0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.14/0.15 % Command : run_Leo-III %s %d 0.14/0.36 % Computer : n016.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1440 0.14/0.36 % WCLimit : 180 0.14/0.36 % DateTime : Mon Jul 3 09:08:35 EDT 2023 0.14/0.36 % CPUTime : 0.94/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 2.17/1.17 % [INFO] Parsing done (324ms). 2.17/1.18 % [INFO] Running in sequential loop mode. 2.90/1.39 % [INFO] eprover registered as external prover. 2.90/1.39 % [INFO] cvc4 registered as external prover. 2.90/1.39 % [INFO] Scanning for conjecture ... 3.16/1.52 % [INFO] Found a conjecture and 1224 axioms. Running axiom selection ... 3.95/1.69 % [INFO] Axiom selection finished. Selected 832 axioms (removed 392 axioms). 4.96/1.98 % [INFO] Problem is higher-order (TPTP THF). 4.96/2.01 % [INFO] Type checking passed. 4.96/2.01 % [CONFIG] Using configuration: timeout(180) with strategy. Searching for refutation ... 122.75/29.31 % External prover 'cvc4' found a proof! 122.75/29.31 % [INFO] Killing All external provers ... 122.75/29.31 % Time passed: 28799ms (effective reasoning time: 28132ms) 122.75/29.31 % Solved by strategy 122.75/29.32 % Axioms used in derivation (832): fact_804_IntI, fact_1073_Int__Collect__mono, fact_347_pigeonhole__infinite, fact_1051_Diff__partition, fact_1077_distrib__imp2, fact_1060_diff__single__insert, fact_412_Un__absorb, fact_227_finite__subset, fact_463_insert__is__Un, fact_1088_fun__upd__image, fact_344_pigeonhole__infinite, fact_1056_Un__Int__assoc__eq, fact_945_Diff__empty, fact_290_singleton__conv, fact_57_finite__surj, fact_1114_not__Some__eq, fact_957_insert__Diff__if, fact_863_Collect__conj__eq, fact_897_inf__absorb1, fact_1197_UNIV__I, fact_952_finite__Diff2, fact_792_folding__one_Oremove, fact_396_Un__assoc, fact_544_rev__predicate1D, fact_145_insertI1, fact_149_subset__trans, fact_729_folding__one_Oinsert, 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fact_1013_Un__Int__crazy, fact_598_sup__left__idem, fact_763_evalc__elim__cases_I6_J, fact_1186_option_Oexhaust, fact_550_sup1I1, fact_176_imageI, fact_833_IntD2, fact_994_insert__inter__insert, fact_524_bot__fun__def, fact_1183_inj__on__iff__surj, fact_497_order__eq__iff, fact_447_Un__absorb1, fact_153_set__mp, fact_584_inf__sup__aci_I5_J, fact_134_insert__Collect, fact_978_Un__Diff__cancel, fact_987_Int__insert__left__if0, fact_333_finite_Osimps, fact_335_pigeonhole__infinite, fact_1045_finite__Diff__insert, fact_652_sup__least, fact_1099_minus__fold__remove, fact_907_inf__greatest, fact_750_mk__disjoint__insert, fact_599_sup_Oleft__commute, fact_628_sup__ge2, fact_148_equalityE, fact_428_finite__UnI, fact_468_xt1_I5_J, fact_1156_union__fold__insert, fact_631_le__iff__sup, fact_49_insert__dom, fact_79_subsetD, fact_772_evalc__WHILE__case, fact_700_com_Osimps_I17_J, fact_1054_image__Int__subset, fact_604_inf__sup__aci_I7_J, fact_644_sup__absorb1, fact_1121_inj__on__Un__image__eq__iff, fact_882_inf__le2, fact_1084_flat__lub__def, fact_47_image__constant, fact_84_image__eqI, fact_405_Un__commute, fact_161_equalityD2, fact_726_the__elem__def, fact_107_all__not__in__conv, fact_625_inf__sup__ord_I4_J, fact_1057_if__image__distrib, fact_562_Option_Oset_Osimps_I2_J, fact_796_is__none__code_I2_J, fact_1036_insert__Diff__single, fact_684_folding__one__idem_Oinsert__idem, fact_1070_dom__override__on, fact_1196_UNIV__I, fact_1115_not__None__eq, fact_285_Collect__conv__if2, fact_241_Collect__def, fact_489_order__antisym__conv, fact_270_domI, fact_262_image__insert, fact_1033_Diff__insert__absorb, fact_112_empty__def, fact_237_mem__def, fact_1053_Diff__subset__conv, fact_608_sup_Oassoc, fact_363_image__subsetI, fact_647_le__supI, fact_35_finite__Collect__conjI, fact_1173_WT_OBody, fact_127_insert__iff, fact_409_Un__def, fact_307_finite__subset__induct, fact_416_Collect__disj__eq, fact_1151_finite__surj__inj, fact_455_image__Un, fact_2_weaken, fact_830_DiffD2, fact_1067_finite__empty__induct, fact_581_sup_Ocommute, fact_912_le__infE, fact_188_singleton__inject, fact_95_empty__iff, help_fequal_2_1_fequal_000tc__Com__Ostate_T, fact_156_set__rev__mp, fact_436_Un__insert__left, fact_988_Int__insert__left__if0, fact_383_UnE, fact_395_Un__assoc, fact_467_xt1_I6_J, fact_368_order__refl, fact_596_sup__left__idem, fact_138_insert__Collect, fact_358_the__elem__eq, fact_4_cut, fact_58_finite__surj, fact_545_rev__predicate1D, fact_571_sup__eq__bot__iff, fact_839_DiffD1, fact_352_domD, conj_4, fact_1011_Int__lower1, fact_170_rev__image__eqI, fact_1152_inj__on__image__Int, fact_696_folding__one__idem_Oidem, fact_997_Int__insert__left, fact_708_com_Osimps_I49_J, fact_417_Un__empty, fact_578_sup__idem, fact_256_insert__image, fact_1140_Option_Oset_Osimps_I1_J, fact_19_finite__imageI, fact_1188_Cantor__Bernstein__aux, fact_979_Un__Diff__cancel, fact_486_ord__eq__le__trans, fact_503_le__bot, fact_18_finite__imageI, fact_7_MGT__BodyN, fact_164_set__eq__subset, fact_972_Diff__subset, fact_118_insertI2, fact_539_conseq12, fact_380_UnCI, fact_1189_image__vimage__subset, fact_494_order__eq__refl, fact_117_insertI2, fact_205_empty__not__insert, fact_958_insert__Diff__if, fact_1098_minus__fold__remove, fact_332_finite_Osimps, fact_831_DiffD2, fact_836_IntD1, fact_403_Un__left__absorb, fact_500_option_Oinject, fact_1034_Diff__insert__absorb, fact_917_inf__bot__right, fact_529_finite__pointwise, fact_528_finite__pointwise, fact_155_set__rev__mp, fact_1080_distrib__imp1, conj_0, fact_560_Option_Oset_Osimps_I2_J, fact_753_Set_Oset__insert, fact_162_equalityD1, fact_461_insert__is__Un, fact_502_Body1, fact_1004_Int__greatest, fact_797_is__none__code_I2_J, fact_514_bot__least, conj_5, fact_709_com_Osimps_I48_J, fact_1012_Int__lower1, fact_669_ospec, fact_177_imageI, fact_867_Diff__Int, fact_86_equals0D, fact_229_finite__subset, fact_281_Collect__conv__if2, fact_527_finite__pointwise, fact_768_evalc_OWhileTrue, fact_234_insert__mono, fact_699_com_Osimps_I13_J, fact_1187_Cantor__Bernstein__aux, fact_200_insert__not__empty, fact_1039_Diff__insert2, fact_492_order__eq__refl, fact_982_Int__insert__left__if1, fact_568_sup__eq__bot__iff, fact_877_inf__le1, fact_617_inf__sup__ord_I3_J, fact_822_inf__Int__eq, fact_859_Int__Collect, fact_530_escape, fact_927_sup__inf__absorb, fact_46_image__constant, fact_17_finite__imageI, fact_1119_domIff, fact_398_Un__iff, fact_302_imageE, fact_175_imageI, fact_97_empty__Collect__eq, fact_182_finite__Collect__disjI, fact_271_domI, fact_451_Un__upper2, fact_586_inf__sup__aci_I5_J, fact_674_folding__one__idem_Ounion__idem, fact_885_le__iff__inf, fact_253_subset__insertI, fact_440_Un__mono, fact_446_Un__absorb1, fact_391_ball__Un, fact_482_ord__le__eq__trans, fact_1061_diff__single__insert, fact_916_inf__bot__right, fact_680_hoare__derivs_OSkip, fact_14_finite__imageI, fact_702_com_Osimps_I47_J, fact_1024_distrib__inf__le, fact_218_image__empty, fact_985_Int__insert__right__if1, fact_1182_inj__on__iff__surj, fact_894_le__infI2, fact_82_image__eqI, fact_818_finite__Diff, fact_967_Int__empty__left, fact_286_singleton__conv, fact_553_pred__subset__eq, fact_1018_Int__Un__distrib2, fact_1010_Int__lower2 122.75/29.32 % No. of inferences in proof: 1705 122.75/29.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 28799 ms resp. 28132 ms w/o parsing 123.96/29.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 123.96/29.66 thf(com_type, type, com: $tType). 123.96/29.66 thf(pname_type, type, pname: $tType). 123.96/29.66 thf(state_type, type, state: $tType). 123.96/29.66 thf(hoare_1708887482_state_type, type, hoare_1708887482_state: $tType). 123.96/29.66 thf(option_com_type, type, option_com: $tType). 123.96/29.66 thf(option_pname_type, type, option_pname: $tType). 123.96/29.66 thf(option1624383643_state_type, type, option1624383643_state: $tType). 123.96/29.66 thf(wt_type, type, wt: (com > $o)). 123.96/29.66 thf(wT_bodies_type, type, wT_bodies: $o). 123.96/29.66 thf(body_type, type, body: (pname > option_com)). 123.96/29.66 thf(body_1_type, type, body_1: (pname > com)). 123.96/29.66 thf(skip_type, type, skip: com). 123.96/29.66 thf(semi_type, type, semi: (com > (com > com))). 123.96/29.66 thf(while_type, type, while: ((state > $o) > (com > com))). 123.96/29.66 thf(finite138924780name_o_type, type, finite138924780name_o: (((pname > $o) > ((pname > $o) > (pname > $o))) > $o)). 123.96/29.66 thf(finite2034616076tate_o_type, type, finite2034616076tate_o: (((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o))) > $o)). 123.96/29.66 thf(finite662762081tate_o_type, type, finite662762081tate_o: ((hoare_1708887482_state > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o))) > $o)). 123.96/29.66 thf(finite297249702name_o_type, type, finite297249702name_o: (((pname > $o) > $o) > $o)). 123.96/29.66 thf(finite1329924456tate_o_type, type, finite1329924456tate_o: (((hoare_1708887482_state > $o) > $o) > $o)). 123.96/29.66 thf(finite_finite_pname_type, type, finite_finite_pname: ((pname > $o) > $o)). 123.96/29.66 thf(finite1625599783_state_type, type, finite1625599783_state: ((hoare_1708887482_state > $o) > $o)). 123.96/29.66 thf(finite603803317name_o_type, type, finite603803317name_o: ((pname > ((pname > $o) > (pname > $o))) > ((pname > $o) > ((pname > $o) > (pname > $o))))). 123.96/29.66 thf(finite96880613tate_o_type, type, finite96880613tate_o: ((hoare_1708887482_state > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o))) > ((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o))))). 123.96/29.66 thf(finite309095018_state_type, type, finite309095018_state: ((hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)) > (hoare_1708887482_state > ((hoare_1708887482_state > $o) > hoare_1708887482_state)))). 123.96/29.66 thf(finite2139561282_pname_type, type, finite2139561282_pname: (((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o))) > ((pname > (hoare_1708887482_state > $o)) > ((hoare_1708887482_state > $o) > ((pname > $o) > (hoare_1708887482_state > $o)))))). 123.96/29.66 thf(finite1282449217_pname_type, type, finite1282449217_pname: ((pname > (pname > pname)) > (((pname > $o) > pname) > $o))). 123.96/29.66 thf(finite1615457021_state_type, type, finite1615457021_state: ((hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)) > (((hoare_1708887482_state > $o) > hoare_1708887482_state) > $o))). 123.96/29.66 thf(finite89670078_pname_type, type, finite89670078_pname: ((pname > (pname > pname)) > (((pname > $o) > pname) > $o))). 123.96/29.66 thf(finite1347568576_state_type, type, finite1347568576_state: ((hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)) > (((hoare_1708887482_state > $o) > hoare_1708887482_state) > $o))). 123.96/29.66 thf(fun_up1986763201_state_type, type, fun_up1986763201_state: ((pname > hoare_1708887482_state) > (pname > (hoare_1708887482_state > (pname > hoare_1708887482_state))))). 123.96/29.66 thf(fun_up879233478on_com_type, type, fun_up879233478on_com: ((pname > option_com) > (pname > (option_com > (pname > option_com))))). 123.96/29.66 thf(inj_on11367768on_com_type, type, inj_on11367768on_com: ((com > option_com) > ((com > $o) > $o))). 123.96/29.66 thf(inj_on1553129421_state_type, type, inj_on1553129421_state: ((pname > hoare_1708887482_state) > ((pname > $o) > $o))). 123.96/29.66 thf(inj_on737724108_pname_type, type, inj_on737724108_pname: ((pname > option_pname) > ((pname > $o) > $o))). 123.96/29.66 thf(inj_on1945914667_pname_type, type, inj_on1945914667_pname: ((hoare_1708887482_state > pname) > ((hoare_1708887482_state > $o) > $o))). 123.96/29.66 thf(inj_on632008595_state_type, type, inj_on632008595_state: ((hoare_1708887482_state > hoare_1708887482_state) > ((hoare_1708887482_state > $o) > $o))). 123.96/29.66 thf(inj_on945311362_state_type, type, inj_on945311362_state: ((hoare_1708887482_state > option1624383643_state) > ((hoare_1708887482_state > $o) > $o))). 123.96/29.66 thf(overri1496249029on_com_type, type, overri1496249029on_com: ((pname > option_com) > ((pname > option_com) > ((pname > $o) > (pname > option_com))))). 123.96/29.66 thf(minus_minus_pname_o_type, type, minus_minus_pname_o: ((pname > $o) > ((pname > $o) > (pname > $o)))). 123.96/29.66 thf(minus_2056855718tate_o_type, type, minus_2056855718tate_o: ((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o)))). 123.96/29.66 thf(the_Ho851197897_state_type, type, the_Ho851197897_state: ((hoare_1708887482_state > $o) > hoare_1708887482_state)). 123.96/29.66 thf(hoare_Mirabelle_MGT_type, type, hoare_Mirabelle_MGT: (com > hoare_1708887482_state)). 123.96/29.66 thf(hoare_90032982_state_type, type, hoare_90032982_state: ((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o))). 123.96/29.66 thf(hoare_496444244_state_type, type, hoare_496444244_state: ((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o))). 123.96/29.66 thf(hoare_1160767572gleton_type, type, hoare_1160767572gleton: $o). 123.96/29.66 thf(hoare_858012674_state_type, type, hoare_858012674_state: ((state > (state > $o)) > (com > ((state > (state > $o)) > hoare_1708887482_state)))). 123.96/29.66 thf(if_Hoa1374726218_state_type, type, if_Hoa1374726218_state: ($o > (hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)))). 123.96/29.66 thf(if_option_com_type, type, if_option_com: ($o > (option_com > (option_com > option_com)))). 123.96/29.66 thf(semila1673364395name_o_type, type, semila1673364395name_o: ((pname > $o) > ((pname > $o) > (pname > $o)))). 123.96/29.66 thf(semila129691299tate_o_type, type, semila129691299tate_o: ((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o)))). 123.96/29.66 thf(semila1780557381name_o_type, type, semila1780557381name_o: ((pname > $o) > ((pname > $o) > (pname > $o)))). 123.96/29.66 thf(semila1122118281tate_o_type, type, semila1122118281tate_o: ((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o)))). 123.96/29.66 thf(dom_com_com_type, type, dom_com_com: ((com > option_com) > (com > $o))). 123.96/29.66 thf(dom_pname_com_type, type, dom_pname_com: ((pname > option_com) > (pname > $o))). 123.96/29.66 thf(dom_pname_pname_type, type, dom_pname_pname: ((pname > option_pname) > (pname > $o))). 123.96/29.66 thf(dom_pn1412407212_state_type, type, dom_pn1412407212_state: ((pname > option1624383643_state) > (pname > $o))). 123.96/29.66 thf(dom_Ho1805192458_pname_type, type, dom_Ho1805192458_pname: ((hoare_1708887482_state > option_pname) > (hoare_1708887482_state > $o))). 123.96/29.66 thf(dom_Ho1703271284_state_type, type, dom_Ho1703271284_state: ((hoare_1708887482_state > option1624383643_state) > (hoare_1708887482_state > $o))). 123.96/29.66 thf(restri1382200118me_com_type, type, restri1382200118me_com: ((pname > option_com) > ((pname > $o) > (pname > option_com)))). 123.96/29.66 thf(evalc_type, type, evalc: (com > (state > (state > $o)))). 123.96/29.66 thf(is_none_pname_type, type, is_none_pname: (option_pname > $o)). 123.96/29.66 thf(is_non163157940_state_type, type, is_non163157940_state: (option1624383643_state > $o)). 123.96/29.66 thf(none_com_type, type, none_com: option_com). 123.96/29.66 thf(none_H1106584047_state_type, type, none_H1106584047_state: option1624383643_state). 123.96/29.66 thf(some_com_type, type, some_com: (com > option_com)). 123.96/29.66 thf(some_pname_type, type, some_pname: (pname > option_pname)). 123.96/29.66 thf(some_H1974565227_state_type, type, some_H1974565227_state: (hoare_1708887482_state > option1624383643_state)). 123.96/29.66 thf(set_com_type, type, set_com: (option_com > (com > $o))). 123.96/29.66 thf(set_pname_type, type, set_pname: (option_pname > (pname > $o))). 123.96/29.66 thf(set_Ho525251890_state_type, type, set_Ho525251890_state: (option1624383643_state > (hoare_1708887482_state > $o))). 123.96/29.66 thf(the_com_type, type, the_com: (option_com > com)). 123.96/29.66 thf(the_pname_1_type, type, the_pname_1: (option_pname > pname)). 123.96/29.66 thf(the_Ho963921505_state_type, type, the_Ho963921505_state: (option1624383643_state > hoare_1708887482_state)). 123.96/29.66 thf(bot_bot_com_o_type, type, bot_bot_com_o: (com > $o)). 123.96/29.66 thf(bot_bot_pname_o_type, type, bot_bot_pname_o: (pname > $o)). 123.96/29.66 thf(bot_bo19817387tate_o_type, type, bot_bo19817387tate_o: (hoare_1708887482_state > $o)). 123.96/29.66 thf(bot_bot_o_type, type, bot_bot_o: $o). 123.96/29.66 thf(ord_le1205211808me_o_o_type, type, ord_le1205211808me_o_o: (((pname > $o) > $o) > (((pname > $o) > $o) > $o))). 123.96/29.66 thf(ord_le1728773982te_o_o_type, type, ord_le1728773982te_o_o: (((hoare_1708887482_state > $o) > $o) > (((hoare_1708887482_state > $o) > $o) > $o))). 123.96/29.66 thf(ord_less_eq_pname_o_type, type, ord_less_eq_pname_o: ((pname > $o) > ((pname > $o) > $o))). 123.96/29.66 thf(ord_le777019615tate_o_type, type, ord_le777019615tate_o: ((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o))). 123.96/29.66 thf(top_top_com_o_type, type, top_top_com_o: (com > $o)). 123.96/29.66 thf(top_top_pname_o_type, type, top_top_pname_o: (pname > $o)). 123.96/29.66 thf(top_to832624271tate_o_type, type, top_to832624271tate_o: (hoare_1708887482_state > $o)). 123.96/29.66 thf(partia1256728516_state_type, type, partia1256728516_state: (hoare_1708887482_state > ((hoare_1708887482_state > $o) > hoare_1708887482_state))). 123.96/29.66 thf(collect_pname_o_type, type, collect_pname_o: (((pname > $o) > $o) > ((pname > $o) > $o))). 123.96/29.66 thf(collec219771562tate_o_type, type, collec219771562tate_o: (((hoare_1708887482_state > $o) > $o) > ((hoare_1708887482_state > $o) > $o))). 123.96/29.66 thf(collect_com_type, type, collect_com: ((com > $o) > (com > $o))). 123.96/29.66 thf(collect_pname_type, type, collect_pname: ((pname > $o) > (pname > $o))). 123.96/29.66 thf(collec1568722789_state_type, type, collec1568722789_state: ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o))). 123.96/29.66 thf(image_pname_o_pname_type, type, image_pname_o_pname: (((pname > $o) > pname) > (((pname > $o) > $o) > (pname > $o)))). 123.96/29.66 thf(image_1922967206_state_type, type, image_1922967206_state: (((pname > $o) > hoare_1708887482_state) > (((pname > $o) > $o) > (hoare_1708887482_state > $o)))). 123.96/29.66 thf(image_2051418740_pname_type, type, image_2051418740_pname: (((hoare_1708887482_state > $o) > pname) > (((hoare_1708887482_state > $o) > $o) > (pname > $o)))). 123.96/29.66 thf(image_27005066_state_type, type, image_27005066_state: (((hoare_1708887482_state > $o) > hoare_1708887482_state) > (((hoare_1708887482_state > $o) > $o) > (hoare_1708887482_state > $o)))). 123.96/29.66 thf(image_com_pname_type, type, image_com_pname: ((com > pname) > ((com > $o) > (pname > $o)))). 123.96/29.66 thf(image_934102463_state_type, type, image_934102463_state: ((com > hoare_1708887482_state) > ((com > $o) > (hoare_1708887482_state > $o)))). 123.96/29.66 thf(image_pname_pname_o_type, type, image_pname_pname_o: ((pname > (pname > $o)) > ((pname > $o) > ((pname > $o) > $o)))). 123.96/29.66 thf(image_425134806tate_o_type, type, image_425134806tate_o: ((pname > (hoare_1708887482_state > $o)) > ((pname > $o) > ((hoare_1708887482_state > $o) > $o)))). 123.96/29.66 thf(image_pname_com_type, type, image_pname_com: ((pname > com) > ((pname > $o) > (com > $o)))). 123.96/29.66 thf(image_pname_pname_type, type, image_pname_pname: ((pname > pname) > ((pname > $o) > (pname > $o)))). 123.96/29.66 thf(image_1116629049_state_type, type, image_1116629049_state: ((pname > hoare_1708887482_state) > ((pname > $o) > (hoare_1708887482_state > $o)))). 123.96/29.66 thf(image_1552895654name_o_type, type, image_1552895654name_o: ((hoare_1708887482_state > (pname > $o)) > ((hoare_1708887482_state > $o) > ((pname > $o) > $o)))). 123.96/29.66 thf(image_1551509096tate_o_type, type, image_1551509096tate_o: ((hoare_1708887482_state > (hoare_1708887482_state > $o)) > ((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o)))). 123.96/29.66 thf(image_1509414295_pname_type, type, image_1509414295_pname: ((hoare_1708887482_state > pname) > ((hoare_1708887482_state > $o) > (pname > $o)))). 123.96/29.66 thf(image_757158439_state_type, type, image_757158439_state: ((hoare_1708887482_state > hoare_1708887482_state) > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o)))). 123.96/29.66 thf(insert_pname_type, type, insert_pname: (pname > ((pname > $o) > (pname > $o)))). 123.96/29.66 thf(insert528405184_state_type, type, insert528405184_state: (hoare_1708887482_state > ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o)))). 123.96/29.66 thf(the_elem_pname_type, type, the_elem_pname: ((pname > $o) > pname)). 123.96/29.66 thf(the_el864710747_state_type, type, the_el864710747_state: ((hoare_1708887482_state > $o) > hoare_1708887482_state)). 123.96/29.66 thf(vimage1943311875_state_type, type, vimage1943311875_state: ((pname > hoare_1708887482_state) > ((hoare_1708887482_state > $o) > (pname > $o)))). 123.96/29.66 thf(fequal_pname_type, type, fequal_pname: (pname > (pname > $o))). 123.96/29.66 thf(fequal_state_type, type, fequal_state: (state > (state > $o))). 123.96/29.66 thf(fequal224822779_state_type, type, fequal224822779_state: (hoare_1708887482_state > (hoare_1708887482_state > $o))). 123.96/29.66 thf(member_com_type, type, member_com: (com > ((com > $o) > $o))). 123.96/29.66 thf(member_pname_type, type, member_pname: (pname > ((pname > $o) > $o))). 123.96/29.66 thf(member451959335_state_type, type, member451959335_state: (hoare_1708887482_state > ((hoare_1708887482_state > $o) > $o))). 123.96/29.66 thf(fa_type, type, fa: (hoare_1708887482_state > $o)). 123.96/29.66 thf(pn_type, type, pn: pname). 123.96/29.66 thf(y_type, type, y: com). 123.96/29.66 thf(sk1_type, type, sk1: ((pname > $o) > ((pname > $o) > ((pname > pname) > (pname > $o))))). 123.96/29.66 thf(sk136_type, type, sk136: pname). 123.96/29.66 thf(sk137_type, type, sk137: state). 123.96/29.66 thf(sk138_type, type, sk138: state). 123.96/29.66 thf(sk139_type, type, sk139: hoare_1708887482_state). 123.96/29.66 thf(447,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ A) <= (! [C:hoare_1708887482_state]: ((member451959335_state @ C @ A) <= (member451959335_state @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_subsetI)). 123.96/29.66 thf(2199,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (A)) | ~ (! [C:hoare_1708887482_state]: ((member451959335_state @ C @ (A)) | ~ (member451959335_state @ C @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[447])). 123.96/29.66 thf(346,axiom,((! [A:(pname > (hoare_1708887482_state > $o)),B:(pname > $o)]: (((finite1329924456tate_o @ (image_425134806tate_o @ A @ B)) => (? [C:pname]: ((member_pname @ C @ B) & ~ (finite_finite_pname @ (collect_pname @ (^ [D:pname]: ((member_pname @ D @ B) & ((A @ D) = (A @ C))))))))) <= (~ (finite_finite_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_pigeonhole__infinite)). 123.96/29.66 thf(1879,plain,((! [A:(pname > (hoare_1708887482_state > $o)),B:(pname > $o)]: (((finite1329924456tate_o @ (image_425134806tate_o @ A @ B)) => (? [C:pname]: ((member_pname @ C @ (B)) & ~ (finite_finite_pname @ (collect_pname @ (^ [D:pname]: ((member_pname @ D @ B) & ((A @ D) = (A @ C))))))))) | (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])). 123.96/29.66 thf(261,axiom,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ bot_bot_pname_o) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_sup__bot__right)). 123.96/29.66 thf(1633,plain,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ bot_bot_pname_o) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 123.96/29.66 thf(306,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((A = B) <= (ord_less_eq_pname_o @ B @ A)) <= (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_equalityI)). 123.96/29.66 thf(1767,plain,((! [A:(pname > $o),B:(pname > $o)]: (((A) = (B)) | ~ (ord_less_eq_pname_o @ (B) @ (A)) | ~ (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 123.96/29.66 thf(86,axiom,((! [A:(pname > option_com),B:pname]: (((dom_pname_com @ A) = (insert_pname @ B @ bot_bot_pname_o)) = (? [C:com]: (A = (fun_up879233478on_com @ (^ [D:pname]: (none_com)) @ B @ (some_com @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_dom__eq__singleton__conv)). 123.96/29.66 thf(1105,plain,((! [A:(pname > option_com),B:pname]: (((dom_pname_com @ A) = (insert_pname @ B @ bot_bot_pname_o)) = (? [C:com]: ((A) = (fun_up879233478on_com @ (^ [D:pname]: (none_com)) @ B @ (some_com @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 123.96/29.66 thf(819,axiom,((finite1625599783_state @ bot_bo19817387tate_o)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_finite_OemptyI)). 123.96/29.66 thf(3434,plain,((finite1625599783_state @ (bot_bo19817387tate_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[819])). 123.96/29.66 thf(652,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila129691299tate_o @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_927_sup__inf__absorb)). 123.96/29.66 thf(2876,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila129691299tate_o @ A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[652])). 123.96/29.66 thf(25,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((minus_minus_pname_o @ A @ (insert_pname @ B @ C)) = (minus_minus_pname_o @ (minus_minus_pname_o @ A @ C) @ (insert_pname @ B @ bot_bot_pname_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_Diff__insert)). 123.96/29.66 thf(909,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((minus_minus_pname_o @ A @ (insert_pname @ B @ C)) = (minus_minus_pname_o @ (minus_minus_pname_o @ A @ C) @ (insert_pname @ B @ bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 123.96/29.66 thf(332,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ A @ C) <= (B = A)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_xt1_I4_J)). 123.96/29.66 thf(1840,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (C)) | ~ ((B) = (A)) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 123.96/29.66 thf(554,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_equalityD1)). 123.96/29.66 thf(2559,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) | ~ ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[554])). 123.96/29.66 thf(113,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_sup_Oassoc)). 123.96/29.66 thf(1179,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 123.96/29.66 thf(81,axiom,((! [A:hoare_1708887482_state]: (member451959335_state @ A @ top_to832624271tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1197_UNIV__I)). 123.96/29.66 thf(1092,plain,((! [A:hoare_1708887482_state]: (member451959335_state @ A @ (top_to832624271tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 123.96/29.66 thf(1093,plain,(! [A:hoare_1708887482_state] : ((member451959335_state @ A @ (top_to832624271tate_o)))),inference(cnf,[status(esa)],[1092])). 123.96/29.66 thf(820,axiom,((~ (member451959335_state @ (hoare_Mirabelle_MGT @ y) @ fa))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3)). 123.96/29.66 thf(3435,plain,((~ (member451959335_state @ (hoare_Mirabelle_MGT @ y) @ (fa)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[820])). 123.96/29.66 thf(3436,plain,((~ (member451959335_state @ (hoare_Mirabelle_MGT @ y) @ (fa)))),inference(polarity_switch,[status(thm)],[3435])). 123.96/29.66 thf(3564,plain,(! [A:hoare_1708887482_state] : (((member451959335_state @ A @ (top_to832624271tate_o)) != (member451959335_state @ (hoare_Mirabelle_MGT @ y) @ (fa))))),inference(paramod_ordered,[status(thm)],[1093,3436])). 123.96/29.66 thf(3565,plain,(! [A:hoare_1708887482_state] : ((A != (hoare_Mirabelle_MGT @ y)) | ((fa) != (top_to832624271tate_o)))),inference(simp,[status(thm)],[3564])). 123.96/29.66 thf(3566,plain,(((fa) != (top_to832624271tate_o))),inference(simp,[status(thm)],[3565])). 123.96/29.66 thf(235,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((~ ((ord_less_eq_pname_o @ A @ C) => (~ (ord_less_eq_pname_o @ B @ C)))) <= (ord_less_eq_pname_o @ (semila1780557381name_o @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_le__supE)). 123.96/29.66 thf(1549,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (~ ((ord_less_eq_pname_o @ (A) @ (C)) => (~ (ord_less_eq_pname_o @ (B) @ (C)))) | ~ (ord_less_eq_pname_o @ (semila1780557381name_o @ A @ B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 123.96/29.66 thf(475,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((! [D:hoare_1708887482_state]: ((A @ D) <= (member451959335_state @ D @ B)) & ! [D:hoare_1708887482_state]: ((member451959335_state @ D @ C) => (A @ D))) = (! [D:hoare_1708887482_state]: ((A @ D) <= (member451959335_state @ D @ (semila1122118281tate_o @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_ball__Un)). 123.96/29.66 thf(2280,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((! [D:hoare_1708887482_state]: ((A @ D) | ~ (member451959335_state @ D @ (B))) & ! [D:hoare_1708887482_state]: ((member451959335_state @ D @ (C)) => (A @ D))) = (! [D:hoare_1708887482_state]: ((A @ D) | ~ (member451959335_state @ D @ (semila1122118281tate_o @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[475])). 123.96/29.66 thf(437,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: ((ord_less_eq_pname_o @ C @ D) => ((ord_less_eq_pname_o @ A @ B) => (ord_less_eq_pname_o @ (semila1673364395name_o @ C @ A) @ (semila1673364395name_o @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1001_Int__mono)). 123.96/29.66 thf(2163,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: ((ord_less_eq_pname_o @ (C) @ (D)) => ((ord_less_eq_pname_o @ (A) @ (B)) => (ord_less_eq_pname_o @ (semila1673364395name_o @ C @ A) @ (semila1673364395name_o @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[437])). 123.96/29.66 thf(19,axiom,((! [A:(pname > $o)]: ((minus_minus_pname_o @ A @ A) = bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_941_Diff__cancel)). 123.96/29.66 thf(892,plain,((! [A:(pname > $o)]: ((minus_minus_pname_o @ A @ A) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 123.96/29.66 thf(62,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ (collec219771562tate_o @ (^ [C:(hoare_1708887482_state > $o)]: ((A @ C) | (B @ C))))) = ((finite1329924456tate_o @ (collec219771562tate_o @ B)) & (finite1329924456tate_o @ (collec219771562tate_o @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_finite__Collect__disjI)). 123.96/29.66 thf(1036,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ (collec219771562tate_o @ (^ [C:(hoare_1708887482_state > $o)]: ((A @ C) | (B @ C))))) = ((finite1329924456tate_o @ (collec219771562tate_o @ B)) & (finite1329924456tate_o @ (collec219771562tate_o @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 123.96/29.66 thf(639,axiom,((! [A:(com > $o)]: ((! [B:com]: ~ (member_com @ B @ A)) => (A = bot_bot_com_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_equals0I)). 123.96/29.66 thf(2822,plain,((! [A:(com > $o)]: ((! [B:com]: ~ (member_com @ B @ (A))) => ((A) = (bot_bot_com_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[639])). 123.96/29.66 thf(578,axiom,((! [A:com,B:com]: (skip != (semi @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_com_Osimps_I12_J)). 123.96/29.66 thf(2630,plain,((! [A:com,B:com]: ~ (skip = (semi @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[578])). 123.96/29.66 thf(414,axiom,((! [A:(hoare_1708887482_state > hoare_1708887482_state),B:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (image_757158439_state @ A @ B) @ B) => (((image_757158439_state @ A @ B) = B) <= (inj_on632008595_state @ A @ B))) <= (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_endo__inj__surj)). 123.96/29.66 thf(2094,plain,((! [A:(hoare_1708887482_state > hoare_1708887482_state),B:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (image_757158439_state @ A @ B) @ (B)) => (((image_757158439_state @ A @ B) = (B)) | ~ (inj_on632008595_state @ (A) @ (B)))) | ~ (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[414])). 123.96/29.66 thf(188,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_874_inf__sup__ord_I1_J)). 123.96/29.66 thf(1411,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 123.96/29.66 thf(614,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (insert_pname @ A @ B) @ C) = ((ord_less_eq_pname_o @ B @ C) & (member_pname @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_insert__subset)). 123.96/29.66 thf(2744,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (insert_pname @ A @ B) @ (C)) = ((ord_less_eq_pname_o @ (B) @ (C)) & (member_pname @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[614])). 123.96/29.66 thf(174,axiom,((! [A:(pname > option1624383643_state),B:pname,C:hoare_1708887482_state]: ((member_pname @ B @ (dom_pn1412407212_state @ A)) <= ((A @ B) = (some_H1974565227_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_domI)). 123.96/29.66 thf(1369,plain,((! [A:(pname > option1624383643_state),B:pname,C:hoare_1708887482_state]: ((member_pname @ B @ (dom_pn1412407212_state @ A)) | ~ ((A @ B) = (some_H1974565227_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 123.96/29.66 thf(109,axiom,((! [A:(pname > $o)]: ((! [B:pname]: ~ (A @ B)) = ((collect_pname @ A) = bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Collect__empty__eq)). 123.96/29.66 thf(1168,plain,((! [A:(pname > $o)]: ((! [B:pname]: ~ (A @ B)) = ((collect_pname @ A) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 123.96/29.66 thf(480,axiom,((! [A:((pname > $o) > $o),B:(pname > $o),C:(pname > $o)]: ((finite_finite_pname @ C) => ((((! [D:pname,E:(pname > $o)]: ((finite_finite_pname @ E) => ((member_pname @ D @ B) => ((~ (member_pname @ D @ E)) => ((A @ (insert_pname @ D @ E)) <= (A @ E)))))) => (A @ C)) <= (A @ bot_bot_pname_o)) <= (ord_less_eq_pname_o @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_finite__subset__induct)). 123.96/29.66 thf(2295,plain,((! [A:((pname > $o) > $o),B:(pname > $o),C:(pname > $o)]: ((finite_finite_pname @ (C)) => (((! [D:pname,E:(pname > $o)]: ((finite_finite_pname @ (E)) => ((member_pname @ D @ (B)) => ((~ (member_pname @ D @ (E))) => ((A @ (insert_pname @ D @ E)) | ~ (A @ (E))))))) => (A @ (C))) | ~ (A @ (bot_bot_pname_o)) | ~ (ord_less_eq_pname_o @ (C) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[480])). 123.96/29.66 thf(808,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ B) => (~ (! [C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ C) <= (B = (insert528405184_state @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_753_Set_Oset__insert)). 123.96/29.66 thf(3399,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (B)) => (~ (! [C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (C)) | ~ ((B) = (insert528405184_state @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[808])). 123.96/29.66 thf(469,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((! [D:(pname > $o),E:(pname > $o),F:(pname > $o)]: ((semila1780557381name_o @ D @ (semila1673364395name_o @ E @ F)) = (semila1673364395name_o @ (semila1780557381name_o @ D @ E) @ (semila1780557381name_o @ D @ F)))) => ((semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_distrib__imp2)). 123.96/29.66 thf(2263,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((! [D:(pname > $o),E:(pname > $o),F:(pname > $o)]: ((semila1780557381name_o @ D @ (semila1673364395name_o @ E @ F)) = (semila1673364395name_o @ (semila1780557381name_o @ D @ E) @ (semila1780557381name_o @ D @ F)))) => ((semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])). 123.96/29.66 thf(521,axiom,((! [A:(pname > com),B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => (member_com @ (A @ B) @ (image_pname_com @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_imageI)). 123.96/29.66 thf(2463,plain,((! [A:(pname > com),B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => (member_com @ (A @ B) @ (image_pname_com @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[521])). 123.96/29.66 thf(353,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((member451959335_state @ C @ A) | (member451959335_state @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_Un__def)). 123.96/29.66 thf(1899,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((member451959335_state @ C @ A) | (member451959335_state @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])). 123.96/29.66 thf(159,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ C) = (semila1673364395name_o @ (semila1780557381name_o @ A @ C) @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_Un__Int__distrib2)). 123.96/29.66 thf(1315,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ C) = (semila1673364395name_o @ (semila1780557381name_o @ A @ C) @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 123.96/29.66 thf(627,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ A) = (finite1625599783_state @ (minus_2056855718tate_o @ A @ B))) <= (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_952_finite__Diff2)). 123.96/29.66 thf(2787,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ (A)) = (finite1625599783_state @ (minus_2056855718tate_o @ A @ B))) | ~ (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[627])). 123.96/29.66 thf(534,axiom,((! [A:((hoare_1708887482_state > $o) > pname),B:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ B) => (finite_finite_pname @ (image_2051418740_pname @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI)). 123.96/29.66 thf(2499,plain,((! [A:((hoare_1708887482_state > $o) > pname),B:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ (B)) => (finite_finite_pname @ (image_2051418740_pname @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[534])). 123.96/29.66 thf(528,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((C = A) | (member451959335_state @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_insert__compr)). 123.96/29.66 thf(2480,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((C = A) | (member451959335_state @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[528])). 123.96/29.66 thf(42,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ B) => ((finite_finite_pname @ (minus_minus_pname_o @ A @ B)) = (finite_finite_pname @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_finite__Diff2)). 123.96/29.66 thf(962,plain,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (B)) => ((finite_finite_pname @ (minus_minus_pname_o @ A @ B)) = (finite_finite_pname @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 123.96/29.66 thf(550,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((semila1122118281tate_o @ B @ A @ C) <= (B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_sup1I1)). 123.96/29.66 thf(2544,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((semila1122118281tate_o @ (B) @ (A) @ C) | ~ (B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[550])). 123.96/29.66 thf(35,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((~ (member_pname @ A @ C)) <= (member_pname @ A @ (minus_minus_pname_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_830_DiffD2)). 123.96/29.66 thf(941,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (~ (member_pname @ A @ (C)) | ~ (member_pname @ A @ (minus_minus_pname_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 123.96/29.66 thf(120,axiom,((! [A:hoare_1708887482_state]: ~ (is_non163157940_state @ (some_H1974565227_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_797_is__none__code_I2_J)). 123.96/29.66 thf(1198,plain,((! [A:hoare_1708887482_state]: ~ (is_non163157940_state @ (some_H1974565227_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 123.96/29.66 thf(1199,plain,((~ (? [A:hoare_1708887482_state]: (is_non163157940_state @ (some_H1974565227_state @ A))))),inference(miniscope,[status(thm)],[1198])). 123.96/29.66 thf(1200,plain,(! [A:hoare_1708887482_state] : ((~ (is_non163157940_state @ (some_H1974565227_state @ A))))),inference(cnf,[status(esa)],[1199])). 123.96/29.66 thf(47,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ B) => ((finite1329924456tate_o @ A) <= (ord_le1728773982te_o_o @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_rev__finite__subset)). 123.96/29.66 thf(977,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ (B)) => ((finite1329924456tate_o @ (A)) | ~ (ord_le1728773982te_o_o @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 123.96/29.66 thf(347,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((B = A) => (ord_less_eq_pname_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_xt1_I4_J)). 123.96/29.66 thf(1882,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => (((B) = (A)) => (ord_less_eq_pname_o @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 123.96/29.66 thf(225,axiom,((! [A:pname,B:pname,C:(pname > $o)]: (((A != B) => (member_pname @ A @ C)) <= (member_pname @ A @ (insert_pname @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_insertE)). 123.96/29.66 thf(1522,plain,((! [A:pname,B:pname,C:(pname > $o)]: (((~ (A = B)) => (member_pname @ A @ (C))) | ~ (member_pname @ A @ (insert_pname @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 123.96/29.66 thf(497,axiom,((! [A:pname,B:(pname > $o)]: ((member_pname @ A @ B) => (? [C:(pname > $o)]: ((B = (insert_pname @ A @ C)) & ~ (member_pname @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_749_mk__disjoint__insert)). 123.96/29.66 thf(2381,plain,((! [A:pname,B:(pname > $o)]: ((member_pname @ A @ (B)) => (? [C:(pname > $o)]: (((B) = (insert_pname @ A @ C)) & ~ (member_pname @ A @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[497])). 123.96/29.66 thf(588,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ B) <= (member451959335_state @ A @ (minus_2056855718tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_DiffD1)). 123.96/29.66 thf(2659,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (B)) | ~ (member451959335_state @ A @ (minus_2056855718tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[588])). 123.96/29.66 thf(292,axiom,((! [A:(com > pname),B:com,C:(com > $o)]: ((member_pname @ (A @ B) @ (image_com_pname @ A @ C)) <= (member_com @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_imageI)). 123.96/29.66 thf(1728,plain,((! [A:(com > pname),B:com,C:(com > $o)]: ((member_pname @ (A @ B) @ (image_com_pname @ A @ C)) | ~ (member_com @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 123.96/29.66 thf(696,axiom,((finite662762081tate_o @ insert528405184_state)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_comp__fun__idem__insert)). 123.96/29.66 thf(3012,plain,((finite662762081tate_o @ (insert528405184_state))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[696])). 123.96/29.66 thf(248,axiom,((! [A:(pname > $o)]: ((semila1673364395name_o @ bot_bot_pname_o @ A) = bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_920_inf__bot__left)). 123.96/29.66 thf(1591,plain,((! [A:(pname > $o)]: ((semila1673364395name_o @ bot_bot_pname_o @ A) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 123.96/29.66 thf(98,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: ((ord_less_eq_pname_o @ C @ D) => ((ord_less_eq_pname_o @ A @ B) => (ord_less_eq_pname_o @ (semila1780557381name_o @ C @ A) @ (semila1780557381name_o @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_Un__mono)). 123.96/29.66 thf(1142,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: ((ord_less_eq_pname_o @ (C) @ (D)) => ((ord_less_eq_pname_o @ (A) @ (B)) => (ord_less_eq_pname_o @ (semila1780557381name_o @ C @ A) @ (semila1780557381name_o @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 123.96/29.66 thf(198,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: ((image_1116629049_state @ A @ (semila1780557381name_o @ B @ C)) = (semila1122118281tate_o @ (image_1116629049_state @ A @ B) @ (image_1116629049_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_image__Un)). 123.96/29.66 thf(1437,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: ((image_1116629049_state @ A @ (semila1780557381name_o @ B @ C)) = (semila1122118281tate_o @ (image_1116629049_state @ A @ B) @ (image_1116629049_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 123.96/29.66 thf(111,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((member451959335_state @ C @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ (^ [D:hoare_1708887482_state]: (member451959335_state @ D @ A)) @ (^ [D:hoare_1708887482_state]: (member451959335_state @ D @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_sup__Un__eq)). 123.96/29.66 thf(1173,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((member451959335_state @ C @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ (^ [D:hoare_1708887482_state]: (member451959335_state @ D @ A)) @ (^ [D:hoare_1708887482_state]: (member451959335_state @ D @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 123.96/29.66 thf(105,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ C) => ((member451959335_state @ B @ A) => (member451959335_state @ B @ (semila129691299tate_o @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_IntI)). 123.96/29.66 thf(1158,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (C)) => ((member451959335_state @ B @ (A)) => (member451959335_state @ B @ (semila129691299tate_o @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 123.96/29.66 thf(539,axiom,((! [A:(pname > $o),B:(pname > (pname > pname)),C:((pname > $o) > pname)]: ((((A != bot_bot_pname_o) => ((member_pname @ (C @ A) @ A) <= (! [D:pname,E:pname]: (member_pname @ (B @ D @ E) @ (insert_pname @ D @ (insert_pname @ E @ bot_bot_pname_o)))))) <= (finite_finite_pname @ A)) <= (finite1282449217_pname @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_folding__one_Oclosed)). 123.96/29.66 thf(2512,plain,((! [A:(pname > $o),B:(pname > (pname > pname)),C:((pname > $o) > pname)]: (((~ ((A) = (bot_bot_pname_o))) => ((member_pname @ (C @ (A)) @ (A)) | ~ (! [D:pname,E:pname]: (member_pname @ (B @ D @ E) @ (insert_pname @ D @ (insert_pname @ E @ bot_bot_pname_o)))))) | ~ (finite_finite_pname @ (A)) | ~ (finite1282449217_pname @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[539])). 123.96/29.66 thf(686,axiom,((! [A:(hoare_1708887482_state > option_pname),B:hoare_1708887482_state,C:pname]: (((A @ B) = (some_pname @ C)) => ((insert528405184_state @ B @ (dom_Ho1805192458_pname @ A)) = (dom_Ho1805192458_pname @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_insert__dom)). 123.96/29.66 thf(2976,plain,((! [A:(hoare_1708887482_state > option_pname),B:hoare_1708887482_state,C:pname]: (((A @ B) = (some_pname @ C)) => ((insert528405184_state @ B @ (dom_Ho1805192458_pname @ A)) = (dom_Ho1805192458_pname @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[686])). 123.96/29.66 thf(458,axiom,((bot_bot_com_o = (collect_com @ (^ [A:com]: (($false)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_empty__def)). 123.96/29.66 thf(2231,plain,(((bot_bot_com_o) = (collect_com @ (^ [A:com]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[458])). 123.96/29.66 thf(74,axiom,((! [A:(hoare_1708887482_state > option1624383643_state),B:hoare_1708887482_state,C:hoare_1708887482_state]: ((member451959335_state @ B @ (dom_Ho1703271284_state @ A)) <= ((A @ B) = (some_H1974565227_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_domI)). 123.96/29.66 thf(1068,plain,((! [A:(hoare_1708887482_state > option1624383643_state),B:hoare_1708887482_state,C:hoare_1708887482_state]: ((member451959335_state @ B @ (dom_Ho1703271284_state @ A)) | ~ ((A @ B) = (some_H1974565227_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 123.96/29.66 thf(501,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (semila129691299tate_o @ B @ A)) <= ((finite1625599783_state @ B) | (finite1625599783_state @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_finite__Int)). 123.96/29.66 thf(2395,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (semila129691299tate_o @ B @ A)) | ~ ((finite1625599783_state @ (B)) | (finite1625599783_state @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])). 123.96/29.66 thf(406,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((member_pname @ A @ C) <= (member_pname @ A @ B)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_in__mono)). 123.96/29.66 thf(2062,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (C)) | ~ (member_pname @ A @ (B)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])). 123.96/29.66 thf(565,axiom,((! [A:(pname > (pname > $o)),B:(pname > $o)]: (((finite297249702name_o @ (image_pname_pname_o @ A @ B)) => (? [C:pname]: (~ (finite_finite_pname @ (collect_pname @ (^ [D:pname]: ((member_pname @ D @ B) & ((A @ D) = (A @ C)))))) & (member_pname @ C @ B)))) <= (~ (finite_finite_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_pigeonhole__infinite)). 123.96/29.66 thf(2590,plain,((! [A:(pname > (pname > $o)),B:(pname > $o)]: (((finite297249702name_o @ (image_pname_pname_o @ A @ B)) => (? [C:pname]: (~ (finite_finite_pname @ (collect_pname @ (^ [D:pname]: ((member_pname @ D @ B) & ((A @ D) = (A @ C)))))) & (member_pname @ C @ (B))))) | (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[565])). 123.96/29.66 thf(185,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila129691299tate_o @ (minus_2056855718tate_o @ A @ B) @ (minus_2056855718tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_Diff__Un)). 123.96/29.66 thf(1401,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila129691299tate_o @ (minus_2056855718tate_o @ A @ B) @ (minus_2056855718tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 123.96/29.66 thf(378,axiom,((! [A:(hoare_1708887482_state > (hoare_1708887482_state > $o)),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ B) => (finite1329924456tate_o @ (image_1551509096tate_o @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__imageI)). 123.96/29.66 thf(1971,plain,((! [A:(hoare_1708887482_state > (hoare_1708887482_state > $o)),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (B)) => (finite1329924456tate_o @ (image_1551509096tate_o @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])). 123.96/29.66 thf(316,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) => ((finite_finite_pname @ A) <= (finite_finite_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_finite__subset)). 123.96/29.66 thf(1793,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) => ((finite_finite_pname @ (A)) | ~ (finite_finite_pname @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 123.96/29.66 thf(229,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1673364395name_o @ B @ C)) = (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_sup__inf__distrib1)). 123.96/29.66 thf(1533,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1673364395name_o @ B @ C)) = (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 123.96/29.66 thf(285,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ B) => ((semila129691299tate_o @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_inf__absorb1)). 123.96/29.66 thf(1705,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) => ((semila129691299tate_o @ A @ B) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 123.96/29.66 thf(275,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ A @ (semila1780557381name_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_Un__upper2)). 123.96/29.66 thf(1671,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (A) @ (semila1780557381name_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 123.96/29.66 thf(822,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((((member451959335_state @ B @ A) => (ord_le777019615tate_o @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) @ C)) & ((ord_le777019615tate_o @ A @ C) <= (~ (member451959335_state @ B @ A)))) = (ord_le777019615tate_o @ A @ (insert528405184_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1064_subset__insert__iff)). 123.96/29.66 thf(3439,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((((member451959335_state @ B @ (A)) => (ord_le777019615tate_o @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) @ (C))) & ((ord_le777019615tate_o @ (A) @ (C)) | (member451959335_state @ B @ (A)))) = (ord_le777019615tate_o @ (A) @ (insert528405184_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[822])). 123.96/29.66 thf(269,axiom,((! [A:pname]: ~ (member_pname @ A @ bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_emptyE)). 123.96/29.66 thf(1655,plain,((! [A:pname]: ~ (member_pname @ A @ (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 123.96/29.66 thf(96,axiom,((! [A:((pname > $o) > hoare_1708887482_state),B:((pname > $o) > $o)]: ((finite1625599783_state @ (image_1922967206_state @ A @ B)) <= (finite297249702name_o @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__imageI)). 123.96/29.66 thf(1137,plain,((! [A:((pname > $o) > hoare_1708887482_state),B:((pname > $o) > $o)]: ((finite1625599783_state @ (image_1922967206_state @ (A) @ (B))) | ~ (finite297249702name_o @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 123.96/29.66 thf(156,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (insert_pname @ A @ B) @ (insert_pname @ A @ C)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_insert__mono)). 