axiom,((! [A:(set_a > $o),B:set_a,C:(set_a > $o)]: (((! [D:set_a]: ((ord_less_eq_set_a @ D @ B) <= (A @ D))) => ((C @ (order_Greatest_set_a @ A)) <= (! [D:set_a]: (((! [E:set_a]: ((ord_less_eq_set_a @ E @ D) <= (A @ E))) => (C @ D)) <= (A @ D))))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_GreatestI2__order)). 132.20/30.71 thf(592,plain,((! [A:(set_a > $o),B:set_a,C:(set_a > $o)]: (((! [D:set_a]: ((ord_less_eq_set_a @ D @ B) | ~ (A @ D))) => ((C @ (order_Greatest_set_a @ (A))) | ~ (! [D:set_a]: (((! [E:set_a]: ((ord_less_eq_set_a @ E @ D) | ~ (A @ E))) => (C @ D)) | ~ (A @ D))))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 132.20/30.71 thf(11647,plain,((sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C))) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true))))) | ((ord_le516598614nres_a) != (ord_le516598614nres_a))),inference(paramod_ordered,[status(thm)],[1064,9348])). 132.20/30.71 thf(11648,plain,((sk7 @ (^ [A:($o > refine424419629nres_a)]: ($true))) | ((^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ! [C:$o]: (ord_le519537037nres_a @ (A @ C) @ (B @ C))) = (^ [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le519537037nres_a @ (A @ $false) @ (B @ $false)) & (ord_le519537037nres_a @ (A @ $true) @ (B @ $true)))))),inference(pattern_uni,[status(thm)],[11647:[]])). 132.20/30.71 thf(294,axiom,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ top_to231829469nres_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_nres__order__simps_I3_J)). 132.20/30.71 thf(1417,plain,((! [A:refine424419629nres_a]: (ord_le519537037nres_a @ A @ top_to231829469nres_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 132.20/30.71 thf(175,axiom,((! [A:$o,B:($o > refine424419629nres_a),C:($o > refine424419629nres_a),D:($o > refine424419629nres_a),E:($o > refine424419629nres_a)]: (((ord_le516598614nres_a @ B @ C) <= (A)) => (((ord_le516598614nres_a @ D @ E) <= (~ (A))) => (ord_le516598614nres_a @ (if_o_R1705037948nres_a @ A @ B @ D) @ (if_o_R1705037948nres_a @ A @ C @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Refine__Misc_Oif__mono)). 132.20/30.71 thf(940,plain,((! [A:$o,B:($o > refine424419629nres_a),C:($o > refine424419629nres_a),D:($o > refine424419629nres_a),E:($o > refine424419629nres_a)]: (((ord_le516598614nres_a @ (B) @ (C)) | ~ (A)) => (((ord_le516598614nres_a @ (D) @ (E)) | (A)) => (ord_le516598614nres_a @ (if_o_R1705037948nres_a @ A @ B @ D) @ (if_o_R1705037948nres_a @ A @ C @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 132.20/30.71 thf(314,axiom,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((partia906949161nres_a @ top_to231829469nres_a @ A @ B) => (ord_le519537037nres_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_flat__ord__compat_I2_J)). 132.20/30.71 thf(1490,plain,((! [A:refine424419629nres_a,B:refine424419629nres_a]: ((partia906949161nres_a @ top_to231829469nres_a @ A @ B) => (ord_le519537037nres_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 132.20/30.71 thf(128,axiom,((! [A:refine787176636t_unit,B:refine424419629nres_a,C:(a > refine787176636t_unit)]: (((refine412683989fail_a @ B) <= (refine579265252t_unit @ A)) => ((ord_le1051254044t_unit @ (refine96995669t_unit @ B @ C) @ A) <= (! [D:a]: (((refine1001002027nres_a @ B @ D) => (ord_le1051254044t_unit @ (C @ D) @ A)) <= (refine412683989fail_a @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_pw__bind__leI)). 132.20/30.71 thf(775,plain,((! [A:refine787176636t_unit,B:refine424419629nres_a,C:(a > refine787176636t_unit)]: (((refine412683989fail_a @ B) | ~ (refine579265252t_unit @ A)) => ((ord_le1051254044t_unit @ (refine96995669t_unit @ B @ (C)) @ A) | ~ (! [D:a]: (((refine1001002027nres_a @ B @ D) => (ord_le1051254044t_unit @ (C @ D) @ A)) | ~ (refine412683989fail_a @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 132.20/30.71 thf(122,axiom,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ A @ B) => ((ord_le516598614nres_a @ B @ A) => (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_dual__order_Oantisym)). 