0.00/0.00 % Leo-III: Strategy 1 (for '60') 33.99/12.55 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 33.99/12.55 % [INFO] Parsing done (328ms). 33.99/12.55 % [INFO] Running in sequential loop mode. 33.99/12.55 % [CONFIG] Using configuration: timeout(60) with strategy 33.99/12.55 % [INFO] eprover registered as external prover. 33.99/12.55 % [INFO] cvc4 registered as external prover. 33.99/12.55 % [INFO] Parsing finished. Scanning for conjecture ... 33.99/12.55 % [INFO] Found a conjecture and 354 axioms. Running axiom selection ... 33.99/12.55 % [INFO] Axiom selection finished. Selected 327 axioms (removed 27 axioms). 33.99/12.55 % [INFO] Problem is higher-order (TPTP THF). 33.99/12.55 % [INFO] Type checking passed. Searching for refutation ... 33.99/12.55 % External prover 'cvc4' found a proof! 33.99/12.55 % [INFO] Killing All external provers ... 33.99/12.55 % Time passed: 8957ms (effective reasoning time: 8174ms) 33.99/12.55 % Solved by strategy 33.99/12.55 % Axioms used in derivation (327): fact_1_renumber, fact_48_converse__rtranclE, fact_60_rtranclE, fact_92_mem__Collect__eq, fact_115_prod_Oinject, fact_275_listrel_OCons, fact_238_self__append__conv, fact_287_listrel_Osimps, fact_288_listrel_Osimps, fact_235_append_Oassoc, fact_230_listrel_Ocases, fact_24_tranclD, fact_151_Zero__neq__Suc, fact_186_n__lists__Nil, fact_274_listrel_OCons, fact_156_list_Odistinct_I1_J, fact_81_trancl__trans, fact_39_converse__rtrancl__into__rtrancl, fact_19_converse__rtranclE2, fact_349_lexord__same__pref__if__irrefl, fact_111_old_Oprod_Oinject, fact_62_trancl_Otrancl__into__trancl, fact_208_gen__length__code_I2_J, fact_69_trancl__into__trancl2, fact_100_rtrancl__into__trancl2, fact_148_diff__induct, fact_45_rtrancl_Ortrancl__refl, fact_229_listrel_Ocases, fact_205_com_Odistinct_I11_J, fact_114_prod_Oinject, fact_262_listrel__Nil2, fact_248_append__eq__append__conv2, fact_135_old_Oprod_Oexhaust, fact_155_not0__implies__Suc, fact_13_inf__def, fact_211_com_Oinject_I4_J, fact_99_rtrancl__trancl__trancl, fact_157_list_OdiscI, fact_296_Cons__listrel1__Cons, fact_140_Suc__inject, fact_116_execs_Ointros_I2_J, conj_3, fact_50_rtrancl_Oinducts, fact_301_not__listrel1__Nil, fact_43_converse__rtrancl__induct, fact_110_old_Oprod_Oinject, fact_213_while__termiE, fact_321_listrel1E, fact_214_exec_OWhileFalse, fact_243_append_Oright__neutral, fact_160_neq__Nil__conv, fact_325_rtrancl__listrel1__ConsI2, fact_224_exec1E_I5_J, fact_165_transpose_Ocases, fact_173_shuffles_Ocases, fact_322_listrel1E, fact_272_listrel__Cons1, fact_311_Cons__listrel1E1, fact_77_trancl_Oinducts, fact_170_list__nonempty__induct, fact_145_old_Onat_Odistinct_I1_J, fact_254_append__Cons, fact_22_converse__rtrancl__induct2, fact_83_trancl_Osimps, fact_324_rtrancl__listrel1__ConsI2, fact_158_list_Oexhaust, fact_188_exec1_ODo, fact_130_Pair__inject, fact_75_r__r__into__trancl, fact_56_rtrancl_Osimps, fact_166_remdups__adj_Ocases, fact_332_lexord__cons__cons, fact_139_not__Cons__self2, fact_240_self__append__conv2, fact_175_successively_Ocases, fact_42_rtrancl_Ortrancl__into__rtrancl, fact_283_listrel_Oinducts, fact_282_listrel_Oinducts, fact_222_termi__while, fact_55_rtrancl_Osimps, fact_255_rev__nonempty__induct, fact_57_rtrancl_Ocases, fact_26_rtranclD, fact_76_r__r__into__trancl, fact_270_listrel__Cons1, fact_215_exec_OWhileTrue, fact_11_trancl__induct