123.96/29.66 thf(1310,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (insert_pname @ A @ B) @ (insert_pname @ A @ C)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 123.96/29.66 thf(396,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila1122118281tate_o @ B @ C)) => ((~ (member451959335_state @ A @ B)) => (member451959335_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_UnE)). 123.96/29.66 thf(2035,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila1122118281tate_o @ B @ C)) => ((~ (member451959335_state @ A @ (B))) => (member451959335_state @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])). 123.96/29.66 thf(295,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_inf__sup__ord_I2_J)). 123.96/29.66 thf(1735,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 123.96/29.66 thf(517,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (semila1780557381name_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_sup_Ocommute)). 123.96/29.66 thf(2448,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (semila1780557381name_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[517])). 123.96/29.66 thf(143,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila129691299tate_o @ B @ C)) => (~ ((~ (member451959335_state @ A @ C)) <= (member451959335_state @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_802_IntE)). 123.96/29.66 thf(1275,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila129691299tate_o @ B @ C)) => (~ (~ (member451959335_state @ A @ (C)) | ~ (member451959335_state @ A @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 123.96/29.66 thf(577,axiom,((! [A:com]: (bot_bot_o = (bot_bot_com_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_bot__fun__def)). 123.96/29.66 thf(2627,plain,((! [A:com]: (bot_bot_o = (bot_bot_com_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[577])). 123.96/29.66 thf(769,axiom,((! [A:pname,B:(pname > option_com)]: (((B @ A) != none_com) = (member_pname @ A @ (dom_pname_com @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_domIff)). 123.96/29.66 thf(3253,plain,((! [A:pname,B:(pname > option_com)]: ((~ ((B @ A) = none_com)) = (member_pname @ A @ (dom_pname_com @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[769])). 123.96/29.66 thf(304,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ C) = (semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C))) = (ord_le777019615tate_o @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_Un__Int__assoc__eq)). 123.96/29.66 thf(1761,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ C) = (semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C))) = (ord_le777019615tate_o @ (C) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 123.96/29.66 thf(37,axiom,((! [A:(pname > pname),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (image_pname_pname @ A @ C) @ B) <= (! [D:pname]: ((member_pname @ D @ C) => (member_pname @ (A @ D) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_image__subsetI)). 123.96/29.66 thf(945,plain,((! [A:(pname > pname),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (image_pname_pname @ A @ C) @ (B)) | ~ (! [D:pname]: ((member_pname @ D @ (C)) => (member_pname @ (A @ D) @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 123.96/29.66 thf(170,axiom,((! [A:(pname > $o),B:pname]: ((((collect_pname @ (^ [C:pname]: ((B = C) & (A @ C)))) = (insert_pname @ B @ bot_bot_pname_o)) <= (A @ B)) & (((collect_pname @ (^ [C:pname]: ((B = C) & (A @ C)))) = bot_bot_pname_o) <= (~ (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_Collect__conv__if2)). 123.96/29.66 thf(1354,plain,((! [A:(pname > $o),B:pname]: ((((collect_pname @ (^ [C:pname]: ((B = C) & (A @ C)))) = (insert_pname @ B @ bot_bot_pname_o)) | ~ (A @ B)) & (((collect_pname @ (^ [C:pname]: ((B = C) & (A @ C)))) = (bot_bot_pname_o)) | (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 123.96/29.66 thf(31,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: (((ord_less_eq_pname_o @ A @ B) => (ord_less_eq_pname_o @ (minus_minus_pname_o @ C @ B) @ (minus_minus_pname_o @ D @ A))) <= (ord_less_eq_pname_o @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_Diff__mono)). 123.96/29.66 thf(930,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: (((ord_less_eq_pname_o @ (A) @ (B)) => (ord_less_eq_pname_o @ (minus_minus_pname_o @ C @ B) @ (minus_minus_pname_o @ D @ A))) | ~ (ord_less_eq_pname_o @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 123.96/29.66 thf(314,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => (ord_le777019615tate_o @ (semila129691299tate_o @ B @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_892_le__infI1)). 123.96/29.66 thf(1788,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => (ord_le777019615tate_o @ (semila129691299tate_o @ B @ A) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 123.96/29.66 thf(194,axiom,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((B @ C) => (semila1780557381name_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_sup1I2)). 123.96/29.66 thf(1426,plain,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((B @ C) => (semila1780557381name_o @ (A) @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 123.96/29.66 thf(388,axiom,((! [A:(hoare_1708887482_state > $o),B:(pname > $o)]: ((B != bot_bot_pname_o) => ((? [C:(pname > hoare_1708887482_state)]: ((inj_on1553129421_state @ C @ B) & (ord_le777019615tate_o @ (image_1116629049_state @ C @ B) @ A))) = (? [C:(hoare_1708887482_state > pname)]: ((image_1509414295_pname @ C @ A) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1183_inj__on__iff__surj)). 123.96/29.66 thf(1999,plain,((! [A:(hoare_1708887482_state > $o),B:(pname > $o)]: ((~ ((B) = (bot_bot_pname_o))) => ((? [C:(pname > hoare_1708887482_state)]: ((inj_on1553129421_state @ (C) @ (B)) & (ord_le777019615tate_o @ (image_1116629049_state @ C @ B) @ (A)))) = (? [C:(hoare_1708887482_state > pname)]: ((image_1509414295_pname @ C @ A) = (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])). 123.96/29.66 thf(481,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((! [D:pname]: ((A @ D) <= (member_pname @ D @ B)) & ! [D:pname]: ((member_pname @ D @ C) => (A @ D))) = (! [D:pname]: ((A @ D) <= (member_pname @ D @ (semila1780557381name_o @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_ball__Un)). 123.96/29.66 thf(2316,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((! [D:pname]: ((A @ D) | ~ (member_pname @ D @ (B))) & ! [D:pname]: ((member_pname @ D @ (C)) => (A @ D))) = (! [D:pname]: ((A @ D) | ~ (member_pname @ D @ (semila1780557381name_o @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])). 123.96/29.66 thf(119,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_Int__lower2)). 123.96/29.66 thf(1196,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 123.96/29.66 thf(330,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (minus_2056855718tate_o @ B @ C)) = ((member451959335_state @ A @ B) & ~ (member451959335_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_846_Diff__iff)). 123.96/29.66 thf(1835,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (minus_2056855718tate_o @ B @ C)) = ((member451959335_state @ A @ (B)) & ~ (member451959335_state @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 123.96/29.66 thf(763,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((((((minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = bot_bo19817387tate_o) => ((D @ (insert528405184_state @ A @ B)) = A)) & (((D @ (insert528405184_state @ A @ B)) = (C @ A @ (D @ (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o))))) <= ((minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)) != bot_bo19817387tate_o))) <= (finite1625599783_state @ B)) <= (finite1615457021_state @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_788_folding__one_Oinsert__remove)). 123.96/29.66 thf(3236,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: (((((minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = (bot_bo19817387tate_o)) => ((D @ (insert528405184_state @ A @ B)) = A)) & (((D @ (insert528405184_state @ A @ B)) = (C @ A @ (D @ (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o))))) | ((minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = (bot_bo19817387tate_o)))) | ~ (finite1625599783_state @ (B)) | ~ (finite1615457021_state @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[763])). 123.96/29.66 thf(606,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (ord_less_eq_pname_o @ (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ A @ C)) @ (semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1024_distrib__inf__le)). 123.96/29.66 thf(2723,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (ord_less_eq_pname_o @ (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ A @ C)) @ (semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[606])). 123.96/29.66 thf(401,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((! [C:hoare_1708887482_state]: ((member451959335_state @ C @ A) => (! [D:hoare_1708887482_state]: ((member451959335_state @ D @ B) => (C != D))))) = ((semila129691299tate_o @ A @ B) = bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_961_disjoint__iff__not__equal)). 123.96/29.66 thf(2046,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((! [C:hoare_1708887482_state]: ((member451959335_state @ C @ (A)) => (! [D:hoare_1708887482_state]: ((member451959335_state @ D @ (B)) => (~ (C = D)))))) = ((semila129691299tate_o @ A @ B) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])). 123.96/29.66 thf(357,axiom,((! [A:(pname > hoare_1708887482_state),B:(hoare_1708887482_state > $o),C:(pname > $o)]: ((ord_le777019615tate_o @ (image_1116629049_state @ A @ C) @ B) <= (! [D:pname]: ((member451959335_state @ (A @ D) @ B) <= (member_pname @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_image__subsetI)). 123.96/29.66 thf(1914,plain,((! [A:(pname > hoare_1708887482_state),B:(hoare_1708887482_state > $o),C:(pname > $o)]: ((ord_le777019615tate_o @ (image_1116629049_state @ A @ C) @ (B)) | ~ (! [D:pname]: ((member451959335_state @ (A @ D) @ (B)) | ~ (member_pname @ D @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])). 123.96/29.66 thf(93,axiom,((! [A:pname]: ((the_elem_pname @ (insert_pname @ A @ bot_bot_pname_o)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_the__elem__eq)). 123.96/29.66 thf(1127,plain,((! [A:pname]: ((the_elem_pname @ (insert_pname @ A @ bot_bot_pname_o)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 123.96/29.66 thf(767,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((hoare_90032982_state @ B @ (insert528405184_state @ C @ bot_bo19817387tate_o)) => ((hoare_90032982_state @ B @ (insert528405184_state @ C @ A)) <= (hoare_90032982_state @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert)). 123.96/29.66 thf(3249,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((hoare_90032982_state @ (B) @ (insert528405184_state @ C @ bot_bo19817387tate_o)) => ((hoare_90032982_state @ (B) @ (insert528405184_state @ C @ A)) | ~ (hoare_90032982_state @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[767])). 123.96/29.66 thf(4,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((minus_minus_pname_o @ A @ B) = (finite603803317name_o @ (^ [C:pname,D:(pname > $o)]: (minus_minus_pname_o @ D @ (insert_pname @ C @ bot_bot_pname_o))) @ A @ B)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1098_minus__fold__remove)). 123.96/29.66 thf(841,plain,((! [A:(pname > $o),B:(pname > $o)]: (((minus_minus_pname_o @ A @ B) = (finite603803317name_o @ (^ [C:pname,D:(pname > $o)]: (minus_minus_pname_o @ D @ (insert_pname @ C @ bot_bot_pname_o))) @ A @ B)) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 123.96/29.66 thf(66,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ (minus_minus_pname_o @ A @ B) @ (semila1673364395name_o @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_Un__Diff__Int)). 123.96/29.66 thf(1046,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ (minus_minus_pname_o @ A @ B) @ (semila1673364395name_o @ A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 123.96/29.66 thf(736,axiom,((! [A:(pname > hoare_1708887482_state),B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => ((insert528405184_state @ (A @ B) @ (image_1116629049_state @ A @ C)) = (image_1116629049_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_insert__image)). 123.96/29.66 thf(3140,plain,((! [A:(pname > hoare_1708887482_state),B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => ((insert528405184_state @ (A @ B) @ (image_1116629049_state @ A @ C)) = (image_1116629049_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[736])). 123.96/29.66 thf(638,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ B @ C)) @ (semila1673364395name_o @ C @ A)) = (semila1673364395name_o @ (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ B @ C)) @ (semila1780557381name_o @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_Un__Int__crazy)). 123.96/29.66 thf(2819,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ B @ C)) @ (semila1673364395name_o @ C @ A)) = (semila1673364395name_o @ (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ B @ C)) @ (semila1780557381name_o @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[638])). 123.96/29.66 thf(257,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ C) @ (semila129691299tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_936_inf__sup__distrib2)). 123.96/29.66 thf(1623,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ C) @ (semila129691299tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 123.96/29.66 thf(679,axiom,(((body @ pn) = (some_com @ y))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5)). 123.96/29.66 thf(2956,plain,(((body @ pn) = (some_com @ y))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[679])). 123.96/29.66 thf(2957,plain,(((some_com @ y) = (body @ pn))),inference(lifteq,[status(thm)],[2956])). 123.96/29.66 thf(569,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_inf__sup__ord_I1_J)). 123.96/29.66 thf(2603,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[569])). 123.96/29.66 thf(816,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: ((B = bot_bot_pname_o) = (bot_bo19817387tate_o = (image_1116629049_state @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_empty__is__image)). 123.96/29.66 thf(3425,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: (((B) = (bot_bot_pname_o)) = ((bot_bo19817387tate_o) = (image_1116629049_state @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[816])). 123.96/29.66 thf(398,axiom,((! [A:pname]: (member_pname @ A @ top_top_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1196_UNIV__I)). 123.96/29.66 thf(2039,plain,((! [A:pname]: (member_pname @ A @ (top_top_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[398])). 123.96/29.66 thf(729,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ B) => ((B != bot_bo19817387tate_o) => ((! [C:hoare_1708887482_state]: (A @ (insert528405184_state @ C @ bot_bo19817387tate_o))) => ((! [C:hoare_1708887482_state,D:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ D) => ((((A @ D) => (A @ (insert528405184_state @ C @ D))) <= (~ (member451959335_state @ C @ D))) <= (D != bot_bo19817387tate_o)))) => (A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_finite__ne__induct)). 123.96/29.66 thf(3116,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (B)) => ((~ ((B) = (bot_bo19817387tate_o))) => ((! [C:hoare_1708887482_state]: (A @ (insert528405184_state @ C @ bot_bo19817387tate_o))) => ((! [C:hoare_1708887482_state,D:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (D)) => (((A @ (D)) => (A @ (insert528405184_state @ C @ D))) | (member451959335_state @ C @ (D)) | ((D) = (bot_bo19817387tate_o))))) => (A @ (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[729])). 123.96/29.66 thf(707,axiom,((! [A:(hoare_1708887482_state > $o),B:(state > (state > $o)),C:pname,D:(state > (state > $o))]: ((hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ B @ (body_1 @ C) @ D) @ bot_bo19817387tate_o)) <= (hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ B @ (the_com @ (body @ C)) @ D) @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_weak__Body)). 123.96/29.66 thf(3046,plain,((! [A:(hoare_1708887482_state > $o),B:(state > (state > $o)),C:pname,D:(state > (state > $o))]: ((hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ B @ (body_1 @ C) @ D) @ bot_bo19817387tate_o)) | ~ (hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ B @ (the_com @ (body @ C)) @ D) @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[707])). 123.96/29.66 thf(618,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Un__left__absorb)). 123.96/29.66 thf(2755,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[618])). 123.96/29.66 thf(343,axiom,((! [A:(pname > hoare_1708887482_state),B:pname,C:(pname > $o)]: ((inj_on1553129421_state @ A @ (insert_pname @ B @ C)) = (~ (member451959335_state @ (A @ B) @ (image_1116629049_state @ A @ (minus_minus_pname_o @ C @ (insert_pname @ B @ bot_bot_pname_o)))) & (inj_on1553129421_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_inj__on__insert)). 123.96/29.66 thf(1871,plain,((! [A:(pname > hoare_1708887482_state),B:pname,C:(pname > $o)]: ((inj_on1553129421_state @ (A) @ (insert_pname @ B @ C)) = (~ (member451959335_state @ (A @ B) @ (image_1116629049_state @ A @ (minus_minus_pname_o @ C @ (insert_pname @ B @ bot_bot_pname_o)))) & (inj_on1553129421_state @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 123.96/29.66 thf(600,axiom,((! [A:com,B:com,C:state,D:state]: ((~ (! [E:state]: ((~ (evalc @ B @ E @ D)) <= (evalc @ A @ C @ E)))) <= (evalc @ (semi @ A @ B) @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_evalc__elim__cases_I4_J)). 123.96/29.66 thf(2708,plain,((! [A:com,B:com,C:state,D:state]: (~ (! [E:state]: (~ (evalc @ B @ E @ D) | ~ (evalc @ A @ C @ E))) | ~ (evalc @ (semi @ A @ B) @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[600])). 123.96/29.66 thf(535,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ B @ (semila129691299tate_o @ C @ A)) <= (ord_le777019615tate_o @ B @ A)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1004_Int__greatest)). 123.96/29.66 thf(2501,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (semila129691299tate_o @ C @ A)) | ~ (ord_le777019615tate_o @ (B) @ (A)) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[535])). 123.96/29.66 thf(339,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((((finite_finite_pname @ A) => ((A != bot_bot_pname_o) => (((D @ (semila1780557381name_o @ B @ A)) = (C @ (D @ B) @ (D @ A))) <= ((semila1673364395name_o @ B @ A) = bot_bot_pname_o)))) <= (B != bot_bot_pname_o)) <= (finite_finite_pname @ B)) <= (finite1282449217_pname @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_folding__one_Ounion__disjoint)). 123.96/29.66 thf(1860,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((finite_finite_pname @ (A)) => ((~ ((A) = (bot_bot_pname_o))) => (((D @ (semila1780557381name_o @ B @ A)) = (C @ (D @ (B)) @ (D @ (A)))) | ~ ((semila1673364395name_o @ B @ A) = (bot_bot_pname_o))))) | ((B) = (bot_bot_pname_o)) | ~ (finite_finite_pname @ (B)) | ~ (finite1282449217_pname @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 123.96/29.66 thf(221,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (semila1780557381name_o @ A @ B) @ C) = ((ord_less_eq_pname_o @ A @ C) & (ord_less_eq_pname_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_le__sup__iff)). 123.96/29.66 thf(1511,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (semila1780557381name_o @ A @ B) @ (C)) = ((ord_less_eq_pname_o @ (A) @ (C)) & (ord_less_eq_pname_o @ (B) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 123.96/29.66 thf(158,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ A @ C)) @ (semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1025_distrib__inf__le)). 123.96/29.66 thf(1313,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ A @ C)) @ (semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 123.96/29.66 thf(424,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (semila1122118281tate_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_sup_Ocommute)). 123.96/29.66 thf(2126,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (semila1122118281tate_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])). 123.96/29.66 thf(706,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o))) = (insert528405184_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1037_insert__Diff__single)). 123.96/29.66 thf(3043,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o))) = (insert528405184_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[706])). 123.96/29.66 thf(558,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ (insert_pname @ A @ C)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_subset__insertI2)). 123.96/29.66 thf(2571,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (insert_pname @ A @ C)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[558])). 123.96/29.66 thf(586,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => (ord_less_eq_pname_o @ B @ (semila1780557381name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_le__supI2)). 123.96/29.66 thf(2654,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => (ord_less_eq_pname_o @ (B) @ (semila1780557381name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[586])). 123.96/29.66 thf(259,axiom,((! [A:pname,B:(pname > $o)]: ((member_pname @ A @ B) => ((insert_pname @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_insert__absorb)). 123.96/29.66 thf(1628,plain,((! [A:pname,B:(pname > $o)]: ((member_pname @ A @ (B)) => ((insert_pname @ A @ B) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 123.96/29.66 thf(69,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((if_Hoa1374726218_state @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate)). 123.96/29.66 thf(1055,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((if_Hoa1374726218_state @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 123.96/29.66 thf(823,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: ((ord_le777019615tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) => ((A = (insert528405184_state @ B @ bot_bo19817387tate_o)) | (A = bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_subset__singletonD)). 123.96/29.66 thf(3442,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: ((ord_le777019615tate_o @ (A) @ (insert528405184_state @ B @ bot_bo19817387tate_o)) => (((A) = (insert528405184_state @ B @ bot_bo19817387tate_o)) | ((A) = (bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[823])). 123.96/29.66 thf(597,axiom,((! [A:(hoare_1708887482_state > pname),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((image_1509414295_pname @ A @ (insert528405184_state @ B @ C)) = (insert_pname @ (A @ B) @ (image_1509414295_pname @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_image__insert)). 123.96/29.66 thf(2698,plain,((! [A:(hoare_1708887482_state > pname),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((image_1509414295_pname @ A @ (insert528405184_state @ B @ C)) = (insert_pname @ (A @ B) @ (image_1509414295_pname @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[597])). 123.96/29.66 thf(732,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (member451959335_state @ A @ (insert528405184_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_insertI1)). 123.96/29.66 thf(3131,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (member451959335_state @ A @ (insert528405184_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[732])). 123.96/29.66 thf(811,axiom,((! [A:pname,B:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ (insert528405184_state @ (hoare_Mirabelle_MGT @ (body_1 @ A)) @ B) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ (the_com @ (body @ A))) @ bot_bo19817387tate_o)) => (hoare_90032982_state @ B @ (insert528405184_state @ (hoare_Mirabelle_MGT @ (body_1 @ A)) @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_MGT__BodyN)). 123.96/29.66 thf(3410,plain,((! [A:pname,B:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ (insert528405184_state @ (hoare_Mirabelle_MGT @ (body_1 @ A)) @ B) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ (the_com @ (body @ A))) @ bot_bo19817387tate_o)) => (hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ (body_1 @ A)) @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[811])). 123.96/29.66 thf(244,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: (((ord_le777019615tate_o @ B @ A) => (A @ C)) <= (B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_rev__predicate1D)). 123.96/29.66 thf(1577,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: (((ord_le777019615tate_o @ (B) @ (A)) => (A @ C)) | ~ (B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 123.96/29.66 thf(779,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ bot_bo19817387tate_o @ A) = bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_921_inf__bot__left)). 123.96/29.66 thf(3280,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ bot_bo19817387tate_o @ A) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[779])). 123.96/29.66 thf(329,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ A @ C) & (ord_le777019615tate_o @ B @ C)) = (ord_le777019615tate_o @ (semila1122118281tate_o @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_le__sup__iff)). 123.96/29.66 thf(1832,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (A) @ (C)) & (ord_le777019615tate_o @ (B) @ (C))) = (ord_le777019615tate_o @ (semila1122118281tate_o @ A @ B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 123.96/29.66 thf(658,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((! [C:hoare_1708887482_state]: ((A @ C) <= (B @ C))) => (ord_le777019615tate_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_predicate1I)). 123.96/29.66 thf(2897,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((! [C:hoare_1708887482_state]: ((A @ C) | ~ (B @ C))) => (ord_le777019615tate_o @ (B) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[658])). 123.96/29.66 thf(233,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: (((ord_less_eq_pname_o @ A @ B) => (ord_less_eq_pname_o @ (semila1780557381name_o @ C @ A) @ (semila1780557381name_o @ D @ B))) <= (ord_less_eq_pname_o @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_sup__mono)). 123.96/29.66 thf(1545,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: (((ord_less_eq_pname_o @ (A) @ (B)) => (ord_less_eq_pname_o @ (semila1780557381name_o @ C @ A) @ (semila1780557381name_o @ D @ B))) | ~ (ord_less_eq_pname_o @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 123.96/29.66 thf(22,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => ((~ (member_pname @ B @ A)) => (member_pname @ B @ (minus_minus_pname_o @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_DiffI)). 123.96/29.66 thf(902,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => ((~ (member_pname @ B @ (A))) => (member_pname @ B @ (minus_minus_pname_o @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 123.96/29.66 thf(318,axiom,((! [A:(pname > $o),B:hoare_1708887482_state,C:(pname > hoare_1708887482_state),D:pname]: (((member_pname @ D @ A) => (member451959335_state @ B @ (image_1116629049_state @ C @ A))) <= (B = (C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_image__eqI)). 123.96/29.66 thf(1800,plain,((! [A:(pname > $o),B:hoare_1708887482_state,C:(pname > hoare_1708887482_state),D:pname]: (((member_pname @ D @ (A)) => (member451959335_state @ B @ (image_1116629049_state @ C @ A))) | ~ (B = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 123.96/29.66 thf(622,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((member451959335_state @ C @ A) & (member451959335_state @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_Int__def)). 123.96/29.66 thf(2767,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((member451959335_state @ C @ A) & (member451959335_state @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[622])). 123.96/29.66 thf(494,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ A @ B) <= (ord_less_eq_pname_o @ A @ C)) <= (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_xt1_I3_J)). 123.96/29.66 thf(2373,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) | ~ (ord_less_eq_pname_o @ (A) @ (C)) | ~ ((B) = (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[494])). 123.96/29.66 thf(761,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1615457021_state @ C @ D) => ((((B != bot_bo19817387tate_o) => ((D @ (insert528405184_state @ A @ B)) = (C @ A @ (D @ B)))) <= (~ (member451959335_state @ A @ B))) <= (finite1625599783_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_folding__one_Oinsert)). 123.96/29.66 thf(3216,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1615457021_state @ (C) @ (D)) => (((~ ((B) = (bot_bo19817387tate_o))) => ((D @ (insert528405184_state @ A @ B)) = (C @ A @ (D @ (B))))) | (member451959335_state @ A @ (B)) | ~ (finite1625599783_state @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[761])). 123.96/29.66 thf(184,axiom,((! [A:(pname > $o),B:(hoare_1708887482_state > pname),C:(hoare_1708887482_state > $o)]: ((ord_less_eq_pname_o @ A @ (image_1509414295_pname @ B @ C)) = (? [D:(hoare_1708887482_state > $o)]: ((A = (image_1509414295_pname @ B @ D)) & (ord_le777019615tate_o @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_subset__image__iff)). 123.96/29.66 thf(1398,plain,((! [A:(pname > $o),B:(hoare_1708887482_state > pname),C:(hoare_1708887482_state > $o)]: ((ord_less_eq_pname_o @ (A) @ (image_1509414295_pname @ B @ C)) = (? [D:(hoare_1708887482_state > $o)]: (((A) = (image_1509414295_pname @ B @ D)) & (ord_le777019615tate_o @ (D) @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 123.96/29.66 thf(669,axiom,((! [A:(hoare_1708887482_state > $o)]: ((? [B:hoare_1708887482_state]: (member451959335_state @ B @ A)) = (A != bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_ex__in__conv)). 123.96/29.66 thf(2929,plain,((! [A:(hoare_1708887482_state > $o)]: ((? [B:hoare_1708887482_state]: (member451959335_state @ B @ (A))) = (~ ((A) = (bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[669])). 123.96/29.66 thf(241,axiom,((! [A:com]: (bot_bot_o = (bot_bot_com_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_bot__apply)). 123.96/29.66 thf(1568,plain,((! [A:com]: (bot_bot_o = (bot_bot_com_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 123.96/29.66 thf(542,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ B @ A) => (ord_less_eq_pname_o @ B @ (semila1673364395name_o @ C @ A))) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_903_le__infI)). 123.96/29.66 thf(2520,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ (B) @ (A)) => (ord_less_eq_pname_o @ (B) @ (semila1673364395name_o @ C @ A))) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[542])). 123.96/29.66 thf(308,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => ((ord_le777019615tate_o @ B @ A) <= (ord_le777019615tate_o @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_subset__trans)). 123.96/29.66 thf(1773,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => ((ord_le777019615tate_o @ (B) @ (A)) | ~ (ord_le777019615tate_o @ (C) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 123.96/29.66 thf(310,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (semila1780557381name_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_Un__commute)). 123.96/29.66 thf(1778,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (semila1780557381name_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 123.96/29.66 thf(84,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (semila1673364395name_o @ B @ C)) = ((member_pname @ A @ C) & (member_pname @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_Int__iff)). 123.96/29.66 thf(1100,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (semila1673364395name_o @ B @ C)) = ((member_pname @ A @ (C)) & (member_pname @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 123.96/29.66 thf(350,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (semila1780557381name_o @ B @ C)) => ((member_pname @ A @ C) <= (~ (member_pname @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_UnE)). 123.96/29.66 thf(1892,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (semila1780557381name_o @ B @ C)) => ((member_pname @ A @ (C)) | (member_pname @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])). 123.96/29.66 thf(829,axiom,((bot_bo19817387tate_o = (collec1568722789_state @ (^ [A:hoare_1708887482_state]: (($false)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_empty__def)). 123.96/29.66 thf(3463,plain,(((bot_bo19817387tate_o) = (collec1568722789_state @ (^ [A:hoare_1708887482_state]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[829])). 123.96/29.66 thf(178,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((B = bot_bot_pname_o) & (A = bot_bot_pname_o)) = ((semila1780557381name_o @ A @ B) = bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_sup__eq__bot__iff)). 123.96/29.66 thf(1379,plain,((! [A:(pname > $o),B:(pname > $o)]: ((((B) = (bot_bot_pname_o)) & ((A) = (bot_bot_pname_o))) = ((semila1780557381name_o @ A @ B) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 123.96/29.66 thf(439,axiom,((! [A:(pname > $o)]: ((semila1673364395name_o @ A @ bot_bot_pname_o) = bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_963_Int__empty__right)). 123.96/29.66 thf(2169,plain,((! [A:(pname > $o)]: ((semila1673364395name_o @ A @ bot_bot_pname_o) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[439])). 123.96/29.66 thf(504,axiom,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((member_pname @ C @ (semila1673364395name_o @ A @ B)) = (semila1673364395name_o @ (^ [D:pname]: (member_pname @ D @ A)) @ (^ [D:pname]: (member_pname @ D @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_821_inf__Int__eq)). 123.96/29.66 thf(2403,plain,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((member_pname @ C @ (semila1673364395name_o @ A @ B)) = (semila1673364395name_o @ (^ [D:pname]: (member_pname @ D @ A)) @ (^ [D:pname]: (member_pname @ D @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[504])). 123.96/29.66 thf(222,axiom,((! [A:pname,B:pname]: (((insert_pname @ A @ bot_bot_pname_o) = (insert_pname @ B @ bot_bot_pname_o)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_singleton__inject)). 123.96/29.66 thf(1514,plain,((! [A:pname,B:pname]: (((insert_pname @ A @ bot_bot_pname_o) = (insert_pname @ B @ bot_bot_pname_o)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 123.96/29.66 thf(135,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (semila1673364395name_o @ B @ C)) => (member_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_IntD1)). 123.96/29.66 thf(1247,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (semila1673364395name_o @ B @ C)) => (member_pname @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 123.96/29.66 thf(402,axiom,((! [A:pname]: ~ (is_none_pname @ (some_pname @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_796_is__none__code_I2_J)). 123.96/29.66 thf(2049,plain,((! [A:pname]: ~ (is_none_pname @ (some_pname @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])). 123.96/29.66 thf(392,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_Sup__fin_Oidem)). 123.96/29.66 thf(2024,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[392])). 123.96/29.66 thf(264,axiom,((! [A:state,B:com,C:state,D:(state > $o),E:state]: (((evalc @ B @ E @ C) => ((evalc @ (while @ D @ B) @ C @ A) => (evalc @ (while @ D @ B) @ E @ A))) <= (D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_evalc_OWhileTrue)). 123.96/29.66 thf(1641,plain,((! [A:state,B:com,C:state,D:(state > $o),E:state]: (((evalc @ B @ E @ C) => ((evalc @ (while @ (D) @ B) @ C @ A) => (evalc @ (while @ (D) @ B) @ E @ A))) | ~ (D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 123.96/29.66 thf(690,axiom,((! [A:(pname > option_com),B:pname,C:com]: (((insert_pname @ B @ (dom_pname_com @ A)) = (dom_pname_com @ A)) <= ((A @ B) = (some_com @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_insert__dom)). 123.96/29.66 thf(2989,plain,((! [A:(pname > option_com),B:pname,C:com]: (((insert_pname @ B @ (dom_pname_com @ A)) = (dom_pname_com @ A)) | ~ ((A @ B) = (some_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[690])). 123.96/29.66 thf(375,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((? [D:hoare_1708887482_state]: ((A @ D) & (member451959335_state @ D @ C)) | ? [D:hoare_1708887482_state]: ((A @ D) & (member451959335_state @ D @ B))) = (? [D:hoare_1708887482_state]: ((member451959335_state @ D @ (semila1122118281tate_o @ B @ C)) & (A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_bex__Un)). 123.96/29.66 thf(1963,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((? [D:hoare_1708887482_state]: ((A @ D) & (member451959335_state @ D @ (C))) | ? [D:hoare_1708887482_state]: ((A @ D) & (member451959335_state @ D @ (B)))) = (? [D:hoare_1708887482_state]: ((member451959335_state @ D @ (semila1122118281tate_o @ B @ C)) & (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])). 123.96/29.66 thf(130,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: ((finite1282449217_pname @ C @ D) => ((finite_finite_pname @ B) => ((finite_finite_pname @ A) => (((C @ (D @ (semila1780557381name_o @ B @ A)) @ (D @ (semila1673364395name_o @ B @ A))) = (C @ (D @ B) @ (D @ A))) <= ((semila1673364395name_o @ B @ A) != bot_bot_pname_o))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_folding__one_Ounion__inter)). 123.96/29.66 thf(1232,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: ((finite1282449217_pname @ (C) @ (D)) => ((finite_finite_pname @ (B)) => ((finite_finite_pname @ (A)) => (((C @ (D @ (semila1780557381name_o @ B @ A)) @ (D @ (semila1673364395name_o @ B @ A))) = (C @ (D @ (B)) @ (D @ (A)))) | ((semila1673364395name_o @ B @ A) = (bot_bot_pname_o)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 123.96/29.66 thf(774,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ B @ A) => (hoare_90032982_state @ A @ C)) <= (hoare_90032982_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_thin)). 123.96/29.66 thf(3268,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (B) @ (A)) => (hoare_90032982_state @ (A) @ (C))) | ~ (hoare_90032982_state @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[774])). 123.96/29.66 thf(520,axiom,((! [A:(pname > $o),B:(pname > $o),C:((pname > $o) > (pname > $o)),D:(pname > $o)]: (((ord_less_eq_pname_o @ A @ D) => ((! [E:(pname > $o),F:(pname > $o)]: ((ord_less_eq_pname_o @ (C @ F) @ (C @ E)) <= (ord_less_eq_pname_o @ F @ E))) => (ord_less_eq_pname_o @ (C @ A) @ B))) <= (B = (C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_xt1_I15_J)). 123.96/29.66 thf(2456,plain,((! [A:(pname > $o),B:(pname > $o),C:((pname > $o) > (pname > $o)),D:(pname > $o)]: (((ord_less_eq_pname_o @ (A) @ (D)) => ((! [E:(pname > $o),F:(pname > $o)]: ((ord_less_eq_pname_o @ (C @ F) @ (C @ E)) | ~ (ord_less_eq_pname_o @ (F) @ (E)))) => (ord_less_eq_pname_o @ (C @ A) @ (B)))) | ~ ((B) = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[520])). 123.96/29.66 thf(29,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ (minus_minus_pname_o @ A @ B) @ B) = (semila1780557381name_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_976_Un__Diff__cancel2)). 123.96/29.66 thf(924,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ (minus_minus_pname_o @ A @ B) @ B) = (semila1780557381name_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 123.96/29.66 thf(818,axiom,((! [A:com]: ((hoare_Mirabelle_MGT @ A) = (hoare_858012674_state @ fequal_state @ A @ (evalc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_MGT__def)). 123.96/29.66 thf(3431,plain,((! [A:com]: ((hoare_Mirabelle_MGT @ A) = (hoare_858012674_state @ (fequal_state) @ A @ (evalc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[818])). 123.96/29.66 thf(272,axiom,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o)]: ((~ (finite1625599783_state @ B)) => ((finite_finite_pname @ (image_1509414295_pname @ A @ B)) => (? [C:hoare_1708887482_state]: ((member451959335_state @ C @ B) & ~ (finite1625599783_state @ (collec1568722789_state @ (^ [D:hoare_1708887482_state]: ((member451959335_state @ D @ B) & ((A @ D) = (A @ C)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_pigeonhole__infinite)). 123.96/29.66 thf(1664,plain,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o)]: ((~ (finite1625599783_state @ (B))) => ((finite_finite_pname @ (image_1509414295_pname @ A @ B)) => (? [C:hoare_1708887482_state]: ((member451959335_state @ C @ (B)) & ~ (finite1625599783_state @ (collec1568722789_state @ (^ [D:hoare_1708887482_state]: ((member451959335_state @ D @ B) & ((A @ D) = (A @ C)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 123.96/29.66 thf(393,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_Un__assoc)). 123.96/29.66 thf(2027,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[393])). 123.96/29.66 thf(755,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (((minus_2056855718tate_o @ (insert528405184_state @ A @ B) @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = B) <= (~ (member451959335_state @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1034_Diff__insert__absorb)). 123.96/29.66 thf(3199,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (((minus_2056855718tate_o @ (insert528405184_state @ A @ B) @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = (B)) | (member451959335_state @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[755])). 123.96/29.66 thf(743,axiom,((! [A:(pname > hoare_1708887482_state),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (image_1116629049_state @ A @ (vimage1943311875_state @ A @ B)) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1189_image__vimage__subset)). 123.96/29.66 thf(3163,plain,((! [A:(pname > hoare_1708887482_state),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (image_1116629049_state @ A @ (vimage1943311875_state @ A @ B)) @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[743])). 123.96/29.66 thf(102,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ C) => ((member451959335_state @ B @ (minus_2056855718tate_o @ C @ A)) <= (~ (member451959335_state @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_DiffI)). 123.96/29.66 thf(1151,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (C)) => ((member451959335_state @ B @ (minus_2056855718tate_o @ C @ A)) | (member451959335_state @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 123.96/29.66 thf(800,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: (((image_1116629049_state @ A @ B) = bot_bo19817387tate_o) = (B = bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_image__is__empty)). 123.96/29.66 thf(3357,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: (((image_1116629049_state @ A @ B) = (bot_bo19817387tate_o)) = ((B) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[800])). 123.96/29.66 thf(3567,plain,(((fa @ sk139) != (top_to832624271tate_o @ sk139))),inference(func_ext,[status(esa)],[3566])). 123.96/29.66 thf(3569,plain,((fa @ sk139) | (top_to832624271tate_o @ sk139)),inference(bool_ext,[status(thm)],[3567])). 123.96/29.66 thf(487,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((ord_less_eq_pname_o @ B @ (semila1673364395name_o @ C @ A)) <= (ord_less_eq_pname_o @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_Int__greatest)). 123.96/29.66 thf(2335,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => ((ord_less_eq_pname_o @ (B) @ (semila1673364395name_o @ C @ A)) | ~ (ord_less_eq_pname_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[487])). 123.96/29.66 thf(626,axiom,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o),C:(pname > hoare_1708887482_state),D:(pname > $o)]: ? [E:(pname > $o)]: ((ord_less_eq_pname_o @ E @ D) & ? [F:(pname > hoare_1708887482_state)]: (! [G:pname]: (((G = (A @ (F @ G))) & (member451959335_state @ (F @ G) @ (minus_2056855718tate_o @ B @ (image_1116629049_state @ C @ E)))) <= (member_pname @ G @ (minus_minus_pname_o @ D @ E))) & ! [G:pname]: ((member_pname @ G @ E) => ((F @ G) = (C @ G)))) & ! [F:pname]: ((~ (member_pname @ F @ (image_1509414295_pname @ A @ (minus_2056855718tate_o @ B @ (image_1116629049_state @ C @ E))))) <= (member_pname @ F @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1187_Cantor__Bernstein__aux)). 123.96/29.66 thf(2777,plain,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o),C:(pname > hoare_1708887482_state),D:(pname > $o)]: ? [E:(pname > $o)]: ((ord_less_eq_pname_o @ (E) @ (D)) & ? [F:(pname > hoare_1708887482_state)]: (! [G:pname]: (((G = (A @ (F @ G))) & (member451959335_state @ (F @ G) @ (minus_2056855718tate_o @ B @ (image_1116629049_state @ C @ E)))) | ~ (member_pname @ G @ (minus_minus_pname_o @ D @ E))) & ! [G:pname]: ((member_pname @ G @ (E)) => ((F @ G) = (C @ G)))) & ! [F:pname]: (~ (member_pname @ F @ (image_1509414295_pname @ A @ (minus_2056855718tate_o @ B @ (image_1116629049_state @ C @ E)))) | ~ (member_pname @ F @ (E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[626])). 123.96/29.66 thf(115,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((C = A) => (ord_less_eq_pname_o @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_ord__le__eq__trans)). 123.96/29.66 thf(1183,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => (((C) = (A)) => (ord_less_eq_pname_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 123.96/29.66 thf(442,axiom,((! [A:(pname > $o)]: (inj_on737724108_pname @ some_pname @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1103_inj__Some)). 123.96/29.66 thf(2178,plain,((! [A:(pname > $o)]: (inj_on737724108_pname @ (some_pname) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[442])). 123.96/29.66 thf(455,axiom,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_sup__idem)). 123.96/29.66 thf(2222,plain,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])). 123.96/29.66 thf(418,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_Int__lower1)). 123.96/29.66 thf(2105,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[418])). 123.96/29.66 thf(717,axiom,((! [A:(state > (state > $o)),B:(hoare_1708887482_state > $o),C:com,D:(state > (state > $o))]: ((hoare_90032982_state @ B @ (insert528405184_state @ (hoare_858012674_state @ D @ C @ A) @ bot_bo19817387tate_o)) <= (! [E:state,F:state]: ((? [G:(state > (state > $o)),H:(state > (state > $o))]: ((hoare_90032982_state @ B @ (insert528405184_state @ (hoare_858012674_state @ G @ C @ H) @ bot_bo19817387tate_o)) & ! [I:state]: ((A @ E @ I) <= (! [J:state]: ((G @ J @ F) => (H @ J @ I)))))) <= (D @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_conseq)). 123.96/29.66 thf(3075,plain,((! [A:(state > (state > $o)),B:(hoare_1708887482_state > $o),C:com,D:(state > (state > $o))]: ((hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_858012674_state @ D @ C @ A) @ bot_bo19817387tate_o)) | ~ (! [E:state,F:state]: (? [G:(state > (state > $o)),H:(state > (state > $o))]: ((hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_858012674_state @ G @ C @ H) @ bot_bo19817387tate_o)) & ! [I:state]: ((A @ E @ I) | ~ (! [J:state]: ((G @ J @ F) => (H @ J @ I))))) | ~ (D @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[717])). 123.96/29.66 thf(201,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ C) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_le__infI2)). 123.96/29.66 thf(1450,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ (C)) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 123.96/29.66 thf(175,axiom,((! [A:(com > $o)]: (inj_on11367768on_com @ some_com @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_inj__Some)). 123.96/29.66 thf(1373,plain,((! [A:(com > $o)]: (inj_on11367768on_com @ (some_com) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 123.96/29.66 thf(692,axiom,((! [A:hoare_1708887482_state,B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => ((image_1116629049_state @ (^ [D:pname]: (A)) @ C) = (insert528405184_state @ A @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_image__constant)). 123.96/29.66 thf(2996,plain,((! [A:hoare_1708887482_state,B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => ((image_1116629049_state @ (^ [D:pname]: (A)) @ C) = (insert528405184_state @ A @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[692])). 123.96/29.66 thf(191,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (semila1780557381name_o @ A @ B)) = ((finite_finite_pname @ A) & (finite_finite_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_finite__Un)). 123.96/29.66 thf(1418,plain,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (semila1780557381name_o @ A @ B)) = ((finite_finite_pname @ (A)) & (finite_finite_pname @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 123.96/29.66 thf(518,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (minus_2056855718tate_o @ B @ A)) <= (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_819_finite__Diff)). 123.96/29.66 thf(2451,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (minus_2056855718tate_o @ B @ A)) | ~ (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[518])). 123.96/29.66 thf(460,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ B @ (semila1780557381name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_inf__sup__aci_I7_J)). 123.96/29.66 thf(2236,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ B @ (semila1780557381name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[460])). 123.96/29.66 thf(374,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((collect_pname @ (^ [C:pname]: ((A @ C) | (B @ C)))) = (semila1780557381name_o @ (collect_pname @ A) @ (collect_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_Collect__disj__eq)). 123.96/29.66 thf(1960,plain,((! [A:(pname > $o),B:(pname > $o)]: ((collect_pname @ (^ [C:pname]: ((A @ C) | (B @ C)))) = (semila1780557381name_o @ (collect_pname @ A) @ (collect_pname @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])). 123.96/29.66 thf(782,axiom,((! [A:pname,B:com,C:com]: ((body_1 @ A) != (semi @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_com_Osimps_I49_J)). 123.96/29.66 thf(3290,plain,((! [A:pname,B:com,C:com]: ~ ((body_1 @ A) = (semi @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[782])). 123.96/29.66 thf(405,axiom,((! [A:(pname > $o)]: ((A = bot_bot_pname_o) <= (! [B:pname]: ~ (member_pname @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_equals0I)). 123.96/29.66 thf(2058,plain,((! [A:(pname > $o)]: (((A) = (bot_bot_pname_o)) | ~ (! [B:pname]: ~ (member_pname @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[405])). 123.96/29.66 thf(492,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (semila1780557381name_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_inf__sup__aci_I5_J)). 123.96/29.66 thf(2367,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (semila1780557381name_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[492])). 123.96/29.66 thf(177,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ A @ (semila1780557381name_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_inf__sup__ord_I4_J)). 123.96/29.66 thf(1377,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (A) @ (semila1780557381name_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 123.96/29.66 thf(529,axiom,((! [A:((pname > $o) > pname),B:((pname > $o) > $o)]: ((finite297249702name_o @ B) => (finite_finite_pname @ (image_pname_o_pname @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI)). 123.96/29.66 thf(2483,plain,((! [A:((pname > $o) > pname),B:((pname > $o) > $o)]: ((finite297249702name_o @ (B)) => (finite_finite_pname @ (image_pname_o_pname @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[529])). 123.96/29.66 thf(348,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ B @ (semila1780557381name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_sup_Oleft__commute)). 123.96/29.66 thf(1886,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ B @ (semila1780557381name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 123.96/29.66 thf(169,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((~ ((member451959335_state @ A @ C) <= (member451959335_state @ A @ B))) <= (member451959335_state @ A @ (minus_2056855718tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_808_DiffE)). 123.96/29.66 thf(1351,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (~ ((member451959335_state @ A @ (C)) | ~ (member451959335_state @ A @ (B))) | ~ (member451959335_state @ A @ (minus_2056855718tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 123.96/29.66 thf(389,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((C = A) | (member451959335_state @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_insert__compr__raw)). 