132.20/30.71 thf(755,plain,((! [A:($o > refine424419629nres_a),B:($o > refine424419629nres_a)]: ((ord_le516598614nres_a @ (A) @ (B)) => ((ord_le516598614nres_a @ (B) @ (A)) => ((B) = (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 132.20/30.71 thf(209,axiom,((! [A:(a > $o),B:a]: ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ A)) @ B) = (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nf__inres__SPEC)). 132.20/30.71 thf(1069,plain,((! [A:(a > $o),B:a]: ((refine1312857699nres_a @ (refine1198353288_RES_a @ (collect_a @ (A))) @ B) = (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 132.20/30.71 thf(24618,plain,($false),inference(e,[status(thm)],[645,1322,1501,629,1469,760,6231,5329,909,1899,893,518,962,555,1956,365,1369,1190,479,1105,16576,347,1729,666,1295,1686,352,12500,1596,683,730,1522,3377,1401,1422,1073,13424,449,878,21834,1041,1486,523,1158,15770,18233,9191,1142,1269,614,677,6522,1426,385,1137,6939,7697,1735,500,715,1275,472,1233,698,1063,14301,1222,1164,797,15791,16630,1196,1001,13209,973,1386,1366,1095,404,782,18834,1441,1409,14909,1298,372,1264,1455,934,1462,5279,802,344,14002,638,1892,1319,1013,881,15338,1100,4008,9768,1922,817,12443,1347,17181,14913,448,1494,1465,16448,834,15409,20978,1183,480,443,17171,2996,16293,1151,1581,353,6438,1215,20368,866,998,1943,15041,1242,527,602,981,1169,397,877,692,1072,453,1394,7645,396,1526,411,17189,1074,9720,380,678,661,1199,366,5281,12673,1206,452,512,439,16297,16292,1047,1057,334,957,952,1519,1123,820,561,1370,1343,6328,1883,1560,625,4994,1178,1159,15999,551,1281,1392,12571,916,13551,852,1555,583,830,456,842,578,1234,1143,948,18172,1328,1375,1064,725,1096,610,420,499,11923,5313,18613,2692,1498,14914,488,1292,669,642,526,637,1810,970,1744,706,1419,328,471,686,476,1016,1207,622,393,515,1451,1530,1266,2355,1050,569,6988,503,701,9348,984,14670,6171,343,13436,360,805,508,14008,921,541,398,16296,794,718,1187,674,12677,926,906,425,513,16188,824,4874,1483,3079,17695,745,573,689,444,1374,375,1278,11578,1154,423,1007,843,772,1388,875,958,1256,1226,1428,1669,382,1058,1332,335,3091,1356,672,14667,1139,445,22298,936,5282,498,466,1092,704,21802,350,6261,9439,604,406,1853,1524,2906,737,434,4374,1175,20327,12676,377,1589,1492,1603,362,451,567,1722,1144,1571,599,1439,477,758,15015,483,1325,895,1177,1061,1112,890,1667,367,552,535,14016,19737,330,912,959,827,10925,2592,1477,1364,1496,6180,431,653,1044,1245,455,883,722,1304,1203,1467,663,374,1081,11579,17244,355,754,490,675,426,1166,680,9514,812,1509,5358,458,14594,525,855,1516,872,887,414,1566,327,705,1611,1053,673,1987,1300,441,370,502,1235,463,338,470,808,544,331,19628,14545,1579,13983,14631,1427,1670,11636,446,497,14906,656,1802,19001,1284,1585,978,991,1617,465,1459,931,482,1157,581,759,2209,844,1108,1316,1084,556,6408,976,14037,903,1010,14015,588,1903,1062,1101,14041,632,401,786,995,896,748,568,378,929,1308,1193,6277,1212,763,383,899,346,549,536,9321,1161,433,510,2142,752,12702,833,405,14984,867,603,950,1097,835,18555,1229,1148,1673,422,1248,865,1480,564,358,1056,1710,635,696,955,7648,415,341,1495,1657,11557,437,1335,1172,474,3479,767,532,1065,987,1352,575,860,1537,1378,10877,1713,442,1399,607,395,839,1431,1004,9335,9370,1120,16368,18939,20977,337,354,923,659,543,17076,639,491,1449,592,11648,1417,1367,940,1490,775,755,676,454,1069])). 132.20/30.71 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 132.20/30.71 % [INFO] Killing All external provers ... 132.20/30.71 WARNING: TreeLimitedRun lost 48.14s, total lost is 48.14s 132.20/30.71 FINAL WATCH: 115.3 CPU 24.6 WC 132.20/30.71 Killed 2 orphans 132.20/30.71 Killed 4 orphans 132.20/30.71 EOF