2, fact_93_Collect__mem__eq, fact_67_trancl__trans__induct, fact_291_snoc__listrel1__snoc__iff, fact_49_rtrancl_Oinducts, fact_40_converse__rtrancl__into__rtrancl, fact_71_irrefl__trancl__rD, fact_226_nths__singleton, fact_167_sorted__wrt_Oinduct, fact_58_rtrancl_Ocases, fact_41_rtrancl_Ortrancl__into__rtrancl, fact_218_com_Odistinct_I13_J, fact_3_renumber__aux, fact_149_zero__induct, fact_233_append__same__eq, fact_336_lexord__linear, fact_297_Cons__listrel1__Cons, fact_216_termi_OWhileFalse, fact_98_rtrancl__trancl__trancl, fact_143_nat_Odistinct_I1_J, fact_199_com_Oinject_I3_J, fact_250_eq__Nil__appendI, fact_221_gen__length__code_I1_J, fact_219_termi_OWhileTrue, fact_331_concat__append, fact_21_converse__rtrancl__induct2, fact_68_trancl__trans__induct, fact_88_tranclE, fact_37_r__into__trancl_H, fact_244_nths__nil, fact_314_Cons__listrel1E2, fact_122_termis_Osimps_I1_J, fact_66_trancl_Or__into__trancl, fact_196_product__lists_Osimps_I1_J, fact_154_old_Onat_Oinducts, fact_78_trancl_Oinducts, fact_338_lexord__irreflexive, fact_152_Zero__not__Suc, fact_237_append__self__conv, fact_117_execs_Ocases, fact_72_irrefl__trancl__rD, fact_183_exec1__pres__termis, fact_345_lexord__append__leftD, fact_16_rtrancl__induct2, fact_295_bind__simps_I1_J, fact_177_prod__cases3, fact_134_old_Oprod_Oexhaust, fact_85_trancl_Ocases, conj_2, fact_256_append__eq__Cons__conv, fact_15_rtrancl__induct2, fact_263_listrel__rtrancl__trans, fact_267_listrel__Cons2, fact_206_exec1_OIfFalse, fact_189_n__lists_Osimps_I1_J, fact_142_inf__cases, fact_280_exec1__drop__suffix__aux, fact_144_old_Onat_Odistinct_I2_J, fact_329_lexord__append__left__rightI, fact_246_listrel__rtrancl__refl, fact_342_concat_Osimps_I2_J, fact_172_splice_Ocases, fact_306_maps__simps_I2_J, fact_5_execs__pres__termi, fact_276_listrel_OCons, fact_261_listrel__Nil1, fact_347_lexord__append__rightI, fact_28_tranclD2, fact_200_exec_OIfTrue, fact_108_list_Oinject, fact_253_Cons__eq__appendI, fact_161_list__induct2_H, fact_74_converse__tranclE, fact_168_remdups__adj_Oinduct, fact_44_converse__rtrancl__induct, fact_178_prod__cases3, fact_150_Suc__neq__Zero, fact_344_lexord__append__leftD, fact_27_tranclD2, fact_300_listrel1I2, fact_104_exec1s__impl__execs, fact_302_not__Nil__listrel1, fact_64_converse__trancl__induct, fact_127_prod__cases, fact_53_rtrancl__trans, fact_335_lexord__Nil__left, fact_180_prod__induct3, fact_217_com_Odistinct_I5_J, fact_7_rtrancl__trancl__absorb, fact_153_old_Onat_Oexhaust, fact_38_r__into__trancl_H, fact_182_prod__induct4, fact_12_trancl__induct2, fact_120_termis_Osimps_I2_J, fact_318_listrel1I, fact_136_old_Oprod_Oinducts, fact_128_prod__cases, fact_34_r__into__rtrancl, fact_319_listrel1I, fact_341_lexord__Nil__right, fact_268_listrel__Cons2, fact_190_termi_OSemi, fact_279_exec1__only1, fact_119_execs_Oinducts, fact_241_Nil__is__append__conv, fact_292_snoc__listrel1__snoc__iff, fact_73_converse__tranclE, fact_260_listrel_ONil, fact_265_app__exec, fact_31_rtrancl__eq__or__trancl, fact_35_rtrancl__idemp, fact_61_trancl_Otrancl__into__trancl, fact_32_rtrancl__eq__or__trancl, fact_227_app__execs, fact_184_exec1E_I3_J, fact_29_trancl__into__rtrancl, fact_316_listrel__reflcl__if__listrel1, fact_0_exec1E_I1_J, fact_146_nat_OdiscI, fact_63_converse__trancl__induct, fact_159_list_Oinducts, fact_23_tranclD, fact_162_splice_Oinduct, fact_271_listrel