123.96/29.66 thf(2002,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((C = A) | (member451959335_state @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])). 123.96/29.66 thf(197,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((A = B) => (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_order__eq__refl)). 123.96/29.66 thf(1433,plain,((! [A:(pname > $o),B:(pname > $o)]: (((A) = (B)) => (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 123.96/29.66 thf(121,axiom,((! [A:(pname > hoare_1708887482_state),B:pname,C:(pname > $o)]: ((member451959335_state @ (A @ B) @ (image_1116629049_state @ A @ C)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_imageI)). 123.96/29.66 thf(1201,plain,((! [A:(pname > hoare_1708887482_state),B:pname,C:(pname > $o)]: ((member451959335_state @ (A @ B) @ (image_1116629049_state @ A @ C)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 123.96/29.66 thf(633,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (insert_pname @ A @ B)) = (insert_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_insert__absorb2)). 123.96/29.66 thf(2804,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (insert_pname @ A @ B)) = (insert_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[633])). 123.96/29.66 thf(282,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ (semila1673364395name_o @ A @ C) @ (semila1673364395name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_935_inf__sup__distrib2)). 123.96/29.66 thf(1697,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ (semila1673364395name_o @ A @ C) @ (semila1673364395name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 123.96/29.66 thf(759,axiom,((! [A:pname,B:hoare_1708887482_state,C:(pname > hoare_1708887482_state),D:(pname > $o)]: (((inj_on1553129421_state @ (fun_up1986763201_state @ C @ A @ B) @ D) <= (~ (member451959335_state @ B @ (image_1116629049_state @ C @ D)))) <= (inj_on1553129421_state @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_inj__on__fun__updI)). 123.96/29.66 thf(3211,plain,((! [A:pname,B:hoare_1708887482_state,C:(pname > hoare_1708887482_state),D:(pname > $o)]: ((inj_on1553129421_state @ (fun_up1986763201_state @ C @ A @ B) @ (D)) | (member451959335_state @ B @ (image_1116629049_state @ C @ D)) | ~ (inj_on1553129421_state @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[759])). 123.96/29.66 thf(450,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ (insert_pname @ A @ B) @ (insert_pname @ A @ C)) = (insert_pname @ A @ (semila1673364395name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_insert__inter__insert)). 123.96/29.66 thf(2205,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ (insert_pname @ A @ B) @ (insert_pname @ A @ C)) = (insert_pname @ A @ (semila1673364395name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[450])). 123.96/29.66 thf(688,axiom,((! [A:(hoare_1708887482_state > $o)]: ((A = bot_bo19817387tate_o) <= (! [B:hoare_1708887482_state]: ~ (member451959335_state @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_equals0I)). 123.96/29.66 thf(2982,plain,((! [A:(hoare_1708887482_state > $o)]: (((A) = (bot_bo19817387tate_o)) | ~ (! [B:hoare_1708887482_state]: ~ (member451959335_state @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[688])). 123.96/29.66 thf(240,axiom,((! [A:option_com]: ((~ (! [B:com]: (A != (some_com @ B)))) <= (A != none_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1184_option_Oexhaust)). 123.96/29.66 thf(1564,plain,((! [A:option_com]: (~ (! [B:com]: ~ (A = (some_com @ B))) | (A = none_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 123.96/29.66 thf(352,axiom,((! [A:pname,B:pname,C:pname,D:pname]: ((((A = C) & (B = D)) | ((A = D) & (B = C))) = ((insert_pname @ A @ (insert_pname @ B @ bot_bot_pname_o)) = (insert_pname @ C @ (insert_pname @ D @ bot_bot_pname_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_doubleton__eq__iff)). 123.96/29.66 thf(1896,plain,((! [A:pname,B:pname,C:pname,D:pname]: ((((A = C) & (B = D)) | ((A = D) & (B = C))) = ((insert_pname @ A @ (insert_pname @ B @ bot_bot_pname_o)) = (insert_pname @ C @ (insert_pname @ D @ bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 123.96/29.66 thf(14,axiom,((! [A:(com > $o)]: (((collect_com @ A) = bot_bot_com_o) = (! [B:com]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Collect__empty__eq)). 123.96/29.66 thf(877,plain,((! [A:(com > $o)]: (((collect_com @ A) = (bot_bot_com_o)) = (! [B:com]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 123.96/29.66 thf(75,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ A @ B)) = (semila1780557381name_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_inf__sup__aci_I8_J)). 123.96/29.66 thf(1072,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ A @ B)) = (semila1780557381name_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 123.96/29.66 thf(704,axiom,((! [A:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ bot_bo19817387tate_o) => (A = bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_le__bot)). 123.96/29.66 thf(3036,plain,((! [A:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (bot_bo19817387tate_o)) => ((A) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[704])). 123.96/29.66 thf(182,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: ((finite1625599783_state @ (image_1116629049_state @ A @ B)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI)). 123.96/29.66 thf(1394,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: ((finite1625599783_state @ (image_1116629049_state @ A @ B)) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 123.96/29.66 thf(624,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ C) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_894_le__infI2)). 123.96/29.66 thf(2772,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ (C)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[624])). 123.96/29.66 thf(741,axiom,((! [A:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ bot_bo19817387tate_o) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_945_Diff__empty)). 123.96/29.66 thf(3157,plain,((! [A:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ bot_bo19817387tate_o) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[741])). 123.96/29.66 thf(462,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (semila1780557381name_o @ C @ A)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_UnI1)). 123.96/29.66 thf(2242,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (semila1780557381name_o @ C @ A)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[462])). 123.96/29.66 thf(167,axiom,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_Sup__fin_Oidem)). 123.96/29.66 thf(1345,plain,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 123.96/29.66 thf(51,axiom,((! [A:(pname > $o),B:(pname > pname),C:(pname > $o)]: (((finite_finite_pname @ A) <= (ord_less_eq_pname_o @ A @ (image_pname_pname @ B @ C))) <= (finite_finite_pname @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_finite__surj)). 123.96/29.66 thf(988,plain,((! [A:(pname > $o),B:(pname > pname),C:(pname > $o)]: ((finite_finite_pname @ (A)) | ~ (ord_less_eq_pname_o @ (A) @ (image_pname_pname @ B @ C)) | ~ (finite_finite_pname @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 123.96/29.66 thf(631,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((((C = A) = ((insert_pname @ B @ C) = (insert_pname @ B @ A))) <= (~ (member_pname @ B @ A))) <= (~ (member_pname @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_insert__ident)). 123.96/29.66 thf(2799,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((((C) = (A)) = ((insert_pname @ B @ C) = (insert_pname @ B @ A))) | (member_pname @ B @ (A)) | (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[631])). 123.96/29.66 thf(477,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila129691299tate_o @ B @ C)) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_933_sup__inf__distrib1)). 123.96/29.66 thf(2286,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila129691299tate_o @ B @ C)) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])). 123.96/29.66 thf(417,axiom,((! [A:(pname > $o),B:((pname > $o) > pname),C:((pname > $o) > $o)]: ((finite297249702name_o @ C) => ((ord_less_eq_pname_o @ A @ (image_pname_o_pname @ B @ C)) => (finite_finite_pname @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_finite__surj)). 123.96/29.66 thf(2103,plain,((! [A:(pname > $o),B:((pname > $o) > pname),C:((pname > $o) > $o)]: ((finite297249702name_o @ (C)) => ((ord_less_eq_pname_o @ (A) @ (image_pname_o_pname @ (B) @ (C))) => (finite_finite_pname @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[417])). 123.96/29.66 thf(616,axiom,((! [A:state,B:state]: ((evalc @ skip @ A @ B) => (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_765_evalc__elim__cases_I1_J)). 123.96/29.66 thf(2750,plain,((! [A:state,B:state]: ((evalc @ skip @ A @ B) => (B = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[616])). 123.96/29.66 thf(678,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => (ord_le777019615tate_o @ B @ (insert528405184_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_subset__insertI2)). 123.96/29.66 thf(2954,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => (ord_le777019615tate_o @ (B) @ (insert528405184_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[678])). 123.96/29.66 thf(251,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ B @ A) = B) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_Un__absorb2)). 123.96/29.66 thf(1604,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ B @ A) = (B)) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 123.96/29.66 thf(723,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((member451959335_state @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_singletonE)). 123.96/29.66 thf(3097,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((member451959335_state @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[723])). 123.96/29.66 thf(525,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ C @ A) => (ord_le777019615tate_o @ B @ A)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_order__trans)). 123.96/29.66 thf(2473,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (C) @ (A)) => (ord_le777019615tate_o @ (B) @ (A))) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[525])). 123.96/29.66 thf(154,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((member_pname @ A @ C) <= (member_pname @ A @ B)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_subsetD)). 123.96/29.66 thf(1306,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (C)) | ~ (member_pname @ A @ (B)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 123.96/29.66 thf(491,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: ((finite89670078_pname @ C @ D) => ((finite_finite_pname @ B) => (((((D @ (semila1780557381name_o @ B @ A)) = (C @ (D @ B) @ (D @ A))) <= (A != bot_bot_pname_o)) <= (finite_finite_pname @ A)) <= (B != bot_bot_pname_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_folding__one__idem_Ounion__idem)). 123.96/29.66 thf(2364,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: ((finite89670078_pname @ (C) @ (D)) => ((finite_finite_pname @ (B)) => (((D @ (semila1780557381name_o @ B @ A)) = (C @ (D @ (B)) @ (D @ (A)))) | ((A) = (bot_bot_pname_o)) | ~ (finite_finite_pname @ (A)) | ((B) = (bot_bot_pname_o))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[491])). 123.96/29.66 thf(103,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ A) <= (ord_le777019615tate_o @ A @ B)) <= (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_rev__finite__subset)). 123.96/29.66 thf(1153,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (A)) | ~ (ord_le777019615tate_o @ (A) @ (B)) | ~ (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 123.96/29.66 thf(165,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (collec1568722789_state @ B) @ (collec1568722789_state @ A)) <= (! [C:hoare_1708887482_state]: ((B @ C) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_Collect__mono)). 123.96/29.66 thf(1338,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (collec1568722789_state @ B) @ (collec1568722789_state @ A)) | ~ (! [C:hoare_1708887482_state]: ((B @ C) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 123.96/29.66 thf(286,axiom,((! [A:(pname > $o)]: ((collect_pname @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_Collect__def)). 123.96/29.66 thf(1708,plain,((! [A:(pname > $o)]: ((collect_pname @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 123.96/29.66 thf(628,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ A @ B) = B) = (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_le__iff__sup)). 123.96/29.66 thf(2790,plain,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ A @ B) = (B)) = (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[628])). 123.96/29.66 thf(342,axiom,((! [A:(hoare_1708887482_state > pname)]: ((image_1509414295_pname @ A @ bot_bo19817387tate_o) = bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_image__empty)). 123.96/29.66 thf(1868,plain,((! [A:(hoare_1708887482_state > pname)]: ((image_1509414295_pname @ A @ bot_bo19817387tate_o) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 123.96/29.66 thf(262,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ A @ (semila1122118281tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_Un__upper1)). 123.96/29.66 thf(1636,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (A) @ (semila1122118281tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 123.96/29.66 thf(293,axiom,((! [A:(hoare_1708887482_state > $o),B:(pname > hoare_1708887482_state),C:(pname > $o)]: ((ord_le777019615tate_o @ A @ (image_1116629049_state @ B @ C)) = (? [D:(pname > $o)]: ((A = (image_1116629049_state @ B @ D)) & (ord_less_eq_pname_o @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_subset__image__iff)). 123.96/29.66 thf(1730,plain,((! [A:(hoare_1708887482_state > $o),B:(pname > hoare_1708887482_state),C:(pname > $o)]: ((ord_le777019615tate_o @ (A) @ (image_1116629049_state @ B @ C)) = (? [D:(pname > $o)]: (((A) = (image_1116629049_state @ B @ D)) & (ord_less_eq_pname_o @ (D) @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 123.96/29.66 thf(340,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ B @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_Un__left__commute)). 123.96/29.66 thf(1863,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ B @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])). 123.96/29.66 thf(773,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (insert528405184_state @ A @ B) @ C) = (insert528405184_state @ A @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_Un__insert__left)). 123.96/29.66 thf(3265,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (insert528405184_state @ A @ B) @ C) = (insert528405184_state @ A @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[773])). 123.96/29.66 thf(583,axiom,((wt @ skip)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_WT_OSkip)). 123.96/29.66 thf(2646,plain,((wt @ skip)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[583])). 123.96/29.66 thf(312,axiom,(((set_com @ none_com) = bot_bot_com_o)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1138_Option_Oset_Osimps_I1_J)). 123.96/29.66 thf(1783,plain,(((set_com @ none_com) = (bot_bot_com_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 123.96/29.66 thf(611,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((ord_less_eq_pname_o @ (minus_minus_pname_o @ A @ (insert_pname @ B @ bot_bot_pname_o)) @ C) => ((member_pname @ B @ A) => (ord_less_eq_pname_o @ A @ (insert_pname @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1060_diff__single__insert)). 123.96/29.66 thf(2737,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((ord_less_eq_pname_o @ (minus_minus_pname_o @ A @ (insert_pname @ B @ bot_bot_pname_o)) @ (C)) => ((member_pname @ B @ (A)) => (ord_less_eq_pname_o @ (A) @ (insert_pname @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[611])). 123.96/29.66 thf(2232,plain,(((collect_com @ (^ [A:com]: (($false)))) = (bot_bot_com_o))),inference(lifteq,[status(thm)],[2231])). 123.96/29.66 thf(710,axiom,((! [A:pname,B:(hoare_1708887482_state > $o),C:(pname > (state > (state > $o))),D:(pname > (state > (state > $o))),E:(pname > $o)]: ((hoare_90032982_state @ (semila1122118281tate_o @ B @ (image_1116629049_state @ (^ [F:pname]: (hoare_858012674_state @ (C @ F) @ (body_1 @ F) @ (D @ F))) @ E)) @ (image_1116629049_state @ (^ [F:pname]: (hoare_858012674_state @ (C @ F) @ (the_com @ (body @ F)) @ (D @ F))) @ E)) => ((member_pname @ A @ E) => (hoare_90032982_state @ B @ (insert528405184_state @ (hoare_858012674_state @ (C @ A) @ (body_1 @ A) @ (D @ A)) @ bot_bo19817387tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_Body1)). 123.96/29.66 thf(3054,plain,((! [A:pname,B:(hoare_1708887482_state > $o),C:(pname > (state > (state > $o))),D:(pname > (state > (state > $o))),E:(pname > $o)]: ((hoare_90032982_state @ (semila1122118281tate_o @ B @ (image_1116629049_state @ (^ [F:pname]: (hoare_858012674_state @ (C @ F) @ (body_1 @ F) @ (D @ F))) @ E)) @ (image_1116629049_state @ (^ [F:pname]: (hoare_858012674_state @ (C @ F) @ (the_com @ (body @ F)) @ (D @ F))) @ E)) => ((member_pname @ A @ (E)) => (hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_858012674_state @ (C @ A) @ (body_1 @ A) @ (D @ A)) @ bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[710])). 123.96/29.66 thf(599,axiom,((! [A:com]: ~ (member_com @ A @ bot_bot_com_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_emptyE)). 123.96/29.66 thf(2705,plain,((! [A:com]: ~ (member_com @ A @ (bot_bot_com_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[599])). 123.96/29.66 thf(181,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((((semila1673364395name_o @ C @ (insert_pname @ B @ A)) = (insert_pname @ B @ (semila1673364395name_o @ C @ A))) <= (member_pname @ B @ C)) & (((semila1673364395name_o @ C @ (insert_pname @ B @ A)) = (semila1673364395name_o @ C @ A)) <= (~ (member_pname @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_999_Int__insert__right)). 123.96/29.66 thf(1387,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((((semila1673364395name_o @ C @ (insert_pname @ B @ A)) = (insert_pname @ B @ (semila1673364395name_o @ C @ A))) | ~ (member_pname @ B @ (C))) & (((semila1673364395name_o @ C @ (insert_pname @ B @ A)) = (semila1673364395name_o @ C @ A)) | (member_pname @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 123.96/29.66 thf(127,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((ord_less_eq_pname_o @ A @ B) & (ord_less_eq_pname_o @ B @ A)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_set__eq__subset)). 123.96/29.66 thf(1223,plain,((! [A:(pname > $o),B:(pname > $o)]: (((ord_less_eq_pname_o @ (A) @ (B)) & (ord_less_eq_pname_o @ (B) @ (A))) = ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 123.96/29.66 thf(80,axiom,((! [A:(hoare_1708887482_state > $o)]: (inj_on945311362_state @ some_H1974565227_state @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_inj__Some)). 123.96/29.66 thf(1090,plain,((! [A:(hoare_1708887482_state > $o)]: (inj_on945311362_state @ (some_H1974565227_state) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 123.96/29.66 thf(1091,plain,(! [A:(hoare_1708887482_state > $o)] : ((inj_on945311362_state @ (some_H1974565227_state) @ (A)))),inference(cnf,[status(esa)],[1090])). 123.96/29.66 thf(474,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: (((A @ C) <= (~ (B @ C))) => (semila1122118281tate_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_sup1CI)). 123.96/29.66 thf(2277,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: (((A @ C) | (B @ C)) => (semila1122118281tate_o @ (A) @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[474])). 123.96/29.66 thf(277,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((member_pname @ B @ C) => ((semila1673364395name_o @ (insert_pname @ B @ A) @ C) = (insert_pname @ B @ (semila1673364395name_o @ A @ C)))) & (((semila1673364395name_o @ (insert_pname @ B @ A) @ C) = (semila1673364395name_o @ A @ C)) <= (~ (member_pname @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_996_Int__insert__left)). 123.96/29.66 thf(1676,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((member_pname @ B @ (C)) => ((semila1673364395name_o @ (insert_pname @ B @ A) @ C) = (insert_pname @ B @ (semila1673364395name_o @ A @ C)))) & (((semila1673364395name_o @ (insert_pname @ B @ A) @ C) = (semila1673364395name_o @ A @ C)) | (member_pname @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 123.96/29.66 thf(218,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ (minus_2056855718tate_o @ A @ C) @ (minus_2056855718tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_975_Un__Diff)). 123.96/29.66 thf(1502,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ (minus_2056855718tate_o @ A @ C) @ (minus_2056855718tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 123.96/29.66 thf(805,axiom,((! [A:pname]: (skip != (body_1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_com_Osimps_I18_J)). 123.96/29.66 thf(3371,plain,((! [A:pname]: ~ (skip = (body_1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[805])). 123.96/29.66 thf(740,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),C:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: (((finite1625599783_state @ A) => (((! [D:hoare_1708887482_state,E:hoare_1708887482_state]: (member451959335_state @ (B @ D @ E) @ (insert528405184_state @ D @ (insert528405184_state @ E @ bot_bo19817387tate_o)))) => (member451959335_state @ (C @ A) @ A)) <= (A != bot_bo19817387tate_o))) <= (finite1615457021_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_folding__one_Oclosed)). 123.96/29.66 thf(3154,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),C:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: (((finite1625599783_state @ (A)) => (((! [D:hoare_1708887482_state,E:hoare_1708887482_state]: (member451959335_state @ (B @ D @ E) @ (insert528405184_state @ D @ (insert528405184_state @ E @ bot_bo19817387tate_o)))) => (member451959335_state @ (C @ (A)) @ (A))) | ((A) = (bot_bo19817387tate_o)))) | ~ (finite1615457021_state @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[740])). 123.96/29.66 thf(689,axiom,((! [A:(pname > (state > (state > $o))),B:(pname > (state > (state > $o))),C:(hoare_1708887482_state > $o),D:(pname > (state > (state > $o))),E:(pname > com),F:(pname > (state > (state > $o))),G:(pname > $o)]: ((((hoare_90032982_state @ C @ (image_1116629049_state @ (^ [H:pname]: (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H))) @ G)) <= (hoare_90032982_state @ C @ (image_1116629049_state @ (^ [H:pname]: (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H))) @ G))) <= (! [H:pname]: ((hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H)) @ bot_bo19817387tate_o)) <= (hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H)) @ bot_bo19817387tate_o))))) <= (finite_finite_pname @ G)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_finite__pointwise)). 123.96/29.66 thf(2986,plain,((! [A:(pname > (state > (state > $o))),B:(pname > (state > (state > $o))),C:(hoare_1708887482_state > $o),D:(pname > (state > (state > $o))),E:(pname > com),F:(pname > (state > (state > $o))),G:(pname > $o)]: ((hoare_90032982_state @ (C) @ (image_1116629049_state @ (^ [H:pname]: (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H))) @ G)) | ~ (hoare_90032982_state @ (C) @ (image_1116629049_state @ (^ [H:pname]: (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H))) @ G)) | ~ (! [H:pname]: ((hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H)) @ bot_bo19817387tate_o)) | ~ (hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H)) @ bot_bo19817387tate_o)))) | ~ (finite_finite_pname @ (G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[689])). 123.96/29.66 thf(731,axiom,(((dom_pname_com @ (^ [A:pname]: (none_com))) = bot_bot_pname_o)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1137_dom__empty)). 123.96/29.66 thf(3129,plain,(((dom_pname_com @ (^ [A:pname]: (none_com))) = (bot_bot_pname_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[731])). 123.96/29.66 thf(3130,plain,(((dom_pname_com @ (^ [A:pname]: (none_com))) = (bot_bot_pname_o))),inference(lifteq,[status(thm)],[3129])). 123.96/29.66 thf(1,conjecture,((hoare_90032982_state @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_7)). 123.96/29.66 thf(2,negated_conjecture,((~ (hoare_90032982_state @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)))),inference(neg_conjecture,[status(cth)],[1])). 123.96/29.66 thf(835,plain,((~ (hoare_90032982_state @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 123.96/29.66 thf(3503,plain,((~ (hoare_90032982_state @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ bot_bot_pname_o) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o))) | ((dom_pname_com @ body) != (dom_pname_com @ (^ [A:pname]: (none_com))))),inference(paramod_ordered,[status(thm)],[3130,835])). 123.96/29.66 thf(3505,plain,((~ (hoare_90032982_state @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ bot_bot_pname_o) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o))) | ((^ [A:pname]: (body)) != (^ [A:pname,B:pname]: (none_com))) | ((^ [A:pname]: (A)) != (^ [A:pname]: (A)))),inference(simp,[status(thm)],[3503])). 123.96/29.66 thf(3507,plain,((~ (hoare_90032982_state @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ bot_bot_pname_o) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o))) | ((^ [A:pname]: (body)) != (^ [A:pname,B:pname]: (none_com)))),inference(simp,[status(thm)],[3505])). 123.96/29.66 thf(3514,plain,(((body @ sk136) != none_com) | (~ (hoare_90032982_state @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ bot_bot_pname_o) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)))),inference(func_ext,[status(esa)],[3507])). 123.96/29.66 thf(832,axiom,((! [A:pname,B:pname]: ((A = B) = ((body_1 @ A) = (body_1 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_com_Osimps_I6_J)). 123.96/29.66 thf(3471,plain,((! [A:pname,B:pname]: ((A = B) = ((body_1 @ A) = (body_1 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[832])). 123.96/29.66 thf(64,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: ((ord_le1205211808me_o_o @ A @ B) => ((finite297249702name_o @ B) => (finite297249702name_o @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_finite__subset)). 123.96/29.66 thf(1042,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: ((ord_le1205211808me_o_o @ (A) @ (B)) => ((finite297249702name_o @ (B)) => (finite297249702name_o @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 123.96/29.66 thf(549,axiom,((! [A:(hoare_1708887482_state > (hoare_1708887482_state > $o)),B:(hoare_1708887482_state > $o)]: (((finite1329924456tate_o @ (image_1551509096tate_o @ A @ B)) => (? [C:hoare_1708887482_state]: (~ (finite1625599783_state @ (collec1568722789_state @ (^ [D:hoare_1708887482_state]: ((member451959335_state @ D @ B) & ((A @ D) = (A @ C)))))) & (member451959335_state @ C @ B)))) <= (~ (finite1625599783_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_pigeonhole__infinite)). 123.96/29.66 thf(2541,plain,((! [A:(hoare_1708887482_state > (hoare_1708887482_state > $o)),B:(hoare_1708887482_state > $o)]: (((finite1329924456tate_o @ (image_1551509096tate_o @ A @ B)) => (? [C:hoare_1708887482_state]: (~ (finite1625599783_state @ (collec1568722789_state @ (^ [D:hoare_1708887482_state]: ((member451959335_state @ D @ B) & ((A @ D) = (A @ C)))))) & (member451959335_state @ C @ (B))))) | (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[549])). 123.96/29.66 thf(224,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((A = B) = ((some_H1974565227_state @ A) = (some_H1974565227_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_option_Oinject)). 123.96/29.66 thf(1519,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((A = B) = ((some_H1974565227_state @ A) = (some_H1974565227_state @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 123.96/29.66 thf(567,axiom,((! [A:pname,B:(pname > $o)]: (bot_bot_pname_o != (insert_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_empty__not__insert)). 123.96/29.66 thf(2596,plain,((! [A:pname,B:(pname > $o)]: ~ ((bot_bot_pname_o) = (insert_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[567])). 123.96/29.66 thf(125,axiom,((! [A:(com > $o)]: ((? [B:com]: (member_com @ B @ A)) = (A != bot_bot_com_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ex__in__conv)). 123.96/29.66 thf(1217,plain,((! [A:(com > $o)]: ((? [B:com]: (member_com @ B @ (A))) = (~ ((A) = (bot_bot_com_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 123.96/29.66 thf(432,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (collect_pname @ (^ [C:pname]: ((member_pname @ C @ A) | (member_pname @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_Un__def)). 123.96/29.66 thf(2147,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (collect_pname @ (^ [C:pname]: ((member_pname @ C @ A) | (member_pname @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[432])). 123.96/29.66 thf(326,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (collect_pname @ (^ [C:pname]: ((C = A) | (member_pname @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_insert__compr)). 123.96/29.66 thf(1824,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (collect_pname @ (^ [C:pname]: ((C = A) | (member_pname @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 123.96/29.66 thf(433,axiom,((! [A:state,B:com,C:state,D:state]: ((evalc @ B @ C @ D) => ((evalc @ B @ C @ A) => (A = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_770_com__det)). 123.96/29.66 thf(2150,plain,((! [A:state,B:com,C:state,D:state]: ((evalc @ B @ C @ D) => ((evalc @ B @ C @ A) => (A = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[433])). 123.96/29.66 thf(426,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ (semila129691299tate_o @ B @ C)) = ((ord_le777019615tate_o @ A @ B) & (ord_le777019615tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_889_le__inf__iff)). 123.96/29.66 thf(2132,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (semila129691299tate_o @ B @ C)) = ((ord_le777019615tate_o @ (A) @ (B)) & (ord_le777019615tate_o @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[426])). 123.96/29.66 thf(656,axiom,((! [A:(state > $o),B:com,C:com,D:com]: ((while @ A @ B) != (semi @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_com_Osimps_I47_J)). 123.96/29.66 thf(2890,plain,((! [A:(state > $o),B:com,C:com,D:com]: ~ ((while @ (A) @ B) = (semi @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[656])). 123.96/29.66 thf(794,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((~ (member451959335_state @ A @ B)) <= (B = bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_equals0D)). 123.96/29.66 thf(3339,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (~ (member451959335_state @ A @ (B)) | ~ ((B) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[794])). 123.96/29.66 thf(132,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ B) => ((semila1122118281tate_o @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_Un__absorb1)). 123.96/29.66 thf(1238,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) => ((semila1122118281tate_o @ A @ B) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 123.96/29.66 thf(680,axiom,((! [A:hoare_1708887482_state]: ((the_el864710747_state @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_the__elem__eq)). 123.96/29.66 thf(2958,plain,((! [A:hoare_1708887482_state]: ((the_el864710747_state @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[680])). 123.96/29.66 thf(516,axiom,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((((B != bot_bot_pname_o) => ((D @ (insert_pname @ A @ B)) = (C @ A @ (D @ B)))) <= (~ (member_pname @ A @ B))) <= (finite_finite_pname @ B)) <= (finite1282449217_pname @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_folding__one_Oinsert)). 123.96/29.66 thf(2445,plain,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((~ ((B) = (bot_bot_pname_o))) => ((D @ (insert_pname @ A @ B)) = (C @ A @ (D @ (B))))) | (member_pname @ A @ (B)) | ~ (finite_finite_pname @ (B)) | ~ (finite1282449217_pname @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[516])). 123.96/29.66 thf(359,axiom,((! [A:pname,B:pname]: ((member_pname @ A @ (insert_pname @ B @ bot_bot_pname_o)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_singletonE)). 123.96/29.66 thf(1920,plain,((! [A:pname,B:pname]: ((member_pname @ A @ (insert_pname @ B @ bot_bot_pname_o)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[359])). 123.96/29.66 thf(150,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: (((finite1625599783_state @ (image_1116629049_state @ A @ B)) => (? [C:pname]: ((member_pname @ C @ B) & ~ (finite_finite_pname @ (collect_pname @ (^ [D:pname]: ((member_pname @ D @ B) & ((A @ D) = (A @ C))))))))) <= (~ (finite_finite_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_pigeonhole__infinite)). 123.96/29.66 thf(1296,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: (((finite1625599783_state @ (image_1116629049_state @ A @ B)) => (? [C:pname]: ((member_pname @ C @ (B)) & ~ (finite_finite_pname @ (collect_pname @ (^ [D:pname]: ((member_pname @ D @ B) & ((A @ D) = (A @ C))))))))) | (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 123.96/29.66 thf(18,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((minus_minus_pname_o @ A @ (semila1673364395name_o @ B @ C)) = (semila1780557381name_o @ (minus_minus_pname_o @ A @ B) @ (minus_minus_pname_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_866_Diff__Int)). 123.96/29.66 thf(889,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((minus_minus_pname_o @ A @ (semila1673364395name_o @ B @ C)) = (semila1780557381name_o @ (minus_minus_pname_o @ A @ B) @ (minus_minus_pname_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 123.96/29.66 thf(123,axiom,((! [A:(pname > $o),B:com,C:(pname > com),D:pname]: (((member_com @ B @ (image_pname_com @ C @ A)) <= (member_pname @ D @ A)) <= (B = (C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_image__eqI)). 123.96/29.66 thf(1210,plain,((! [A:(pname > $o),B:com,C:(pname > com),D:pname]: ((member_com @ B @ (image_pname_com @ C @ A)) | ~ (member_pname @ D @ (A)) | ~ (B = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 123.96/29.66 thf(118,axiom,((! [A:pname,B:(pname > $o)]: ((B = bot_bot_pname_o) => (~ (member_pname @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_equals0D)). 123.96/29.66 thf(1192,plain,((! [A:pname,B:(pname > $o)]: (((B) = (bot_bot_pname_o)) => (~ (member_pname @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 123.96/29.66 thf(1193,plain,(! [B:(pname > $o),A:pname] : ((~ ((B) = (bot_bot_pname_o))) | (~ (member_pname @ A @ (B))))),inference(cnf,[status(esa)],[1192])). 123.96/29.66 thf(1194,plain,(! [B:(pname > $o),A:pname] : (((B) != (bot_bot_pname_o)) | (~ (member_pname @ A @ (B))))),inference(lifteq,[status(thm)],[1193])). 123.96/29.66 thf(1195,plain,(! [A:pname] : ((~ (member_pname @ A @ (bot_bot_pname_o))))),inference(simp,[status(thm)],[1194])). 123.96/29.66 thf(531,axiom,((! [A:com]: (member_com @ A @ top_top_com_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1195_UNIV__I)). 123.96/29.66 thf(2492,plain,((! [A:com]: (member_com @ A @ (top_top_com_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[531])). 123.96/29.66 thf(457,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((~ (member451959335_state @ B @ C)) => ((ord_le777019615tate_o @ C @ A) = (ord_le777019615tate_o @ C @ (insert528405184_state @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_subset__insert)). 123.96/29.66 thf(2228,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((~ (member451959335_state @ B @ (C))) => ((ord_le777019615tate_o @ (C) @ (A)) = (ord_le777019615tate_o @ (C) @ (insert528405184_state @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])). 123.96/29.66 thf(148,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_inf__sup__aci_I8_J)). 123.96/29.66 thf(1291,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 123.96/29.66 thf(46,axiom,((! [A:(pname > pname),B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => ((insert_pname @ (A @ B) @ (image_pname_pname @ A @ C)) = (image_pname_pname @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_insert__image)). 123.96/29.66 thf(974,plain,((! [A:(pname > pname),B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => ((insert_pname @ (A @ B) @ (image_pname_pname @ A @ C)) = (image_pname_pname @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 123.96/29.66 thf(824,axiom,((! [A:hoare_1708887482_state]: ((bot_bo19817387tate_o @ A) = (member451959335_state @ A @ bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_bot__empty__eq)). 123.96/29.66 thf(3445,plain,((! [A:hoare_1708887482_state]: ((bot_bo19817387tate_o @ A) = (member451959335_state @ A @ (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[824])). 123.96/29.66 thf(6,axiom,((! [A:(pname > (pname > $o)),B:(pname > $o),C:((pname > $o) > $o)]: (((? [D:(pname > $o)]: ((C = (image_pname_pname_o @ A @ D)) & (finite_finite_pname @ D) & (ord_less_eq_pname_o @ D @ B))) <= (ord_le1205211808me_o_o @ C @ (image_pname_pname_o @ A @ B))) <= (finite297249702name_o @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_finite__subset__image)). 123.96/29.66 thf(847,plain,((! [A:(pname > (pname > $o)),B:(pname > $o),C:((pname > $o) > $o)]: (? [D:(pname > $o)]: (((C) = (image_pname_pname_o @ A @ D)) & (finite_finite_pname @ (D)) & (ord_less_eq_pname_o @ (D) @ (B))) | ~ (ord_le1205211808me_o_o @ (C) @ (image_pname_pname_o @ A @ B)) | ~ (finite297249702name_o @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 123.96/29.66 thf(619,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) => ((ord_less_eq_pname_o @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_order__antisym__conv)). 123.96/29.66 thf(2758,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) => ((ord_less_eq_pname_o @ (B) @ (A)) = ((B) = (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[619])). 123.96/29.66 thf(651,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_Un__absorb)). 123.96/29.66 thf(2873,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[651])). 123.96/29.66 thf(809,axiom,((! [A:(state > $o),B:com,C:pname]: ((while @ A @ B) != (body_1 @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_com_Osimps_I58_J)). 123.96/29.66 thf(3403,plain,((! [A:(state > $o),B:com,C:pname]: ~ ((while @ (A) @ B) = (body_1 @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[809])). 123.96/29.66 thf(377,axiom,((! [A:(com > $o)]: ((A = bot_bot_com_o) = (! [B:com]: ~ (member_com @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_all__not__in__conv)). 123.96/29.66 thf(1968,plain,((! [A:(com > $o)]: (((A) = (bot_bot_com_o)) = (! [B:com]: ~ (member_com @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])). 123.96/29.66 thf(7,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1673364395name_o @ A @ (minus_minus_pname_o @ B @ A)) = bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_Diff__disjoint)). 123.96/29.66 thf(852,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1673364395name_o @ A @ (minus_minus_pname_o @ B @ A)) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 123.96/29.66 thf(237,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((~ ((member_pname @ A @ B) => (~ (member_pname @ A @ C)))) <= (member_pname @ A @ (semila1673364395name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_IntE)). 123.96/29.66 thf(1555,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (~ ((member_pname @ A @ (B)) => (~ (member_pname @ A @ (C)))) | ~ (member_pname @ A @ (semila1673364395name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 123.96/29.66 thf(486,axiom,((! [A:option_com]: ((A = none_com) = (! [B:com]: (A != (some_com @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1112_not__Some__eq)). 123.96/29.66 thf(2332,plain,((! [A:option_com]: ((A = none_com) = (! [B:com]: ~ (A = (some_com @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])). 123.96/29.66 thf(640,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((member451959335_state @ A @ C) <= (member451959335_state @ A @ B)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_in__mono)). 123.96/29.66 thf(2826,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (C)) | ~ (member451959335_state @ A @ (B)) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[640])). 123.96/29.66 thf(790,axiom,(((set_Ho525251890_state @ none_H1106584047_state) = bot_bo19817387tate_o)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1140_Option_Oset_Osimps_I1_J)). 123.96/29.66 thf(3314,plain,(((set_Ho525251890_state @ none_H1106584047_state) = (bot_bo19817387tate_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[790])). 123.96/29.66 thf(784,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ B @ C) => ((hoare_90032982_state @ A @ B) => (hoare_90032982_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cut)). 123.96/29.66 thf(3297,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ (B) @ (C)) => ((hoare_90032982_state @ (A) @ (B)) => (hoare_90032982_state @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[784])). 123.96/29.66 thf(714,axiom,((ord_le777019615tate_o @ fa @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ A)))) @ (dom_pname_com @ body)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4)). 123.96/29.66 thf(3065,plain,((ord_le777019615tate_o @ (fa) @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ A)))) @ (dom_pname_com @ body)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[714])). 123.96/29.66 thf(797,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ bot_bo19817387tate_o) = bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_Int__empty__right)). 123.96/29.66 thf(3349,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ bot_bo19817387tate_o) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[797])). 123.96/29.66 thf(408,axiom,((! [A:(state > $o),B:com,C:state,D:state]: ((((A @ C) <= (D = C)) => (~ ((A @ C) => (! [E:state]: ((evalc @ B @ C @ E) => (~ (evalc @ (while @ A @ B) @ E @ D))))))) <= (evalc @ (while @ A @ B) @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_evalc__WHILE__case)). 123.96/29.66 thf(2068,plain,((! [A:(state > $o),B:com,C:state,D:state]: ((((A @ C) | ~ (D = C)) => (~ ((A @ C) => (! [E:state]: ((evalc @ B @ C @ E) => (~ (evalc @ (while @ (A) @ B) @ E @ D))))))) | ~ (evalc @ (while @ (A) @ B) @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])). 123.96/29.66 thf(324,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((ord_less_eq_pname_o @ B @ A) <= (ord_less_eq_pname_o @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_subset__trans)). 123.96/29.66 thf(1819,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => ((ord_less_eq_pname_o @ (B) @ (A)) | ~ (ord_less_eq_pname_o @ (C) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 123.96/29.66 thf(701,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((((B != bot_bo19817387tate_o) => ((D @ (insert528405184_state @ A @ B)) = (C @ A @ (D @ B)))) <= (finite1625599783_state @ B)) <= (finite1347568576_state @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_folding__one__idem_Oinsert__idem)). 123.96/29.66 thf(3028,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: (((~ ((B) = (bot_bo19817387tate_o))) => ((D @ (insert528405184_state @ A @ B)) = (C @ A @ (D @ (B))))) | ~ (finite1625599783_state @ (B)) | ~ (finite1347568576_state @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[701])). 123.96/29.66 thf(709,axiom,((! [A:pname,B:(state > $o),C:com]: ((body_1 @ A) != (while @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_com_Osimps_I59_J)). 123.96/29.66 thf(3050,plain,((! [A:pname,B:(state > $o),C:com]: ~ ((body_1 @ A) = (while @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[709])). 123.96/29.66 thf(145,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ B @ A) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_equalityD2)). 123.96/29.66 thf(1281,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (A)) | ~ ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 123.96/29.66 thf(613,axiom,((! [A:option_com]: ((A = none_com) = ((set_com @ A) = bot_bot_com_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_set__empty__eq)). 123.96/29.66 thf(2741,plain,((! [A:option_com]: ((A = none_com) = ((set_com @ A) = (bot_bot_com_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[613])). 123.96/29.66 thf(703,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ (collec1568722789_state @ B)) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((~ (C = A)) => (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_insert__Collect)). 123.96/29.66 thf(3033,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ (collec1568722789_state @ B)) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((~ (C = A)) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[703])). 123.96/29.66 thf(297,axiom,((! [A:(state > $o),B:com]: (skip != (while @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_com_Osimps_I16_J)). 123.96/29.66 thf(1740,plain,((! [A:(state > $o),B:com]: ~ (skip = (while @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 123.96/29.66 thf(356,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: (((ord_less_eq_pname_o @ (semila1673364395name_o @ C @ (collect_pname @ B)) @ (semila1673364395name_o @ D @ (collect_pname @ A))) <= (! [E:pname]: ((member_pname @ E @ C) => ((B @ E) => (A @ E))))) <= (ord_less_eq_pname_o @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_Int__Collect__mono)). 123.96/29.66 thf(1910,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: ((ord_less_eq_pname_o @ (semila1673364395name_o @ C @ (collect_pname @ B)) @ (semila1673364395name_o @ D @ (collect_pname @ A))) | ~ (! [E:pname]: ((member_pname @ E @ (C)) => ((B @ E) => (A @ E)))) | ~ (ord_less_eq_pname_o @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])). 123.96/29.66 thf(382,axiom,((finite138924780name_o @ semila1780557381name_o)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_comp__fun__idem__sup)). 123.96/29.66 thf(1983,plain,((finite138924780name_o @ (semila1780557381name_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])). 123.96/29.66 thf(13,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ A @ (semila1780557381name_o @ B @ C)) = (ord_less_eq_pname_o @ (minus_minus_pname_o @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_Diff__subset__conv)). 123.96/29.66 thf(874,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (semila1780557381name_o @ B @ C)) = (ord_less_eq_pname_o @ (minus_minus_pname_o @ A @ B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 123.96/29.66 thf(319,axiom,((! [A:(pname > $o)]: ((? [B:pname,C:(pname > $o)]: ((A = (insert_pname @ B @ C)) & ~ (member_pname @ B @ C))) = (A != bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_nonempty__iff)). 123.96/29.66 thf(1804,plain,((! [A:(pname > $o)]: ((? [B:pname,C:(pname > $o)]: (((A) = (insert_pname @ B @ C)) & ~ (member_pname @ B @ (C)))) = (~ ((A) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 123.96/29.66 thf(645,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o)),D:(hoare_1708887482_state > $o)]: ((((ord_le777019615tate_o @ (C @ A) @ B) <= (! [E:(hoare_1708887482_state > $o),F:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ F @ E) => (ord_le777019615tate_o @ (C @ F) @ (C @ E))))) <= (ord_le777019615tate_o @ A @ D)) <= (B = (C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_760_xt1_I15_J)). 123.96/29.66 thf(2841,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o)),D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (C @ A) @ (B)) | ~ (! [E:(hoare_1708887482_state > $o),F:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (F) @ (E)) => (ord_le777019615tate_o @ (C @ F) @ (C @ E)))) | ~ (ord_le777019615tate_o @ (A) @ (D)) | ~ ((B) = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[645])). 123.96/29.66 thf(88,axiom,((! [A:pname]: (bot_bot_o = (bot_bot_pname_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_bot__fun__def)). 123.96/29.66 thf(1111,plain,((! [A:pname]: (bot_bot_o = (bot_bot_pname_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 123.96/29.66 thf(247,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ A) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_equalityD2)). 123.96/29.66 thf(1587,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (A)) | ~ ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 123.96/29.66 thf(538,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (semila1122118281tate_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_inf__sup__aci_I5_J)). 123.96/29.66 thf(2509,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (semila1122118281tate_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[538])). 123.96/29.66 thf(302,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((semila1673364395name_o @ A @ B) = A) <= (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_897_inf__absorb1)). 123.96/29.66 thf(1755,plain,((! [A:(pname > $o),B:(pname > $o)]: (((semila1673364395name_o @ A @ B) = (A)) | ~ (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 123.96/29.66 thf(90,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ C) = (semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C))) = (ord_less_eq_pname_o @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_Un__Int__assoc__eq)). 123.96/29.66 thf(1118,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ C) = (semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C))) = (ord_less_eq_pname_o @ (C) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 123.96/29.66 thf(757,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (insert528405184_state @ B @ C)) = (insert528405184_state @ B @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_Un__insert__right)). 123.96/29.66 thf(3205,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (insert528405184_state @ B @ C)) = (insert528405184_state @ B @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[757])). 123.96/29.66 thf(540,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ B @ A) => (ord_less_eq_pname_o @ B @ (semila1673364395name_o @ C @ A))) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_906_inf__greatest)). 123.96/29.66 thf(2515,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ (B) @ (A)) => (ord_less_eq_pname_o @ (B) @ (semila1673364395name_o @ C @ A))) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[540])). 123.96/29.66 thf(416,axiom,((! [A:com]: ~ (member_com @ A @ bot_bot_com_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_empty__iff)). 123.96/29.66 thf(2100,plain,((! [A:com]: ~ (member_com @ A @ (bot_bot_com_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])). 123.96/29.66 thf(141,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => ((ord_le777019615tate_o @ C @ A) => ((minus_2056855718tate_o @ C @ (minus_2056855718tate_o @ A @ B)) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_969_double__diff)). 123.96/29.66 thf(1270,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => ((ord_le777019615tate_o @ (C) @ (A)) => ((minus_2056855718tate_o @ C @ (minus_2056855718tate_o @ A @ B)) = (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 123.96/29.66 thf(138,axiom,((! [A:(com > $o),B:hoare_1708887482_state,C:(com > hoare_1708887482_state),D:com]: ((B = (C @ D)) => ((member_com @ D @ A) => (member451959335_state @ B @ (image_934102463_state @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_image__eqI)). 123.96/29.66 thf(1259,plain,((! [A:(com > $o),B:hoare_1708887482_state,C:(com > hoare_1708887482_state),D:com]: ((B = (C @ D)) => ((member_com @ D @ (A)) => (member451959335_state @ B @ (image_934102463_state @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 123.96/29.66 thf(495,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => ((ord_le777019615tate_o @ B @ A) => (ord_le777019615tate_o @ B @ (semila129691299tate_o @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_904_le__infI)). 123.96/29.66 thf(2377,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => ((ord_le777019615tate_o @ (B) @ (A)) => (ord_le777019615tate_o @ (B) @ (semila129691299tate_o @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[495])). 123.96/29.66 thf(38,axiom,((! [A:((pname > $o) > $o)]: ((collect_pname_o @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_Collect__def)). 123.96/29.66 thf(948,plain,((! [A:((pname > $o) > $o)]: ((collect_pname_o @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 123.96/29.66 thf(176,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (semila129691299tate_o @ C @ A) @ (semila129691299tate_o @ D @ B)) <= (ord_le777019615tate_o @ A @ B)) <= (ord_le777019615tate_o @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_Int__mono)). 