__Cons1, fact_197_subseqs_Osimps_I1_J, fact_266_listrel__Cons2, fact_169_successively_Oinduct, fact_79_trancl__induct, fact_113_prod_Oinject, fact_286_listrel_Osimps, fact_284_listrel_Oinducts, fact_80_trancl__induct, fact_187_exec1E_I2_J, fact_129_prod__cases, fact_101_rtrancl__into__trancl2, fact_97_trancl__rtrancl__trancl, fact_133_old_Oprod_Oexhaust, fact_124_surj__pair, fact_126_surj__pair, fact_259_rev__induct, fact_25_rtranclD, fact_2_renumber, fact_107_nat_Oinject, fact_131_Pair__inject, fact_30_trancl__into__rtrancl, fact_4_renumber__aux, fact_95_Collect__mem__eq, fact_109_exec1s__impl__exec, fact_137_old_Oprod_Oinducts, fact_185_exec1_OSemi, fact_278_exec1__only1__aux, fact_90_mem__Collect__eq, fact_33_r__into__rtrancl, fact_18_converse__rtranclE2, fact_236_append__Nil2, fact_123_zero__reorient, fact_65_trancl_Or__into__trancl, fact_96_trancl__rtrancl__trancl, conj_1, fact_181_prod__induct3, fact_313_Cons__listrel1E2, fact_86_trancl_Ocases, fact_234_append__assoc, fact_239_append__self__conv2, fact_252_append_Oleft__neutral, fact_232_same__append__eq, fact_251_append__Nil, fact_179_prod__cases4, fact_327_concat__eq__append__conv, fact_94_Collect__mem__eq, fact_102_rtrancl__into__trancl1, fact_164_shuffles_Oinduct, fact_225_exec1_OWhileTrue, fact_249_append__eq__appendI, fact_304_listrel__rtrancl__eq__rtrancl__listrel1, fact_46_rtrancl_Ortrancl__refl, fact_84_trancl_Osimps, fact_163_induct__list012, fact_147_nat__induct, fact_201_exec_OIfFalse, fact_348_concat__eq__appendD, fact_299_rtrancl__listrel1__ConsI1, fact_54_rtrancl__trans, fact_202_termi_OIfTrue, fact_118_execs_Osimps, fact_171_map__tailrec__rev_Oinduct, fact_106_old_Onat_Oinject, fact_112_old_Oprod_Oinject, fact_192_com_Oinject_I1_J, fact_198_exec1E_I4_J, fact_290_bind__simps_I2_J, fact_47_converse__rtranclE, fact_203_termi_OIfFalse, fact_303_append__listrel1I, fact_333_lexord__cons__cons, fact_228_listrel_Ocases, fact_138_old_Oprod_Oinducts, fact_89_termi__impl__not__inf, fact_308_listrel1I1, fact_105_execs__pres__termis, fact_310_Cons__listrel1E1, fact_223_termi__while__lemma, fact_176_exec__impl__execs, fact_36_rtrancl__idemp, fact_204_com_Odistinct_I3_J, fact_103_rtrancl__into__trancl1, fact_52_rtrancl__induct, fact_258_rev__exhaust, fact_59_rtranclE, fact_91_mem__Collect__eq, conj_0, fact_340_concat_Osimps_I1_J, fact_87_tranclE, fact_6_rtrancl__trancl__absorb, fact_343_lexord__append__leftI, fact_210_exec1_OWhileFalse, fact_328_lexord__append__left__rightI, fact_194_exec_ODo, fact_307_listrel1I1, fact_132_Pair__inject, fact_195_exec_OSemi, fact_257_Cons__eq__append__conv, fact_8_trancl__rtrancl__absorb, fact_207_exec1_OIfTrue, fact_70_trancl__into__trancl2, fact_212_com_Odistinct_I19_J, fact_82_trancl__trans, fact_245_append1__eq__conv, fact_220_while__termiE2, fact_191_com_Oinject_I2_J, fact_242_append__is__Nil__conv, fact_193_com_Odistinct_I1_J, fact_51_rtrancl__induct, fact_209_insert__Nil, fact_174_sorted__wrt_Ocases, fact_281_exec1__drop__suffix, fact_294_maps__simps_I1_J, fact_141_n__not__Suc__n, fact_121_execs_Ointros_I1_J, fact_125_surj__pair, fact_9_trancl__rtrancl__absorb 33.99/12.55 % No. of inferences in proof: 658 33.99/12.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8957 ms resp. 8174 ms w/o parsing 33.99/12.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 33.99/12.55 thf(set_Pr541394119_state_type, type, set_Pr541394119_state: $tType). 