123.96/29.66 thf(1375,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (semila129691299tate_o @ C @ A) @ (semila129691299tate_o @ D @ B)) | ~ (ord_le777019615tate_o @ (A) @ (B)) | ~ (ord_le777019615tate_o @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 123.96/29.66 thf(685,axiom,((! [A:(pname > hoare_1708887482_state),B:pname,C:(pname > $o)]: ((image_1116629049_state @ A @ (insert_pname @ B @ C)) = (insert528405184_state @ (A @ B) @ (image_1116629049_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_image__insert)). 123.96/29.66 thf(2973,plain,((! [A:(pname > hoare_1708887482_state),B:pname,C:(pname > $o)]: ((image_1116629049_state @ A @ (insert_pname @ B @ C)) = (insert528405184_state @ (A @ B) @ (image_1116629049_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[685])). 123.96/29.66 thf(91,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > option_pname)]: ((? [C:pname]: ((B @ A) = (some_pname @ C))) <= (member451959335_state @ A @ (dom_Ho1805192458_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_domD)). 123.96/29.66 thf(1121,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > option_pname)]: (? [C:pname]: ((B @ A) = (some_pname @ C)) | ~ (member451959335_state @ A @ (dom_Ho1805192458_pname @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 123.96/29.66 thf(737,axiom,((! [A:com,B:(hoare_1708887482_state > $o)]: ((hoare_1160767572gleton) => (((hoare_90032982_state @ B @ (insert528405184_state @ (hoare_Mirabelle_MGT @ A) @ bot_bo19817387tate_o)) <= (wt @ A)) <= (! [C:pname]: ((hoare_90032982_state @ B @ (insert528405184_state @ (hoare_Mirabelle_MGT @ (body_1 @ C)) @ bot_bo19817387tate_o)) <= (member_pname @ C @ (dom_pname_com @ body)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_MGF__lemma1)). 123.96/29.66 thf(3143,plain,((! [A:com,B:(hoare_1708887482_state > $o)]: ((hoare_1160767572gleton) => ((hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ A) @ bot_bo19817387tate_o)) | ~ (wt @ A) | ~ (! [C:pname]: ((hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ (body_1 @ C)) @ bot_bo19817387tate_o)) | ~ (member_pname @ C @ (dom_pname_com @ body)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[737])). 123.96/29.66 thf(171,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((member451959335_state @ B @ A) <= (~ (member451959335_state @ B @ C))) => (member451959335_state @ B @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_UnCI)). 123.96/29.66 thf(1361,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((member451959335_state @ B @ (A)) | (member451959335_state @ B @ (C))) => (member451959335_state @ B @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 123.96/29.66 thf(367,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ C) <= (member_pname @ A @ (semila1673364395name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_IntD2)). 123.96/29.66 thf(1942,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (C)) | ~ (member_pname @ A @ (semila1673364395name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])). 123.96/29.66 thf(810,axiom,((! [A:com]: ((hoare_1160767572gleton) => ((wT_bodies) => ((wt @ A) => (hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ A) @ bot_bo19817387tate_o))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_MGF)). 123.96/29.66 thf(3407,plain,((! [A:com]: ((hoare_1160767572gleton) => ((wT_bodies) => ((wt @ A) => (hoare_90032982_state @ (bot_bo19817387tate_o) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ A) @ bot_bo19817387tate_o))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[810])). 123.96/29.66 thf(114,axiom,((finite_finite_pname @ bot_bot_pname_o)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_finite_OemptyI)). 123.96/29.66 thf(1182,plain,((finite_finite_pname @ (bot_bot_pname_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 123.96/29.66 thf(722,axiom,((! [A:hoare_1708887482_state]: ((bot_bo19817387tate_o @ A) = bot_bot_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_bot__apply)). 123.96/29.66 thf(3094,plain,((! [A:hoare_1708887482_state]: ((bot_bo19817387tate_o @ A) = bot_bot_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[722])). 123.96/29.66 thf(590,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ A @ (semila1673364395name_o @ B @ C)) => (~ ((~ (ord_less_eq_pname_o @ A @ C)) <= (ord_less_eq_pname_o @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_912_le__infE)). 123.96/29.66 thf(2666,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (semila1673364395name_o @ B @ C)) => (~ (~ (ord_less_eq_pname_o @ (A) @ (C)) | ~ (ord_less_eq_pname_o @ (A) @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[590])). 123.96/29.66 thf(349,axiom,((! [A:(com > hoare_1708887482_state)]: ((image_934102463_state @ A @ bot_bot_com_o) = bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_image__empty)). 123.96/29.66 thf(1889,plain,((! [A:(com > hoare_1708887482_state)]: ((image_934102463_state @ A @ bot_bot_com_o) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 123.96/29.66 thf(63,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((minus_minus_pname_o @ (insert_pname @ B @ A) @ C) = (minus_minus_pname_o @ A @ C)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_954_insert__Diff1)). 123.96/29.66 thf(1039,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((minus_minus_pname_o @ (insert_pname @ B @ A) @ C) = (minus_minus_pname_o @ A @ C)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 123.96/29.66 thf(215,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) => ((semila1780557381name_o @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_sup__absorb1)). 123.96/29.66 thf(1493,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) => ((semila1780557381name_o @ B @ A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 123.96/29.66 thf(278,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((member_pname @ A @ B) => (member_pname @ A @ C)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_set__mp)). 123.96/29.66 thf(1683,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((member_pname @ A @ (B)) => (member_pname @ A @ (C))) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 123.96/29.66 thf(106,axiom,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_subset__refl)). 123.96/29.66 thf(1160,plain,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ (A) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 123.96/29.66 thf(789,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ B) = (semila1122118281tate_o @ (insert528405184_state @ A @ bot_bo19817387tate_o) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_insert__is__Un)). 123.96/29.66 thf(3311,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ B) = (semila1122118281tate_o @ (insert528405184_state @ A @ bot_bo19817387tate_o) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[789])). 123.96/29.66 thf(60,axiom,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: ((finite1282449217_pname @ C @ D) => ((finite_finite_pname @ B) => ((((minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o)) = bot_bot_pname_o) => ((D @ (insert_pname @ A @ B)) = A)) & (((minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o)) != bot_bot_pname_o) => ((D @ (insert_pname @ A @ B)) = (C @ A @ (D @ (minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_787_folding__one_Oinsert__remove)). 123.96/29.66 thf(1028,plain,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: ((finite1282449217_pname @ (C) @ (D)) => ((finite_finite_pname @ (B)) => ((((minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o)) = (bot_bot_pname_o)) => ((D @ (insert_pname @ A @ B)) = A)) & ((~ ((minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o)) = (bot_bot_pname_o))) => ((D @ (insert_pname @ A @ B)) = (C @ A @ (D @ (minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 123.96/29.66 thf(77,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ B @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_sup_Oleft__commute)). 123.96/29.66 thf(1082,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ B @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 123.96/29.66 thf(510,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(hoare_1708887482_state > pname),D:(hoare_1708887482_state > $o)]: ? [E:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ E @ D) & ? [F:(hoare_1708887482_state > pname)]: (! [G:hoare_1708887482_state]: (((G = (A @ (F @ G))) & (member_pname @ (F @ G) @ (minus_minus_pname_o @ B @ (image_1509414295_pname @ C @ E)))) <= (member451959335_state @ G @ (minus_2056855718tate_o @ D @ E))) & ! [G:hoare_1708887482_state]: (((F @ G) = (C @ G)) <= (member451959335_state @ G @ E))) & ! [F:hoare_1708887482_state]: ((~ (member451959335_state @ F @ (image_1116629049_state @ A @ (minus_minus_pname_o @ B @ (image_1509414295_pname @ C @ E))))) <= (member451959335_state @ F @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1188_Cantor__Bernstein__aux)). 123.96/29.66 thf(2419,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(hoare_1708887482_state > pname),D:(hoare_1708887482_state > $o)]: ? [E:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (E) @ (D)) & ? [F:(hoare_1708887482_state > pname)]: (! [G:hoare_1708887482_state]: (((G = (A @ (F @ G))) & (member_pname @ (F @ G) @ (minus_minus_pname_o @ B @ (image_1509414295_pname @ C @ E)))) | ~ (member451959335_state @ G @ (minus_2056855718tate_o @ D @ E))) & ! [G:hoare_1708887482_state]: (((F @ G) = (C @ G)) | ~ (member451959335_state @ G @ (E)))) & ! [F:hoare_1708887482_state]: (~ (member451959335_state @ F @ (image_1116629049_state @ A @ (minus_minus_pname_o @ B @ (image_1509414295_pname @ C @ E)))) | ~ (member451959335_state @ F @ (E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[510])). 123.96/29.66 thf(76,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((A = B) => (~ ((~ (ord_less_eq_pname_o @ B @ A)) <= (ord_less_eq_pname_o @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_equalityE)). 123.96/29.66 thf(1075,plain,((! [A:(pname > $o),B:(pname > $o)]: (((A) = (B)) => (~ (~ (ord_less_eq_pname_o @ (B) @ (A)) | ~ (ord_less_eq_pname_o @ (A) @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 123.96/29.66 thf(193,axiom,((! [A:(pname > $o),B:((hoare_1708887482_state > $o) > pname),C:((hoare_1708887482_state > $o) > $o)]: (((finite_finite_pname @ A) <= (ord_less_eq_pname_o @ A @ (image_2051418740_pname @ B @ C))) <= (finite1329924456tate_o @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_finite__surj)). 123.96/29.66 thf(1424,plain,((! [A:(pname > $o),B:((hoare_1708887482_state > $o) > pname),C:((hoare_1708887482_state > $o) > $o)]: ((finite_finite_pname @ (A)) | ~ (ord_less_eq_pname_o @ (A) @ (image_2051418740_pname @ (B) @ (C))) | ~ (finite1329924456tate_o @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 123.96/29.66 thf(695,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ A @ C) => (hoare_90032982_state @ B @ A)) <= (hoare_90032982_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_weaken)). 123.96/29.66 thf(3010,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (A) @ (C)) => (hoare_90032982_state @ (B) @ (A))) | ~ (hoare_90032982_state @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[695])). 123.96/29.66 thf(283,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ A @ (semila1780557381name_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_inf__sup__ord_I3_J)). 123.96/29.66 thf(1700,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (A) @ (semila1780557381name_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 123.96/29.66 thf(365,axiom,((! [A:pname]: ~ (member_pname @ A @ bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_empty__iff)). 123.96/29.66 thf(1937,plain,((! [A:pname]: ~ (member_pname @ A @ (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])). 123.96/29.66 thf(321,axiom,((! [A:option1624383643_state]: ((? [B:hoare_1708887482_state]: (A = (some_H1974565227_state @ B))) = (A != none_H1106584047_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1117_not__None__eq)). 123.96/29.66 thf(1810,plain,((! [A:option1624383643_state]: ((? [B:hoare_1708887482_state]: (A = (some_H1974565227_state @ B))) = (~ (A = none_H1106584047_state))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 123.96/29.66 thf(440,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => ((member451959335_state @ A @ C) <= (member451959335_state @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_set__mp)). 123.96/29.66 thf(2172,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => ((member451959335_state @ A @ (C)) | ~ (member451959335_state @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[440])). 123.96/29.66 thf(817,axiom,((! [A:(hoare_1708887482_state > $o),B:(state > (state > $o)),C:com,D:(state > (state > $o)),E:$o]: ((hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ (^ [F:state,G:state]: ((B @ F @ G) & (E))) @ C @ D) @ bot_bo19817387tate_o)) <= ((hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ B @ C @ D) @ bot_bo19817387tate_o)) <= (E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_constant)). 123.96/29.66 thf(3428,plain,((! [A:(hoare_1708887482_state > $o),B:(state > (state > $o)),C:com,D:(state > (state > $o)),E:$o]: ((hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ (^ [F:state,G:state]: ((B @ F @ G) & (E))) @ C @ D) @ bot_bo19817387tate_o)) | ~ ((hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ B @ C @ D) @ bot_bo19817387tate_o)) | ~ (E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[817])). 123.96/29.66 thf(124,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1615457021_state @ C @ D) => ((finite1625599783_state @ B) => ((((C @ (D @ (semila1122118281tate_o @ B @ A)) @ (D @ (semila129691299tate_o @ B @ A))) = (C @ (D @ B) @ (D @ A))) <= ((semila129691299tate_o @ B @ A) != bot_bo19817387tate_o)) <= (finite1625599783_state @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_779_folding__one_Ounion__inter)). 123.96/29.66 thf(1214,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1615457021_state @ (C) @ (D)) => ((finite1625599783_state @ (B)) => (((C @ (D @ (semila1122118281tate_o @ B @ A)) @ (D @ (semila129691299tate_o @ B @ A))) = (C @ (D @ (B)) @ (D @ (A)))) | ((semila129691299tate_o @ B @ A) = (bot_bo19817387tate_o)) | ~ (finite1625599783_state @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 123.96/29.66 thf(753,axiom,((! [A:(hoare_1708887482_state > $o),B:(state > (state > $o)),C:(state > $o),D:com]: (hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ (^ [E:state,F:state]: ((B @ E @ F) & ~ (C @ F))) @ (while @ C @ D) @ B) @ bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_LoopF)). 123.96/29.66 thf(3194,plain,((! [A:(hoare_1708887482_state > $o),B:(state > (state > $o)),C:(state > $o),D:com]: (hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ (^ [E:state,F:state]: ((B @ E @ F) & ~ (C @ F))) @ (while @ C @ D) @ B) @ bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[753])). 123.96/29.66 thf(783,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((A != B) => (member451959335_state @ A @ C)) <= (member451959335_state @ A @ (insert528405184_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_insertE)). 123.96/29.66 thf(3294,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((~ (A = B)) => (member451959335_state @ A @ (C))) | ~ (member451959335_state @ A @ (insert528405184_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[783])). 123.96/29.66 thf(104,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ B @ A) & (ord_le777019615tate_o @ A @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_order__eq__iff)). 123.96/29.66 thf(1155,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (B) @ (A)) & (ord_le777019615tate_o @ (A) @ (B))) = ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 123.96/29.66 thf(298,axiom,((! [A:(com > hoare_1708887482_state),B:(com > $o)]: ((B = bot_bot_com_o) = ((image_934102463_state @ A @ B) = bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_image__is__empty)). 123.96/29.66 thf(1744,plain,((! [A:(com > hoare_1708887482_state),B:(com > $o)]: (((B) = (bot_bot_com_o)) = ((image_934102463_state @ A @ B) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 123.96/29.66 thf(3,axiom,((! [A:(pname > pname),B:(pname > $o),C:(pname > $o)]: (((? [D:(pname > $o)]: ((finite_finite_pname @ D) & (C = (image_pname_pname @ A @ D)) & (ord_less_eq_pname_o @ D @ B))) <= (ord_less_eq_pname_o @ C @ (image_pname_pname @ A @ B))) <= (finite_finite_pname @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_finite__subset__image)). 123.96/29.66 thf(836,plain,((! [A:(pname > pname),B:(pname > $o),C:(pname > $o)]: (? [D:(pname > $o)]: ((finite_finite_pname @ (D)) & ((C) = (image_pname_pname @ A @ D)) & (ord_less_eq_pname_o @ (D) @ (B))) | ~ (ord_less_eq_pname_o @ (C) @ (image_pname_pname @ A @ B)) | ~ (finite_finite_pname @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 123.96/29.66 thf(837,plain,(! [C:(pname > $o),B:(pname > $o),A:(pname > pname)] : ((ord_less_eq_pname_o @ (sk1 @ C @ B @ A) @ (B)) | (~ (ord_less_eq_pname_o @ (C) @ (image_pname_pname @ A @ B))) | (~ (finite_finite_pname @ (C))))),inference(cnf,[status(esa)],[836])). 123.96/29.66 thf(210,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ (semila1673364395name_o @ A @ C) @ (semila1673364395name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_Int__Un__distrib2)). 123.96/29.66 thf(1478,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ (semila1673364395name_o @ A @ C) @ (semila1673364395name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 123.96/29.66 thf(712,axiom,((! [A:hoare_1708887482_state]: (bot_bot_o = (bot_bo19817387tate_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_bot__fun__def)). 123.96/29.66 thf(3059,plain,((! [A:hoare_1708887482_state]: (bot_bot_o = (bot_bo19817387tate_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[712])). 123.96/29.66 thf(236,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((A = B) = ((ord_less_eq_pname_o @ A @ B) & (ord_less_eq_pname_o @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_order__eq__iff)). 123.96/29.66 thf(1552,plain,((! [A:(pname > $o),B:(pname > $o)]: (((A) = (B)) = ((ord_less_eq_pname_o @ (A) @ (B)) & (ord_less_eq_pname_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 123.96/29.66 thf(533,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_882_inf__le2)). 123.96/29.66 thf(2497,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[533])). 123.96/29.66 thf(556,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (minus_2056855718tate_o @ B @ A)) = (semila1122118281tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979_Un__Diff__cancel)). 123.96/29.66 thf(2566,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (minus_2056855718tate_o @ B @ A)) = (semila1122118281tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[556])). 123.96/29.66 thf(369,axiom,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ (insert_pname @ A @ C)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_insertI2)). 123.96/29.66 thf(1947,plain,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ (insert_pname @ A @ C)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])). 123.96/29.66 thf(383,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ C) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ C) @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_939_sup__inf__distrib2)). 123.96/29.66 thf(1984,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ C) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ C) @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])). 123.96/29.66 thf(403,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((semila1780557381name_o @ A @ (insert_pname @ B @ C)) = (insert_pname @ B @ (semila1780557381name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_Un__insert__right)). 123.96/29.66 thf(2052,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((semila1780557381name_o @ A @ (insert_pname @ B @ C)) = (insert_pname @ B @ (semila1780557381name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[403])). 123.96/29.66 thf(289,axiom,((! [A:(pname > (pname > $o)),B:(pname > $o)]: ((finite297249702name_o @ (image_pname_pname_o @ A @ B)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__imageI)). 123.96/29.66 thf(1720,plain,((! [A:(pname > (pname > $o)),B:(pname > $o)]: ((finite297249702name_o @ (image_pname_pname_o @ A @ B)) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 123.96/29.66 thf(429,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ B) => (finite1625599783_state @ A)) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_finite__subset)). 123.96/29.66 thf(2140,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ (B)) => (finite1625599783_state @ (A))) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])). 123.96/29.66 thf(162,axiom,((! [A:(pname > option_com),B:pname,C:option_com]: (((C = none_com) => ((dom_pname_com @ (fun_up879233478on_com @ A @ B @ C)) = (minus_minus_pname_o @ (dom_pname_com @ A) @ (insert_pname @ B @ bot_bot_pname_o)))) & ((C != none_com) => ((dom_pname_com @ (fun_up879233478on_com @ A @ B @ C)) = (insert_pname @ B @ (dom_pname_com @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1175_dom__fun__upd)). 123.96/29.66 thf(1324,plain,((! [A:(pname > option_com),B:pname,C:option_com]: (((C = none_com) => ((dom_pname_com @ (fun_up879233478on_com @ A @ B @ C)) = (minus_minus_pname_o @ (dom_pname_com @ A) @ (insert_pname @ B @ bot_bot_pname_o)))) & ((~ (C = none_com)) => ((dom_pname_com @ (fun_up879233478on_com @ A @ B @ C)) = (insert_pname @ B @ (dom_pname_com @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 123.96/29.66 thf(89,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((! [D:(hoare_1708887482_state > $o),E:(hoare_1708887482_state > $o),F:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ D @ (semila129691299tate_o @ E @ F)) = (semila129691299tate_o @ (semila1122118281tate_o @ D @ E) @ (semila1122118281tate_o @ D @ F)))) => ((semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_distrib__imp2)). 123.96/29.66 thf(1114,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((! [D:(hoare_1708887482_state > $o),E:(hoare_1708887482_state > $o),F:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ D @ (semila129691299tate_o @ E @ F)) = (semila129691299tate_o @ (semila1122118281tate_o @ D @ E) @ (semila1122118281tate_o @ D @ F)))) => ((semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 123.96/29.66 thf(139,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) != bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_insert__not__empty)). 123.96/29.66 thf(1263,plain,((! [A:pname,B:(pname > $o)]: ~ ((insert_pname @ A @ B) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 123.96/29.66 thf(54,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: ((ord_le1728773982te_o_o @ A @ B) => ((finite1329924456tate_o @ B) => (finite1329924456tate_o @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_finite__subset)). 123.96/29.66 thf(997,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: ((ord_le1728773982te_o_o @ (A) @ (B)) => ((finite1329924456tate_o @ (B)) => (finite1329924456tate_o @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 123.96/29.66 thf(670,axiom,((! [A:(hoare_1708887482_state > $o)]: ((the_el864710747_state @ A) = (the_Ho851197897_state @ (^ [B:hoare_1708887482_state]: (A = (insert528405184_state @ B @ bot_bo19817387tate_o))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_the__elem__def)). 123.96/29.66 thf(2932,plain,((! [A:(hoare_1708887482_state > $o)]: ((the_el864710747_state @ (A)) = (the_Ho851197897_state @ (^ [B:hoare_1708887482_state]: (A = (insert528405184_state @ B @ bot_bo19817387tate_o))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[670])). 123.96/29.66 thf(50,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((finite_finite_pname @ (minus_minus_pname_o @ A @ C)) = (finite_finite_pname @ (minus_minus_pname_o @ A @ (insert_pname @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_finite__Diff__insert)). 123.96/29.66 thf(985,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((finite_finite_pname @ (minus_minus_pname_o @ A @ C)) = (finite_finite_pname @ (minus_minus_pname_o @ A @ (insert_pname @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 123.96/29.66 thf(228,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (semila1122118281tate_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_Un__commute)). 123.96/29.66 thf(1530,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (semila1122118281tate_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 123.96/29.66 thf(231,axiom,((! [A:pname,B:(pname > option_pname)]: ((? [C:pname]: ((B @ A) = (some_pname @ C))) <= (member_pname @ A @ (dom_pname_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_domD)). 123.96/29.66 thf(1539,plain,((! [A:pname,B:(pname > option_pname)]: (? [C:pname]: ((B @ A) = (some_pname @ C)) | ~ (member_pname @ A @ (dom_pname_pname @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 123.96/29.66 thf(203,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1615457021_state @ C @ D) => ((finite1625599783_state @ B) => ((~ (member451959335_state @ A @ B)) => ((D @ (insert528405184_state @ A @ B)) = (finite309095018_state @ C @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1165_folding__one_Oeq__fold_H)). 123.96/29.66 thf(1456,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1615457021_state @ (C) @ (D)) => ((finite1625599783_state @ (B)) => ((~ (member451959335_state @ A @ (B))) => ((D @ (insert528405184_state @ A @ B)) = (finite309095018_state @ (C) @ A @ (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 123.96/29.66 thf(179,axiom,((! [A:com,B:option_com]: ((member_com @ A @ (set_com @ B)) = (B = (some_com @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_elem__set)). 123.96/29.66 thf(1382,plain,((! [A:com,B:option_com]: ((member_com @ A @ (set_com @ B)) = (B = (some_com @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 123.96/29.66 thf(799,axiom,((! [A:hoare_1708887482_state]: ((set_Ho525251890_state @ (some_H1974565227_state @ A)) = (insert528405184_state @ A @ bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_Option_Oset_Osimps_I2_J)). 123.96/29.66 thf(3354,plain,((! [A:hoare_1708887482_state]: ((set_Ho525251890_state @ (some_H1974565227_state @ A)) = (insert528405184_state @ A @ bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[799])). 123.96/29.66 thf(434,axiom,((! [A:pname,B:(pname > $o)]: ((B @ A) = (member_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_mem__def)). 123.96/29.66 thf(2153,plain,((! [A:pname,B:(pname > $o)]: ((B @ A) = (member_pname @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[434])). 123.96/29.66 thf(659,axiom,((! [A:hoare_1708887482_state,B:option1624383643_state]: ((member451959335_state @ A @ (set_Ho525251890_state @ B)) = (B = (some_H1974565227_state @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_elem__set)). 123.96/29.66 thf(2900,plain,((! [A:hoare_1708887482_state,B:option1624383643_state]: ((member451959335_state @ A @ (set_Ho525251890_state @ B)) = (B = (some_H1974565227_state @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[659])). 123.96/29.66 thf(363,axiom,(((? [A:state,B:state]: (A != B)) = hoare_1160767572gleton)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_state__not__singleton__def)). 123.96/29.66 thf(1932,plain,(((? [A:state,B:state]: ~ (A = B)) = hoare_1160767572gleton)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[363])). 123.96/29.66 thf(522,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) => ((ord_less_eq_pname_o @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_order__antisym)). 123.96/29.66 thf(2465,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) => ((ord_less_eq_pname_o @ (B) @ (A)) => ((A) = (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[522])). 123.96/29.66 thf(71,axiom,((! [A:(hoare_1708887482_state > $o),B:((pname > $o) > hoare_1708887482_state),C:((pname > $o) > $o)]: (((finite1625599783_state @ A) <= (ord_le777019615tate_o @ A @ (image_1922967206_state @ B @ C))) <= (finite297249702name_o @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_finite__surj)). 123.96/29.66 thf(1060,plain,((! [A:(hoare_1708887482_state > $o),B:((pname > $o) > hoare_1708887482_state),C:((pname > $o) > $o)]: ((finite1625599783_state @ (A)) | ~ (ord_le777019615tate_o @ (A) @ (image_1922967206_state @ (B) @ (C))) | ~ (finite297249702name_o @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 123.96/29.66 thf(336,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: (((B @ C) <= (~ (A @ C))) <= (semila1122118281tate_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_sup1E)). 123.96/29.66 thf(1852,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((B @ C) | (A @ C) | ~ (semila1122118281tate_o @ (A) @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 123.96/29.66 thf(636,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => (ord_le777019615tate_o @ B @ (semila1122118281tate_o @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_le__supI1)). 123.96/29.66 thf(2813,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => (ord_le777019615tate_o @ (B) @ (semila1122118281tate_o @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[636])). 123.96/29.66 thf(344,axiom,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ bot_bot_pname_o @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_bot__least)). 123.96/29.66 thf(1874,plain,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ (bot_bot_pname_o) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])). 123.96/29.66 thf(728,axiom,((finite_finite_pname @ (dom_pname_com @ body))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_finite__dom__body)). 123.96/29.66 thf(3115,plain,((finite_finite_pname @ (dom_pname_com @ body))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[728])). 123.96/29.66 thf(766,axiom,((! [A:com,B:(state > (state > $o)),C:(hoare_1708887482_state > $o),D:(state > (state > $o)),E:com,F:(state > (state > $o))]: ((hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ D @ E @ F) @ bot_bo19817387tate_o)) => ((hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ F @ A @ B) @ bot_bo19817387tate_o)) => (hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ D @ (semi @ E @ A) @ B) @ bot_bo19817387tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_Comp)). 123.96/29.66 thf(3247,plain,((! [A:com,B:(state > (state > $o)),C:(hoare_1708887482_state > $o),D:(state > (state > $o)),E:com,F:(state > (state > $o))]: ((hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ D @ E @ F) @ bot_bo19817387tate_o)) => ((hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ F @ A @ B) @ bot_bo19817387tate_o)) => (hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ D @ (semi @ E @ A) @ B) @ bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[766])). 123.96/29.66 thf(648,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ B @ (semila129691299tate_o @ C @ A)) <= (ord_le777019615tate_o @ B @ A)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_907_inf__greatest)). 123.96/29.66 thf(2862,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (semila129691299tate_o @ C @ A)) | ~ (ord_le777019615tate_o @ (B) @ (A)) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[648])). 123.96/29.66 thf(493,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ B) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_mem__def)). 123.96/29.66 thf(2370,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])). 123.96/29.66 thf(226,axiom,((! [A:(pname > $o)]: ((semila1673364395name_o @ A @ bot_bot_pname_o) = bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_916_inf__bot__right)). 123.96/29.66 thf(1525,plain,((! [A:(pname > $o)]: ((semila1673364395name_o @ A @ bot_bot_pname_o) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 123.96/29.66 thf(160,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ B) = B) = (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_le__iff__sup)). 123.96/29.66 thf(1318,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ B) = (B)) = (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 123.96/29.66 thf(668,axiom,((! [A:((pname > $o) > (state > (state > $o))),B:((pname > $o) > (state > (state > $o))),C:(hoare_1708887482_state > $o),D:((pname > $o) > (state > (state > $o))),E:((pname > $o) > com),F:((pname > $o) > (state > (state > $o))),G:((pname > $o) > $o)]: ((finite297249702name_o @ G) => ((! [H:(pname > $o)]: ((hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H)) @ bot_bo19817387tate_o)) <= (hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H)) @ bot_bo19817387tate_o)))) => ((hoare_90032982_state @ C @ (image_1922967206_state @ (^ [H:(pname > $o)]: (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H))) @ G)) => (hoare_90032982_state @ C @ (image_1922967206_state @ (^ [H:(pname > $o)]: (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H))) @ G))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_finite__pointwise)). 123.96/29.66 thf(2926,plain,((! [A:((pname > $o) > (state > (state > $o))),B:((pname > $o) > (state > (state > $o))),C:(hoare_1708887482_state > $o),D:((pname > $o) > (state > (state > $o))),E:((pname > $o) > com),F:((pname > $o) > (state > (state > $o))),G:((pname > $o) > $o)]: ((finite297249702name_o @ (G)) => ((! [H:(pname > $o)]: ((hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H)) @ bot_bo19817387tate_o)) | ~ (hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H)) @ bot_bo19817387tate_o)))) => ((hoare_90032982_state @ (C) @ (image_1922967206_state @ (^ [H:(pname > $o)]: (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H))) @ (G))) => (hoare_90032982_state @ (C) @ (image_1922967206_state @ (^ [H:(pname > $o)]: (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H))) @ (G)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[668])). 123.96/29.66 thf(449,axiom,((! [A:(state > $o),B:com]: ((wt @ (while @ A @ B)) <= (wt @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_While)). 123.96/29.66 thf(2203,plain,((! [A:(state > $o),B:com]: ((wt @ (while @ (A) @ B)) | ~ (wt @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[449])). 123.96/29.66 thf(451,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (semila129691299tate_o @ C @ (collec1568722789_state @ B)) @ (semila129691299tate_o @ D @ (collec1568722789_state @ A))) <= (! [E:hoare_1708887482_state]: (((B @ E) => (A @ E)) <= (member451959335_state @ E @ C)))) <= (ord_le777019615tate_o @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1073_Int__Collect__mono)). 123.96/29.66 thf(2208,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (semila129691299tate_o @ C @ (collec1568722789_state @ B)) @ (semila129691299tate_o @ D @ (collec1568722789_state @ A))) | ~ (! [E:hoare_1708887482_state]: (((B @ E) => (A @ E)) | ~ (member451959335_state @ E @ (C)))) | ~ (ord_le777019615tate_o @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[451])). 123.96/29.66 thf(682,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ B) != bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_insert__not__empty)). 123.96/29.66 thf(2963,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ~ ((insert528405184_state @ A @ B) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[682])). 123.96/29.66 thf(207,axiom,((! [A:com,B:(com > $o),C:option_com]: ((! [D:com]: ((B @ D) <= (member_com @ D @ (set_com @ C)))) => ((C = (some_com @ A)) => (B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_ospec)). 123.96/29.66 thf(1466,plain,((! [A:com,B:(com > $o),C:option_com]: ((! [D:com]: ((B @ D) | ~ (member_com @ D @ (set_com @ C)))) => ((C = (some_com @ A)) => (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 123.96/29.66 thf(815,axiom,((! [A:((hoare_1708887482_state > $o) > (state > (state > $o))),B:((hoare_1708887482_state > $o) > (state > (state > $o))),C:(hoare_1708887482_state > $o),D:((hoare_1708887482_state > $o) > (state > (state > $o))),E:((hoare_1708887482_state > $o) > com),F:((hoare_1708887482_state > $o) > (state > (state > $o))),G:((hoare_1708887482_state > $o) > $o)]: (((! [H:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H)) @ bot_bo19817387tate_o)) <= (hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H)) @ bot_bo19817387tate_o)))) => ((hoare_90032982_state @ C @ (image_27005066_state @ (^ [H:(hoare_1708887482_state > $o)]: (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H))) @ G)) <= (hoare_90032982_state @ C @ (image_27005066_state @ (^ [H:(hoare_1708887482_state > $o)]: (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H))) @ G)))) <= (finite1329924456tate_o @ G)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_finite__pointwise)). 123.96/29.66 thf(3422,plain,((! [A:((hoare_1708887482_state > $o) > (state > (state > $o))),B:((hoare_1708887482_state > $o) > (state > (state > $o))),C:(hoare_1708887482_state > $o),D:((hoare_1708887482_state > $o) > (state > (state > $o))),E:((hoare_1708887482_state > $o) > com),F:((hoare_1708887482_state > $o) > (state > (state > $o))),G:((hoare_1708887482_state > $o) > $o)]: (((! [H:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H)) @ bot_bo19817387tate_o)) | ~ (hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H)) @ bot_bo19817387tate_o)))) => ((hoare_90032982_state @ (C) @ (image_27005066_state @ (^ [H:(hoare_1708887482_state > $o)]: (hoare_858012674_state @ (A @ H) @ (E @ H) @ (B @ H))) @ (G))) | ~ (hoare_90032982_state @ (C) @ (image_27005066_state @ (^ [H:(hoare_1708887482_state > $o)]: (hoare_858012674_state @ (D @ H) @ (E @ H) @ (F @ H))) @ (G))))) | ~ (finite1329924456tate_o @ (G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[815])). 123.96/29.66 thf(574,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ C @ D) => ((finite1625599783_state @ B) => ((B != bot_bo19817387tate_o) => ((finite1625599783_state @ A) => (((D @ (semila1122118281tate_o @ B @ A)) = (C @ (D @ B) @ (D @ A))) <= (A != bot_bo19817387tate_o)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_folding__one__idem_Ounion__idem)). 123.96/29.66 thf(2617,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ (C) @ (D)) => ((finite1625599783_state @ (B)) => ((~ ((B) = (bot_bo19817387tate_o))) => ((finite1625599783_state @ (A)) => (((D @ (semila1122118281tate_o @ B @ A)) = (C @ (D @ (B)) @ (D @ (A)))) | ((A) = (bot_bo19817387tate_o))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[574])). 123.96/29.66 thf(589,axiom,((! [A:(state > $o),B:com]: ((while @ A @ B) != skip))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_com_Osimps_I17_J)). 123.96/29.66 thf(2662,plain,((! [A:(state > $o),B:com]: ~ ((while @ (A) @ B) = skip))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[589])). 123.96/29.66 thf(387,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((semila1673364395name_o @ (insert_pname @ B @ A) @ C) = (semila1673364395name_o @ A @ C)) <= (~ (member_pname @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_987_Int__insert__left__if0)). 123.96/29.66 thf(1996,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((semila1673364395name_o @ (insert_pname @ B @ A) @ C) = (semila1673364395name_o @ A @ C)) | (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])). 123.96/29.66 thf(545,axiom,((! [A:pname]: ((set_pname @ (some_pname @ A)) = (insert_pname @ A @ bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_Option_Oset_Osimps_I2_J)). 123.96/29.66 thf(2529,plain,((! [A:pname]: ((set_pname @ (some_pname @ A)) = (insert_pname @ A @ bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[545])). 123.96/29.66 thf(662,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (collect_pname @ B) @ (collect_pname @ A)) <= (! [C:pname]: ((B @ C) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_Collect__mono)). 123.96/29.66 thf(2909,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (collect_pname @ B) @ (collect_pname @ A)) | ~ (! [C:pname]: ((B @ C) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[662])). 123.96/29.66 thf(738,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ B) => ((minus_2056855718tate_o @ A @ B) = (finite96880613tate_o @ (^ [C:hoare_1708887482_state,D:(hoare_1708887482_state > $o)]: (minus_2056855718tate_o @ D @ (insert528405184_state @ C @ bot_bo19817387tate_o))) @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_minus__fold__remove)). 123.96/29.66 thf(3147,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (B)) => ((minus_2056855718tate_o @ A @ B) = (finite96880613tate_o @ (^ [C:hoare_1708887482_state,D:(hoare_1708887482_state > $o)]: (minus_2056855718tate_o @ D @ (insert528405184_state @ C @ bot_bo19817387tate_o))) @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[738])). 123.96/29.66 thf(827,axiom,((! [A:(state > (state > $o)),B:(state > (state > $o)),C:com]: ((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ C) @ bot_bo19817387tate_o)) => ((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_858012674_state @ A @ C @ B) @ bot_bo19817387tate_o)) <= (hoare_496444244_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_858012674_state @ A @ C @ B) @ bot_bo19817387tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_MGF__complete)). 123.96/29.66 thf(3454,plain,((! [A:(state > (state > $o)),B:(state > (state > $o)),C:com]: ((hoare_90032982_state @ (bot_bo19817387tate_o) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ C) @ bot_bo19817387tate_o)) => ((hoare_90032982_state @ (bot_bo19817387tate_o) @ (insert528405184_state @ (hoare_858012674_state @ A @ C @ B) @ bot_bo19817387tate_o)) | ~ (hoare_496444244_state @ (bot_bo19817387tate_o) @ (insert528405184_state @ (hoare_858012674_state @ A @ C @ B) @ bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[827])). 123.96/29.66 thf(579,axiom,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_sup_Oidem)). 123.96/29.66 thf(2634,plain,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[579])). 123.96/29.66 thf(338,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ (minus_2056855718tate_o @ B @ A)) = B) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_Diff__partition)). 123.96/29.66 thf(1857,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ (minus_2056855718tate_o @ B @ A)) = (B)) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 123.96/29.66 thf(133,axiom,((! [A:pname,B:pname,C:(pname > $o)]: (((A = B) | (member_pname @ A @ C)) = (member_pname @ A @ (insert_pname @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_insert__iff)). 123.96/29.66 thf(1241,plain,((! [A:pname,B:pname,C:(pname > $o)]: (((A = B) | (member_pname @ A @ (C))) = (member_pname @ A @ (insert_pname @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 123.96/29.66 thf(551,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ B @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_sup__left__commute)). 123.96/29.66 thf(2546,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ B @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[551])). 123.96/29.66 thf(1933,plain,(((? [A:state,B:state]: ~ (A = B)) = hoare_1160767572gleton)),inference(lifteq,[status(thm)],[1932])). 123.96/29.66 thf(157,axiom,(hoare_1160767572gleton),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 123.96/29.66 thf(1312,plain,(hoare_1160767572gleton),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 123.96/29.66 thf(3561,plain,((? [A:state,B:state]: ~ (A = B))),inference(rewrite,[status(thm)],[1933,1312])). 123.96/29.66 thf(3562,plain,((~ (sk137 = sk138))),inference(cnf,[status(esa)],[3561])). 123.96/29.66 thf(3563,plain,((sk138 != sk137)),inference(lifteq,[status(thm)],[3562])). 123.96/29.66 thf(620,axiom,((! [A:option1624383643_state]: ((~ (! [B:hoare_1708887482_state]: (A != (some_H1974565227_state @ B)))) <= (A != none_H1106584047_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_option_Oexhaust)). 123.96/29.66 thf(2761,plain,((! [A:option1624383643_state]: (~ (! [B:hoare_1708887482_state]: ~ (A = (some_H1974565227_state @ B))) | (A = none_H1106584047_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[620])). 123.96/29.66 thf(655,axiom,((! [A:(pname > hoare_1708887482_state),B:hoare_1708887482_state,C:pname,D:(pname > $o)]: ((((image_1116629049_state @ (fun_up1986763201_state @ A @ C @ B) @ D) = (insert528405184_state @ B @ (image_1116629049_state @ A @ (minus_minus_pname_o @ D @ (insert_pname @ C @ bot_bot_pname_o))))) <= (member_pname @ C @ D)) & ((~ (member_pname @ C @ D)) => ((image_1116629049_state @ (fun_up1986763201_state @ A @ C @ B) @ D) = (image_1116629049_state @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_fun__upd__image)). 123.96/29.66 thf(2883,plain,((! [A:(pname > hoare_1708887482_state),B:hoare_1708887482_state,C:pname,D:(pname > $o)]: ((((image_1116629049_state @ (fun_up1986763201_state @ A @ C @ B) @ D) = (insert528405184_state @ B @ (image_1116629049_state @ A @ (minus_minus_pname_o @ D @ (insert_pname @ C @ bot_bot_pname_o))))) | ~ (member_pname @ C @ (D))) & ((~ (member_pname @ C @ (D))) => ((image_1116629049_state @ (fun_up1986763201_state @ A @ C @ B) @ D) = (image_1116629049_state @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[655])). 123.96/29.66 thf(28,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ (collect_pname_o @ A)) & (finite297249702name_o @ (collect_pname_o @ B))) = (finite297249702name_o @ (collect_pname_o @ (^ [C:(pname > $o)]: ((A @ C) | (B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_finite__Collect__disjI)). 123.96/29.66 thf(921,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ (collect_pname_o @ A)) & (finite297249702name_o @ (collect_pname_o @ B))) = (finite297249702name_o @ (collect_pname_o @ (^ [C:(pname > $o)]: ((A @ C) | (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 123.96/29.66 thf(787,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ bot_bo19817387tate_o) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_sup__bot__right)). 123.96/29.66 thf(3306,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ bot_bo19817387tate_o) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[787])). 123.96/29.66 thf(334,axiom,((! [A:(pname > $o)]: ((semila1673364395name_o @ bot_bot_pname_o @ A) = bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_966_Int__empty__left)). 123.96/29.66 thf(1846,plain,((! [A:(pname > $o)]: ((semila1673364395name_o @ bot_bot_pname_o @ A) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 123.96/29.66 thf(116,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: (ord_le777019615tate_o @ (minus_2056855718tate_o @ (image_1116629049_state @ A @ B) @ (image_1116629049_state @ A @ C)) @ (image_1116629049_state @ A @ (minus_minus_pname_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_image__diff__subset)). 123.96/29.66 thf(1187,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: (ord_le777019615tate_o @ (minus_2056855718tate_o @ (image_1116629049_state @ A @ B) @ (image_1116629049_state @ A @ C)) @ (image_1116629049_state @ A @ (minus_minus_pname_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 123.96/29.66 thf(664,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila129691299tate_o @ B @ C)) => (member451959335_state @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_IntD2)). 123.96/29.66 thf(2915,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila129691299tate_o @ B @ C)) => (member451959335_state @ A @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[664])). 123.96/29.66 thf(506,axiom,((! [A:(pname > $o)]: ((A = bot_bot_pname_o) <= (ord_less_eq_pname_o @ A @ bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_le__bot)). 123.96/29.66 thf(2408,plain,((! [A:(pname > $o)]: (((A) = (bot_bot_pname_o)) | ~ (ord_less_eq_pname_o @ (A) @ (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])). 123.96/29.66 thf(629,axiom,((! [A:com,B:(com > $o)]: ((~ (member_com @ A @ B)) <= (B = bot_bot_com_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_equals0D)). 123.96/29.66 thf(2793,plain,((! [A:com,B:(com > $o)]: (~ (member_com @ A @ (B)) | ~ ((B) = (bot_bot_com_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[629])). 123.96/29.66 thf(412,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((semila129691299tate_o @ C @ (insert528405184_state @ B @ A)) = (semila129691299tate_o @ C @ A)) <= (~ (member451959335_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_Int__insert__right__if0)). 123.96/29.66 thf(2089,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((semila129691299tate_o @ C @ (insert528405184_state @ B @ A)) = (semila129691299tate_o @ C @ A)) | (member451959335_state @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])). 123.96/29.66 thf(751,axiom,((! [A:(hoare_1708887482_state > $o),B:(pname > (state > (state > $o))),C:(pname > (state > (state > $o))),D:(pname > $o)]: ((hoare_90032982_state @ A @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (body_1 @ E) @ (C @ E))) @ D)) <= (hoare_90032982_state @ (semila1122118281tate_o @ A @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (body_1 @ E) @ (C @ E))) @ D)) @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (the_com @ (body @ E)) @ (C @ E))) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_hoare__derivs_OBody)). 123.96/29.66 thf(3190,plain,((! [A:(hoare_1708887482_state > $o),B:(pname > (state > (state > $o))),C:(pname > (state > (state > $o))),D:(pname > $o)]: ((hoare_90032982_state @ (A) @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (body_1 @ E) @ (C @ E))) @ D)) | ~ (hoare_90032982_state @ (semila1122118281tate_o @ A @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (body_1 @ E) @ (C @ E))) @ D)) @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (the_com @ (body @ E)) @ (C @ E))) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[751])). 123.96/29.66 thf(43,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ (collect_pname_o @ A)) | (finite297249702name_o @ (collect_pname_o @ B))) => (finite297249702name_o @ (collect_pname_o @ (^ [C:(pname > $o)]: ((B @ C) & (A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_finite__Collect__conjI)). 123.96/29.66 thf(965,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ (collect_pname_o @ A)) | (finite297249702name_o @ (collect_pname_o @ B))) => (finite297249702name_o @ (collect_pname_o @ (^ [C:(pname > $o)]: ((B @ C) & (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 123.96/29.66 thf(500,axiom,((! [A:hoare_1708887482_state,B:(com > hoare_1708887482_state),C:(com > $o)]: ((member451959335_state @ A @ (image_934102463_state @ B @ C)) => (~ (! [D:com]: ((A = (B @ D)) => (~ (member_com @ D @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_imageE)). 123.96/29.66 thf(2391,plain,((! [A:hoare_1708887482_state,B:(com > hoare_1708887482_state),C:(com > $o)]: ((member451959335_state @ A @ (image_934102463_state @ B @ C)) => (~ (! [D:com]: ((A = (B @ D)) => (~ (member_com @ D @ (C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[500])). 123.96/29.66 thf(563,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > option1624383643_state)]: ((? [C:hoare_1708887482_state]: ((B @ A) = (some_H1974565227_state @ C))) <= (member451959335_state @ A @ (dom_Ho1703271284_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_domD)). 123.96/29.66 thf(2585,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > option1624383643_state)]: (? [C:hoare_1708887482_state]: ((B @ A) = (some_H1974565227_state @ C)) | ~ (member451959335_state @ A @ (dom_Ho1703271284_state @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[563])). 123.96/29.66 thf(142,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ (semila1122118281tate_o @ A @ C)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_le__supI2)). 123.96/29.66 thf(1273,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (semila1122118281tate_o @ A @ C)) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 123.96/29.66 thf(772,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((A = B) <= ((insert528405184_state @ A @ bot_bo19817387tate_o) = (insert528405184_state @ B @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_singleton__inject)). 123.96/29.66 thf(3262,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((A = B) | ~ ((insert528405184_state @ A @ bot_bo19817387tate_o) = (insert528405184_state @ B @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[772])). 123.96/29.66 thf(657,axiom,((! [A:pname,B:pname]: (((some_pname @ A) = (some_pname @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_option_Oinject)). 123.96/29.66 thf(2894,plain,((! [A:pname,B:pname]: (((some_pname @ A) = (some_pname @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[657])). 123.96/29.66 thf(807,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((((D @ (insert528405184_state @ A @ B)) = (finite309095018_state @ C @ A @ B)) <= (finite1625599783_state @ B)) <= (finite1347568576_state @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_folding__one__idem_Oeq__fold__idem_H)). 123.96/29.66 thf(3396,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: (((D @ (insert528405184_state @ A @ B)) = (finite309095018_state @ (C) @ A @ (B))) | ~ (finite1625599783_state @ (B)) | ~ (finite1347568576_state @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[807])). 123.96/29.66 thf(260,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => ((member_pname @ B @ A) => (member_pname @ B @ (semila1673364395name_o @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_IntI)). 123.96/29.66 thf(1631,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => ((member_pname @ B @ (A)) => (member_pname @ B @ (semila1673364395name_o @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 123.96/29.66 thf(431,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ C))) = (finite1625599783_state @ (minus_2056855718tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1046_finite__Diff__insert)). 123.96/29.66 thf(2144,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ C))) = (finite1625599783_state @ (minus_2056855718tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])). 123.96/29.66 thf(24,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o))) = (insert_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1036_insert__Diff__single)). 123.96/29.66 thf(906,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o))) = (insert_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 123.96/29.66 thf(144,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ B @ C) & (member451959335_state @ A @ C)) = (ord_le777019615tate_o @ (insert528405184_state @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_insert__subset)). 123.96/29.66 thf(1278,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (B) @ (C)) & (member451959335_state @ A @ (C))) = (ord_le777019615tate_o @ (insert528405184_state @ A @ B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 123.96/29.66 thf(355,axiom,((! [A:hoare_1708887482_state,B:(com > hoare_1708887482_state),C:com,D:(com > $o)]: (((A = (B @ C)) => (member451959335_state @ A @ (image_934102463_state @ B @ D))) <= (member_com @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_rev__image__eqI)). 123.96/29.66 thf(1906,plain,((! [A:hoare_1708887482_state,B:(com > hoare_1708887482_state),C:com,D:(com > $o)]: (((A = (B @ C)) => (member451959335_state @ A @ (image_934102463_state @ B @ D))) | ~ (member_com @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[355])). 123.96/29.66 thf(305,axiom,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((semila1780557381name_o @ (^ [D:pname]: (member_pname @ D @ A)) @ (^ [D:pname]: (member_pname @ D @ B)) @ C) = (member_pname @ C @ (semila1780557381name_o @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_sup__Un__eq)). 123.96/29.66 thf(1764,plain,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((semila1780557381name_o @ (^ [D:pname]: (member_pname @ D @ A)) @ (^ [D:pname]: (member_pname @ D @ B)) @ C) = (member_pname @ C @ (semila1780557381name_o @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 123.96/29.66 thf(508,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (semila1780557381name_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_sup__commute)). 123.96/29.66 thf(2413,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ B) = (semila1780557381name_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])). 123.96/29.66 thf(100,axiom,((! [A:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ A) => (finite1329924456tate_o @ (collec219771562tate_o @ (^ [B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__Collect__subsets)). 123.96/29.66 thf(1146,plain,((! [A:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (A)) => (finite1329924456tate_o @ (collec219771562tate_o @ (^ [B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 123.96/29.66 thf(479,axiom,((! [A:pname]: ((collect_pname @ (fequal_pname @ A)) = (insert_pname @ A @ bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_singleton__conv2)). 123.96/29.66 thf(2292,plain,((! [A:pname]: ((collect_pname @ (fequal_pname @ A)) = (insert_pname @ A @ bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])). 123.96/29.66 thf(553,axiom,((! [A:pname]: ((collect_pname @ (^ [B:pname]: (B = A))) = (insert_pname @ A @ bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_singleton__conv)). 123.96/29.66 thf(2556,plain,((! [A:pname]: ((collect_pname @ (^ [B:pname]: (B = A))) = (insert_pname @ A @ bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[553])). 123.96/29.66 thf(85,axiom,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_order__refl)). 123.96/29.66 thf(1103,plain,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ (A) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 123.96/29.66 thf(465,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ A @ C) => (ord_le777019615tate_o @ (semila1122118281tate_o @ B @ A) @ C)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_le__supI)). 123.96/29.66 thf(2253,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (A) @ (C)) => (ord_le777019615tate_o @ (semila1122118281tate_o @ B @ A) @ (C))) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])). 123.96/29.66 thf(473,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (ord_less_eq_pname_o @ (semila1780557381name_o @ A @ (semila1673364395name_o @ B @ C)) @ (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_distrib__sup__le)). 123.96/29.66 thf(2275,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (ord_less_eq_pname_o @ (semila1780557381name_o @ A @ (semila1673364395name_o @ B @ C)) @ (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[473])). 123.96/29.66 thf(395,axiom,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_less_eq_pname_o @ (image_1509414295_pname @ A @ B) @ (image_1509414295_pname @ A @ C)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_image__mono)). 123.96/29.66 thf(2033,plain,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_less_eq_pname_o @ (image_1509414295_pname @ A @ B) @ (image_1509414295_pname @ A @ C)) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])). 123.96/29.66 thf(718,axiom,((! [A:pname]: ((wt @ (body_1 @ A)) <= ((body @ A) != none_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1173_WT_OBody)). 123.96/29.66 thf(3079,plain,((! [A:pname]: ((wt @ (body_1 @ A)) | ((body @ A) = none_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[718])). 123.96/29.66 thf(299,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_883_inf__le2)). 123.96/29.66 thf(1747,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 123.96/29.66 thf(673,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ bot_bo19817387tate_o) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_Un__empty__right)). 123.96/29.66 thf(2941,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ bot_bo19817387tate_o) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[673])). 123.96/29.66 thf(806,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ C) => ((ord_le777019615tate_o @ C @ B) => (((A @ C) <= (! [D:hoare_1708887482_state,E:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ E) => ((((A @ E) => (A @ (insert528405184_state @ D @ E))) <= (~ (member451959335_state @ D @ E))) <= (member451959335_state @ D @ B))))) <= (A @ bot_bo19817387tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_finite__subset__induct)). 123.96/29.66 thf(3375,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (C)) => ((ord_le777019615tate_o @ (C) @ (B)) => ((A @ (C)) | ~ (! [D:hoare_1708887482_state,E:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (E)) => (((A @ (E)) => (A @ (insert528405184_state @ D @ E))) | (member451959335_state @ D @ (E)) | ~ (member451959335_state @ D @ (B))))) | ~ (A @ (bot_bo19817387tate_o))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[806])). 123.96/29.66 thf(610,axiom,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ bot_bot_pname_o) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_Un__empty__right)). 123.96/29.66 thf(2734,plain,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ bot_bot_pname_o) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[610])). 123.96/29.66 thf(726,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (insert528405184_state @ A @ B)) <= (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite_OinsertI)). 123.96/29.66 thf(3111,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (insert528405184_state @ A @ B)) | ~ (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[726])). 123.96/29.66 thf(777,axiom,((! [A:(hoare_1708887482_state > $o),B:com]: (((hoare_90032982_state @ A @ (insert528405184_state @ (hoare_Mirabelle_MGT @ B) @ bot_bo19817387tate_o)) <= (hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ (^ [C:state,D:state]: ! [E:state]: ((evalc @ B @ D @ E) => (C = E))) @ B @ fequal_state) @ bot_bo19817387tate_o))) <= (hoare_1160767572gleton)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_757_MGT__alternD)). 123.96/29.66 thf(3274,plain,((! [A:(hoare_1708887482_state > $o),B:com]: ((hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ B) @ bot_bo19817387tate_o)) | ~ (hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ (^ [C:state,D:state]: ! [E:state]: ((evalc @ B @ D @ E) => (C = E))) @ B @ fequal_state) @ bot_bo19817387tate_o)) | ~ (hoare_1160767572gleton)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[777])). 123.96/29.66 thf(795,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (((insert528405184_state @ A @ (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o))) = B) <= (member451959335_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1031_insert__Diff)). 123.96/29.66 thf(3343,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (((insert528405184_state @ A @ (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o))) = (B)) | ~ (member451959335_state @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[795])). 123.96/29.66 thf(468,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => ((semila1673364395name_o @ (insert_pname @ B @ A) @ C) = (insert_pname @ B @ (semila1673364395name_o @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_981_Int__insert__left__if1)). 123.96/29.66 thf(2260,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => ((semila1673364395name_o @ (insert_pname @ B @ A) @ C) = (insert_pname @ B @ (semila1673364395name_o @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])). 123.96/29.66 thf(23,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ B) => (finite_finite_pname @ (minus_minus_pname_o @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_818_finite__Diff)). 123.96/29.66 thf(904,plain,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (B)) => (finite_finite_pname @ (minus_minus_pname_o @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 123.96/29.66 thf(672,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ B) => ((insert528405184_state @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insert__absorb)). 123.96/29.66 thf(2938,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (B)) => ((insert528405184_state @ A @ B) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[672])). 123.96/29.66 thf(456,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (semila1780557381name_o @ (insert_pname @ A @ bot_bot_pname_o) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_insert__is__Un)). 123.96/29.66 thf(2225,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (semila1780557381name_o @ (insert_pname @ A @ bot_bot_pname_o) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[456])). 123.96/29.66 thf(1784,plain,(((set_com @ none_com) = (bot_bot_com_o))),inference(lifteq,[status(thm)],[1783])). 123.96/29.66 thf(544,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_order__eq__refl)). 123.96/29.66 thf(2525,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) | ~ ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[544])). 123.96/29.66 thf(301,axiom,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: ((finite89670078_pname @ C @ D) => (((member_pname @ A @ B) => ((C @ A @ (D @ B)) = (D @ B))) <= (finite_finite_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_folding__one__idem_Oin__idem)). 123.96/29.66 thf(1752,plain,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: ((finite89670078_pname @ (C) @ (D)) => (((member_pname @ A @ (B)) => ((C @ A @ (D @ (B))) = (D @ (B)))) | ~ (finite_finite_pname @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 123.96/29.66 thf(780,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (bot_bo19817387tate_o != (insert528405184_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_empty__not__insert)). 123.96/29.66 thf(3283,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ~ ((bot_bo19817387tate_o) = (insert528405184_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[780])). 123.96/29.66 thf(776,axiom,((! [A:(state > (state > $o)),B:pname,C:(state > (state > $o)),D:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ (insert528405184_state @ (hoare_858012674_state @ A @ (body_1 @ B) @ C) @ D) @ (insert528405184_state @ (hoare_858012674_state @ A @ (the_com @ (body @ B)) @ C) @ bot_bo19817387tate_o)) => (hoare_90032982_state @ D @ (insert528405184_state @ (hoare_858012674_state @ A @ (body_1 @ B) @ C) @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_BodyN)). 123.96/29.66 thf(3272,plain,((! [A:(state > (state > $o)),B:pname,C:(state > (state > $o)),D:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ (insert528405184_state @ (hoare_858012674_state @ A @ (body_1 @ B) @ C) @ D) @ (insert528405184_state @ (hoare_858012674_state @ A @ (the_com @ (body @ B)) @ C) @ bot_bo19817387tate_o)) => (hoare_90032982_state @ (D) @ (insert528405184_state @ (hoare_858012674_state @ A @ (body_1 @ B) @ C) @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[776])). 123.96/29.66 thf(603,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) => ((semila1673364395name_o @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_inf__absorb2)). 123.96/29.66 thf(2716,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) => ((semila1673364395name_o @ B @ A) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[603])). 123.96/29.66 thf(92,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ C) => ((semila129691299tate_o @ (insert528405184_state @ B @ A) @ C) = (insert528405184_state @ B @ (semila129691299tate_o @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_Int__insert__left__if1)). 123.96/29.66 thf(1124,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (C)) => ((semila129691299tate_o @ (insert528405184_state @ B @ A) @ C) = (insert528405184_state @ B @ (semila129691299tate_o @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 123.96/29.66 thf(760,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),C:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: (((C @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = A) <= (finite1615457021_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_folding__one_Osingleton)). 123.96/29.66 thf(3213,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),C:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: (((C @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = A) | ~ (finite1615457021_state @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[760])). 123.96/29.66 thf(684,axiom,((! [A:(hoare_1708887482_state > $o)]: (((collec1568722789_state @ A) = bot_bo19817387tate_o) = (! [B:hoare_1708887482_state]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Collect__empty__eq)). 123.96/29.66 thf(2970,plain,((! [A:(hoare_1708887482_state > $o)]: (((collec1568722789_state @ A) = (bot_bo19817387tate_o)) = (! [B:hoare_1708887482_state]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[684])). 123.96/29.66 thf(57,axiom,((! [A:((pname > $o) > pname),B:((pname > $o) > $o),C:(pname > $o)]: ((finite_finite_pname @ C) => ((? [D:((pname > $o) > $o)]: ((C = (image_pname_o_pname @ A @ D)) & (finite297249702name_o @ D) & (ord_le1205211808me_o_o @ D @ B))) <= (ord_less_eq_pname_o @ C @ (image_pname_o_pname @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_finite__subset__image)). 123.96/29.66 thf(1007,plain,((! [A:((pname > $o) > pname),B:((pname > $o) > $o),C:(pname > $o)]: ((finite_finite_pname @ (C)) => (? [D:((pname > $o) > $o)]: (((C) = (image_pname_o_pname @ (A) @ (D))) & (finite297249702name_o @ (D)) & (ord_le1205211808me_o_o @ (D) @ (B))) | ~ (ord_less_eq_pname_o @ (C) @ (image_pname_o_pname @ (A) @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 123.96/29.66 thf(792,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > $o)]: (((A @ bot_bo19817387tate_o) => ((! [C:hoare_1708887482_state,D:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ D) => ((~ (member451959335_state @ C @ D)) => ((A @ (insert528405184_state @ C @ D)) <= (A @ D))))) => (A @ B))) <= (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_finite__induct)). 123.96/29.66 thf(3319,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > $o)]: (((A @ (bot_bo19817387tate_o)) => ((! [C:hoare_1708887482_state,D:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (D)) => ((~ (member451959335_state @ C @ (D))) => ((A @ (insert528405184_state @ C @ D)) | ~ (A @ (D)))))) => (A @ (B)))) | ~ (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[792])). 123.96/29.66 thf(256,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_sup__assoc)). 123.96/29.66 thf(1620,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 123.96/29.66 thf(530,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ B @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_inf__sup__aci_I7_J)). 123.96/29.66 thf(2489,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ B @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[530])). 123.96/29.66 thf(268,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ A @ B) = B) <= (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_Un__absorb1)). 123.96/29.66 thf(1652,plain,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ A @ B) = (B)) | ~ (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 123.96/29.66 thf(362,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_inf__sup__aci_I6_J)). 123.96/29.66 thf(1929,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])). 123.96/29.66 thf(317,axiom,((! [A:((pname > $o) > hoare_1708887482_state),B:((pname > $o) > $o),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ C) => ((ord_le777019615tate_o @ C @ (image_1922967206_state @ A @ B)) => (? [D:((pname > $o) > $o)]: ((finite297249702name_o @ D) & (C = (image_1922967206_state @ A @ D)) & (ord_le1205211808me_o_o @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_finite__subset__image)). 123.96/29.66 thf(1795,plain,((! [A:((pname > $o) > hoare_1708887482_state),B:((pname > $o) > $o),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (C)) => ((ord_le777019615tate_o @ (C) @ (image_1922967206_state @ (A) @ (B))) => (? [D:((pname > $o) > $o)]: ((finite297249702name_o @ (D)) & ((C) = (image_1922967206_state @ (A) @ (D))) & (ord_le1205211808me_o_o @ (D) @ (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 123.96/29.66 thf(502,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ B) => ((semila129691299tate_o @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1006_Int__absorb1)). 123.96/29.66 thf(2398,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) => ((semila129691299tate_o @ B @ A) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])). 123.96/29.66 thf(128,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ C) @ (semila129691299tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1018_Int__Un__distrib2)). 123.96/29.66 thf(1226,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ C) @ (semila129691299tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 123.96/29.66 thf(213,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ A @ B) => (ord_le777019615tate_o @ (minus_2056855718tate_o @ C @ B) @ (minus_2056855718tate_o @ D @ A))) <= (ord_le777019615tate_o @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_971_Diff__mono)). 123.96/29.66 thf(1488,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (A) @ (B)) => (ord_le777019615tate_o @ (minus_2056855718tate_o @ C @ B) @ (minus_2056855718tate_o @ D @ A))) | ~ (ord_le777019615tate_o @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 123.96/29.66 thf(596,axiom,((! [A:(pname > pname),B:(pname > $o)]: ((~ (finite_finite_pname @ B)) => ((finite_finite_pname @ (image_pname_pname @ A @ B)) => (? [C:pname]: (~ (finite_finite_pname @ (collect_pname @ (^ [D:pname]: ((member_pname @ D @ B) & ((A @ D) = (A @ C)))))) & (member_pname @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_pigeonhole__infinite)). 123.96/29.66 thf(2695,plain,((! [A:(pname > pname),B:(pname > $o)]: ((~ (finite_finite_pname @ (B))) => ((finite_finite_pname @ (image_pname_pname @ A @ B)) => (? [C:pname]: (~ (finite_finite_pname @ (collect_pname @ (^ [D:pname]: ((member_pname @ D @ B) & ((A @ D) = (A @ C)))))) & (member_pname @ C @ (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[596])). 123.96/29.66 thf(137,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((minus_2056855718tate_o @ (insert528405184_state @ B @ A) @ C) = (minus_2056855718tate_o @ A @ C)) <= (member451959335_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_955_insert__Diff1)). 123.96/29.66 thf(1256,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((minus_2056855718tate_o @ (insert528405184_state @ B @ A) @ C) = (minus_2056855718tate_o @ A @ C)) | ~ (member451959335_state @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 123.96/29.66 thf(195,axiom,((! [A:(pname > $o)]: ((ord_less_eq_pname_o @ A @ bot_bot_pname_o) = (A = bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_bot__unique)). 123.96/29.66 thf(1428,plain,((! [A:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (bot_bot_pname_o)) = ((A) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 123.96/29.66 thf(97,axiom,((! [A:(pname > $o)]: ((semila1780557381name_o @ bot_bot_pname_o @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_sup__bot__left)). 123.96/29.66 thf(1139,plain,((! [A:(pname > $o)]: ((semila1780557381name_o @ bot_bot_pname_o @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 123.96/29.66 thf(274,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ (semila1780557381name_o @ C @ A)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_le__supI1)). 123.96/29.66 thf(1669,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (semila1780557381name_o @ C @ A)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 123.96/29.66 thf(758,axiom,((! [A:(pname > option_com)]: ((! [B:pname]: ((A @ B) = none_com)) = ((dom_pname_com @ A) = bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1136_dom__eq__empty__conv)). 123.96/29.66 thf(3208,plain,((! [A:(pname > option_com)]: ((! [B:pname]: ((A @ B) = none_com)) = ((dom_pname_com @ A) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[758])). 123.96/29.66 thf(70,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > (hoare_1708887482_state > $o)),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ C) => ((ord_le1728773982te_o_o @ A @ (image_1551509096tate_o @ B @ C)) => (finite1329924456tate_o @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_finite__surj)). 123.96/29.66 thf(1058,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > (hoare_1708887482_state > $o)),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (C)) => ((ord_le1728773982te_o_o @ (A) @ (image_1551509096tate_o @ B @ C)) => (finite1329924456tate_o @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 123.96/29.66 thf(163,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ A @ B) <= (ord_le777019615tate_o @ A @ C)) <= (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_xt1_I3_J)). 123.96/29.66 thf(1332,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) | ~ (ord_le777019615tate_o @ (A) @ (C)) | ~ ((B) = (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 123.96/29.66 thf(27,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (minus_minus_pname_o @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_972_Diff__subset)). 123.96/29.66 thf(919,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (minus_minus_pname_o @ A @ B) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 123.96/29.66 thf(206,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_877_inf__le1)). 123.96/29.66 thf(1464,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 123.96/29.66 thf(786,axiom,((! [A:(state > (state > $o)),B:(state > (state > $o)),C:(hoare_1708887482_state > $o),D:(state > (state > $o)),E:com,F:(state > (state > $o))]: ((hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ D @ E @ F) @ bot_bo19817387tate_o)) => ((hoare_90032982_state @ C @ (insert528405184_state @ (hoare_858012674_state @ B @ E @ A) @ bot_bo19817387tate_o)) <= (! [G:state,H:state]: ((! [I:state]: ((! [J:state]: ((F @ J @ I) <= (D @ J @ H))) => (A @ G @ I))) <= (B @ G @ H))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_conseq12)). 123.96/29.66 thf(3302,plain,((! [A:(state > (state > $o)),B:(state > (state > $o)),C:(hoare_1708887482_state > $o),D:(state > (state > $o)),E:com,F:(state > (state > $o))]: ((hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ D @ E @ F) @ bot_bo19817387tate_o)) => ((hoare_90032982_state @ (C) @ (insert528405184_state @ (hoare_858012674_state @ B @ E @ A) @ bot_bo19817387tate_o)) | ~ (! [G:state,H:state]: (! [I:state]: ((! [J:state]: ((F @ J @ I) | ~ (D @ J @ H))) => (A @ G @ I)) | ~ (B @ G @ H))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[786])). 123.96/29.66 thf(263,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (semila1780557381name_o @ (collect_pname @ (^ [C:pname]: (C = A))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_insert__def)). 123.96/29.66 thf(1638,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (semila1780557381name_o @ (collect_pname @ (^ [C:pname]: (C = A))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 123.96/29.66 thf(671,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > hoare_1708887482_state),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ C @ D) => ((((A != bot_bo19817387tate_o) => ((B @ (D @ A)) = (D @ (image_757158439_state @ B @ A)))) <= (finite1625599783_state @ A)) <= (! [E:hoare_1708887482_state,F:hoare_1708887482_state]: ((B @ (C @ E @ F)) = (C @ (B @ E) @ (B @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_folding__one__idem_Ohom__commute)). 123.96/29.66 thf(2935,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > hoare_1708887482_state),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ (C) @ (D)) => (((~ ((A) = (bot_bo19817387tate_o))) => ((B @ (D @ (A))) = (D @ (image_757158439_state @ B @ A)))) | ~ (finite1625599783_state @ (A)) | ~ (! [E:hoare_1708887482_state,F:hoare_1708887482_state]: ((B @ (C @ E @ F)) = (C @ (B @ E) @ (B @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[671])). 123.96/29.66 thf(294,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (semila1122118281tate_o @ C @ A)) <= (member451959335_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_UnI1)). 123.96/29.66 thf(1733,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (semila1122118281tate_o @ C @ A)) | ~ (member451959335_state @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 123.96/29.66 thf(515,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((A = B) = ((ord_le777019615tate_o @ B @ A) & (ord_le777019615tate_o @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_set__eq__subset)). 123.96/29.66 thf(2442,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((A) = (B)) = ((ord_le777019615tate_o @ (B) @ (A)) & (ord_le777019615tate_o @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])). 123.96/29.66 thf(617,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ A @ (semila1780557381name_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_Un__upper1)). 123.96/29.66 thf(2753,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (A) @ (semila1780557381name_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[617])). 123.96/29.66 thf(404,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((finite_finite_pname @ (collect_pname @ B)) | (finite_finite_pname @ (collect_pname @ A))) => (finite_finite_pname @ (collect_pname @ (^ [C:pname]: ((B @ C) & (A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_finite__Collect__conjI)). 123.96/29.66 thf(2055,plain,((! [A:(pname > $o),B:(pname > $o)]: (((finite_finite_pname @ (collect_pname @ B)) | (finite_finite_pname @ (collect_pname @ A))) => (finite_finite_pname @ (collect_pname @ (^ [C:pname]: ((B @ C) & (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])). 123.96/29.66 thf(559,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ (semila1122118281tate_o @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_924_inf__sup__absorb)). 123.96/29.66 thf(2573,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ (semila1122118281tate_o @ A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[559])). 123.96/29.66 thf(482,axiom,((! [A:(pname > $o)]: ((? [B:pname]: (member_pname @ B @ A)) = (A != bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_ex__in__conv)). 123.96/29.66 thf(2319,plain,((! [A:(pname > $o)]: ((? [B:pname]: (member_pname @ B @ (A))) = (~ ((A) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[482])). 123.96/29.66 thf(48,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: (((finite1329924456tate_o @ (collec219771562tate_o @ A)) | (finite1329924456tate_o @ (collec219771562tate_o @ B))) => (finite1329924456tate_o @ (collec219771562tate_o @ (^ [C:(hoare_1708887482_state > $o)]: ((B @ C) & (A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_finite__Collect__conjI)). 123.96/29.66 thf(979,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: (((finite1329924456tate_o @ (collec219771562tate_o @ A)) | (finite1329924456tate_o @ (collec219771562tate_o @ B))) => (finite1329924456tate_o @ (collec219771562tate_o @ (^ [C:(hoare_1708887482_state > $o)]: ((B @ C) & (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 123.96/29.66 thf(410,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (semila129691299tate_o @ C @ A) @ (semila129691299tate_o @ D @ B)) <= (ord_le777019615tate_o @ A @ B)) <= (ord_le777019615tate_o @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_910_inf__mono)). 123.96/29.66 thf(2084,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (semila129691299tate_o @ C @ A) @ (semila129691299tate_o @ D @ B)) | ~ (ord_le777019615tate_o @ (A) @ (B)) | ~ (ord_le777019615tate_o @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[410])). 123.96/29.66 thf(351,axiom,((! [A:(com > hoare_1708887482_state),B:com,C:(com > $o)]: ((member_com @ B @ C) => (member451959335_state @ (A @ B) @ (image_934102463_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_imageI)). 123.96/29.66 thf(1894,plain,((! [A:(com > hoare_1708887482_state),B:com,C:(com > $o)]: ((member_com @ B @ (C)) => (member451959335_state @ (A @ B) @ (image_934102463_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])). 123.96/29.66 thf(580,axiom,((! [A:(hoare_1708887482_state > pname),B:(pname > $o),C:(hoare_1708887482_state > $o)]: ((ord_less_eq_pname_o @ (image_1509414295_pname @ A @ C) @ B) <= (! [D:hoare_1708887482_state]: ((member451959335_state @ D @ C) => (member_pname @ (A @ D) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_image__subsetI)). 123.96/29.66 thf(2637,plain,((! [A:(hoare_1708887482_state > pname),B:(pname > $o),C:(hoare_1708887482_state > $o)]: ((ord_less_eq_pname_o @ (image_1509414295_pname @ A @ C) @ (B)) | ~ (! [D:hoare_1708887482_state]: ((member451959335_state @ D @ (C)) => (member_pname @ (A @ D) @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[580])). 123.96/29.66 thf(243,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: (((inj_on1553129421_state @ A @ B) & (inj_on1553129421_state @ A @ C) & ((semila129691299tate_o @ (image_1116629049_state @ A @ (minus_minus_pname_o @ B @ C)) @ (image_1116629049_state @ A @ (minus_minus_pname_o @ C @ B))) = bot_bo19817387tate_o)) = (inj_on1553129421_state @ A @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_inj__on__Un)). 123.96/29.66 thf(1574,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: (((inj_on1553129421_state @ (A) @ (B)) & (inj_on1553129421_state @ (A) @ (C)) & ((semila129691299tate_o @ (image_1116629049_state @ A @ (minus_minus_pname_o @ B @ C)) @ (image_1116629049_state @ A @ (minus_minus_pname_o @ C @ B))) = (bot_bo19817387tate_o))) = (inj_on1553129421_state @ (A) @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 123.96/29.66 thf(464,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:option1624383643_state]: ((! [D:hoare_1708887482_state]: ((B @ D) <= (member451959335_state @ D @ (set_Ho525251890_state @ C)))) => ((C = (some_H1974565227_state @ A)) => (B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_ospec)). 123.96/29.66 thf(2246,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:option1624383643_state]: ((! [D:hoare_1708887482_state]: ((B @ D) | ~ (member451959335_state @ D @ (set_Ho525251890_state @ C)))) => ((C = (some_H1974565227_state @ A)) => (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[464])). 123.96/29.66 thf(675,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((member451959335_state @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_singleton__iff)). 123.96/29.66 thf(2945,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((member451959335_state @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[675])). 123.96/29.66 thf(15,axiom,((! [A:(com > $o)]: ((! [B:com]: ~ (A @ B)) = (bot_bot_com_o = (collect_com @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_empty__Collect__eq)). 123.96/29.66 thf(880,plain,((! [A:(com > $o)]: ((! [B:com]: ~ (A @ B)) = ((bot_bot_com_o) = (collect_com @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 123.96/29.66 thf(632,axiom,((! [A:(pname > $o)]: ((finite297249702name_o @ (collect_pname_o @ (^ [B:(pname > $o)]: (ord_less_eq_pname_o @ B @ A)))) <= (finite_finite_pname @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__Collect__subsets)). 123.96/29.66 thf(2802,plain,((! [A:(pname > $o)]: ((finite297249702name_o @ (collect_pname_o @ (^ [B:(pname > $o)]: (ord_less_eq_pname_o @ B @ A)))) | ~ (finite_finite_pname @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[632])). 123.96/29.66 thf(10,axiom,((! [A:(hoare_1708887482_state > (hoare_1708887482_state > $o)),B:(hoare_1708887482_state > $o),C:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ C) => ((? [D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ D @ B) & (finite1625599783_state @ D) & (C = (image_1551509096tate_o @ A @ D)))) <= (ord_le1728773982te_o_o @ C @ (image_1551509096tate_o @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_finite__subset__image)). 123.96/29.66 thf(863,plain,((! [A:(hoare_1708887482_state > (hoare_1708887482_state > $o)),B:(hoare_1708887482_state > $o),C:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ (C)) => (? [D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (D) @ (B)) & (finite1625599783_state @ (D)) & ((C) = (image_1551509096tate_o @ A @ D))) | ~ (ord_le1728773982te_o_o @ (C) @ (image_1551509096tate_o @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 123.96/29.66 thf(605,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ A @ (semila1122118281tate_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_inf__sup__ord_I4_J)). 123.96/29.66 thf(2721,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (A) @ (semila1122118281tate_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[605])). 123.96/29.66 thf(798,axiom,((! [A:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ bot_bo19817387tate_o @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_bot__least)). 123.96/29.66 thf(3352,plain,((! [A:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (bot_bo19817387tate_o) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[798])). 123.96/29.66 thf(548,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((A @ C) | (B @ C)))) = (semila1122118281tate_o @ (collec1568722789_state @ A) @ (collec1568722789_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_Collect__disj__eq)). 123.96/29.66 thf(2538,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((A @ C) | (B @ C)))) = (semila1122118281tate_o @ (collec1568722789_state @ A) @ (collec1568722789_state @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[548])). 123.96/29.66 thf(187,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (^ [C:pname]: (member_pname @ C @ A)) @ (^ [C:pname]: (member_pname @ C @ B))) = (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_pred__subset__eq)). 123.96/29.66 thf(1408,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (^ [C:pname]: (member_pname @ C @ A)) @ (^ [C:pname]: (member_pname @ C @ B))) = (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 123.96/29.66 thf(527,axiom,((bot_bot_pname_o = (collect_pname @ (^ [A:pname]: (($false)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_empty__def)). 123.96/29.66 thf(2478,plain,(((bot_bot_pname_o) = (collect_pname @ (^ [A:pname]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[527])). 123.96/29.66 thf(768,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ A @ B) => (hoare_496444244_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_hoare__sound)). 123.96/29.67 thf(3251,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ (A) @ (B)) => (hoare_496444244_state @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[768])). 123.96/29.67 thf(625,axiom,((! [A:pname,B:pname,C:(pname > $o)]: ((insert_pname @ A @ (insert_pname @ B @ C)) = (insert_pname @ B @ (insert_pname @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_insert__commute)). 123.96/29.67 thf(2774,plain,((! [A:pname,B:pname,C:(pname > $o)]: ((insert_pname @ A @ (insert_pname @ B @ C)) = (insert_pname @ B @ (insert_pname @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[625])). 123.96/29.67 thf(781,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ (insert528405184_state @ A @ B)) = (insert528405184_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_insert__absorb2)). 123.96/29.67 thf(3287,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ (insert528405184_state @ A @ B)) = (insert528405184_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[781])). 123.96/29.67 thf(661,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ B @ C)) @ (semila129691299tate_o @ C @ A)) = (semila129691299tate_o @ (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ B @ C)) @ (semila1122118281tate_o @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_Un__Int__crazy)). 123.96/29.67 thf(2906,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ B @ C)) @ (semila129691299tate_o @ C @ A)) = (semila129691299tate_o @ (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ B @ C)) @ (semila1122118281tate_o @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[661])). 123.96/29.67 thf(814,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: (((A = C) | (B @ C)) = (insert528405184_state @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_insert__code)). 123.96/29.67 thf(3419,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: (((A = C) | (B @ C)) = (insert528405184_state @ A @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[814])). 123.96/29.67 thf(415,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ A @ B) = bot_bot_pname_o) = ((B = bot_bot_pname_o) & (A = bot_bot_pname_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_Un__empty)). 123.96/29.67 thf(2097,plain,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ A @ B) = (bot_bot_pname_o)) = (((B) = (bot_bot_pname_o)) & ((A) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])). 123.96/29.67 thf(775,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((member451959335_state @ B @ A) => (ord_le777019615tate_o @ A @ (insert528405184_state @ B @ C))) <= (ord_le777019615tate_o @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1061_diff__single__insert)). 123.96/29.67 thf(3270,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((member451959335_state @ B @ (A)) => (ord_le777019615tate_o @ (A) @ (insert528405184_state @ B @ C))) | ~ (ord_le777019615tate_o @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[775])). 123.96/29.67 thf(467,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ C) => ((semila129691299tate_o @ C @ (insert528405184_state @ B @ A)) = (insert528405184_state @ B @ (semila129691299tate_o @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_985_Int__insert__right__if1)). 123.96/29.67 thf(2257,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (C)) => ((semila129691299tate_o @ C @ (insert528405184_state @ B @ A)) = (insert528405184_state @ B @ (semila129691299tate_o @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])). 123.96/29.67 thf(52,axiom,((! [A:(pname > (hoare_1708887482_state > $o)),B:(pname > $o),C:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ C) => ((ord_le1728773982te_o_o @ C @ (image_425134806tate_o @ A @ B)) => (? [D:(pname > $o)]: ((ord_less_eq_pname_o @ D @ B) & (finite_finite_pname @ D) & (C = (image_425134806tate_o @ A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_finite__subset__image)). 123.96/29.67 thf(990,plain,((! [A:(pname > (hoare_1708887482_state > $o)),B:(pname > $o),C:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ (C)) => ((ord_le1728773982te_o_o @ (C) @ (image_425134806tate_o @ A @ B)) => (? [D:(pname > $o)]: ((ord_less_eq_pname_o @ (D) @ (B)) & (finite_finite_pname @ (D)) & ((C) = (image_425134806tate_o @ A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 123.96/29.67 thf(831,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((member451959335_state @ A @ C) | (A = B)) = (member451959335_state @ A @ (insert528405184_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_insert__iff)). 123.96/29.67 thf(3468,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((member451959335_state @ A @ (C)) | (A = B)) = (member451959335_state @ A @ (insert528405184_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[831])). 123.96/29.67 thf(232,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (minus_2056855718tate_o @ A @ B) @ C) = (ord_le777019615tate_o @ A @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_Diff__subset__conv)). 123.96/29.67 thf(1542,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (minus_2056855718tate_o @ A @ B) @ (C)) = (ord_le777019615tate_o @ (A) @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 123.96/29.67 thf(290,axiom,((! [A:(state > (state > $o)),B:com,C:(state > (state > $o)),D:(state > (state > $o)),E:com,F:(state > (state > $o))]: (((A = D) & (C = F) & (B = E)) = ((hoare_858012674_state @ A @ B @ C) = (hoare_858012674_state @ D @ E @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_triple_Oinject)). 123.96/29.67 thf(1722,plain,((! [A:(state > (state > $o)),B:com,C:(state > (state > $o)),D:(state > (state > $o)),E:com,F:(state > (state > $o))]: ((((A) = (D)) & ((C) = (F)) & (B = E)) = ((hoare_858012674_state @ (A) @ B @ (C)) = (hoare_858012674_state @ (D) @ E @ (F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 123.96/29.67 thf(591,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((B = A) <= (ord_less_eq_pname_o @ B @ A)) <= (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_xt1_I5_J)). 123.96/29.67 thf(2669,plain,((! [A:(pname > $o),B:(pname > $o)]: (((B) = (A)) | ~ (ord_less_eq_pname_o @ (B) @ (A)) | ~ (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[591])). 123.96/29.67 thf(99,axiom,((! [A:pname,B:(pname > $o)]: ((finite_finite_pname @ B) => (finite_finite_pname @ (insert_pname @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite_OinsertI)). 123.96/29.67 thf(1144,plain,((! [A:pname,B:(pname > $o)]: ((finite_finite_pname @ (B)) => (finite_finite_pname @ (insert_pname @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 123.96/29.67 thf(280,axiom,((! [A:hoare_1708887482_state]: (none_H1106584047_state != (some_H1974565227_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1108_option_Osimps_I2_J)). 123.96/29.67 thf(1690,plain,((! [A:hoare_1708887482_state]: ~ (none_H1106584047_state = (some_H1974565227_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 123.96/29.67 thf(715,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (insert528405184_state @ A @ C)) <= ((B = A) <= (~ (member451959335_state @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_insertCI)). 123.96/29.67 thf(3066,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (insert528405184_state @ A @ C)) | ~ ((B = A) | (member451959335_state @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[715])). 123.96/29.67 thf(242,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((minus_2056855718tate_o @ A @ B) = A) <= ((semila129691299tate_o @ A @ B) = bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_Diff__triv)). 123.96/29.67 thf(1571,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((minus_2056855718tate_o @ A @ B) = (A)) | ~ ((semila129691299tate_o @ A @ B) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 123.96/29.67 thf(650,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1010_Int__lower2)). 123.96/29.67 thf(2871,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[650])). 123.96/29.67 thf(446,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ A @ (semila1122118281tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_inf__sup__ord_I3_J)). 123.96/29.67 thf(2197,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (A) @ (semila1122118281tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[446])). 123.96/29.67 thf(742,axiom,((! [A:(state > (state > $o)),B:(hoare_1708887482_state > $o),C:(state > (state > $o)),D:com,E:(state > (state > $o))]: (((hoare_90032982_state @ B @ (insert528405184_state @ (hoare_858012674_state @ C @ D @ A) @ bot_bo19817387tate_o)) <= (! [F:state,G:state]: ((E @ F @ G) => (A @ F @ G)))) <= (hoare_90032982_state @ B @ (insert528405184_state @ (hoare_858012674_state @ C @ D @ E) @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_conseq2)). 123.96/29.67 thf(3160,plain,((! [A:(state > (state > $o)),B:(hoare_1708887482_state > $o),C:(state > (state > $o)),D:com,E:(state > (state > $o))]: ((hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_858012674_state @ C @ D @ A) @ bot_bo19817387tate_o)) | ~ (! [F:state,G:state]: ((E @ F @ G) => (A @ F @ G))) | ~ (hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_858012674_state @ C @ D @ E) @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[742])). 123.96/29.67 thf(762,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ B) => ((A @ B) => ((! [C:hoare_1708887482_state,D:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ D) => (((A @ (minus_2056855718tate_o @ D @ (insert528405184_state @ C @ bot_bo19817387tate_o))) <= (A @ D)) <= (member451959335_state @ C @ D)))) => (A @ bot_bo19817387tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_finite__empty__induct)). 123.96/29.67 thf(3219,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (B)) => ((A @ (B)) => ((! [C:hoare_1708887482_state,D:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (D)) => ((A @ (minus_2056855718tate_o @ D @ (insert528405184_state @ C @ bot_bo19817387tate_o))) | ~ (A @ (D)) | ~ (member451959335_state @ C @ (D))))) => (A @ (bot_bo19817387tate_o))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[762])). 123.96/29.67 thf(570,axiom,((! [A:(pname > $o)]: ((A = bot_bot_pname_o) = (! [B:pname]: ~ (member_pname @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_all__not__in__conv)). 123.96/29.67 thf(2605,plain,((! [A:(pname > $o)]: (((A) = (bot_bot_pname_o)) = (! [B:pname]: ~ (member_pname @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[570])). 123.96/29.67 thf(733,axiom,((! [A:hoare_1708887482_state]: ~ (member451959335_state @ A @ bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_emptyE)). 123.96/29.67 thf(3133,plain,((! [A:hoare_1708887482_state]: ~ (member451959335_state @ A @ (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[733])). 123.96/29.67 thf(425,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila129691299tate_o @ A @ B) = A) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_Int__absorb2)). 123.96/29.67 thf(2129,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila129691299tate_o @ A @ B) = (A)) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])). 123.96/29.67 thf(386,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ B @ A) = B) <= (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_Un__absorb2)). 123.96/29.67 thf(1993,plain,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ B @ A) = (B)) | ~ (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])). 123.96/29.67 thf(470,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) => ((semila1780557381name_o @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_sup__absorb2)). 123.96/29.67 thf(2267,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) => ((semila1780557381name_o @ A @ B) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[470])). 123.96/29.67 thf(325,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((! [C:pname]: ((member_pname @ C @ A) <= (member_pname @ C @ B))) => (ord_less_eq_pname_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_subsetI)). 123.96/29.67 thf(1821,plain,((! [A:(pname > $o),B:(pname > $o)]: ((! [C:pname]: ((member_pname @ C @ (A)) | ~ (member_pname @ C @ (B)))) => (ord_less_eq_pname_o @ (B) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 123.96/29.67 thf(107,axiom,((! [A:state,B:state]: ((A = B) | ~ (fequal_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Ostate_T)). 123.96/29.67 thf(1162,plain,((! [A:state,B:state]: ((A = B) | ~ (fequal_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 123.96/29.67 thf(744,axiom,((! [A:(pname > $o),B:(hoare_1708887482_state > $o)]: (((? [C:(pname > hoare_1708887482_state)]: ((image_1116629049_state @ C @ A) = B)) = (? [C:(hoare_1708887482_state > pname)]: ((inj_on1945914667_pname @ C @ B) & (ord_less_eq_pname_o @ (image_1509414295_pname @ C @ B) @ A)))) <= (B != bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_inj__on__iff__surj)). 123.96/29.67 thf(3165,plain,((! [A:(pname > $o),B:(hoare_1708887482_state > $o)]: (((? [C:(pname > hoare_1708887482_state)]: ((image_1116629049_state @ C @ A) = (B))) = (? [C:(hoare_1708887482_state > pname)]: ((inj_on1945914667_pname @ (C) @ (B)) & (ord_less_eq_pname_o @ (image_1509414295_pname @ C @ B) @ (A))))) | ((B) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[744])). 123.96/29.67 thf(752,axiom,((! [A:pname,B:state,C:state]: ((evalc @ (body_1 @ A) @ B @ C) => (evalc @ (the_com @ (body @ A)) @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_evalc__elim__cases_I6_J)). 123.96/29.67 thf(3192,plain,((! [A:pname,B:state,C:state]: ((evalc @ (body_1 @ A) @ B @ C) => (evalc @ (the_com @ (body @ A)) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[752])). 123.96/29.67 thf(166,axiom,((! [A:com]: (none_com != (some_com @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1106_option_Osimps_I2_J)). 123.96/29.67 thf(1341,plain,((! [A:com]: ~ (none_com = (some_com @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 123.96/29.67 thf(1342,plain,((~ (? [A:com]: (none_com = (some_com @ A))))),inference(miniscope,[status(thm)],[1341])). 123.96/29.67 thf(1343,plain,(! [A:com] : ((~ (none_com = (some_com @ A))))),inference(cnf,[status(esa)],[1342])). 123.96/29.67 thf(1344,plain,(! [A:com] : (((some_com @ A) != none_com))),inference(lifteq,[status(thm)],[1343])). 123.96/29.67 thf(443,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_sup__assoc)). 123.96/29.67 thf(2180,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[443])). 123.96/29.67 thf(828,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: (((ord_le777019615tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) => ((partia1256728516_state @ B @ A) = B)) & (((partia1256728516_state @ B @ A) = (the_Ho851197897_state @ (^ [C:hoare_1708887482_state]: (member451959335_state @ C @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)))))) <= (~ (ord_le777019615tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_flat__lub__def)). 123.96/29.67 thf(3456,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: (((ord_le777019615tate_o @ (A) @ (insert528405184_state @ B @ bot_bo19817387tate_o)) => ((partia1256728516_state @ B @ (A)) = B)) & (((partia1256728516_state @ B @ (A)) = (the_Ho851197897_state @ (^ [C:hoare_1708887482_state]: (member451959335_state @ C @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)))))) | (ord_le777019615tate_o @ (A) @ (insert528405184_state @ B @ bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[828])). 123.96/29.67 thf(273,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => ((member451959335_state @ A @ B) => (member451959335_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_subsetD)). 