33.99/12.55 thf(produc2046512871_state_type, type, produc2046512871_state: $tType). 33.99/12.55 thf(set_Pr1325664839_state_type, type, set_Pr1325664839_state: $tType). 33.99/12.55 thf(produc1586269031_state_type, type, produc1586269031_state: $tType). 33.99/12.55 thf(set_Pr2096893127_state_type, type, set_Pr2096893127_state: $tType). 33.99/12.55 thf(produc186437863_state_type, type, produc186437863_state: $tType). 33.99/12.55 thf(set_Pr1142642759_state_type, type, set_Pr1142642759_state: $tType). 33.99/12.55 thf(produc1225889383_state_type, type, produc1225889383_state: $tType). 33.99/12.55 thf(list_P890094829_state_type, type, list_P890094829_state: $tType). 33.99/12.55 thf(set_Pr1165141447_state_type, type, set_Pr1165141447_state: $tType). 33.99/12.55 thf(produc410756839_state_type, type, produc410756839_state: $tType). 33.99/12.55 thf(set_Pr391631483_state_type, type, set_Pr391631483_state: $tType). 33.99/12.55 thf(produc1393453339_state_type, type, produc1393453339_state: $tType). 33.99/12.55 thf(produc2058209240st_com_type, type, produc2058209240st_com: $tType). 33.99/12.55 thf(set_Pr602326075st_com_type, type, set_Pr602326075st_com: $tType). 33.99/12.55 thf(list_P1040014977_state_type, type, list_P1040014977_state: $tType). 33.99/12.55 thf(set_Pr849496667_state_type, type, set_Pr849496667_state: $tType). 33.99/12.55 thf(produc258871771st_com_type, type, produc258871771st_com: $tType). 33.99/12.55 thf(produc2041926651_state_type, type, produc2041926651_state: $tType). 33.99/12.55 thf(set_Pr1822651163om_com_type, type, set_Pr1822651163om_com: $tType). 33.99/12.55 thf(product_prod_com_com_type, type, product_prod_com_com: $tType). 33.99/12.55 thf(list_list_com_type, type, list_list_com: $tType). 33.99/12.55 thf(list_state_type, type, list_state: $tType). 33.99/12.55 thf(set_state_type, type, set_state: $tType). 33.99/12.55 thf(list_com_type, type, list_com: $tType). 33.99/12.55 thf(set_nat_type, type, set_nat: $tType). 33.99/12.55 thf(state_type, type, state: $tType). 33.99/12.55 thf(com_type, type, com: $tType). 33.99/12.55 thf(nat_type, type, nat: $tType). 33.99/12.55 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 33.99/12.55 thf(append_list_com_type, type, append_list_com: (list_list_com > (list_list_com > list_list_com))). 33.99/12.55 thf(append_com_type, type, append_com: (list_com > (list_com > list_com))). 33.99/12.55 thf(append982487830_state_type, type, append982487830_state: (list_P1040014977_state > (list_P1040014977_state > list_P1040014977_state))). 33.99/12.55 thf(bind_com_com_type, type, bind_com_com: (list_com > ((com > list_com) > list_com))). 33.99/12.55 thf(concat_com_type, type, concat_com: (list_list_com > list_com)). 33.99/12.55 thf(gen_length_com_type, type, gen_length_com: (nat > (list_com > nat))). 33.99/12.55 thf(insert_com_type, type, insert_com: (com > (list_com > list_com))). 33.99/12.55 thf(lexord_com_type, type, lexord_com: (set_Pr1822651163om_com > set_Pr602326075st_com)). 33.99/12.55 thf(lexord1062073966_state_type, type, lexord1062073966_state: (set_Pr1165141447_state > set_Pr1142642759_state)). 33.99/12.55 thf(cons_list_com_type, type, cons_list_com: (list_com > (list_list_com > list_list_com))). 33.99/12.55 thf(cons_com_type, type, cons_com: (com > (list_com > list_com))). 