123.96/29.67 thf(1667,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => ((member451959335_state @ A @ (B)) => (member451959335_state @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 123.96/29.67 thf(667,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((~ (member451959335_state @ B @ C)) => ((~ (member451959335_state @ B @ A)) => ((C = A) = ((insert528405184_state @ B @ C) = (insert528405184_state @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_insert__ident)). 123.96/29.67 thf(2923,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((~ (member451959335_state @ B @ (C))) => ((~ (member451959335_state @ B @ (A))) => (((C) = (A)) = ((insert528405184_state @ B @ C) = (insert528405184_state @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[667])). 123.96/29.67 thf(331,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((ord_less_eq_pname_o @ (semila1780557381name_o @ B @ A) @ C) <= (ord_less_eq_pname_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_Un__least)). 123.96/29.67 thf(1838,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => ((ord_less_eq_pname_o @ (semila1780557381name_o @ B @ A) @ (C)) | ~ (ord_less_eq_pname_o @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 123.96/29.67 thf(566,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1673364395name_o @ A @ (semila1780557381name_o @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_923_inf__sup__absorb)). 123.96/29.67 thf(2593,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1673364395name_o @ A @ (semila1780557381name_o @ A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[566])). 123.96/29.67 thf(20,axiom,((! [A:pname,B:(pname > (pname > pname)),C:((pname > $o) > pname)]: ((finite89670078_pname @ B @ C) => ((B @ A @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_folding__one__idem_Oidem)). 123.96/29.67 thf(895,plain,((! [A:pname,B:(pname > (pname > pname)),C:((pname > $o) > pname)]: ((finite89670078_pname @ (B) @ (C)) => ((B @ A @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 123.96/29.67 thf(826,axiom,((! [A:hoare_1708887482_state]: ~ (member451959335_state @ A @ bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_empty__iff)). 123.96/29.67 thf(3451,plain,((! [A:hoare_1708887482_state]: ~ (member451959335_state @ A @ (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[826])). 123.96/29.67 thf(478,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((! [C:pname]: ((A @ C) <= (B @ C))) => (ord_less_eq_pname_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_predicate1I)). 123.96/29.67 thf(2289,plain,((! [A:(pname > $o),B:(pname > $o)]: ((! [C:pname]: ((A @ C) | ~ (B @ C))) => (ord_less_eq_pname_o @ (B) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])). 123.96/29.67 thf(584,axiom,((! [A:com,B:(pname > com),C:pname,D:(pname > $o)]: (((A = (B @ C)) => (member_com @ A @ (image_pname_com @ B @ D))) <= (member_pname @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_rev__image__eqI)). 123.96/29.67 thf(2647,plain,((! [A:com,B:(pname > com),C:pname,D:(pname > $o)]: (((A = (B @ C)) => (member_com @ A @ (image_pname_com @ B @ D))) | ~ (member_pname @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[584])). 123.96/29.67 thf(36,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:(pname > (hoare_1708887482_state > $o)),C:(pname > $o)]: ((finite_finite_pname @ C) => ((ord_le1728773982te_o_o @ A @ (image_425134806tate_o @ B @ C)) => (finite1329924456tate_o @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_finite__surj)). 123.96/29.67 thf(943,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:(pname > (hoare_1708887482_state > $o)),C:(pname > $o)]: ((finite_finite_pname @ (C)) => ((ord_le1728773982te_o_o @ (A) @ (image_425134806tate_o @ B @ C)) => (finite1329924456tate_o @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 123.96/29.67 thf(58,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (minus_minus_pname_o @ B @ C)) = ((member_pname @ A @ B) & ~ (member_pname @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_Diff__iff)). 123.96/29.67 thf(1022,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (minus_minus_pname_o @ B @ C)) = ((member_pname @ A @ (B)) & ~ (member_pname @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 123.96/29.67 thf(32,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ C @ A) => ((minus_minus_pname_o @ C @ (minus_minus_pname_o @ A @ B)) = B)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_double__diff)). 123.96/29.67 thf(932,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ (C) @ (A)) => ((minus_minus_pname_o @ C @ (minus_minus_pname_o @ A @ B)) = (B))) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 123.96/29.67 thf(371,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((~ ((~ (ord_le777019615tate_o @ A @ C)) <= (ord_le777019615tate_o @ A @ B))) <= (ord_le777019615tate_o @ A @ (semila129691299tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_913_le__infE)). 123.96/29.67 thf(1952,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (~ (~ (ord_le777019615tate_o @ (A) @ (C)) | ~ (ord_le777019615tate_o @ (A) @ (B))) | ~ (ord_le777019615tate_o @ (A) @ (semila129691299tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[371])). 123.96/29.67 thf(739,axiom,((! [A:pname,B:com]: (((wt @ B) <= ((body @ A) = (some_com @ B))) <= (wT_bodies)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_WT__bodiesD)). 123.96/29.67 thf(3150,plain,((! [A:pname,B:com]: ((wt @ B) | ~ ((body @ A) = (some_com @ B)) | ~ (wT_bodies)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[739])). 123.96/29.67 thf(485,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila129691299tate_o @ B @ A) = A) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_901_inf__absorb2)). 123.96/29.67 thf(2329,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila129691299tate_o @ B @ A) = (A)) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[485])). 123.96/29.67 thf(623,axiom,((! [A:(pname > (hoare_1708887482_state > $o)),B:(pname > $o)]: ((finite_finite_pname @ B) => (finite1329924456tate_o @ (image_425134806tate_o @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__imageI)). 123.96/29.67 thf(2770,plain,((! [A:(pname > (hoare_1708887482_state > $o)),B:(pname > $o)]: ((finite_finite_pname @ (B)) => (finite1329924456tate_o @ (image_425134806tate_o @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[623])). 123.96/29.67 thf(361,axiom,((! [A:(com > hoare_1708887482_state),B:(com > $o)]: ((bot_bo19817387tate_o = (image_934102463_state @ A @ B)) = (B = bot_bot_com_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_empty__is__image)). 123.96/29.67 thf(1926,plain,((! [A:(com > hoare_1708887482_state),B:(com > $o)]: (((bot_bo19817387tate_o) = (image_934102463_state @ A @ B)) = ((B) = (bot_bot_com_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])). 123.96/29.67 thf(411,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (minus_2056855718tate_o @ A @ B) @ B) = (semila1122118281tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_Un__Diff__cancel2)). 123.96/29.67 thf(2086,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (minus_2056855718tate_o @ A @ B) @ B) = (semila1122118281tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[411])). 123.96/29.67 thf(265,axiom,((! [A:hoare_1708887482_state,B:(pname > hoare_1708887482_state),C:(pname > $o)]: ((member451959335_state @ A @ (image_1116629049_state @ B @ C)) => (~ (! [D:pname]: ((A = (B @ D)) => (~ (member_pname @ D @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_imageE)). 123.96/29.67 thf(1643,plain,((! [A:hoare_1708887482_state,B:(pname > hoare_1708887482_state),C:(pname > $o)]: ((member451959335_state @ A @ (image_1116629049_state @ B @ C)) => (~ (! [D:pname]: ((A = (B @ D)) => (~ (member_pname @ D @ (C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 123.96/29.67 thf(16,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((minus_minus_pname_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ (minus_minus_pname_o @ A @ C) @ (minus_minus_pname_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_974_Un__Diff)). 123.96/29.67 thf(883,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((minus_minus_pname_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ (minus_minus_pname_o @ A @ C) @ (minus_minus_pname_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 123.96/29.67 thf(407,axiom,((! [A:pname,B:(pname > $o)]: ((~ (! [C:(pname > $o)]: ((B = (insert_pname @ A @ C)) => (member_pname @ A @ C)))) <= (member_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_752_Set_Oset__insert)). 123.96/29.67 thf(2064,plain,((! [A:pname,B:(pname > $o)]: (~ (! [C:(pname > $o)]: (((B) = (insert_pname @ A @ C)) => (member_pname @ A @ (C)))) | ~ (member_pname @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])). 123.96/29.67 thf(112,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > hoare_1708887482_state),D:(pname > $o)]: ((inj_on1553129421_state @ C @ D) => (((ord_less_eq_pname_o @ A @ D) => ((image_1116629049_state @ C @ (semila1673364395name_o @ B @ A)) = (semila129691299tate_o @ (image_1116629049_state @ C @ B) @ (image_1116629049_state @ C @ A)))) <= (ord_less_eq_pname_o @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1152_inj__on__image__Int)). 123.96/29.67 thf(1176,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > hoare_1708887482_state),D:(pname > $o)]: ((inj_on1553129421_state @ (C) @ (D)) => (((ord_less_eq_pname_o @ (A) @ (D)) => ((image_1116629049_state @ C @ (semila1673364395name_o @ B @ A)) = (semila129691299tate_o @ (image_1116629049_state @ C @ B) @ (image_1116629049_state @ C @ A)))) | ~ (ord_less_eq_pname_o @ (B) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 123.96/29.67 thf(547,axiom,((! [A:(pname > $o)]: ((semila1780557381name_o @ bot_bot_pname_o @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_Un__empty__left)). 123.96/29.67 thf(2535,plain,((! [A:(pname > $o)]: ((semila1780557381name_o @ bot_bot_pname_o @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[547])). 123.96/29.67 thf(216,axiom,((! [A:(hoare_1708887482_state > hoare_1708887482_state),B:(hoare_1708887482_state > $o)]: ((~ (finite1625599783_state @ B)) => ((finite1625599783_state @ (image_757158439_state @ A @ B)) => (? [C:hoare_1708887482_state]: (~ (finite1625599783_state @ (collec1568722789_state @ (^ [D:hoare_1708887482_state]: ((member451959335_state @ D @ B) & ((A @ D) = (A @ C)))))) & (member451959335_state @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_pigeonhole__infinite)). 123.96/29.67 thf(1496,plain,((! [A:(hoare_1708887482_state > hoare_1708887482_state),B:(hoare_1708887482_state > $o)]: ((~ (finite1625599783_state @ (B))) => ((finite1625599783_state @ (image_757158439_state @ A @ B)) => (? [C:hoare_1708887482_state]: (~ (finite1625599783_state @ (collec1568722789_state @ (^ [D:hoare_1708887482_state]: ((member451959335_state @ D @ B) & ((A @ D) = (A @ C)))))) & (member451959335_state @ C @ (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 123.96/29.67 thf(379,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((B = C) => ((ord_le777019615tate_o @ B @ A) <= (ord_le777019615tate_o @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_ord__eq__le__trans)). 123.96/29.67 thf(1973,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((B) = (C)) => ((ord_le777019615tate_o @ (B) @ (A)) | ~ (ord_le777019615tate_o @ (C) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])). 123.96/29.67 thf(537,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ A @ B) & (ord_less_eq_pname_o @ A @ C)) = (ord_less_eq_pname_o @ A @ (semila1673364395name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_888_le__inf__iff)). 123.96/29.67 thf(2506,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ (A) @ (B)) & (ord_less_eq_pname_o @ (A) @ (C))) = (ord_less_eq_pname_o @ (A) @ (semila1673364395name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[537])). 123.96/29.67 thf(26,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((member_pname @ B @ C) => ((minus_minus_pname_o @ (insert_pname @ B @ A) @ C) = (minus_minus_pname_o @ A @ C))) & ((~ (member_pname @ B @ C)) => ((minus_minus_pname_o @ (insert_pname @ B @ A) @ C) = (insert_pname @ B @ (minus_minus_pname_o @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_957_insert__Diff__if)). 123.96/29.67 thf(912,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((member_pname @ B @ (C)) => ((minus_minus_pname_o @ (insert_pname @ B @ A) @ C) = (minus_minus_pname_o @ A @ C))) & ((~ (member_pname @ B @ (C))) => ((minus_minus_pname_o @ (insert_pname @ B @ A) @ C) = (insert_pname @ B @ (minus_minus_pname_o @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 123.96/29.67 thf(110,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((C @ A) <= (B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_predicate1D)). 123.96/29.67 thf(1171,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => ((C @ A) | ~ (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 123.96/29.67 thf(183,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ A @ B) => (ord_le777019615tate_o @ (semila1122118281tate_o @ C @ A) @ (semila1122118281tate_o @ D @ B))) <= (ord_le777019615tate_o @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_Un__mono)). 123.96/29.67 thf(1396,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (A) @ (B)) => (ord_le777019615tate_o @ (semila1122118281tate_o @ C @ A) @ (semila1122118281tate_o @ D @ B))) | ~ (ord_le777019615tate_o @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 123.96/29.67 thf(607,axiom,((! [A:(pname > $o)]: ((! [B:pname]: ~ (A @ B)) = (bot_bot_pname_o = (collect_pname @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_empty__Collect__eq)). 123.96/29.67 thf(2725,plain,((! [A:(pname > $o)]: ((! [B:pname]: ~ (A @ B)) = ((bot_bot_pname_o) = (collect_pname @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[607])). 123.96/29.67 thf(503,axiom,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((B @ C) => ((A @ C) <= (ord_less_eq_pname_o @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_rev__predicate1D)). 123.96/29.67 thf(2401,plain,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((B @ C) => ((A @ C) | ~ (ord_less_eq_pname_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[503])). 123.96/29.67 thf(249,axiom,((! [A:(hoare_1708887482_state > (pname > $o)),B:(hoare_1708887482_state > $o)]: ((~ (finite1625599783_state @ B)) => ((? [C:hoare_1708887482_state]: ((member451959335_state @ C @ B) & ~ (finite1625599783_state @ (collec1568722789_state @ (^ [D:hoare_1708887482_state]: ((member451959335_state @ D @ B) & ((A @ D) = (A @ C)))))))) <= (finite297249702name_o @ (image_1552895654name_o @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_pigeonhole__infinite)). 123.96/29.67 thf(1594,plain,((! [A:(hoare_1708887482_state > (pname > $o)),B:(hoare_1708887482_state > $o)]: ((~ (finite1625599783_state @ (B))) => (? [C:hoare_1708887482_state]: ((member451959335_state @ C @ (B)) & ~ (finite1625599783_state @ (collec1568722789_state @ (^ [D:hoare_1708887482_state]: ((member451959335_state @ D @ B) & ((A @ D) = (A @ C))))))) | ~ (finite297249702name_o @ (image_1552895654name_o @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 123.96/29.67 thf(452,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((B = A) = (ord_le777019615tate_o @ B @ A)) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_order__antisym__conv)). 123.96/29.67 thf(2212,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((((B) = (A)) = (ord_le777019615tate_o @ (B) @ (A))) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[452])). 123.96/29.67 thf(41,axiom,((! [A:((hoare_1708887482_state > $o) > $o)]: ((collec219771562tate_o @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_Collect__def)). 123.96/29.67 thf(959,plain,((! [A:((hoare_1708887482_state > $o) > $o)]: ((collec219771562tate_o @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 123.96/29.67 thf(621,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => (ord_less_eq_pname_o @ (semila1673364395name_o @ B @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_891_le__infI1)). 123.96/29.67 thf(2765,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => (ord_less_eq_pname_o @ (semila1673364395name_o @ B @ A) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[621])). 123.96/29.67 thf(65,axiom,((! [A:((pname > $o) > $o),B:(pname > (pname > $o)),C:(pname > $o)]: ((finite_finite_pname @ C) => ((ord_le1205211808me_o_o @ A @ (image_pname_pname_o @ B @ C)) => (finite297249702name_o @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_finite__surj)). 123.96/29.67 thf(1044,plain,((! [A:((pname > $o) > $o),B:(pname > (pname > $o)),C:(pname > $o)]: ((finite_finite_pname @ (C)) => ((ord_le1205211808me_o_o @ (A) @ (image_pname_pname_o @ B @ C)) => (finite297249702name_o @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 123.96/29.67 thf(575,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1673364395name_o @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_sup__inf__absorb)). 123.96/29.67 thf(2620,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1673364395name_o @ A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[575])). 123.96/29.67 thf(11,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) => ((semila1780557381name_o @ A @ (minus_minus_pname_o @ B @ A)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_Diff__partition)). 123.96/29.67 thf(868,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) => ((semila1780557381name_o @ A @ (minus_minus_pname_o @ B @ A)) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 123.96/29.67 thf(200,axiom,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o),C:(pname > $o)]: ((finite_finite_pname @ C) => ((ord_less_eq_pname_o @ C @ (image_1509414295_pname @ A @ B)) => (? [D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ D @ B) & (C = (image_1509414295_pname @ A @ D)) & (finite1625599783_state @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_finite__subset__image)). 123.96/29.67 thf(1445,plain,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o),C:(pname > $o)]: ((finite_finite_pname @ (C)) => ((ord_less_eq_pname_o @ (C) @ (image_1509414295_pname @ A @ B)) => (? [D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (D) @ (B)) & ((C) = (image_1509414295_pname @ A @ D)) & (finite1625599783_state @ (D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 123.96/29.67 thf(227,axiom,((! [A:(hoare_1708887482_state > $o),B:(pname > hoare_1708887482_state),C:(pname > $o)]: ((finite_finite_pname @ C) => ((ord_le777019615tate_o @ A @ (image_1116629049_state @ B @ C)) => (finite1625599783_state @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_finite__surj)). 123.96/29.67 thf(1528,plain,((! [A:(hoare_1708887482_state > $o),B:(pname > hoare_1708887482_state),C:(pname > $o)]: ((finite_finite_pname @ (C)) => ((ord_le777019615tate_o @ (A) @ (image_1116629049_state @ B @ C)) => (finite1625599783_state @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 123.96/29.67 thf(764,axiom,((! [A:(pname > option_com),B:(pname > $o)]: ((dom_pname_com @ (restri1382200118me_com @ A @ B)) = (semila1673364395name_o @ (dom_pname_com @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1190_dom__restrict)). 123.96/29.67 thf(3241,plain,((! [A:(pname > option_com),B:(pname > $o)]: ((dom_pname_com @ (restri1382200118me_com @ A @ B)) = (semila1673364395name_o @ (dom_pname_com @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[764])). 123.96/29.67 thf(630,axiom,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ bot_bot_pname_o @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_empty__subsetI)). 123.96/29.67 thf(2797,plain,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ (bot_bot_pname_o) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[630])). 123.96/29.67 thf(698,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ (insert528405184_state @ B @ C)) = (minus_2056855718tate_o @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1040_Diff__insert2)). 123.96/29.67 thf(3016,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ (insert528405184_state @ B @ C)) = (minus_2056855718tate_o @ (minus_2056855718tate_o @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[698])). 123.96/29.67 thf(309,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ C @ D) => ((finite1625599783_state @ B) => (((ord_le777019615tate_o @ A @ B) => ((C @ (D @ A) @ (D @ B)) = (D @ B))) <= (A != bot_bo19817387tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_folding__one__idem_Osubset__idem)). 123.96/29.67 thf(1775,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ (C) @ (D)) => ((finite1625599783_state @ (B)) => (((ord_le777019615tate_o @ (A) @ (B)) => ((C @ (D @ (A)) @ (D @ (B))) = (D @ (B)))) | ((A) = (bot_bo19817387tate_o))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 123.96/29.67 thf(463,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_876_inf__le1)). 123.96/29.67 thf(2244,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (semila1673364395name_o @ A @ B) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[463])). 123.96/29.67 thf(391,axiom,((! [A:(pname > $o),B:pname]: (ord_less_eq_pname_o @ A @ (insert_pname @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_subset__insertI)). 123.96/29.67 thf(2022,plain,((! [A:(pname > $o),B:pname]: (ord_less_eq_pname_o @ (A) @ (insert_pname @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[391])). 123.96/29.67 thf(802,axiom,((! [A:(hoare_1708887482_state > $o),B:com,C:(state > (state > $o)),D:(state > (state > $o))]: ((hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ D @ B @ C) @ bot_bo19817387tate_o)) <= (! [E:state,F:state]: ((D @ E @ F) => (hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ (^ [G:state,H:state]: (H = F)) @ B @ (^ [G:state]: (C @ E))) @ bot_bo19817387tate_o))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_escape)). 123.96/29.67 thf(3363,plain,((! [A:(hoare_1708887482_state > $o),B:com,C:(state > (state > $o)),D:(state > (state > $o))]: ((hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ D @ B @ C) @ bot_bo19817387tate_o)) | ~ (! [E:state,F:state]: ((D @ E @ F) => (hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ (^ [G:state,H:state]: (H = F)) @ B @ (^ [G:state]: (C @ E))) @ bot_bo19817387tate_o))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[802])). 123.96/29.67 thf(172,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ B) = ((semila129691299tate_o @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_886_le__iff__inf)). 123.96/29.67 thf(1364,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) = ((semila129691299tate_o @ A @ B) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 123.96/29.67 thf(683,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ (insert528405184_state @ B @ C)) = (minus_2056855718tate_o @ (minus_2056855718tate_o @ A @ C) @ (insert528405184_state @ B @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_Diff__insert)). 123.96/29.67 thf(2967,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ (insert528405184_state @ B @ C)) = (minus_2056855718tate_o @ (minus_2056855718tate_o @ A @ C) @ (insert528405184_state @ B @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[683])). 123.96/29.67 thf(136,axiom,((! [A:((hoare_1708887482_state > $o) > hoare_1708887482_state),B:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ B) => (finite1625599783_state @ (image_27005066_state @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__imageI)). 123.96/29.67 thf(1250,plain,((! [A:((hoare_1708887482_state > $o) > hoare_1708887482_state),B:((hoare_1708887482_state > $o) > $o)]: ((finite1329924456tate_o @ (B)) => (finite1625599783_state @ (image_27005066_state @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 123.96/29.67 thf(3511,plain,(! [A:com] : (((body @ pn) != none_com) | ((some_com @ y) != (some_com @ A)))),inference(paramod_ordered,[status(thm)],[2957,1344])). 123.96/29.67 thf(3512,plain,(((body @ pn) != none_com)),inference(pattern_uni,[status(thm)],[3511:[bind(A, $thf(y))]])). 123.96/29.67 thf(748,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: (((B = C) = ((image_1116629049_state @ A @ B) = (image_1116629049_state @ A @ C))) <= (inj_on1553129421_state @ A @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1121_inj__on__Un__image__eq__iff)). 123.96/29.67 thf(3178,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: ((((B) = (C)) = ((image_1116629049_state @ A @ B) = (image_1116629049_state @ A @ C))) | ~ (inj_on1553129421_state @ (A) @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[748])). 123.96/29.67 thf(693,axiom,((! [A:hoare_1708887482_state,B:(pname > $o)]: (((B = bot_bot_pname_o) => ((image_1116629049_state @ (^ [C:pname]: (A)) @ B) = bot_bo19817387tate_o)) & ((B != bot_bot_pname_o) => ((image_1116629049_state @ (^ [C:pname]: (A)) @ B) = (insert528405184_state @ A @ bot_bo19817387tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_image__constant__conv)). 123.96/29.67 thf(2999,plain,((! [A:hoare_1708887482_state,B:(pname > $o)]: ((((B) = (bot_bot_pname_o)) => ((image_1116629049_state @ (^ [C:pname]: (A)) @ B) = (bot_bo19817387tate_o))) & ((~ ((B) = (bot_bot_pname_o))) => ((image_1116629049_state @ (^ [C:pname]: (A)) @ B) = (insert528405184_state @ A @ bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[693])). 123.96/29.67 thf(435,axiom,((! [A:(com > option_com),B:com,C:com]: ((member_com @ B @ (dom_com_com @ A)) <= ((A @ B) = (some_com @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_domI)). 123.96/29.67 thf(2156,plain,((! [A:(com > option_com),B:com,C:com]: ((member_com @ B @ (dom_com_com @ A)) | ~ ((A @ B) = (some_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[435])). 123.96/29.67 thf(281,axiom,((! [A:pname]: ((member_pname @ A @ bot_bot_pname_o) = (bot_bot_pname_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_bot__empty__eq)). 123.96/29.67 thf(1694,plain,((! [A:pname]: ((member_pname @ A @ (bot_bot_pname_o)) = (bot_bot_pname_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 123.96/29.67 thf(595,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ A @ B) => (ord_le777019615tate_o @ (semila1122118281tate_o @ C @ A) @ (semila1122118281tate_o @ D @ B))) <= (ord_le777019615tate_o @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_sup__mono)). 123.96/29.67 thf(2693,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (A) @ (B)) => (ord_le777019615tate_o @ (semila1122118281tate_o @ C @ A) @ (semila1122118281tate_o @ D @ B))) | ~ (ord_le777019615tate_o @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[595])). 123.96/29.67 thf(258,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ A @ (semila1122118281tate_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_Un__upper2)). 123.96/29.67 thf(1626,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (A) @ (semila1122118281tate_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 123.96/29.67 thf(461,axiom,((! [A:hoare_1708887482_state,B:(pname > hoare_1708887482_state),C:(pname > $o)]: ((? [D:pname]: ((A = (B @ D)) & (member_pname @ D @ C))) = (member451959335_state @ A @ (image_1116629049_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_image__iff)). 123.96/29.67 thf(2239,plain,((! [A:hoare_1708887482_state,B:(pname > hoare_1708887482_state),C:(pname > $o)]: ((? [D:pname]: ((A = (B @ D)) & (member_pname @ D @ (C)))) = (member451959335_state @ A @ (image_1116629049_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[461])). 123.96/29.67 thf(702,axiom,((! [A:pname,B:state,C:state]: ((evalc @ (the_com @ (body @ A)) @ B @ C) => (evalc @ (body_1 @ A) @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764_evalc_OBody)). 123.96/29.67 thf(3031,plain,((! [A:pname,B:state,C:state]: ((evalc @ (the_com @ (body @ A)) @ B @ C) => (evalc @ (body_1 @ A) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[702])). 123.96/29.67 thf(122,axiom,((! [A:pname,B:(pname > $o),C:option_pname]: (((C = (some_pname @ A)) => (B @ A)) <= (! [D:pname]: ((member_pname @ D @ (set_pname @ C)) => (B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_ospec)). 123.96/29.67 thf(1203,plain,((! [A:pname,B:(pname > $o),C:option_pname]: (((C = (some_pname @ A)) => (B @ A)) | ~ (! [D:pname]: ((member_pname @ D @ (set_pname @ C)) => (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 123.96/29.67 thf(536,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((member451959335_state @ A @ B) | (member451959335_state @ A @ C)) = (member451959335_state @ A @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_Un__iff)). 123.96/29.67 thf(2503,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((member451959335_state @ A @ (B)) | (member451959335_state @ A @ (C))) = (member451959335_state @ A @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[536])). 123.96/29.67 thf(34,axiom,((! [A:((pname > $o) > $o),B:(hoare_1708887482_state > (pname > $o)),C:(hoare_1708887482_state > $o)]: (((finite297249702name_o @ A) <= (ord_le1205211808me_o_o @ A @ (image_1552895654name_o @ B @ C))) <= (finite1625599783_state @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_finite__surj)). 123.96/29.67 thf(939,plain,((! [A:((pname > $o) > $o),B:(hoare_1708887482_state > (pname > $o)),C:(hoare_1708887482_state > $o)]: ((finite297249702name_o @ (A)) | ~ (ord_le1205211808me_o_o @ (A) @ (image_1552895654name_o @ B @ C)) | ~ (finite1625599783_state @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 123.96/29.67 thf(44,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (minus_minus_pname_o @ B @ A)) = (semila1780557381name_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_Un__Diff__cancel)). 123.96/29.67 thf(968,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (minus_minus_pname_o @ B @ A)) = (semila1780557381name_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 123.96/29.67 thf(562,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ A @ B)) = (semila1780557381name_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_sup__left__idem)). 123.96/29.67 thf(2582,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ A @ B)) = (semila1780557381name_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[562])). 123.96/29.67 thf(67,axiom,((! [A:pname,B:pname]: ((A = B) | ~ (fequal_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T)). 123.96/29.67 thf(1049,plain,((! [A:pname,B:pname]: ((A = B) | ~ (fequal_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 123.96/29.67 thf(390,axiom,((! [A:((pname > $o) > $o),B:(pname > $o)]: ((finite_finite_pname @ B) => ((A @ bot_bot_pname_o) => ((A @ B) <= (! [C:pname,D:(pname > $o)]: ((finite_finite_pname @ D) => (((A @ D) => (A @ (insert_pname @ C @ D))) <= (~ (member_pname @ C @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_finite__induct)). 123.96/29.67 thf(2005,plain,((! [A:((pname > $o) > $o),B:(pname > $o)]: ((finite_finite_pname @ (B)) => ((A @ (bot_bot_pname_o)) => ((A @ (B)) | ~ (! [C:pname,D:(pname > $o)]: ((finite_finite_pname @ (D)) => (((A @ (D)) => (A @ (insert_pname @ C @ D))) | (member_pname @ C @ (D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])). 123.96/29.67 thf(189,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (semila1780557381name_o @ A @ C)) <= ((~ (member_pname @ B @ C)) => (member_pname @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_UnCI)). 123.96/29.67 thf(1413,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (semila1780557381name_o @ A @ C)) | ~ ((~ (member_pname @ B @ (C))) => (member_pname @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 123.96/29.67 thf(303,axiom,((! [A:(pname > $o)]: ((ord_less_eq_pname_o @ A @ bot_bot_pname_o) = (A = bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_subset__empty)). 123.96/29.67 thf(1758,plain,((! [A:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (bot_bot_pname_o)) = ((A) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 123.96/29.67 thf(419,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (semila1122118281tate_o @ A @ B)) = ((finite1625599783_state @ A) & (finite1625599783_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_finite__Un)). 123.96/29.67 thf(2107,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (semila1122118281tate_o @ A @ B)) = ((finite1625599783_state @ (A)) & (finite1625599783_state @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])). 123.96/29.67 thf(30,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: ((ord_le1205211808me_o_o @ (collect_pname_o @ B) @ (collect_pname_o @ A)) <= (! [C:(pname > $o)]: ((A @ C) <= (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_Collect__mono)). 123.96/29.67 thf(927,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: ((ord_le1205211808me_o_o @ (collect_pname_o @ B) @ (collect_pname_o @ A)) | ~ (! [C:(pname > $o)]: ((A @ (C)) | ~ (B @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 123.96/29.67 thf(397,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (semila1780557381name_o @ A @ C)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_UnI2)). 123.96/29.67 thf(2037,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (semila1780557381name_o @ A @ C)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[397])). 123.96/29.67 thf(385,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (insert_pname @ A @ B) @ C) = (insert_pname @ A @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_Un__insert__left)). 123.96/29.67 thf(1990,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (insert_pname @ A @ B) @ C) = (insert_pname @ A @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])). 123.96/29.67 thf(708,axiom,((! [A:(hoare_1708887482_state > $o),B:(pname > $o)]: ((hoare_90032982_state @ (semila1122118281tate_o @ A @ (image_1116629049_state @ (^ [C:pname]: (hoare_Mirabelle_MGT @ (body_1 @ C))) @ B)) @ (image_1116629049_state @ (^ [C:pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ C)))) @ B)) => ((finite_finite_pname @ B) => (hoare_90032982_state @ A @ (image_1116629049_state @ (^ [C:pname]: (hoare_Mirabelle_MGT @ (body_1 @ C))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_MGT__Body)). 123.96/29.67 thf(3048,plain,((! [A:(hoare_1708887482_state > $o),B:(pname > $o)]: ((hoare_90032982_state @ (semila1122118281tate_o @ A @ (image_1116629049_state @ (^ [C:pname]: (hoare_Mirabelle_MGT @ (body_1 @ C))) @ B)) @ (image_1116629049_state @ (^ [C:pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ C)))) @ B)) => ((finite_finite_pname @ (B)) => (hoare_90032982_state @ (A) @ (image_1116629049_state @ (^ [C:pname]: (hoare_Mirabelle_MGT @ (body_1 @ C))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[708])). 123.96/29.67 thf(448,axiom,((finite1625599783_state @ fa)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)). 123.96/29.67 thf(2202,plain,((finite1625599783_state @ (fa))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[448])). 123.96/29.67 thf(234,axiom,((! [A:(state > $o),B:com]: ((wt @ (while @ A @ B)) => (wt @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_WTs__elim__cases_I6_J)). 123.96/29.67 thf(1547,plain,((! [A:(state > $o),B:com]: ((wt @ (while @ (A) @ B)) => (wt @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 123.96/29.67 thf(307,axiom,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((image_1509414295_pname @ A @ (semila1122118281tate_o @ B @ C)) = (semila1780557381name_o @ (image_1509414295_pname @ A @ B) @ (image_1509414295_pname @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_image__Un)). 123.96/29.67 thf(1770,plain,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((image_1509414295_pname @ A @ (semila1122118281tate_o @ B @ C)) = (semila1780557381name_o @ (image_1509414295_pname @ A @ B) @ (image_1509414295_pname @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 123.96/29.67 thf(8,axiom,((! [A:(hoare_1708887482_state > (pname > $o)),B:(hoare_1708887482_state > $o),C:((pname > $o) > $o)]: ((finite297249702name_o @ C) => ((? [D:(hoare_1708887482_state > $o)]: ((C = (image_1552895654name_o @ A @ D)) & (finite1625599783_state @ D) & (ord_le777019615tate_o @ D @ B))) <= (ord_le1205211808me_o_o @ C @ (image_1552895654name_o @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_finite__subset__image)). 123.96/29.67 thf(855,plain,((! [A:(hoare_1708887482_state > (pname > $o)),B:(hoare_1708887482_state > $o),C:((pname > $o) > $o)]: ((finite297249702name_o @ (C)) => (? [D:(hoare_1708887482_state > $o)]: (((C) = (image_1552895654name_o @ A @ D)) & (finite1625599783_state @ (D)) & (ord_le777019615tate_o @ (D) @ (B))) | ~ (ord_le1205211808me_o_o @ (C) @ (image_1552895654name_o @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 123.96/29.67 thf(3315,plain,(((set_Ho525251890_state @ none_H1106584047_state) = (bot_bo19817387tate_o))),inference(lifteq,[status(thm)],[3314])). 123.96/29.67 thf(253,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ C) = (semila1673364395name_o @ (semila1780557381name_o @ A @ C) @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_938_sup__inf__distrib2)). 123.96/29.67 thf(1611,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ C) = (semila1673364395name_o @ (semila1780557381name_o @ A @ C) @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 123.96/29.67 thf(719,axiom,((! [A:(state > (state > $o)),B:(hoare_1708887482_state > $o),C:(state > (state > $o)),D:com,E:(state > (state > $o))]: (((! [F:state,G:state]: ((C @ F @ G) <= (A @ F @ G))) => (hoare_90032982_state @ B @ (insert528405184_state @ (hoare_858012674_state @ A @ D @ E) @ bot_bo19817387tate_o))) <= (hoare_90032982_state @ B @ (insert528405184_state @ (hoare_858012674_state @ C @ D @ E) @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_conseq1)). 123.96/29.67 thf(3082,plain,((! [A:(state > (state > $o)),B:(hoare_1708887482_state > $o),C:(state > (state > $o)),D:com,E:(state > (state > $o))]: (((! [F:state,G:state]: ((C @ F @ G) | ~ (A @ F @ G))) => (hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_858012674_state @ A @ D @ E) @ bot_bo19817387tate_o))) | ~ (hoare_90032982_state @ (B) @ (insert528405184_state @ (hoare_858012674_state @ C @ D @ E) @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[719])). 123.96/29.67 thf(45,axiom,((! [A:(pname > $o),B:(pname > pname),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((! [E:pname,F:pname]: ((B @ (C @ E @ F)) = (C @ (B @ E) @ (B @ F)))) => (((A != bot_bot_pname_o) => ((B @ (D @ A)) = (D @ (image_pname_pname @ B @ A)))) <= (finite_finite_pname @ A))) <= (finite89670078_pname @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_721_folding__one__idem_Ohom__commute)). 123.96/29.67 thf(971,plain,((! [A:(pname > $o),B:(pname > pname),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((! [E:pname,F:pname]: ((B @ (C @ E @ F)) = (C @ (B @ E) @ (B @ F)))) => (((~ ((A) = (bot_bot_pname_o))) => ((B @ (D @ (A))) = (D @ (image_pname_pname @ B @ A)))) | ~ (finite_finite_pname @ (A)))) | ~ (finite89670078_pname @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 123.96/29.67 thf(564,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: (((inj_on1553129421_state @ A @ B) => (finite_finite_pname @ B)) <= (finite1625599783_state @ (image_1116629049_state @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_finite__imageD)). 123.96/29.67 thf(2588,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: (((inj_on1553129421_state @ (A) @ (B)) => (finite_finite_pname @ (B))) | ~ (finite1625599783_state @ (image_1116629049_state @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[564])). 123.96/29.67 thf(266,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ A @ (semila1122118281tate_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_sup__ge2)). 123.96/29.67 thf(1647,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (A) @ (semila1122118281tate_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 123.96/29.67 thf(40,axiom,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: ((((member_pname @ A @ B) => ((((D @ B) = (C @ A @ (D @ (minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o))))) <= ((minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o)) != bot_bot_pname_o)) & (((D @ B) = A) <= ((minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o)) = bot_bot_pname_o)))) <= (finite_finite_pname @ B)) <= (finite1282449217_pname @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_792_folding__one_Oremove)). 123.96/29.67 thf(954,plain,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((member_pname @ A @ (B)) => ((((D @ (B)) = (C @ A @ (D @ (minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o))))) | ((minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o)) = (bot_bot_pname_o))) & (((D @ (B)) = A) | ~ ((minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o)) = (bot_bot_pname_o))))) | ~ (finite_finite_pname @ (B)) | ~ (finite1282449217_pname @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 123.96/29.67 thf(140,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((semila1673364395name_o @ C @ (insert_pname @ B @ A)) = (insert_pname @ B @ (semila1673364395name_o @ C @ A))) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_Int__insert__right__if1)). 123.96/29.67 thf(1267,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((semila1673364395name_o @ C @ (insert_pname @ B @ A)) = (insert_pname @ B @ (semila1673364395name_o @ C @ A))) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 123.96/29.67 thf(436,axiom,((! [A:pname]: (bot_bot_o = (bot_bot_pname_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_bot__apply)). 123.96/29.67 thf(2160,plain,((! [A:pname]: (bot_bot_o = (bot_bot_pname_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[436])). 123.96/29.67 thf(59,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((minus_minus_pname_o @ A @ (insert_pname @ B @ C)) = (minus_minus_pname_o @ (minus_minus_pname_o @ A @ (insert_pname @ B @ bot_bot_pname_o)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039_Diff__insert2)). 123.96/29.67 thf(1025,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((minus_minus_pname_o @ A @ (insert_pname @ B @ C)) = (minus_minus_pname_o @ (minus_minus_pname_o @ A @ (insert_pname @ B @ bot_bot_pname_o)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 123.96/29.67 thf(557,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((B @ C) => (semila1122118281tate_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_sup1I2)). 123.96/29.67 thf(2569,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((B @ C) => (semila1122118281tate_o @ (A) @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[557])). 123.96/29.67 thf(825,axiom,((! [A:(hoare_1708887482_state > $o)]: ((A = bot_bo19817387tate_o) = (ord_le777019615tate_o @ A @ bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_subset__empty)). 123.96/29.67 thf(3448,plain,((! [A:(hoare_1708887482_state > $o)]: (((A) = (bot_bo19817387tate_o)) = (ord_le777019615tate_o @ (A) @ (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[825])). 123.96/29.67 thf(413,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ A @ B) => (ord_le777019615tate_o @ A @ C)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_xt1_I6_J)). 123.96/29.67 thf(2092,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (A) @ (B)) => (ord_le777019615tate_o @ (A) @ (C))) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])). 123.96/29.67 thf(438,axiom,((! [A:(hoare_1708887482_state > option_pname),B:hoare_1708887482_state,C:pname]: (((A @ B) = (some_pname @ C)) => (member451959335_state @ B @ (dom_Ho1805192458_pname @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_domI)). 123.96/29.67 thf(2165,plain,((! [A:(hoare_1708887482_state > option_pname),B:hoare_1708887482_state,C:pname]: (((A @ B) = (some_pname @ C)) => (member451959335_state @ B @ (dom_Ho1805192458_pname @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])). 123.96/29.67 thf(666,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: ((finite_finite_pname @ B) => ((image_1116629049_state @ A @ B) = (finite2139561282_pname @ semila1122118281tate_o @ (^ [C:pname]: (insert528405184_state @ (A @ C) @ bot_bo19817387tate_o)) @ bot_bo19817387tate_o @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1102_image__eq__fold__image)). 123.96/29.67 thf(2920,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o)]: ((finite_finite_pname @ (B)) => ((image_1116629049_state @ A @ B) = (finite2139561282_pname @ (semila1122118281tate_o) @ (^ [C:pname]: (insert528405184_state @ (A @ C) @ bot_bo19817387tate_o)) @ bot_bo19817387tate_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[666])). 123.96/29.67 thf(756,axiom,((! [A:hoare_1708887482_state]: ((collec1568722789_state @ (^ [B:hoare_1708887482_state]: (B = A))) = (insert528405184_state @ A @ bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_singleton__conv)). 123.96/29.67 thf(3202,plain,((! [A:hoare_1708887482_state]: ((collec1568722789_state @ (^ [B:hoare_1708887482_state]: (B = A))) = (insert528405184_state @ A @ bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[756])). 123.96/29.67 thf(131,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((semila1673364395name_o @ C @ (insert_pname @ B @ A)) = (semila1673364395name_o @ C @ A)) <= (~ (member_pname @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_Int__insert__right__if0)). 123.96/29.67 thf(1235,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((semila1673364395name_o @ C @ (insert_pname @ B @ A)) = (semila1673364395name_o @ C @ A)) | (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 123.96/29.67 thf(488,axiom,((! [A:(pname > option_com),B:(pname > option_com),C:(pname > $o)]: ((dom_pname_com @ (overri1496249029on_com @ A @ B @ C)) = (semila1780557381name_o @ (minus_minus_pname_o @ (dom_pname_com @ A) @ (collect_pname @ (^ [D:pname]: (member_pname @ D @ (minus_minus_pname_o @ C @ (dom_pname_com @ B)))))) @ (collect_pname @ (^ [D:pname]: (member_pname @ D @ (semila1673364395name_o @ C @ (dom_pname_com @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_dom__override__on)). 123.96/29.67 thf(2337,plain,((! [A:(pname > option_com),B:(pname > option_com),C:(pname > $o)]: ((dom_pname_com @ (overri1496249029on_com @ A @ B @ C)) = (semila1780557381name_o @ (minus_minus_pname_o @ (dom_pname_com @ A) @ (collect_pname @ (^ [D:pname]: (member_pname @ D @ (minus_minus_pname_o @ C @ (dom_pname_com @ B)))))) @ (collect_pname @ (^ [D:pname]: (member_pname @ D @ (semila1673364395name_o @ C @ (dom_pname_com @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[488])). 123.96/29.67 thf(812,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ bot_bo19817387tate_o @ A) = bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_Int__empty__left)). 123.96/29.67 thf(3412,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ bot_bo19817387tate_o @ A) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[812])). 123.96/29.67 thf(146,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ C) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ C) @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1016_Un__Int__distrib2)). 123.96/29.67 thf(1285,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ C) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ C) @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 123.96/29.67 thf(164,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((ord_less_eq_pname_o @ A @ B) => (finite_finite_pname @ A)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_rev__finite__subset)). 123.96/29.67 thf(1336,plain,((! [A:(pname > $o),B:(pname > $o)]: (((ord_less_eq_pname_o @ (A) @ (B)) => (finite_finite_pname @ (A))) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 123.96/29.67 thf(587,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ (collec1568722789_state @ B)) & (finite1625599783_state @ (collec1568722789_state @ A))) = (finite1625599783_state @ (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((A @ C) | (B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_finite__Collect__disjI)). 123.96/29.67 thf(2656,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ (collec1568722789_state @ B)) & (finite1625599783_state @ (collec1568722789_state @ A))) = (finite1625599783_state @ (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((A @ C) | (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[587])). 123.96/29.67 thf(287,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((C @ A) <= (B @ A)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_predicate1D)). 123.96/29.67 thf(1711,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((C @ A) | ~ (B @ A) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 123.96/29.67 thf(699,axiom,((! [A:hoare_1708887482_state,B:(com > $o)]: ((((image_934102463_state @ (^ [C:com]: (A)) @ B) = (insert528405184_state @ A @ bot_bo19817387tate_o)) <= (B != bot_bot_com_o)) & (((image_934102463_state @ (^ [C:com]: (A)) @ B) = bot_bo19817387tate_o) <= (B = bot_bot_com_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_image__constant__conv)). 123.96/29.67 thf(3019,plain,((! [A:hoare_1708887482_state,B:(com > $o)]: ((((image_934102463_state @ (^ [C:com]: (A)) @ B) = (insert528405184_state @ A @ bot_bo19817387tate_o)) | ((B) = (bot_bot_com_o))) & (((image_934102463_state @ (^ [C:com]: (A)) @ B) = (bot_bo19817387tate_o)) | ~ ((B) = (bot_bot_com_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[699])). 123.96/29.67 thf(615,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_sup__idem)). 123.96/29.67 thf(2747,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[615])). 123.96/29.67 thf(217,axiom,((! [A:hoare_1708887482_state]: ((the_Ho963921505_state @ (some_H1974565227_state @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_the_Osimps)). 123.96/29.67 thf(1499,plain,((! [A:hoare_1708887482_state]: ((the_Ho963921505_state @ (some_H1974565227_state @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 123.96/29.67 thf(315,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_Un__assoc)). 123.96/29.67 thf(1790,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (semila1122118281tate_o @ A @ B) @ C) = (semila1122118281tate_o @ A @ (semila1122118281tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 123.96/29.67 thf(384,axiom,((! [A:(state > $o),B:com,C:(state > $o),D:com]: (((while @ A @ B) = (while @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_com_Osimps_I5_J)). 123.96/29.67 thf(1987,plain,((! [A:(state > $o),B:com,C:(state > $o),D:com]: (((while @ (A) @ B) = (while @ (C) @ D)) = (((A) = (C)) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])). 123.96/29.67 thf(322,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ (semila129691299tate_o @ B @ C)) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ A @ C))) <= (! [D:(hoare_1708887482_state > $o),E:(hoare_1708887482_state > $o),F:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ D @ (semila1122118281tate_o @ E @ F)) = (semila1122118281tate_o @ (semila129691299tate_o @ D @ E) @ (semila129691299tate_o @ D @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1081_distrib__imp1)). 123.96/29.67 thf(1813,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ (semila129691299tate_o @ B @ C)) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ A @ C))) | ~ (! [D:(hoare_1708887482_state > $o),E:(hoare_1708887482_state > $o),F:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ D @ (semila1122118281tate_o @ E @ F)) = (semila1122118281tate_o @ (semila129691299tate_o @ D @ E) @ (semila129691299tate_o @ D @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 123.96/29.67 thf(152,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_sup_Oleft__idem)). 123.96/29.67 thf(1300,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 123.96/29.67 thf(202,axiom,(((hoare_1160767572gleton) => (! [A:state]: ~ (! [B:state]: (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_single__stateE)). 123.96/29.67 thf(1452,plain,(((hoare_1160767572gleton) => (! [A:state]: ~ (! [B:state]: (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 123.96/29.67 thf(838,plain,(! [C:(pname > $o),B:(pname > $o),A:(pname > pname)] : (((C) = (image_pname_pname @ A @ (sk1 @ C @ B @ A))) | (~ (ord_less_eq_pname_o @ (C) @ (image_pname_pname @ A @ B))) | (~ (finite_finite_pname @ (C))))),inference(cnf,[status(esa)],[836])). 123.96/29.67 thf(840,plain,(! [C:(pname > $o),B:(pname > $o),A:(pname > pname)] : (((C) = (image_pname_pname @ A @ (sk1 @ C @ B @ A))) | (~ (ord_less_eq_pname_o @ (C) @ (image_pname_pname @ A @ B))) | (~ (finite_finite_pname @ (C))))),inference(lifteq,[status(thm)],[838])). 123.96/29.67 thf(313,axiom,((! [A:(com > hoare_1708887482_state),B:com,C:(com > $o)]: (((insert528405184_state @ (A @ B) @ (image_934102463_state @ A @ C)) = (image_934102463_state @ A @ C)) <= (member_com @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_insert__image)). 