33.99/12.55 thf(cons_state_type, type, cons_state: (state > (list_state > list_state))). 33.99/12.55 thf(cons_P465369265_state_type, type, cons_P465369265_state: (produc2041926651_state > (list_P1040014977_state > list_P1040014977_state))). 33.99/12.55 thf(nil_list_com_type, type, nil_list_com: list_list_com). 33.99/12.55 thf(nil_com_type, type, nil_com: list_com). 33.99/12.55 thf(nil_state_type, type, nil_state: list_state). 33.99/12.55 thf(nil_Pr1844458753_state_type, type, nil_Pr1844458753_state: list_P1040014977_state). 33.99/12.55 thf(listrel1_com_type, type, listrel1_com: (set_Pr1822651163om_com > set_Pr602326075st_com)). 33.99/12.55 thf(listre1738592858_state_type, type, listre1738592858_state: (set_Pr1165141447_state > set_Pr1142642759_state)). 33.99/12.55 thf(listre1268245261_state_type, type, listre1268245261_state: (set_Pr849496667_state > set_Pr391631483_state)). 33.99/12.55 thf(listrel_com_com_type, type, listrel_com_com: (set_Pr1822651163om_com > set_Pr602326075st_com)). 33.99/12.55 thf(listre194873521_state_type, type, listre194873521_state: (set_Pr1165141447_state > set_Pr1142642759_state)). 33.99/12.55 thf(maps_com_com_type, type, maps_com_com: ((com > list_com) > (list_com > list_com))). 33.99/12.55 thf(n_lists_com_type, type, n_lists_com: (nat > (list_com > list_list_com))). 33.99/12.55 thf(nths_com_type, type, nths_com: (list_com > (set_nat > list_com))). 33.99/12.55 thf(product_lists_com_type, type, product_lists_com: (list_list_com > list_list_com)). 33.99/12.55 thf(subseqs_com_type, type, subseqs_com: (list_com > list_list_com)). 33.99/12.55 thf(suc_type, type, suc: (nat > nat)). 33.99/12.55 thf(pHoare259243666_exec1_type, type, pHoare259243666_exec1: set_Pr1165141447_state). 33.99/12.55 thf(pHoare259243732_execs_type, type, pHoare259243732_execs: (state > (list_com > (state > $o)))). 33.99/12.55 thf(pHoare2126160787le_inf_type, type, pHoare2126160787le_inf: (list_com > (state > $o))). 33.99/12.55 thf(pHoare806997636termis_type, type, pHoare806997636termis: (list_com > (state > $o))). 33.99/12.55 thf(cond_type, type, cond: ((state > $o) > (com > (com > com)))). 33.99/12.55 thf(do_type, type, do: ((state > set_state) > com)). 33.99/12.55 thf(semi_type, type, semi: (com > (com > com))). 33.99/12.55 thf(while_type, type, while: ((state > $o) > (com > com))). 33.99/12.55 thf(exec_type, type, exec: (state > (com > (state > $o)))). 33.99/12.55 thf(termi_type, type, termi: (com > (state > $o))). 33.99/12.55 thf(produc1914379986st_com_type, type, produc1914379986st_com: ((com > (com > $o)) > (list_com > produc2058209240st_com))). 33.99/12.55 thf(produc1742567891_state_type, type, produc1742567891_state: (list_list_com > (list_state > produc1393453339_state))). 33.99/12.55 thf(produc1307105171st_com_type, type, produc1307105171st_com: (list_com > (list_com > produc258871771st_com))). 33.99/12.55 thf(produc1204172211_state_type, type, produc1204172211_state: (list_com > (state > produc2041926651_state))). 33.99/12.55 thf(produc1298457559_state_type, type, produc1298457559_state: (list_P1040014977_state > (list_P1040014977_state > produc1225889383_state))). 33.99/12.55 thf(product_Pair_com_com_type, type, product_Pair_com_com: (com > (com > product_prod_com_com))). 33.99/12.55 thf(produc1909270103_state_type, type, produc1909270103_state: (produc2041926651_state > (produc2041926651_state > produc410756839_state))). 