123.96/29.67 thf(1785,plain,((! [A:(com > hoare_1708887482_state),B:com,C:(com > $o)]: (((insert528405184_state @ (A @ B) @ (image_934102463_state @ A @ C)) = (image_934102463_state @ A @ C)) | ~ (member_com @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 123.96/29.67 thf(700,axiom,((! [A:(hoare_1708887482_state > $o),B:com]: ((hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ (^ [C:state,D:state]: ! [E:state]: ((evalc @ B @ D @ E) => (C = E))) @ B @ fequal_state) @ bot_bo19817387tate_o)) <= (hoare_90032982_state @ A @ (insert528405184_state @ (hoare_Mirabelle_MGT @ B) @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_MGT__alternI)). 123.96/29.67 thf(3026,plain,((! [A:(hoare_1708887482_state > $o),B:com]: ((hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ (^ [C:state,D:state]: ! [E:state]: ((evalc @ B @ D @ E) => (C = E))) @ B @ fequal_state) @ bot_bo19817387tate_o)) | ~ (hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ B) @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[700])). 123.96/29.67 thf(511,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ A @ (semila1122118281tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_sup__ge1)). 123.96/29.67 thf(2429,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (A) @ (semila1122118281tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[511])). 123.96/29.67 thf(454,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ B) = B) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_sup__absorb2)). 123.96/29.67 thf(2219,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ B) = (B)) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])). 123.96/29.67 thf(381,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ B) = (semila1122118281tate_o @ (collec1568722789_state @ (^ [C:hoare_1708887482_state]: (C = A))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_insert__def)). 123.96/29.67 thf(1980,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ B) = (semila1122118281tate_o @ (collec1568722789_state @ (^ [C:hoare_1708887482_state]: (C = A))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])). 123.96/29.67 thf(328,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_880_inf__sup__ord_I2_J)). 123.96/29.67 thf(1830,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 123.96/29.67 thf(730,axiom,((! [A:(hoare_1708887482_state > $o),B:(pname > (state > (state > $o))),C:(pname > (state > (state > $o))),D:(pname > $o)]: ((hoare_496444244_state @ (semila1122118281tate_o @ A @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (body_1 @ E) @ (C @ E))) @ D)) @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (the_com @ (body @ E)) @ (C @ E))) @ D)) => (hoare_496444244_state @ A @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (body_1 @ E) @ (C @ E))) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_Body__sound__lemma)). 123.96/29.67 thf(3127,plain,((! [A:(hoare_1708887482_state > $o),B:(pname > (state > (state > $o))),C:(pname > (state > (state > $o))),D:(pname > $o)]: ((hoare_496444244_state @ (semila1122118281tate_o @ A @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (body_1 @ E) @ (C @ E))) @ D)) @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (the_com @ (body @ E)) @ (C @ E))) @ D)) => (hoare_496444244_state @ (A) @ (image_1116629049_state @ (^ [E:pname]: (hoare_858012674_state @ (B @ E) @ (body_1 @ E) @ (C @ E))) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[730])). 123.96/29.67 thf(78,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila129691299tate_o @ B @ C)) = ((member451959335_state @ A @ B) & (member451959335_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_Int__iff)). 123.96/29.67 thf(1085,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila129691299tate_o @ B @ C)) = ((member451959335_state @ A @ (B)) & (member451959335_state @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 123.96/29.67 thf(270,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_inf__sup__aci_I6_J)). 123.96/29.67 thf(1658,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 123.96/29.67 thf(483,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((finite_finite_pname @ A) | (finite_finite_pname @ B)) => (finite_finite_pname @ (semila1673364395name_o @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_finite__Int)). 123.96/29.67 thf(2322,plain,((! [A:(pname > $o),B:(pname > $o)]: (((finite_finite_pname @ (A)) | (finite_finite_pname @ (B))) => (finite_finite_pname @ (semila1673364395name_o @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[483])). 123.96/29.67 thf(598,axiom,((! [A:com,B:(pname > com),C:(pname > $o)]: ((member_com @ A @ (image_pname_com @ B @ C)) => (~ (! [D:pname]: ((A = (B @ D)) => (~ (member_pname @ D @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_imageE)). 123.96/29.67 thf(2701,plain,((! [A:com,B:(pname > com),C:(pname > $o)]: ((member_com @ A @ (image_pname_com @ B @ C)) => (~ (! [D:pname]: ((A = (B @ D)) => (~ (member_pname @ D @ (C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[598])). 123.96/29.67 thf(39,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (minus_minus_pname_o @ B @ C)) => (~ ((member_pname @ A @ B) => (member_pname @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_DiffE)). 123.96/29.67 thf(951,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (minus_minus_pname_o @ B @ C)) => (~ ((member_pname @ A @ (B)) => (member_pname @ A @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 123.96/29.67 thf(660,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_sup_Oidem)). 123.96/29.67 thf(2903,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[660])). 123.96/29.67 thf(747,axiom,((! [A:(hoare_1708887482_state > option1624383643_state),B:hoare_1708887482_state,C:hoare_1708887482_state]: (((A @ B) = (some_H1974565227_state @ C)) => ((insert528405184_state @ B @ (dom_Ho1703271284_state @ A)) = (dom_Ho1703271284_state @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_insert__dom)). 123.96/29.67 thf(3174,plain,((! [A:(hoare_1708887482_state > option1624383643_state),B:hoare_1708887482_state,C:hoare_1708887482_state]: (((A @ B) = (some_H1974565227_state @ C)) => ((insert528405184_state @ B @ (dom_Ho1703271284_state @ A)) = (dom_Ho1703271284_state @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[747])). 123.96/29.67 thf(400,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ C) => (member451959335_state @ B @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_UnI2)). 123.96/29.67 thf(2044,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (C)) => (member451959335_state @ B @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[400])). 123.96/29.67 thf(94,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ C @ D) => ((((C @ A @ (D @ B)) = (D @ B)) <= (member451959335_state @ A @ B)) <= (finite1625599783_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_folding__one__idem_Oin__idem)). 123.96/29.67 thf(1130,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ (C) @ (D)) => (((C @ A @ (D @ (B))) = (D @ (B))) | ~ (member451959335_state @ A @ (B)) | ~ (finite1625599783_state @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 123.96/29.67 thf(245,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ A @ B)) = (semila1780557381name_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_sup_Oleft__idem)). 123.96/29.67 thf(1579,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ A @ B)) = (semila1780557381name_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 123.96/29.67 thf(523,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: ((ord_less_eq_pname_o @ C @ D) => ((ord_less_eq_pname_o @ (semila1673364395name_o @ C @ A) @ (semila1673364395name_o @ D @ B)) <= (ord_less_eq_pname_o @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_inf__mono)). 123.96/29.67 thf(2468,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: ((ord_less_eq_pname_o @ (C) @ (D)) => ((ord_less_eq_pname_o @ (semila1673364395name_o @ C @ A) @ (semila1673364395name_o @ D @ B)) | ~ (ord_less_eq_pname_o @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[523])). 123.96/29.67 thf(126,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ (minus_2056855718tate_o @ B @ A)) = bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_Diff__disjoint)). 123.96/29.67 thf(1220,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ (minus_2056855718tate_o @ B @ A)) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 123.96/29.67 thf(507,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ B) => ((finite_finite_pname @ (semila1780557381name_o @ B @ A)) <= (finite_finite_pname @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_finite__UnI)). 123.96/29.67 thf(2411,plain,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (B)) => ((finite_finite_pname @ (semila1780557381name_o @ B @ A)) | ~ (finite_finite_pname @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])). 123.96/29.67 thf(725,axiom,((! [A:(pname > option_com),B:pname,C:com]: ((member_pname @ B @ (dom_pname_com @ A)) <= ((A @ B) = (some_com @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_domI)). 123.96/29.67 thf(3107,plain,((! [A:(pname > option_com),B:pname,C:com]: ((member_pname @ B @ (dom_pname_com @ A)) | ~ ((A @ B) = (some_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[725])). 123.96/29.67 thf(335,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ B) => ((semila1122118281tate_o @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_sup__absorb1)). 123.96/29.67 thf(1849,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) => ((semila1122118281tate_o @ B @ A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 123.96/29.67 thf(230,axiom,((! [A:pname,B:(pname > $o)]: ((finite_finite_pname @ B) = (finite_finite_pname @ (insert_pname @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_finite__insert)). 123.96/29.67 thf(1536,plain,((! [A:pname,B:(pname > $o)]: ((finite_finite_pname @ (B)) = (finite_finite_pname @ (insert_pname @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 123.96/29.67 thf(561,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((~ (member_pname @ B @ C)) => ((ord_less_eq_pname_o @ C @ A) = (ord_less_eq_pname_o @ C @ (insert_pname @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_subset__insert)). 123.96/29.67 thf(2579,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((~ (member_pname @ B @ (C))) => ((ord_less_eq_pname_o @ (C) @ (A)) = (ord_less_eq_pname_o @ (C) @ (insert_pname @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[561])). 123.96/29.67 thf(300,axiom,((! [A:(pname > $o)]: ((finite_finite_pname @ A) = (? [B:(pname > $o),C:pname]: ((finite_finite_pname @ B) & (A = (insert_pname @ C @ B))) | (A = bot_bot_pname_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_finite_Osimps)). 123.96/29.67 thf(1749,plain,((! [A:(pname > $o)]: ((finite_finite_pname @ (A)) = (? [B:(pname > $o),C:pname]: ((finite_finite_pname @ (B)) & ((A) = (insert_pname @ C @ B))) | ((A) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 123.96/29.67 thf(82,axiom,((! [A:pname,B:option_pname]: ((B = (some_pname @ A)) = (member_pname @ A @ (set_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_elem__set)). 123.96/29.67 thf(1094,plain,((! [A:pname,B:option_pname]: ((B = (some_pname @ A)) = (member_pname @ A @ (set_pname @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 123.96/29.67 thf(716,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ B) => (? [C:(hoare_1708887482_state > $o)]: (~ (member451959335_state @ A @ C) & (B = (insert528405184_state @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_750_mk__disjoint__insert)). 123.96/29.67 thf(3071,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (B)) => (? [C:(hoare_1708887482_state > $o)]: (~ (member451959335_state @ A @ (C)) & ((B) = (insert528405184_state @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[716])). 123.96/29.67 thf(770,axiom,((! [A:(hoare_1708887482_state > $o)]: ((A = bot_bo19817387tate_o) = (! [B:hoare_1708887482_state]: ~ (member451959335_state @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_all__not__in__conv)). 123.96/29.67 thf(3256,plain,((! [A:(hoare_1708887482_state > $o)]: (((A) = (bot_bo19817387tate_o)) = (! [B:hoare_1708887482_state]: ~ (member451959335_state @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[770])). 123.96/29.67 thf(634,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) = ((semila1780557381name_o @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_subset__Un__eq)). 123.96/29.67 thf(2807,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) = ((semila1780557381name_o @ A @ B) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[634])). 123.96/29.67 thf(694,axiom,((! [A:pname,B:(pname > option_com)]: ((? [C:com]: ((B @ A) = (some_com @ C))) <= (member_pname @ A @ (dom_pname_com @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_domD)). 123.96/29.67 thf(3007,plain,((! [A:pname,B:(pname > option_com)]: (? [C:com]: ((B @ A) = (some_com @ C)) | ~ (member_pname @ A @ (dom_pname_com @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[694])). 123.96/29.67 thf(255,axiom,((! [A:(hoare_1708887482_state > $o)]: ((collec1568722789_state @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_Collect__def)). 123.96/29.67 thf(1617,plain,((! [A:(hoare_1708887482_state > $o)]: ((collec1568722789_state @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 123.96/29.67 thf(593,axiom,((! [A:((hoare_1708887482_state > $o) > hoare_1708887482_state),B:((hoare_1708887482_state > $o) > $o),C:(hoare_1708887482_state > $o)]: (((? [D:((hoare_1708887482_state > $o) > $o)]: ((ord_le1728773982te_o_o @ D @ B) & (C = (image_27005066_state @ A @ D)) & (finite1329924456tate_o @ D))) <= (ord_le777019615tate_o @ C @ (image_27005066_state @ A @ B))) <= (finite1625599783_state @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_finite__subset__image)). 123.96/29.67 thf(2675,plain,((! [A:((hoare_1708887482_state > $o) > hoare_1708887482_state),B:((hoare_1708887482_state > $o) > $o),C:(hoare_1708887482_state > $o)]: (? [D:((hoare_1708887482_state > $o) > $o)]: ((ord_le1728773982te_o_o @ (D) @ (B)) & ((C) = (image_27005066_state @ (A) @ (D))) & (finite1329924456tate_o @ (D))) | ~ (ord_le777019615tate_o @ (C) @ (image_27005066_state @ (A) @ (B))) | ~ (finite1625599783_state @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[593])). 123.96/29.67 thf(186,axiom,((! [A:com,B:com]: ((semi @ A @ B) != skip))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_com_Osimps_I13_J)). 123.96/29.67 thf(1404,plain,((! [A:com,B:com]: ~ ((semi @ A @ B) = skip))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 123.96/29.67 thf(364,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ B @ A) = (finite603803317name_o @ insert_pname @ A @ B)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_union__fold__insert)). 123.96/29.67 thf(1934,plain,((! [A:(pname > $o),B:(pname > $o)]: (((semila1780557381name_o @ B @ A) = (finite603803317name_o @ (insert_pname) @ A @ B)) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])). 123.96/29.67 thf(676,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((A = bot_bo19817387tate_o) & (B = bot_bo19817387tate_o)) = ((semila1122118281tate_o @ A @ B) = bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_sup__eq__bot__iff)). 123.96/29.67 thf(2948,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((((A) = (bot_bo19817387tate_o)) & ((B) = (bot_bo19817387tate_o))) = ((semila1122118281tate_o @ A @ B) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[676])). 123.96/29.67 thf(644,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ B @ A) => (A = B)) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_order__antisym)). 123.96/29.67 thf(2838,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (B) @ (A)) => ((A) = (B))) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[644])). 123.96/29.67 thf(421,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((A = B) => (~ ((~ (ord_le777019615tate_o @ B @ A)) <= (ord_le777019615tate_o @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_equalityE)). 123.96/29.67 thf(2113,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((A) = (B)) => (~ (~ (ord_le777019615tate_o @ (B) @ (A)) | ~ (ord_le777019615tate_o @ (A) @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[421])). 123.96/29.67 thf(813,axiom,((! [A:pname]: ((body_1 @ A) != skip))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_com_Osimps_I19_J)). 123.96/29.67 thf(3415,plain,((! [A:pname]: ~ ((body_1 @ A) = skip))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[813])). 123.96/29.67 thf(284,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) = ((semila1673364395name_o @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_885_le__iff__inf)). 123.96/29.67 thf(1702,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) = ((semila1673364395name_o @ A @ B) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 123.96/29.67 thf(496,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: (ord_le777019615tate_o @ (image_1116629049_state @ A @ (semila1673364395name_o @ B @ C)) @ (semila129691299tate_o @ (image_1116629049_state @ A @ B) @ (image_1116629049_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1054_image__Int__subset)). 123.96/29.67 thf(2379,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: (ord_le777019615tate_o @ (image_1116629049_state @ A @ (semila1673364395name_o @ B @ C)) @ (semila129691299tate_o @ (image_1116629049_state @ A @ B) @ (image_1116629049_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[496])). 123.96/29.67 thf(490,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((((semila129691299tate_o @ C @ (insert528405184_state @ B @ A)) = (semila129691299tate_o @ C @ A)) <= (~ (member451959335_state @ B @ C))) & ((member451959335_state @ B @ C) => ((semila129691299tate_o @ C @ (insert528405184_state @ B @ A)) = (insert528405184_state @ B @ (semila129691299tate_o @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1000_Int__insert__right)). 123.96/29.67 thf(2357,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((((semila129691299tate_o @ C @ (insert528405184_state @ B @ A)) = (semila129691299tate_o @ C @ A)) | (member451959335_state @ B @ (C))) & ((member451959335_state @ B @ (C)) => ((semila129691299tate_o @ C @ (insert528405184_state @ B @ A)) = (insert528405184_state @ B @ (semila129691299tate_o @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[490])). 123.96/29.67 thf(372,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ C) => ((ord_le777019615tate_o @ C @ A) => (member451959335_state @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_set__rev__mp)). 123.96/29.67 thf(1955,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (C)) => ((ord_le777019615tate_o @ (C) @ (A)) => (member451959335_state @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])). 123.96/29.67 thf(212,axiom,((! [A:com,B:com]: ((A = B) = ((some_com @ A) = (some_com @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_option_Oinject)). 123.96/29.67 thf(1485,plain,((! [A:com,B:com]: ((A = B) = ((some_com @ A) = (some_com @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 123.96/29.67 thf(68,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((minus_minus_pname_o @ A @ B) = (collect_pname @ (^ [C:pname]: ((member_pname @ C @ A) & ~ (member_pname @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_853_set__diff__eq)). 123.96/29.67 thf(1052,plain,((! [A:(pname > $o),B:(pname > $o)]: ((minus_minus_pname_o @ A @ B) = (collect_pname @ (^ [C:pname]: ((member_pname @ C @ A) & ~ (member_pname @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 123.96/29.67 thf(601,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((((member_pname @ B @ A) => (ord_less_eq_pname_o @ (minus_minus_pname_o @ A @ (insert_pname @ B @ bot_bot_pname_o)) @ C)) & ((~ (member_pname @ B @ A)) => (ord_less_eq_pname_o @ A @ C))) = (ord_less_eq_pname_o @ A @ (insert_pname @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1063_subset__insert__iff)). 123.96/29.67 thf(2711,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((((member_pname @ B @ (A)) => (ord_less_eq_pname_o @ (minus_minus_pname_o @ A @ (insert_pname @ B @ bot_bot_pname_o)) @ (C))) & ((~ (member_pname @ B @ (A))) => (ord_less_eq_pname_o @ (A) @ (C)))) = (ord_less_eq_pname_o @ (A) @ (insert_pname @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[601])). 123.96/29.67 thf(608,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila129691299tate_o @ B @ C)) => (member451959335_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_IntD1)). 123.96/29.67 thf(2728,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (semila129691299tate_o @ B @ C)) => (member451959335_state @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[608])). 123.96/29.67 thf(394,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ B) = ((semila1122118281tate_o @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_subset__Un__eq)). 123.96/29.67 thf(2030,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) = ((semila1122118281tate_o @ A @ B) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])). 123.96/29.67 thf(646,axiom,((! [A:(pname > $o),B:pname]: ((((collect_pname @ (^ [C:pname]: ((C = B) & (A @ C)))) = bot_bot_pname_o) <= (~ (A @ B))) & ((A @ B) => ((collect_pname @ (^ [C:pname]: ((C = B) & (A @ C)))) = (insert_pname @ B @ bot_bot_pname_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_Collect__conv__if)). 123.96/29.67 thf(2848,plain,((! [A:(pname > $o),B:pname]: ((((collect_pname @ (^ [C:pname]: ((C = B) & (A @ C)))) = (bot_bot_pname_o)) | (A @ B)) & ((A @ B) => ((collect_pname @ (^ [C:pname]: ((C = B) & (A @ C)))) = (insert_pname @ B @ bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[646])). 123.96/29.67 thf(803,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ B @ A) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_asm)). 123.96/29.67 thf(3366,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((hoare_90032982_state @ (B) @ (A)) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[803])). 123.96/29.67 thf(513,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_930_inf__sup__distrib1)). 123.96/29.67 thf(2435,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[513])). 123.96/29.67 thf(735,axiom,((finite662762081tate_o @ (^ [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_comp__fun__idem__remove)). 123.96/29.67 thf(3139,plain,((finite662762081tate_o @ (^ [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[735])). 123.96/29.67 thf(267,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) => ((semila1673364395name_o @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1005_Int__absorb1)). 123.96/29.67 thf(1649,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) => ((semila1673364395name_o @ B @ A) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 123.96/29.67 thf(2479,plain,(((collect_pname @ (^ [A:pname]: (($false)))) = (bot_bot_pname_o))),inference(lifteq,[status(thm)],[2478])). 123.96/29.67 thf(376,axiom,((! [A:(hoare_1708887482_state > hoare_1708887482_state),B:(hoare_1708887482_state > $o)]: (((inj_on632008595_state @ A @ B) <= (ord_le777019615tate_o @ B @ (image_757158439_state @ A @ B))) <= (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_finite__surj__inj)). 123.96/29.67 thf(1966,plain,((! [A:(hoare_1708887482_state > hoare_1708887482_state),B:(hoare_1708887482_state > $o)]: ((inj_on632008595_state @ (A) @ (B)) | ~ (ord_le777019615tate_o @ (B) @ (image_757158439_state @ A @ B)) | ~ (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[376])). 123.96/29.67 thf(279,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ C) => ((? [D:(pname > $o)]: ((ord_less_eq_pname_o @ D @ B) & (finite_finite_pname @ D) & (C = (image_1116629049_state @ A @ D)))) <= (ord_le777019615tate_o @ C @ (image_1116629049_state @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_finite__subset__image)). 123.96/29.67 thf(1685,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (C)) => (? [D:(pname > $o)]: ((ord_less_eq_pname_o @ (D) @ (B)) & (finite_finite_pname @ (D)) & ((C) = (image_1116629049_state @ A @ D))) | ~ (ord_le777019615tate_o @ (C) @ (image_1116629049_state @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 123.96/29.67 thf(161,axiom,((! [A:pname,B:(pname > $o)]: (((insert_pname @ A @ (minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o))) = B) <= (member_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1030_insert__Diff)). 123.96/29.67 thf(1321,plain,((! [A:pname,B:(pname > $o)]: (((insert_pname @ A @ (minus_minus_pname_o @ B @ (insert_pname @ A @ bot_bot_pname_o))) = (B)) | ~ (member_pname @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 123.96/29.67 thf(333,axiom,((! [A:(hoare_1708887482_state > $o),B:((hoare_1708887482_state > $o) > hoare_1708887482_state),C:((hoare_1708887482_state > $o) > $o)]: (((ord_le777019615tate_o @ A @ (image_27005066_state @ B @ C)) => (finite1625599783_state @ A)) <= (finite1329924456tate_o @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_finite__surj)). 123.96/29.67 thf(1844,plain,((! [A:(hoare_1708887482_state > $o),B:((hoare_1708887482_state > $o) > hoare_1708887482_state),C:((hoare_1708887482_state > $o) > $o)]: (((ord_le777019615tate_o @ (A) @ (image_27005066_state @ (B) @ (C))) => (finite1625599783_state @ (A))) | ~ (finite1329924456tate_o @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 123.96/29.67 thf(750,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ C) => (member451959335_state @ B @ (insert528405184_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_insertI2)). 123.96/29.67 thf(3188,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (C)) => (member451959335_state @ B @ (insert528405184_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[750])). 123.96/29.67 thf(311,axiom,((! [A:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_order__refl)). 123.96/29.67 thf(1781,plain,((! [A:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (A) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 123.96/29.67 thf(420,axiom,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o)]: (((image_1509414295_pname @ A @ B) = bot_bot_pname_o) = (B = bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_image__is__empty)). 123.96/29.67 thf(2110,plain,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o)]: (((image_1509414295_pname @ A @ B) = (bot_bot_pname_o)) = ((B) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[420])). 123.96/29.67 thf(341,axiom,((! [A:com,B:(state > $o),C:state]: ((~ (B @ C)) => (evalc @ (while @ B @ A) @ C @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_769_evalc_OWhileFalse)). 123.96/29.67 thf(1866,plain,((! [A:com,B:(state > $o),C:state]: ((~ (B @ C)) => (evalc @ (while @ (B) @ A) @ C @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 123.96/29.67 thf(320,axiom,((! [A:pname,B:pname,C:(pname > $o)]: (((image_pname_pname @ (^ [D:pname]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_image__constant)). 123.96/29.67 thf(1807,plain,((! [A:pname,B:pname,C:(pname > $o)]: (((image_pname_pname @ (^ [D:pname]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 123.96/29.67 thf(745,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:hoare_1708887482_state,D:hoare_1708887482_state]: ((((B = D) & (A = C)) | ((B = C) & (A = D))) = ((insert528405184_state @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) = (insert528405184_state @ C @ (insert528405184_state @ D @ bot_bo19817387tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_doubleton__eq__iff)). 123.96/29.67 thf(3168,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:hoare_1708887482_state,D:hoare_1708887482_state]: ((((B = D) & (A = C)) | ((B = C) & (A = D))) = ((insert528405184_state @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o)) = (insert528405184_state @ C @ (insert528405184_state @ D @ bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[745])). 123.96/29.67 thf(366,axiom,((! [A:(pname > $o),B:(pname > $o),C:pname]: (((~ (A @ C)) => (B @ C)) <= (semila1780557381name_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_sup1E)). 123.96/29.67 thf(1940,plain,((! [A:(pname > $o),B:(pname > $o),C:pname]: (((~ (A @ C)) => (B @ C)) | ~ (semila1780557381name_o @ (A) @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])). 123.96/29.67 thf(192,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (collect_pname @ B)) = (collect_pname @ (^ [C:pname]: ((~ (C = A)) => (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_insert__Collect)). 123.96/29.67 thf(1421,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (collect_pname @ B)) = (collect_pname @ (^ [C:pname]: ((~ (C = A)) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 123.96/29.67 thf(834,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ bot_bo19817387tate_o) = bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_917_inf__bot__right)). 123.96/29.67 thf(3478,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ bot_bo19817387tate_o) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[834])). 123.96/29.67 thf(204,axiom,((! [A:state,B:state]: ((A != B) | (fequal_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Ostate_T)). 123.96/29.67 thf(1459,plain,((! [A:state,B:state]: (~ (A = B) | (fequal_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 123.96/29.67 thf(721,axiom,((! [A:(pname > hoare_1708887482_state),B:pname]: (member451959335_state @ (A @ B) @ (image_1116629049_state @ A @ top_top_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1198_rangeI)). 123.96/29.67 thf(3092,plain,((! [A:(pname > hoare_1708887482_state),B:pname]: (member451959335_state @ (A @ B) @ (image_1116629049_state @ A @ top_top_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[721])). 123.96/29.67 thf(370,axiom,((! [A:pname,B:(pname > option1624383643_state)]: ((member_pname @ A @ (dom_pn1412407212_state @ B)) => (? [C:hoare_1708887482_state]: ((B @ A) = (some_H1974565227_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_domD)). 123.96/29.67 thf(1949,plain,((! [A:pname,B:(pname > option1624383643_state)]: ((member_pname @ A @ (dom_pn1412407212_state @ B)) => (? [C:hoare_1708887482_state]: ((B @ A) = (some_H1974565227_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[370])). 123.96/29.67 thf(641,axiom,((! [A:pname,B:(com > pname),C:(com > $o)]: ((member_pname @ A @ (image_com_pname @ B @ C)) => (~ (! [D:com]: ((~ (member_com @ D @ C)) <= (A = (B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_imageE)). 123.96/29.67 thf(2828,plain,((! [A:pname,B:(com > pname),C:(com > $o)]: ((member_pname @ A @ (image_com_pname @ B @ C)) => (~ (! [D:com]: (~ (member_com @ D @ (C)) | ~ (A = (B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[641])). 123.96/29.67 thf(323,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ A) => (finite1625599783_state @ (semila1122118281tate_o @ B @ A))) <= (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_finite__UnI)). 123.96/29.67 thf(1817,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ (A)) => (finite1625599783_state @ (semila1122118281tate_o @ B @ A))) | ~ (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 123.96/29.67 thf(746,axiom,((! [A:hoare_1708887482_state,B:com,C:(com > $o)]: (((image_934102463_state @ (^ [D:com]: (A)) @ C) = (insert528405184_state @ A @ bot_bo19817387tate_o)) <= (member_com @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_image__constant)). 123.96/29.67 thf(3171,plain,((! [A:hoare_1708887482_state,B:com,C:(com > $o)]: (((image_934102463_state @ (^ [D:com]: (A)) @ C) = (insert528405184_state @ A @ bot_bo19817387tate_o)) | ~ (member_com @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[746])). 123.96/29.67 thf(453,axiom,((! [A:com]: ((some_com @ A) != none_com))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1109_option_Osimps_I3_J)). 123.96/29.67 thf(2215,plain,((! [A:com]: ~ ((some_com @ A) = none_com))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[453])). 123.96/29.67 thf(223,axiom,((! [A:(hoare_1708887482_state > (pname > $o)),B:(hoare_1708887482_state > $o)]: ((finite297249702name_o @ (image_1552895654name_o @ A @ B)) <= (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__imageI)). 123.96/29.67 thf(1517,plain,((! [A:(hoare_1708887482_state > (pname > $o)),B:(hoare_1708887482_state > $o)]: ((finite297249702name_o @ (image_1552895654name_o @ A @ B)) | ~ (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 123.96/29.67 thf(572,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((semila1780557381name_o @ A @ (semila1673364395name_o @ B @ C)) = (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ A @ C))) <= (! [D:(pname > $o),E:(pname > $o),F:(pname > $o)]: ((semila1673364395name_o @ D @ (semila1780557381name_o @ E @ F)) = (semila1780557381name_o @ (semila1673364395name_o @ D @ E) @ (semila1673364395name_o @ D @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_distrib__imp1)). 123.96/29.67 thf(2611,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((semila1780557381name_o @ A @ (semila1673364395name_o @ B @ C)) = (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ A @ C))) | ~ (! [D:(pname > $o),E:(pname > $o),F:(pname > $o)]: ((semila1673364395name_o @ D @ (semila1780557381name_o @ E @ F)) = (semila1780557381name_o @ (semila1673364395name_o @ D @ E) @ (semila1673364395name_o @ D @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[572])). 123.96/29.67 thf(484,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ C @ A) => (ord_less_eq_pname_o @ B @ A)) <= (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_ord__eq__le__trans)). 123.96/29.67 thf(2325,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ (C) @ (A)) => (ord_less_eq_pname_o @ (B) @ (A))) | ~ ((B) = (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])). 123.96/29.67 thf(117,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1673364395name_o @ B @ C)) = (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_Un__Int__distrib)). 123.96/29.67 thf(1189,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1673364395name_o @ B @ C)) = (semila1673364395name_o @ (semila1780557381name_o @ A @ B) @ (semila1780557381name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 123.96/29.67 thf(796,axiom,((! [A:option1624383643_state]: ((A = none_H1106584047_state) = ((set_Ho525251890_state @ A) = bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_set__empty__eq)). 123.96/29.67 thf(3346,plain,((! [A:option1624383643_state]: ((A = none_H1106584047_state) = ((set_Ho525251890_state @ A) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[796])). 123.96/29.67 thf(711,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ B) => ((semila1122118281tate_o @ B @ A) = (finite96880613tate_o @ insert528405184_state @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_union__fold__insert)). 123.96/29.67 thf(3056,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (B)) => ((semila1122118281tate_o @ B @ A) = (finite96880613tate_o @ (insert528405184_state) @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[711])). 123.96/29.67 thf(5,axiom,((! [A:(pname > $o)]: ((minus_minus_pname_o @ A @ bot_bot_pname_o) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_944_Diff__empty)). 123.96/29.67 thf(844,plain,((! [A:(pname > $o)]: ((minus_minus_pname_o @ A @ bot_bot_pname_o) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 123.96/29.67 thf(582,axiom,((! [A:com,B:(com > $o)]: ((B @ A) = (member_com @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_mem__def)). 123.96/29.67 thf(2643,plain,((! [A:com,B:(com > $o)]: ((B @ A) = (member_com @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[582])). 123.96/29.67 thf(87,axiom,((! [A:pname,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ C) => ((image_1509414295_pname @ (^ [D:hoare_1708887482_state]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_image__constant)). 123.96/29.67 thf(1108,plain,((! [A:pname,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((member451959335_state @ B @ (C)) => ((image_1509414295_pname @ (^ [D:hoare_1708887482_state]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 123.96/29.67 thf(705,axiom,((! [A:com,B:com,C:pname]: ((semi @ A @ B) != (body_1 @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_com_Osimps_I48_J)). 123.96/29.67 thf(3039,plain,((! [A:com,B:com,C:pname]: ~ ((semi @ A @ B) = (body_1 @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[705])). 123.96/29.67 thf(830,axiom,((! [A:(hoare_1708887482_state > $o)]: ((A = bot_bo19817387tate_o) = (ord_le777019615tate_o @ A @ bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_bot__unique)). 123.96/29.67 thf(3465,plain,((! [A:(hoare_1708887482_state > $o)]: (((A) = (bot_bo19817387tate_o)) = (ord_le777019615tate_o @ (A) @ (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[830])). 123.96/29.67 thf(180,axiom,((! [A:state]: (evalc @ skip @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_evalc_OSkip)). 123.96/29.67 thf(1385,plain,((! [A:state]: (evalc @ skip @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 123.96/29.67 thf(472,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => (ord_le777019615tate_o @ (image_1116629049_state @ A @ B) @ (image_1116629049_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_image__mono)). 123.96/29.67 thf(2273,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => (ord_le777019615tate_o @ (image_1116629049_state @ A @ B) @ (image_1116629049_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])). 123.96/29.67 thf(647,axiom,((! [A:((pname > $o) > (pname > $o)),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: ((ord_less_eq_pname_o @ C @ D) => (((A @ C) = B) => ((! [E:(pname > $o),F:(pname > $o)]: ((ord_less_eq_pname_o @ F @ E) => (ord_less_eq_pname_o @ (A @ F) @ (A @ E)))) => (ord_less_eq_pname_o @ B @ (A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_xt1_I16_J)). 123.96/29.67 thf(2855,plain,((! [A:((pname > $o) > (pname > $o)),B:(pname > $o),C:(pname > $o),D:(pname > $o)]: ((ord_less_eq_pname_o @ (C) @ (D)) => (((A @ C) = (B)) => ((! [E:(pname > $o),F:(pname > $o)]: ((ord_less_eq_pname_o @ (F) @ (E)) => (ord_less_eq_pname_o @ (A @ F) @ (A @ E)))) => (ord_less_eq_pname_o @ (B) @ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[647])). 123.96/29.67 thf(211,axiom,((! [A:hoare_1708887482_state,B:(pname > hoare_1708887482_state),C:pname,D:(pname > $o)]: (((member451959335_state @ A @ (image_1116629049_state @ B @ D)) <= (A = (B @ C))) <= (member_pname @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_rev__image__eqI)). 123.96/29.67 thf(1481,plain,((! [A:hoare_1708887482_state,B:(pname > hoare_1708887482_state),C:pname,D:(pname > $o)]: ((member451959335_state @ A @ (image_1116629049_state @ B @ D)) | ~ (A = (B @ C)) | ~ (member_pname @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 123.96/29.67 thf(793,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ (insert528405184_state @ A @ B) @ (insert528405184_state @ A @ C)) = (insert528405184_state @ A @ (semila129691299tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_insert__inter__insert)). 123.96/29.67 thf(3336,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ (insert528405184_state @ A @ B) @ (insert528405184_state @ A @ C)) = (insert528405184_state @ A @ (semila129691299tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[793])). 123.96/29.67 thf(337,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (collect_pname @ (^ [C:pname]: ((C = A) | (member_pname @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_insert__compr__raw)). 123.96/29.67 thf(1854,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (collect_pname @ (^ [C:pname]: ((C = A) | (member_pname @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 123.96/29.67 thf(134,axiom,((! [A:com]: ((the_com @ (some_com @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_the_Osimps)). 123.96/29.67 thf(1244,plain,((! [A:com]: ((the_com @ (some_com @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 123.96/29.67 thf(509,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ (collec1568722789_state @ B)) | (finite1625599783_state @ (collec1568722789_state @ A))) => (finite1625599783_state @ (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((B @ C) & (A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_finite__Collect__conjI)). 123.96/29.67 thf(2416,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((finite1625599783_state @ (collec1568722789_state @ B)) | (finite1625599783_state @ (collec1568722789_state @ A))) => (finite1625599783_state @ (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((B @ C) & (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])). 123.96/29.67 thf(720,axiom,((! [A:(pname > hoare_1708887482_state),B:(pname > hoare_1708887482_state),C:(pname > $o),D:(pname > $o)]: ((((image_1116629049_state @ A @ C) = (image_1116629049_state @ B @ D)) <= (! [E:pname]: ((member_pname @ E @ D) => ((A @ E) = (B @ E))))) <= (C = D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_image__cong)). 123.96/29.67 thf(3085,plain,((! [A:(pname > hoare_1708887482_state),B:(pname > hoare_1708887482_state),C:(pname > $o),D:(pname > $o)]: (((image_1116629049_state @ A @ C) = (image_1116629049_state @ B @ D)) | ~ (! [E:pname]: ((member_pname @ E @ (D)) => ((A @ E) = (B @ E)))) | ~ ((C) = (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[720])). 123.96/29.67 thf(441,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),C:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ B @ C) => ((B @ A @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_folding__one__idem_Oidem)). 123.96/29.67 thf(2174,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),C:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1347568576_state @ (B) @ (C)) => ((B @ A @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])). 123.96/29.67 thf(476,axiom,((! [A:(com > hoare_1708887482_state),B:(hoare_1708887482_state > $o),C:(com > $o)]: ((! [D:com]: ((member451959335_state @ (A @ D) @ B) <= (member_com @ D @ C))) => (ord_le777019615tate_o @ (image_934102463_state @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_image__subsetI)). 123.96/29.67 thf(2283,plain,((! [A:(com > hoare_1708887482_state),B:(hoare_1708887482_state > $o),C:(com > $o)]: ((! [D:com]: ((member451959335_state @ (A @ D) @ (B)) | ~ (member_com @ D @ (C)))) => (ord_le777019615tate_o @ (image_934102463_state @ A @ C) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[476])). 123.96/29.67 thf(499,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (minus_2056855718tate_o @ B @ C)) => (~ (member451959335_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_DiffD2)). 123.96/29.67 thf(2389,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((member451959335_state @ A @ (minus_2056855718tate_o @ B @ C)) => (~ (member451959335_state @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])). 123.96/29.67 thf(209,axiom,((! [A:com,B:com]: ((wt @ B) => ((wt @ A) => (wt @ (semi @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_WT_OSemi)). 123.96/29.67 thf(1476,plain,((! [A:com,B:com]: ((wt @ B) => ((wt @ A) => (wt @ (semi @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 123.96/29.67 thf(427,axiom,((! [A:pname]: ((the_pname_1 @ (some_pname @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_the_Osimps)). 123.96/29.67 thf(2135,plain,((! [A:pname]: ((the_pname_1 @ (some_pname @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])). 123.96/29.67 thf(505,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => ((ord_le777019615tate_o @ A @ C) => (ord_le777019615tate_o @ (semila1122118281tate_o @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_sup__least)). 123.96/29.67 thf(2406,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => ((ord_le777019615tate_o @ (A) @ (C)) => (ord_le777019615tate_o @ (semila1122118281tate_o @ B @ A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])). 123.96/29.67 thf(72,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ B @ (semila1780557381name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_Un__left__commute)). 123.96/29.67 thf(1062,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ B @ (semila1780557381name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 123.96/29.67 thf(546,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((member451959335_state @ A @ B) & (C @ A)) = (member451959335_state @ A @ (semila129691299tate_o @ B @ (collec1568722789_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_Int__Collect)). 123.96/29.67 thf(2532,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((member451959335_state @ A @ (B)) & (C @ A)) = (member451959335_state @ A @ (semila129691299tate_o @ B @ (collec1568722789_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[546])). 123.96/29.67 thf(220,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((~ (member451959335_state @ B @ C)) => ((semila129691299tate_o @ (insert528405184_state @ B @ A) @ C) = (semila129691299tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_Int__insert__left__if0)). 123.96/29.67 thf(1508,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((~ (member451959335_state @ B @ (C))) => ((semila129691299tate_o @ (insert528405184_state @ B @ A) @ C) = (semila129691299tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 123.96/29.67 thf(571,axiom,((! [A:com,B:(com > option_com)]: ((? [C:com]: ((B @ A) = (some_com @ C))) <= (member_com @ A @ (dom_com_com @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_domD)). 123.96/29.67 thf(2608,plain,((! [A:com,B:(com > option_com)]: (? [C:com]: ((B @ A) = (some_com @ C)) | ~ (member_com @ A @ (dom_com_com @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[571])). 123.96/29.67 thf(512,axiom,((! [A:hoare_1708887482_state]: ((some_H1974565227_state @ A) != none_H1106584047_state))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1111_option_Osimps_I3_J)). 123.96/29.67 thf(2431,plain,((! [A:hoare_1708887482_state]: ~ ((some_H1974565227_state @ A) = none_H1106584047_state))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[512])). 123.96/29.67 thf(734,axiom,((! [A:(pname > hoare_1708887482_state)]: ((image_1116629049_state @ A @ bot_bot_pname_o) = bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_image__empty)). 123.96/29.67 thf(3136,plain,((! [A:(pname > hoare_1708887482_state)]: ((image_1116629049_state @ A @ bot_bot_pname_o) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[734])). 123.96/29.67 thf(804,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ (insert528405184_state @ B @ C)) = (insert528405184_state @ B @ (insert528405184_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_insert__commute)). 123.96/29.67 thf(3368,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((insert528405184_state @ A @ (insert528405184_state @ B @ C)) = (insert528405184_state @ B @ (insert528405184_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[804])). 123.96/29.67 thf(53,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: ((finite297249702name_o @ B) => ((finite297249702name_o @ A) <= (ord_le1205211808me_o_o @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_rev__finite__subset)). 123.96/29.67 thf(995,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: ((finite297249702name_o @ (B)) => ((finite297249702name_o @ (A)) | ~ (ord_le1205211808me_o_o @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 123.96/29.67 thf(238,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (^ [C:hoare_1708887482_state]: (member451959335_state @ C @ A)) @ (^ [C:hoare_1708887482_state]: (member451959335_state @ C @ B))) = (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_pred__subset__eq)). 123.96/29.67 thf(1558,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (^ [C:hoare_1708887482_state]: (member451959335_state @ C @ A)) @ (^ [C:hoare_1708887482_state]: (member451959335_state @ C @ B))) = (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 123.96/29.67 thf(674,axiom,((hoare_90032982_state @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ fa)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6)). 123.96/29.67 thf(2944,plain,((hoare_90032982_state @ (image_1116629049_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ (fa))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[674])). 123.96/29.67 thf(409,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ B @ (semila1780557381name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_sup__left__commute)). 123.96/29.67 thf(2081,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ B @ (semila1780557381name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[409])). 123.96/29.67 thf(149,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((ord_less_eq_pname_o @ A @ C) => (ord_less_eq_pname_o @ (semila1780557381name_o @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_sup__least)). 123.96/29.67 thf(1294,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => ((ord_less_eq_pname_o @ (A) @ (C)) => (ord_less_eq_pname_o @ (semila1780557381name_o @ B @ A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 123.96/29.67 thf(199,axiom,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ (insert_pname @ A @ C)) <= ((~ (member_pname @ B @ C)) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_insertCI)). 123.96/29.67 thf(1440,plain,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ (insert_pname @ A @ C)) | ~ ((~ (member_pname @ B @ (C))) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 123.96/29.67 thf(155,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ A @ (semila1780557381name_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_sup__ge1)). 123.96/29.67 thf(1308,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (A) @ (semila1780557381name_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 123.96/29.67 thf(560,axiom,((! [A:pname,B:(pname > $o)]: ((~ (member_pname @ A @ B)) => ((minus_minus_pname_o @ (insert_pname @ A @ B) @ (insert_pname @ A @ bot_bot_pname_o)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1033_Diff__insert__absorb)). 123.96/29.67 thf(2576,plain,((! [A:pname,B:(pname > $o)]: ((~ (member_pname @ A @ (B))) => ((minus_minus_pname_o @ (insert_pname @ A @ B) @ (insert_pname @ A @ bot_bot_pname_o)) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[560])). 123.96/29.67 thf(444,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((A = B) | ~ (fequal224822779_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com)). 123.96/29.67 thf(2183,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((A = B) | ~ (fequal224822779_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[444])). 123.96/29.67 thf(252,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((A = B) => (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_equalityD1)). 123.96/29.67 thf(1607,plain,((! [A:(pname > $o),B:(pname > $o)]: (((A) = (B)) => (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 123.96/29.67 thf(422,axiom,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_Un__absorb)). 123.96/29.67 thf(2120,plain,((! [A:(pname > $o)]: ((semila1780557381name_o @ A @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])). 123.96/29.67 thf(254,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (minus_2056855718tate_o @ A @ B) @ (semila129691299tate_o @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_Un__Diff__Int)). 123.96/29.67 thf(1614,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ (minus_2056855718tate_o @ A @ B) @ (semila129691299tate_o @ A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 123.96/29.67 thf(749,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: ((((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((B = C) & (A @ C)))) = bot_bo19817387tate_o) <= (~ (A @ B))) & ((A @ B) => ((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((B = C) & (A @ C)))) = (insert528405184_state @ B @ bot_bo19817387tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_Collect__conv__if2)). 123.96/29.67 thf(3181,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: ((((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((B = C) & (A @ C)))) = (bot_bo19817387tate_o)) | (A @ B)) & ((A @ B) => ((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((B = C) & (A @ C)))) = (insert528405184_state @ B @ bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[749])). 123.96/29.67 thf(526,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1673364395name_o @ A @ B) = (collect_pname @ (^ [C:pname]: ((member_pname @ C @ A) & (member_pname @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_848_Int__def)). 123.96/29.67 thf(2475,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1673364395name_o @ A @ B) = (collect_pname @ (^ [C:pname]: ((member_pname @ C @ A) & (member_pname @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[526])). 123.96/29.67 thf(663,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (semila1122118281tate_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_sup__commute)). 123.96/29.67 thf(2912,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ B) = (semila1122118281tate_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[663])). 123.96/29.67 thf(399,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((semila129691299tate_o @ (^ [D:hoare_1708887482_state]: (member451959335_state @ D @ A)) @ (^ [D:hoare_1708887482_state]: (member451959335_state @ D @ B)) @ C) = (member451959335_state @ C @ (semila129691299tate_o @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_822_inf__Int__eq)). 123.96/29.67 thf(2041,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((semila129691299tate_o @ (^ [D:hoare_1708887482_state]: (member451959335_state @ D @ A)) @ (^ [D:hoare_1708887482_state]: (member451959335_state @ D @ B)) @ C) = (member451959335_state @ C @ (semila129691299tate_o @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])). 123.96/29.67 thf(21,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((minus_minus_pname_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1673364395name_o @ (minus_minus_pname_o @ A @ B) @ (minus_minus_pname_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_Diff__Un)). 123.96/29.67 thf(899,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((minus_minus_pname_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1673364395name_o @ (minus_minus_pname_o @ A @ B) @ (minus_minus_pname_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 123.96/29.67 thf(271,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (collect_pname @ (^ [C:pname]: ((A @ C) | (B @ C))))) = ((finite_finite_pname @ (collect_pname @ A)) & (finite_finite_pname @ (collect_pname @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_finite__Collect__disjI)). 123.96/29.67 thf(1661,plain,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (collect_pname @ (^ [C:pname]: ((A @ C) | (B @ C))))) = ((finite_finite_pname @ (collect_pname @ A)) & (finite_finite_pname @ (collect_pname @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 123.96/29.67 thf(612,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila1122118281tate_o @ A @ (semila129691299tate_o @ B @ C)) @ (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1028_distrib__sup__le)). 123.96/29.67 thf(2739,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila1122118281tate_o @ A @ (semila129691299tate_o @ B @ C)) @ (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[612])). 123.96/29.67 thf(532,axiom,((! [A:option1624383643_state]: ((! [B:hoare_1708887482_state]: (A != (some_H1974565227_state @ B))) = (A = none_H1106584047_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1114_not__Some__eq)). 123.96/29.67 thf(2494,plain,((! [A:option1624383643_state]: ((! [B:hoare_1708887482_state]: ~ (A = (some_H1974565227_state @ B))) = (A = none_H1106584047_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[532])). 123.96/29.67 thf(665,axiom,((! [A:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ bot_bo19817387tate_o @ A) = bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_empty__Diff)). 123.96/29.67 thf(2917,plain,((! [A:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ bot_bo19817387tate_o @ A) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[665])). 123.96/29.67 thf(576,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (((C = A) => (ord_le777019615tate_o @ B @ A)) <= (ord_le777019615tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_ord__le__eq__trans)). 123.96/29.67 thf(2623,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((((C) = (A)) => (ord_le777019615tate_o @ (B) @ (A))) | ~ (ord_le777019615tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[576])). 123.96/29.67 thf(430,axiom,((! [A:pname,B:(pname > $o)]: (member_pname @ A @ (insert_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_insertI1)). 123.96/29.67 thf(2142,plain,((! [A:pname,B:(pname > $o)]: (member_pname @ A @ (insert_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])). 123.96/29.67 thf(168,axiom,((! [A:(pname > $o),B:(pname > option_com),C:(pname > option_com)]: ((dom_pname_com @ (^ [D:pname]: (if_option_com @ (A @ D) @ (B @ D) @ (C @ D)))) = (semila1780557381name_o @ (semila1673364395name_o @ (dom_pname_com @ B) @ (collect_pname @ A)) @ (semila1673364395name_o @ (dom_pname_com @ C) @ (collect_pname @ (^ [D:pname]: ~ (A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_dom__if)). 123.96/29.67 thf(1348,plain,((! [A:(pname > $o),B:(pname > option_com),C:(pname > option_com)]: ((dom_pname_com @ (^ [D:pname]: (if_option_com @ (A @ D) @ (B @ D) @ (C @ D)))) = (semila1780557381name_o @ (semila1673364395name_o @ (dom_pname_com @ B) @ (collect_pname @ A)) @ (semila1673364395name_o @ (dom_pname_com @ C) @ (collect_pname @ (^ [D:pname]: ~ (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 123.96/29.67 thf(55,axiom,((! [A:((hoare_1708887482_state > $o) > pname),B:((hoare_1708887482_state > $o) > $o),C:(pname > $o)]: ((finite_finite_pname @ C) => ((? [D:((hoare_1708887482_state > $o) > $o)]: ((ord_le1728773982te_o_o @ D @ B) & (finite1329924456tate_o @ D) & (C = (image_2051418740_pname @ A @ D)))) <= (ord_less_eq_pname_o @ C @ (image_2051418740_pname @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_finite__subset__image)). 123.96/29.67 thf(999,plain,((! [A:((hoare_1708887482_state > $o) > pname),B:((hoare_1708887482_state > $o) > $o),C:(pname > $o)]: ((finite_finite_pname @ (C)) => (? [D:((hoare_1708887482_state > $o) > $o)]: ((ord_le1728773982te_o_o @ (D) @ (B)) & (finite1329924456tate_o @ (D)) & ((C) = (image_2051418740_pname @ (A) @ (D)))) | ~ (ord_less_eq_pname_o @ (C) @ (image_2051418740_pname @ (A) @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 123.96/29.67 thf(541,axiom,((! [A:pname,B:(pname > $o),C:pname]: (((B @ C) | (A = C)) = (insert_pname @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_insert__code)). 123.96/29.67 thf(2517,plain,((! [A:pname,B:(pname > $o),C:pname]: (((B @ C) | (A = C)) = (insert_pname @ A @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[541])). 123.96/29.67 thf(291,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1615457021_state @ C @ D) => (((B != bot_bo19817387tate_o) => ((finite1625599783_state @ A) => ((A != bot_bo19817387tate_o) => (((semila129691299tate_o @ B @ A) = bot_bo19817387tate_o) => ((D @ (semila1122118281tate_o @ B @ A)) = (C @ (D @ B) @ (D @ A))))))) <= (finite1625599783_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_784_folding__one_Ounion__disjoint)). 123.96/29.67 thf(1725,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((finite1615457021_state @ (C) @ (D)) => (((~ ((B) = (bot_bo19817387tate_o))) => ((finite1625599783_state @ (A)) => ((~ ((A) = (bot_bo19817387tate_o))) => (((semila129691299tate_o @ B @ A) = (bot_bo19817387tate_o)) => ((D @ (semila1122118281tate_o @ B @ A)) = (C @ (D @ (B)) @ (D @ (A)))))))) | ~ (finite1625599783_state @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 123.96/29.67 thf(373,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_sup_Oassoc)). 123.96/29.67 thf(1957,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1780557381name_o @ (semila1780557381name_o @ A @ B) @ C) = (semila1780557381name_o @ A @ (semila1780557381name_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[373])). 123.96/29.67 thf(498,axiom,((! [A:(com > $o),B:pname,C:(com > pname),D:com]: (((member_com @ D @ A) => (member_pname @ B @ (image_com_pname @ C @ A))) <= (B = (C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_image__eqI)). 123.96/29.67 thf(2385,plain,((! [A:(com > $o),B:pname,C:(com > pname),D:com]: (((member_com @ D @ (A)) => (member_pname @ B @ (image_com_pname @ C @ A))) | ~ (B = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])). 123.96/29.67 thf(466,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => ((ord_less_eq_pname_o @ C @ A) => (member_pname @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_set__rev__mp)). 123.96/29.67 thf(2255,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => ((ord_less_eq_pname_o @ (C) @ (A)) => (member_pname @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[466])). 123.96/29.67 thf(604,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (minus_2056855718tate_o @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_973_Diff__subset)). 123.96/29.67 thf(2719,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (minus_2056855718tate_o @ A @ B) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[604])). 123.96/29.67 thf(3464,plain,(((collec1568722789_state @ (^ [A:hoare_1708887482_state]: (($false)))) = (bot_bo19817387tate_o))),inference(lifteq,[status(thm)],[3463])). 123.96/29.67 thf(677,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((hoare_90032982_state @ A @ C) & (hoare_90032982_state @ A @ (insert528405184_state @ B @ bot_bo19817387tate_o))) <= (hoare_90032982_state @ A @ (insert528405184_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_derivs__insertD)). 123.96/29.67 thf(2951,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((hoare_90032982_state @ (A) @ (C)) & (hoare_90032982_state @ (A) @ (insert528405184_state @ B @ bot_bo19817387tate_o))) | ~ (hoare_90032982_state @ (A) @ (insert528405184_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[677])). 123.96/29.67 thf(345,axiom,((! [A:(pname > $o),B:(pname > option_com),C:pname]: (((B @ C) = none_com) => ((minus_minus_pname_o @ (dom_pname_com @ B) @ (insert_pname @ C @ A)) = (minus_minus_pname_o @ (dom_pname_com @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_dom__minus)). 123.96/29.67 thf(1876,plain,((! [A:(pname > $o),B:(pname > option_com),C:pname]: (((B @ C) = none_com) => ((minus_minus_pname_o @ (dom_pname_com @ B) @ (insert_pname @ C @ A)) = (minus_minus_pname_o @ (dom_pname_com @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])). 123.96/29.67 thf(713,axiom,((! [A:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ A) = bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_942_Diff__cancel)). 123.96/29.67 thf(3062,plain,((! [A:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ A) = (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[713])). 123.96/29.67 thf(423,axiom,((! [A:(hoare_1708887482_state > pname),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((insert_pname @ (A @ B) @ (image_1509414295_pname @ A @ C)) = (image_1509414295_pname @ A @ C)) <= (member451959335_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_insert__image)). 123.96/29.67 thf(2123,plain,((! [A:(hoare_1708887482_state > pname),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((insert_pname @ (A @ B) @ (image_1509414295_pname @ A @ C)) = (image_1509414295_pname @ A @ C)) | ~ (member451959335_state @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[423])). 123.96/29.67 thf(95,axiom,((! [A:hoare_1708887482_state]: ~ (! [B:(state > (state > $o)),C:com,D:(state > (state > $o))]: (A != (hoare_858012674_state @ B @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_triple_Oexhaust)). 123.96/29.67 thf(1133,plain,((! [A:hoare_1708887482_state]: ~ (! [B:(state > (state > $o)),C:com,D:(state > (state > $o))]: ~ (A = (hoare_858012674_state @ (B) @ C @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 123.96/29.67 thf(83,axiom,((! [A:com,B:com]: ((wt @ (semi @ A @ B)) => (~ ((wt @ A) => (~ (wt @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_WTs__elim__cases_I4_J)). 123.96/29.67 thf(1097,plain,((! [A:com,B:com]: ((wt @ (semi @ A @ B)) => (~ ((wt @ A) => (~ (wt @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 123.96/29.67 thf(129,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((member451959335_state @ C @ A) & ~ (member451959335_state @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_set__diff__eq)). 123.96/29.67 thf(1229,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ B) = (collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((member451959335_state @ C @ A) & ~ (member451959335_state @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 123.96/29.67 thf(459,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ A @ B)) = (semila1780557381name_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Un__left__absorb)). 123.96/29.67 thf(2233,plain,((! [A:(pname > $o),B:(pname > $o)]: ((semila1780557381name_o @ A @ (semila1780557381name_o @ A @ B)) = (semila1780557381name_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[459])). 123.96/29.67 thf(543,axiom,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((finite_finite_pname @ B) => ((B != bot_bot_pname_o) => ((D @ (insert_pname @ A @ B)) = (C @ A @ (D @ B))))) <= (finite89670078_pname @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_folding__one__idem_Oinsert__idem)). 123.96/29.67 thf(2522,plain,((! [A:pname,B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((finite_finite_pname @ (B)) => ((~ ((B) = (bot_bot_pname_o))) => ((D @ (insert_pname @ A @ B)) = (C @ A @ (D @ (B)))))) | ~ (finite89670078_pname @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[543])). 123.96/29.67 thf(724,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: (((~ (A @ B)) => ((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((C = B) & (A @ C)))) = bot_bo19817387tate_o)) & (((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((C = B) & (A @ C)))) = (insert528405184_state @ B @ bot_bo19817387tate_o)) <= (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_Collect__conv__if)). 123.96/29.67 thf(3100,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: (((~ (A @ B)) => ((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((C = B) & (A @ C)))) = (bot_bo19817387tate_o))) & (((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((C = B) & (A @ C)))) = (insert528405184_state @ B @ bot_bo19817387tate_o)) | ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[724])). 123.96/29.67 thf(637,axiom,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: ((A != B) | (fequal224822779_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com)). 123.96/29.67 thf(2815,plain,((! [A:hoare_1708887482_state,B:hoare_1708887482_state]: (~ (A = B) | (fequal224822779_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[637])). 123.96/29.67 thf(153,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((~ ((ord_le777019615tate_o @ A @ C) => (~ (ord_le777019615tate_o @ B @ C)))) <= (ord_le777019615tate_o @ (semila1122118281tate_o @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_le__supE)). 123.96/29.67 thf(1303,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: (~ ((ord_le777019615tate_o @ (A) @ (C)) => (~ (ord_le777019615tate_o @ (B) @ (C)))) | ~ (ord_le777019615tate_o @ (semila1122118281tate_o @ A @ B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 123.96/29.67 thf(101,axiom,((! [A:(com > pname),B:(pname > $o),C:(com > $o)]: ((! [D:com]: ((member_pname @ (A @ D) @ B) <= (member_com @ D @ C))) => (ord_less_eq_pname_o @ (image_com_pname @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_image__subsetI)). 123.96/29.67 thf(1148,plain,((! [A:(com > pname),B:(pname > $o),C:(com > $o)]: ((! [D:com]: ((member_pname @ (A @ D) @ (B)) | ~ (member_com @ D @ (C)))) => (ord_less_eq_pname_o @ (image_com_pname @ A @ C) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 123.96/29.67 thf(276,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((finite_finite_pname @ B) => (((ord_less_eq_pname_o @ A @ B) => ((C @ (D @ A) @ (D @ B)) = (D @ B))) <= (A != bot_bot_pname_o))) <= (finite89670078_pname @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_folding__one__idem_Osubset__idem)). 123.96/29.67 thf(1673,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > pname)),D:((pname > $o) > pname)]: (((finite_finite_pname @ (B)) => (((ord_less_eq_pname_o @ (A) @ (B)) => ((C @ (D @ (A)) @ (D @ (B))) = (D @ (B)))) | ((A) = (bot_bot_pname_o)))) | ~ (finite89670078_pname @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 123.96/29.67 thf(788,axiom,((! [A:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ bot_bo19817387tate_o @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_empty__subsetI)). 123.96/29.67 thf(3309,plain,((! [A:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (bot_bo19817387tate_o) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[788])). 123.96/29.67 thf(239,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (semila1780557381name_o @ B @ C)) = ((member_pname @ A @ C) | (member_pname @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_Un__iff)). 123.96/29.67 thf(1561,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (semila1780557381name_o @ B @ C)) = ((member_pname @ A @ (C)) | (member_pname @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 123.96/29.67 thf(208,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ A @ B) => ((semila1673364395name_o @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1007_Int__absorb2)). 123.96/29.67 thf(1473,plain,((! [A:(pname > $o),B:(pname > $o)]: ((ord_less_eq_pname_o @ (A) @ (B)) => ((semila1673364395name_o @ A @ B) = (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 123.96/29.67 thf(73,axiom,((! [A:(pname > $o),B:(pname > hoare_1708887482_state),C:(pname > hoare_1708887482_state),D:(pname > $o)]: ((image_1116629049_state @ (^ [E:pname]: (if_Hoa1374726218_state @ (A @ E) @ (B @ E) @ (C @ E))) @ D) = (semila1122118281tate_o @ (image_1116629049_state @ B @ (semila1673364395name_o @ D @ (collect_pname @ A))) @ (image_1116629049_state @ C @ (semila1673364395name_o @ D @ (collect_pname @ (^ [E:pname]: ~ (A @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1057_if__image__distrib)). 123.96/29.67 thf(1065,plain,((! [A:(pname > $o),B:(pname > hoare_1708887482_state),C:(pname > hoare_1708887482_state),D:(pname > $o)]: ((image_1116629049_state @ (^ [E:pname]: (if_Hoa1374726218_state @ (A @ E) @ (B @ E) @ (C @ E))) @ D) = (semila1122118281tate_o @ (image_1116629049_state @ B @ (semila1673364395name_o @ D @ (collect_pname @ A))) @ (image_1116629049_state @ C @ (semila1673364395name_o @ D @ (collect_pname @ (^ [E:pname]: ~ (A @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 123.96/29.67 thf(585,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ B @ A) => (B = A)) <= (ord_le777019615tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_xt1_I5_J)). 123.96/29.67 thf(2651,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((ord_le777019615tate_o @ (B) @ (A)) => ((B) = (A))) | ~ (ord_le777019615tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[585])). 123.96/29.67 thf(445,axiom,((! [A:((pname > $o) > $o),B:(pname > $o)]: (((((! [C:pname,D:(pname > $o)]: ((((~ (member_pname @ C @ D)) => ((A @ (insert_pname @ C @ D)) <= (A @ D))) <= (D != bot_bot_pname_o)) <= (finite_finite_pname @ D))) => (A @ B)) <= (! [C:pname]: (A @ (insert_pname @ C @ bot_bot_pname_o)))) <= (B != bot_bot_pname_o)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_finite__ne__induct)). 123.96/29.67 thf(2186,plain,((! [A:((pname > $o) > $o),B:(pname > $o)]: (((! [C:pname,D:(pname > $o)]: (((~ (member_pname @ C @ (D))) => ((A @ (insert_pname @ C @ D)) | ~ (A @ (D)))) | ((D) = (bot_bot_pname_o)) | ~ (finite_finite_pname @ (D)))) => (A @ (B))) | ~ (! [C:pname]: (A @ (insert_pname @ C @ bot_bot_pname_o))) | ((B) = (bot_bot_pname_o)) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[445])). 123.96/29.67 thf(778,axiom,((! [A:(pname > option_com)]: ((dom_pname_com @ A) = (collect_pname @ (^ [B:pname]: ~ ((A @ B) = none_com)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1118_dom__def)). 123.96/29.67 thf(3277,plain,((! [A:(pname > option_com)]: ((dom_pname_com @ A) = (collect_pname @ (^ [B:pname]: ~ ((A @ B) = none_com)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[778])). 123.96/29.67 thf(61,axiom,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: ((ord_le1728773982te_o_o @ (collec219771562tate_o @ B) @ (collec219771562tate_o @ A)) <= (! [C:(hoare_1708887482_state > $o)]: ((B @ C) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_Collect__mono)). 123.96/29.67 thf(1033,plain,((! [A:((hoare_1708887482_state > $o) > $o),B:((hoare_1708887482_state > $o) > $o)]: ((ord_le1728773982te_o_o @ (collec219771562tate_o @ B) @ (collec219771562tate_o @ A)) | ~ (! [C:(hoare_1708887482_state > $o)]: ((B @ (C)) => (A @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 123.96/29.67 thf(681,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: (ord_le777019615tate_o @ A @ (insert528405184_state @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_subset__insertI)). 123.96/29.67 thf(2961,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state]: (ord_le777019615tate_o @ (A) @ (insert528405184_state @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[681])). 123.96/29.67 thf(147,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila129691299tate_o @ B @ C)) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1020_Un__Int__distrib)). 123.96/29.67 thf(1288,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila129691299tate_o @ B @ C)) = (semila129691299tate_o @ (semila1122118281tate_o @ A @ B) @ (semila1122118281tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 123.96/29.67 thf(602,axiom,((! [A:com,B:state,C:com,D:state,E:state]: (((evalc @ A @ E @ B) => (evalc @ (semi @ C @ A) @ D @ B)) <= (evalc @ C @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_evalc_OSemi)). 123.96/29.67 thf(2714,plain,((! [A:com,B:state,C:com,D:state,E:state]: (((evalc @ A @ E @ B) => (evalc @ (semi @ C @ A) @ D @ B)) | ~ (evalc @ C @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[602])). 123.96/29.67 thf(754,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ bot_bo19817387tate_o @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_sup__bot__left)). 123.96/29.67 thf(3196,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ bot_bo19817387tate_o @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[754])). 123.96/29.67 thf(489,axiom,((! [A:((pname > $o) > $o),B:(pname > $o)]: ((finite_finite_pname @ B) => ((A @ B) => ((A @ bot_bot_pname_o) <= (! [C:pname,D:(pname > $o)]: ((finite_finite_pname @ D) => ((member_pname @ C @ D) => ((A @ (minus_minus_pname_o @ D @ (insert_pname @ C @ bot_bot_pname_o))) <= (A @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_finite__empty__induct)). 123.96/29.67 thf(2340,plain,((! [A:((pname > $o) > $o),B:(pname > $o)]: ((finite_finite_pname @ (B)) => ((A @ (B)) => ((A @ (bot_bot_pname_o)) | ~ (! [C:pname,D:(pname > $o)]: ((finite_finite_pname @ (D)) => ((member_pname @ C @ (D)) => ((A @ (minus_minus_pname_o @ D @ (insert_pname @ C @ bot_bot_pname_o))) | ~ (A @ (D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[489])). 123.96/29.67 thf(108,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ (semila129691299tate_o @ B @ C)) = (semila1122118281tate_o @ (minus_2056855718tate_o @ A @ B) @ (minus_2056855718tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_867_Diff__Int)). 123.96/29.67 thf(1165,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((minus_2056855718tate_o @ A @ (semila129691299tate_o @ B @ C)) = (semila1122118281tate_o @ (minus_2056855718tate_o @ A @ B) @ (minus_2056855718tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 123.96/29.67 thf(17,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((minus_minus_pname_o @ A @ B) = A) <= ((semila1673364395name_o @ A @ B) = bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_Diff__triv)). 123.96/29.67 thf(886,plain,((! [A:(pname > $o),B:(pname > $o)]: (((minus_minus_pname_o @ A @ B) = (A)) | ~ ((semila1673364395name_o @ A @ B) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 123.96/29.67 thf(552,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((~ (member451959335_state @ B @ C)) => ((minus_2056855718tate_o @ (insert528405184_state @ B @ A) @ C) = (insert528405184_state @ B @ (minus_2056855718tate_o @ A @ C)))) & ((member451959335_state @ B @ C) => ((minus_2056855718tate_o @ (insert528405184_state @ B @ A) @ C) = (minus_2056855718tate_o @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_958_insert__Diff__if)). 123.96/29.67 thf(2549,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((~ (member451959335_state @ B @ (C))) => ((minus_2056855718tate_o @ (insert528405184_state @ B @ A) @ C) = (insert528405184_state @ B @ (minus_2056855718tate_o @ A @ C)))) & ((member451959335_state @ B @ (C)) => ((minus_2056855718tate_o @ (insert528405184_state @ B @ A) @ C) = (minus_2056855718tate_o @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[552])). 123.96/29.67 thf(765,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ B) = bot_bo19817387tate_o) = ((B = bot_bo19817387tate_o) & (A = bot_bo19817387tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_Un__empty)). 123.96/29.67 thf(3244,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (((semila1122118281tate_o @ A @ B) = (bot_bo19817387tate_o)) = (((B) = (bot_bo19817387tate_o)) & ((A) = (bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[765])). 123.96/29.67 thf(380,axiom,((! [A:(pname > $o),B:pname]: ((ord_less_eq_pname_o @ A @ (insert_pname @ B @ bot_bot_pname_o)) => ((A = bot_bot_pname_o) | (A = (insert_pname @ B @ bot_bot_pname_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_subset__singletonD)). 123.96/29.67 thf(1977,plain,((! [A:(pname > $o),B:pname]: ((ord_less_eq_pname_o @ (A) @ (insert_pname @ B @ bot_bot_pname_o)) => (((A) = (bot_bot_pname_o)) | ((A) = (insert_pname @ B @ bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])). 123.96/29.67 thf(327,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > hoare_1708887482_state),D:(pname > $o)]: ((inj_on1553129421_state @ C @ D) => (((ord_less_eq_pname_o @ A @ D) => ((image_1116629049_state @ C @ (minus_minus_pname_o @ B @ A)) = (minus_2056855718tate_o @ (image_1116629049_state @ C @ B) @ (image_1116629049_state @ C @ A)))) <= (ord_less_eq_pname_o @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_inj__on__image__set__diff)). 123.96/29.67 thf(1827,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > hoare_1708887482_state),D:(pname > $o)]: ((inj_on1553129421_state @ (C) @ (D)) => (((ord_less_eq_pname_o @ (A) @ (D)) => ((image_1116629049_state @ C @ (minus_minus_pname_o @ B @ A)) = (minus_2056855718tate_o @ (image_1116629049_state @ C @ B) @ (image_1116629049_state @ C @ A)))) | ~ (ord_less_eq_pname_o @ (B) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 123.96/29.67 thf(9,axiom,((! [A:(pname > $o)]: ((minus_minus_pname_o @ bot_bot_pname_o @ A) = bot_bot_pname_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_empty__Diff)). 123.96/29.67 thf(860,plain,((! [A:(pname > $o)]: ((minus_minus_pname_o @ bot_bot_pname_o @ A) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 123.96/29.67 thf(568,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((? [D:pname]: ((member_pname @ D @ (semila1780557381name_o @ B @ C)) & (A @ D))) = (? [D:pname]: ((member_pname @ D @ B) & (A @ D)) | ? [D:pname]: ((member_pname @ D @ C) & (A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_bex__Un)). 123.96/29.67 thf(2600,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((? [D:pname]: ((member_pname @ D @ (semila1780557381name_o @ B @ C)) & (A @ D))) = (? [D:pname]: ((member_pname @ D @ (B)) & (A @ D)) | ? [D:pname]: ((member_pname @ D @ (C)) & (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[568])). 123.96/29.67 thf(801,axiom,((! [A:(hoare_1708887482_state > $o)]: ((! [B:hoare_1708887482_state]: ~ (A @ B)) = (bot_bo19817387tate_o = (collec1568722789_state @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_empty__Collect__eq)). 123.96/29.67 thf(3360,plain,((! [A:(hoare_1708887482_state > $o)]: ((! [B:hoare_1708887482_state]: ~ (A @ B)) = ((bot_bo19817387tate_o) = (collec1568722789_state @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[801])). 123.96/29.67 thf(246,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: ((((member451959335_state @ A @ B) => ((((minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)) != bot_bo19817387tate_o) => ((D @ B) = (C @ A @ (D @ (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)))))) & (((minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = bot_bo19817387tate_o) => ((D @ B) = A)))) <= (finite1625599783_state @ B)) <= (finite1615457021_state @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_folding__one_Oremove)). 123.96/29.67 thf(1582,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > (hoare_1708887482_state > hoare_1708887482_state)),D:((hoare_1708887482_state > $o) > hoare_1708887482_state)]: (((member451959335_state @ A @ (B)) => (((~ ((minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = (bot_bo19817387tate_o))) => ((D @ (B)) = (C @ A @ (D @ (minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)))))) & (((minus_2056855718tate_o @ B @ (insert528405184_state @ A @ bot_bo19817387tate_o)) = (bot_bo19817387tate_o)) => ((D @ (B)) = A)))) | ~ (finite1625599783_state @ (B)) | ~ (finite1615457021_state @ (C) @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 123.96/29.67 thf(771,axiom,((! [A:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ A) = ((A = bot_bo19817387tate_o) | ? [B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((finite1625599783_state @ B) & (A = (insert528405184_state @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_finite_Osimps)). 123.96/29.67 thf(3259,plain,((! [A:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (A)) = (((A) = (bot_bo19817387tate_o)) | ? [B:(hoare_1708887482_state > $o),C:hoare_1708887482_state]: ((finite1625599783_state @ (B)) & ((A) = (insert528405184_state @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[771])). 123.96/29.67 thf(360,axiom,((! [A:option_com]: ((? [B:com]: (A = (some_com @ B))) = (A != none_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_not__None__eq)). 123.96/29.67 thf(1923,plain,((! [A:option_com]: ((? [B:com]: (A = (some_com @ B))) = (~ (A = none_com))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])). 123.96/29.67 thf(288,axiom,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((~ (member451959335_state @ B @ C)) => ((semila129691299tate_o @ (insert528405184_state @ B @ A) @ C) = (semila129691299tate_o @ A @ C))) & (((semila129691299tate_o @ (insert528405184_state @ B @ A) @ C) = (insert528405184_state @ B @ (semila129691299tate_o @ A @ C))) <= (member451959335_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_997_Int__insert__left)). 123.96/29.67 thf(1713,plain,((! [A:(hoare_1708887482_state > $o),B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((~ (member451959335_state @ B @ (C))) => ((semila129691299tate_o @ (insert528405184_state @ B @ A) @ C) = (semila129691299tate_o @ A @ C))) & (((semila129691299tate_o @ (insert528405184_state @ B @ A) @ C) = (insert528405184_state @ B @ (semila129691299tate_o @ A @ C))) | ~ (member451959335_state @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 123.96/29.67 thf(151,axiom,(wT_bodies),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)). 123.96/29.67 thf(1299,plain,(wT_bodies),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 123.96/29.67 thf(12,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (minus_minus_pname_o @ B @ C)) => (member_pname @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839_DiffD1)). 123.96/29.67 thf(871,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (minus_minus_pname_o @ B @ C)) => (member_pname @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 123.96/29.67 thf(428,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: (((ord_less_eq_pname_o @ B @ A) <= (ord_less_eq_pname_o @ C @ A)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_order__trans)). 123.96/29.67 thf(2138,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (A)) | ~ (ord_less_eq_pname_o @ (C) @ (A)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])). 123.96/29.67 thf(839,plain,(! [C:(pname > $o),B:(pname > $o),A:(pname > pname)] : ((finite_finite_pname @ (sk1 @ C @ B @ A)) | (~ (ord_less_eq_pname_o @ (C) @ (image_pname_pname @ A @ B))) | (~ (finite_finite_pname @ (C))))),inference(cnf,[status(esa)],[836])). 123.96/29.67 thf(635,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((A @ C) & (B @ C)))) = (semila129691299tate_o @ (collec1568722789_state @ A) @ (collec1568722789_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_Collect__conj__eq)). 123.96/29.67 thf(2810,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((collec1568722789_state @ (^ [C:hoare_1708887482_state]: ((A @ C) & (B @ C)))) = (semila129691299tate_o @ (collec1568722789_state @ A) @ (collec1568722789_state @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[635])). 123.96/29.67 thf(609,axiom,((! [A:com]: ((member_com @ A @ bot_bot_com_o) = (bot_bot_com_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_bot__empty__eq)). 123.96/29.67 thf(2731,plain,((! [A:com]: ((member_com @ A @ (bot_bot_com_o)) = (bot_bot_com_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[609])). 123.96/29.67 thf(250,axiom,((! [A:((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o)),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ C @ D) => (((A @ C) = B) => ((! [E:(hoare_1708887482_state > $o),F:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A @ F) @ (A @ E)) <= (ord_le777019615tate_o @ F @ E))) => (ord_le777019615tate_o @ B @ (A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_xt1_I16_J)). 123.96/29.67 thf(1597,plain,((! [A:((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o)),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o),D:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (C) @ (D)) => (((A @ C) = (B)) => ((! [E:(hoare_1708887482_state > $o),F:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A @ F) @ (A @ E)) | ~ (ord_le777019615tate_o @ (F) @ (E)))) => (ord_le777019615tate_o @ (B) @ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 123.96/29.67 thf(649,axiom,((! [A:pname,B:(hoare_1708887482_state > $o)]: ((((image_1509414295_pname @ (^ [C:hoare_1708887482_state]: (A)) @ B) = (insert_pname @ A @ bot_bot_pname_o)) <= (B != bot_bo19817387tate_o)) & ((B = bot_bo19817387tate_o) => ((image_1509414295_pname @ (^ [C:hoare_1708887482_state]: (A)) @ B) = bot_bot_pname_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_image__constant__conv)). 123.96/29.67 thf(2864,plain,((! [A:pname,B:(hoare_1708887482_state > $o)]: ((((image_1509414295_pname @ (^ [C:hoare_1708887482_state]: (A)) @ B) = (insert_pname @ A @ bot_bot_pname_o)) | ((B) = (bot_bo19817387tate_o))) & (((B) = (bot_bo19817387tate_o)) => ((image_1509414295_pname @ (^ [C:hoare_1708887482_state]: (A)) @ B) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[649])). 123.96/29.67 thf(49,axiom,((! [A:pname,B:(pname > (pname > pname)),C:((pname > $o) > pname)]: ((finite1282449217_pname @ B @ C) => ((C @ (insert_pname @ A @ bot_bot_pname_o)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_folding__one_Osingleton)). 123.96/29.67 thf(982,plain,((! [A:pname,B:(pname > (pname > pname)),C:((pname > $o) > pname)]: ((finite1282449217_pname @ (B) @ (C)) => ((C @ (insert_pname @ A @ bot_bot_pname_o)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 123.96/29.67 thf(196,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_Int__lower1)). 123.96/29.67 thf(1431,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (semila129691299tate_o @ A @ B) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 123.96/29.67 thf(56,axiom,((! [A:option_com,B:option_com]: ((if_option_com @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T)). 123.96/29.67 thf(1004,plain,((! [A:option_com,B:option_com]: ((if_option_com @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 123.96/29.67 thf(727,axiom,((! [A:(hoare_1708887482_state > $o),B:(state > (state > $o))]: (hoare_90032982_state @ A @ (insert528405184_state @ (hoare_858012674_state @ B @ skip @ B) @ bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_hoare__derivs_OSkip)). 123.96/29.67 thf(3113,plain,((! [A:(hoare_1708887482_state > $o),B:(state > (state > $o))]: (hoare_90032982_state @ (A) @ (insert528405184_state @ (hoare_858012674_state @ B @ skip @ B) @ bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[727])). 123.96/29.67 thf(354,axiom,((! [A:com,B:com,C:(state > $o),D:com]: ((semi @ A @ B) != (while @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_com_Osimps_I46_J)). 123.96/29.67 thf(1902,plain,((! [A:com,B:com,C:(state > $o),D:com]: ~ ((semi @ A @ B) = (while @ (C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 123.96/29.67 thf(219,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((collect_pname @ (^ [C:pname]: ((A @ C) & (B @ C)))) = (semila1673364395name_o @ (collect_pname @ A) @ (collect_pname @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_Collect__conj__eq)). 123.96/29.67 thf(1505,plain,((! [A:(pname > $o),B:(pname > $o)]: ((collect_pname @ (^ [C:pname]: ((A @ C) & (B @ C)))) = (semila1673364395name_o @ (collect_pname @ A) @ (collect_pname @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 123.96/29.67 thf(471,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_929_inf__sup__distrib1)). 123.96/29.67 thf(2270,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[471])). 123.96/29.67 thf(697,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (insert528405184_state @ A @ B)) = (finite1625599783_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_finite__insert)). 123.96/29.67 thf(3013,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (insert528405184_state @ A @ B)) = (finite1625599783_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[697])). 123.96/29.67 thf(833,axiom,((! [A:pname]: ((wt @ (body_1 @ A)) => (~ (! [B:com]: ((body @ A) != (some_com @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_WTs__elim__cases_I7_J)). 123.96/29.67 thf(3474,plain,((! [A:pname]: ((wt @ (body_1 @ A)) => (~ (! [B:com]: ~ ((body @ A) = (some_com @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[833])). 123.96/29.67 thf(821,axiom,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => (ord_le777019615tate_o @ (insert528405184_state @ A @ B) @ (insert528405184_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_insert__mono)). 123.96/29.67 thf(3437,plain,((! [A:hoare_1708887482_state,B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => (ord_le777019615tate_o @ (insert528405184_state @ A @ B) @ (insert528405184_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[821])). 123.96/29.67 thf(296,axiom,((! [A:com,B:com,C:com,D:com]: (((B = D) & (A = C)) = ((semi @ A @ B) = (semi @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_com_Osimps_I3_J)). 123.96/29.67 thf(1737,plain,((! [A:com,B:com,C:com,D:com]: (((B = D) & (A = C)) = ((semi @ A @ B) = (semi @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 123.96/29.67 thf(642,axiom,((! [A:(pname > $o),B:(hoare_1708887482_state > pname),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ C) => ((finite_finite_pname @ A) <= (ord_less_eq_pname_o @ A @ (image_1509414295_pname @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_finite__surj)). 123.96/29.67 thf(2832,plain,((! [A:(pname > $o),B:(hoare_1708887482_state > pname),C:(hoare_1708887482_state > $o)]: ((finite1625599783_state @ (C)) => ((finite_finite_pname @ (A)) | ~ (ord_less_eq_pname_o @ (A) @ (image_1509414295_pname @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[642])). 123.96/29.67 thf(190,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ B @ C) => ((ord_le777019615tate_o @ A @ C) => (ord_le777019615tate_o @ (semila1122118281tate_o @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_Un__least)). 123.96/29.67 thf(1416,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (B) @ (C)) => ((ord_le777019615tate_o @ (A) @ (C)) => (ord_le777019615tate_o @ (semila1122118281tate_o @ B @ A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 123.96/29.67 thf(519,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1022_Int__Un__distrib)). 123.96/29.67 thf(2453,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o),C:(hoare_1708887482_state > $o)]: ((semila129691299tate_o @ A @ (semila1122118281tate_o @ B @ C)) = (semila1122118281tate_o @ (semila129691299tate_o @ A @ B) @ (semila129691299tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])). 123.96/29.67 thf(691,axiom,((! [A:hoare_1708887482_state]: ((collec1568722789_state @ (fequal224822779_state @ A)) = (insert528405184_state @ A @ bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_singleton__conv2)). 123.96/29.67 thf(2993,plain,((! [A:hoare_1708887482_state]: ((collec1568722789_state @ (fequal224822779_state @ A)) = (insert528405184_state @ A @ bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[691])). 123.96/29.67 thf(524,axiom,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o)]: ((bot_bot_pname_o = (image_1509414295_pname @ A @ B)) = (B = bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_empty__is__image)). 123.96/29.67 thf(2470,plain,((! [A:(hoare_1708887482_state > pname),B:(hoare_1708887482_state > $o)]: (((bot_bot_pname_o) = (image_1509414295_pname @ A @ B)) = ((B) = (bot_bo19817387tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[524])). 123.96/29.67 thf(687,axiom,((! [A:(hoare_1708887482_state > $o)]: (hoare_90032982_state @ A @ bot_bo19817387tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty)). 123.96/29.67 thf(2980,plain,((! [A:(hoare_1708887482_state > $o)]: (hoare_90032982_state @ (A) @ (bot_bo19817387tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[687])). 123.96/29.67 thf(592,axiom,((! [A:pname,B:pname]: ((A = B) = (member_pname @ A @ (insert_pname @ B @ bot_bot_pname_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_singleton__iff)). 123.96/29.67 thf(2672,plain,((! [A:pname,B:pname]: ((A = B) = (member_pname @ A @ (insert_pname @ B @ bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[592])). 123.96/29.67 thf(653,axiom,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ A @ (semila1780557381name_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_sup__ge2)). 123.96/29.67 thf(2879,plain,((! [A:(pname > $o),B:(pname > $o)]: (ord_less_eq_pname_o @ (A) @ (semila1780557381name_o @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[653])). 123.96/29.67 thf(581,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ A @ B) => ((A = B) <= (ord_le777019615tate_o @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_equalityI)). 123.96/29.67 thf(2640,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((ord_le777019615tate_o @ (A) @ (B)) => (((A) = (B)) | ~ (ord_le777019615tate_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[581])). 123.96/29.67 thf(368,axiom,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_sup__left__idem)). 123.96/29.67 thf(1944,plain,((! [A:(hoare_1708887482_state > $o),B:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ A @ (semila1122118281tate_o @ A @ B)) = (semila1122118281tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])). 123.96/29.67 thf(173,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((ord_less_eq_pname_o @ A @ B) => (ord_less_eq_pname_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_xt1_I6_J)). 123.96/29.67 thf(1367,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => ((ord_less_eq_pname_o @ (A) @ (B)) => (ord_less_eq_pname_o @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 123.96/29.67 thf(555,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_Int__Un__distrib)). 123.96/29.67 thf(2563,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((semila1673364395name_o @ A @ (semila1780557381name_o @ B @ C)) = (semila1780557381name_o @ (semila1673364395name_o @ A @ B) @ (semila1673364395name_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[555])). 123.96/29.67 thf(654,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((ord_less_eq_pname_o @ A @ C) => (ord_less_eq_pname_o @ (semila1780557381name_o @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_le__supI)). 123.96/29.67 thf(2881,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => ((ord_less_eq_pname_o @ (A) @ (C)) => (ord_less_eq_pname_o @ (semila1780557381name_o @ B @ A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[654])). 123.96/29.67 thf(33,axiom,((! [A:pname,B:pname]: ((fequal_pname @ A @ B) | (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T)). 123.96/29.67 thf(935,plain,((! [A:pname,B:pname]: ((fequal_pname @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 123.96/29.67 thf(785,axiom,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ bot_bo19817387tate_o @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_Un__empty__left)). 123.96/29.67 thf(3299,plain,((! [A:(hoare_1708887482_state > $o)]: ((semila1122118281tate_o @ bot_bo19817387tate_o @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[785])). 123.96/29.67 thf(594,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((C @ A) & (member_pname @ A @ B)) = (member_pname @ A @ (semila1673364395name_o @ B @ (collect_pname @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_858_Int__Collect)). 123.96/29.67 thf(2690,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((C @ A) & (member_pname @ A @ (B))) = (member_pname @ A @ (semila1673364395name_o @ B @ (collect_pname @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[594])). 123.96/29.67 thf(205,axiom,((finite2034616076tate_o @ semila1122118281tate_o)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_comp__fun__idem__sup)). 123.96/29.67 thf(1463,plain,((finite2034616076tate_o @ (semila1122118281tate_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 123.96/29.67 thf(514,axiom,((! [A:pname,B:(com > pname),C:com,D:(com > $o)]: (((A = (B @ C)) => (member_pname @ A @ (image_com_pname @ B @ D))) <= (member_com @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rev__image__eqI)). 123.96/29.67 thf(2438,plain,((! [A:pname,B:(com > pname),C:com,D:(com > $o)]: (((A = (B @ C)) => (member_pname @ A @ (image_com_pname @ B @ D))) | ~ (member_com @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[514])). 123.96/29.67 thf(214,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((! [C:pname]: ((! [D:pname]: ((member_pname @ D @ B) => (C != D))) <= (member_pname @ C @ A))) = ((semila1673364395name_o @ A @ B) = bot_bot_pname_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_960_disjoint__iff__not__equal)). 123.96/29.67 thf(1490,plain,((! [A:(pname > $o),B:(pname > $o)]: ((! [C:pname]: (! [D:pname]: ((member_pname @ D @ (B)) => (~ (C = D))) | ~ (member_pname @ C @ (A)))) = ((semila1673364395name_o @ A @ B) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 123.96/29.67 thf(573,axiom,((! [A:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_subset__refl)). 123.96/29.67 thf(2615,plain,((! [A:(hoare_1708887482_state > $o)]: (ord_le777019615tate_o @ (A) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[573])). 123.96/29.67 thf(358,axiom,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((semila1780557381name_o @ A @ B @ C) <= ((A @ C) <= (~ (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_sup1CI)). 123.96/29.67 thf(1917,plain,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((semila1780557381name_o @ (A) @ (B) @ C) | ~ ((A @ C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])). 123.96/29.67 thf(791,axiom,((! [A:(hoare_1708887482_state > $o)]: ((? [B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: ((A = (insert528405184_state @ B @ C)) & ~ (member451959335_state @ B @ C))) = (A != bot_bo19817387tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_nonempty__iff)). 123.96/29.67 thf(3316,plain,((! [A:(hoare_1708887482_state > $o)]: ((? [B:hoare_1708887482_state,C:(hoare_1708887482_state > $o)]: (((A) = (insert528405184_state @ B @ C)) & ~ (member451959335_state @ B @ (C)))) = (~ ((A) = (bot_bo19817387tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[791])). 123.96/29.67 thf(643,axiom,((! [A:(pname > option_pname),B:pname,C:pname]: ((member_pname @ B @ (dom_pname_pname @ A)) <= ((A @ B) = (some_pname @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_domI)). 123.96/29.67 thf(2834,plain,((! [A:(pname > option_pname),B:pname,C:pname]: ((member_pname @ B @ (dom_pname_pname @ A)) | ~ ((A @ B) = (some_pname @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[643])). 123.96/29.67 thf(79,axiom,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((semila1780557381name_o @ B @ A @ C) <= (B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_sup1I1)). 123.96/29.67 thf(1088,plain,((! [A:(pname > $o),B:(pname > $o),C:pname]: ((semila1780557381name_o @ (B) @ (A) @ C) | ~ (B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 123.96/29.67 thf(5703,plain,(($false)),inference(cvc4,[status(thm)],[2199,1879,1633,1767,1105,3434,2876,909,1840,2559,1179,3566,1549,2280,2163,892,1036,2822,2630,2094,1411,2744,1369,1168,2295,3399,2263,2463,1899,1315,2787,2499,2480,962,2544,941,1200,977,1882,1522,2381,2659,1728,3012,1591,1142,1437,1173,1158,2512,2976,2231,1068,2395,2062,2590,1401,1971,1793,1533,1705,1671,3439,1655,1137,1310,2035,1735,2448,1275,2627,3253,1761,945,1354,930,1788,1426,1999,2316,1196,1835,3236,2723,2046,1914,1127,3249,841,1046,3140,2819,1623,2957,2603,3425,2039,3116,3046,2755,1871,2708,2501,1860,1511,1313,2126,3043,2571,2654,1628,1055,3442,2698,3131,3410,1577,3280,1832,2897,1545,902,1800,2767,2373,3216,1398,2929,1568,2520,1773,1778,1100,1892,3463,1379,2169,2403,1514,1247,2049,2024,1641,2989,1963,1232,3268,2456,924,3431,1664,2027,3199,3163,1151,3357,3569,2335,2777,1183,2178,2222,2105,3075,1450,1373,2996,1418,2451,2236,1960,3290,2058,2367,1377,2483,1886,1351,2002,1433,1201,2804,1697,3211,2205,2982,1564,1896,877,1072,3036,1394,2772,3157,2242,1345,988,2799,2286,2103,2750,2954,1604,3097,2473,3567,1306,2364,1153,1338,1708,2790,1868,1636,1730,1863,3435,3265,2646,1783,2737,2232,3054,2705,1387,1223,1091,2277,1676,1502,3371,3154,2986,3514,3471,1042,2541,1519,2596,1217,2147,1824,2150,2132,2890,3339,1238,2958,2445,1920,1296,889,1210,1195,2492,2228,1291,974,3445,847,2758,2873,3403,1968,852,1555,2332,2826,3314,3297,3065,3349,2068,1819,3028,3050,1281,2741,3033,1740,1910,1983,874,1804,2841,1111,1587,2509,1755,1118,3205,2515,2100,1270,1259,2377,948,1375,2973,1121,3143,1361,1942,3407,1182,3094,2666,1889,1039,1493,1683,1160,3311,1028,1082,2419,1075,1424,3010,1700,1937,1810,2172,3428,1214,3194,3294,1155,1744,837,1478,3059,1552,2497,2566,1947,1984,2052,1720,2140,1324,1114,1263,997,2932,985,1530,1539,1456,1382,3354,2153,2900,1192,1932,2465,1060,1852,2813,1874,3115,3247,2862,2370,1525,1318,2926,2203,2208,2963,1466,3422,2617,2662,1996,2529,2909,3147,3454,2634,1857,1241,2546,3563,2761,2883,921,3306,1846,1187,2915,2408,2793,2089,3190,965,2391,2585,1273,3262,2894,3396,1631,2144,906,1278,1906,1764,2413,3130,1146,2292,2556,1103,2253,2275,2033,3079,1747,2941,3375,2734,3111,3274,3343,2260,904,2938,2225,1784,2525,1752,3283,3272,2716,1124,3213,2970,1007,3319,1620,2489,1652,1929,1795,2398,1226,1488,2695,1256,1428,1139,1669,1312,3208,1058,1332,1090,919,1464,3302,1638,2935,1733,2442,2753,3436,2055,1092,2573,2319,979,2084,1894,2637,1574,2246,2945,880,2802,863,2721,3352,2538,1408,2478,3251,2774,3287,2906,3419,2097,3270,2257,990,3468,1542,1722,2669,1144,1690,3066,1571,2871,2197,3160,3219,2605,3133,2129,1993,2267,1821,1162,3165,3192,1344,2180,3456,1667,2923,1838,2593,895,3451,2289,2647,943,1022,932,1952,3150,2329,2770,1926,2086,1643,883,2064,1176,2535,1496,1973,2506,912,1171,1198,1396,2725,2401,1594,2212,959,2765,1044,2620,868,1445,1528,3241,2797,3016,1775,2244,2022,3363,1364,2967,1250,3512,3178,2999,2156,1694,2693,1626,2239,3031,1203,2503,939,968,836,2582,1049,2005,1413,1758,2107,927,2037,1990,3048,2202,1547,1770,855,3315,1611,3082,971,2588,1647,954,3129,1267,2160,1025,3507,2569,3448,2092,2165,2920,3202,1235,2337,3412,1285,1336,2656,1711,3019,2747,1499,1790,1987,1813,1300,1452,840,1785,3026,2429,2219,1980,1830,3127,1085,1658,2322,2701,951,2903,3174,2044,1130,1579,2468,1220,2411,3107,1849,1536,2579,1749,1094,3071,3256,2807,3007,1617,2675,1404,1934,2948,2838,2113,3415,1702,2379,2357,1955,1485,1052,2711,2728,2030,2848,3366,2435,3139,1649,2479,1966,1685,1321,1844,3188,1781,2110,1866,1807,3168,1940,1421,3478,1459,3092,1949,2828,1817,3171,2215,1517,2611,2325,1189,3346,3056,844,2643,1108,3039,3465,1385,2273,1341,2855,1481,3336,1854,1244,2416,3085,2174,2283,2389,1476,2135,2406,1062,2532,1508,2608,2431,3136,3368,995,1558,2944,2956,2081,1294,1440,1308,2576,2183,1607,2120,1614,3181,2475,2912,2041,899,1661,2739,2494,2917,2623,2142,1348,999,2517,1725,1957,2385,2255,2719,3464,2951,1876,3062,2123,1133,1097,835,1229,2233,2522,3100,2815,1303,1148,1673,3309,1561,1473,1065,2651,2186,3277,1033,2961,1288,2714,3196,2340,1165,886,2549,3244,1977,1827,860,2600,3360,1582,3259,1923,1713,1299,871,2138,1093,839,2810,2731,1597,2864,982,1431,1004,3113,1902,1505,2270,3013,3474,3437,1737,2832,1416,2453,2993,2470,2980,2672,2879,2640,1944,1367,2563,2881,935,3299,2690,1463,2438,1490,2615,1917,3316,2834,1088])). 123.96/29.67 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 123.96/29.67 % [INFO] Killing All external provers ... 124.07/29.73 EOF