33.99/12.55 thf(produc2065881943_state_type, type, produc2065881943_state: (produc410756839_state > (produc410756839_state > produc186437863_state))). 33.99/12.55 thf(irrefl_com_type, type, irrefl_com: (set_Pr1822651163om_com > $o)). 33.99/12.55 thf(collect_state_type, type, collect_state: ((state > $o) > set_state)). 33.99/12.55 thf(collec300063826_state_type, type, collec300063826_state: ((produc410756839_state > $o) > set_Pr1165141447_state)). 33.99/12.55 thf(collec489924946_state_type, type, collec489924946_state: ((produc186437863_state > $o) > set_Pr2096893127_state)). 33.99/12.55 thf(transi436345274st_com_type, type, transi436345274st_com: (set_Pr602326075st_com > set_Pr602326075st_com)). 33.99/12.55 thf(transi339813252_state_type, type, transi339813252_state: (set_Pr1142642759_state > set_Pr1142642759_state)). 33.99/12.55 thf(transi863150634cl_com_type, type, transi863150634cl_com: (set_Pr1822651163om_com > set_Pr1822651163om_com)). 33.99/12.55 thf(transi1302705790_state_type, type, transi1302705790_state: (set_Pr1165141447_state > set_Pr1165141447_state)). 33.99/12.55 thf(transi463013610_state_type, type, transi463013610_state: (set_Pr2096893127_state > set_Pr2096893127_state)). 33.99/12.55 thf(transi1726587420_state_type, type, transi1726587420_state: (set_Pr1165141447_state > set_Pr1165141447_state)). 33.99/12.55 thf(transi1666849160_state_type, type, transi1666849160_state: (set_Pr2096893127_state > set_Pr2096893127_state)). 33.99/12.55 thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))). 33.99/12.55 thf(member_state_type, type, member_state: (state > (set_state > $o))). 33.99/12.55 thf(member1442949316_state_type, type, member1442949316_state: (produc1393453339_state > (set_Pr391631483_state > $o))). 33.99/12.55 thf(member32358020st_com_type, type, member32358020st_com: (produc258871771st_com > (set_Pr602326075st_com > $o))). 33.99/12.55 thf(member64234660_state_type, type, member64234660_state: (produc2041926651_state > (set_Pr849496667_state > $o))). 33.99/12.55 thf(member1267359376_state_type, type, member1267359376_state: (produc1225889383_state > (set_Pr1142642759_state > $o))). 33.99/12.55 thf(member1333916004om_com_type, type, member1333916004om_com: (product_prod_com_com > (set_Pr1822651163om_com > $o))). 33.99/12.55 thf(member1069318160_state_type, type, member1069318160_state: (produc410756839_state > (set_Pr1165141447_state > $o))). 33.99/12.55 thf(member512523024_state_type, type, member512523024_state: (produc186437863_state > (set_Pr2096893127_state > $o))). 33.99/12.55 thf(c_type, type, c: com). 33.99/12.55 thf(f_type, type, f: (nat > produc2041926651_state)). 33.99/12.55 thf(n_type, type, n: nat). 33.99/12.55 thf(s_type, type, s: state). 33.99/12.55 thf(231,axiom,((! [A:set_Pr1165141447_state,B:produc2041926651_state,C:produc2041926651_state]: ((! [D:produc2041926651_state]: ~ (member1069318160_state @ (produc1909270103_state @ D @ D) @ (transi1726587420_state @ A))) => ((B != C) <= (member1069318160_state @ (produc1909270103_state @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_irrefl__trancl__rD)). 33.99/12.55 thf(1322,plain,((! [A:set_Pr1165141447_state,B:produc2041926651_state,C:produc2041926651_state]: ((! [D:produc2041926651_state]: ~ (member1069318160_state @ (produc1909270103_state @ D @ D) @ (transi1726587420_state @ A))) => (~ (B = C) | ~ (member1069318160_state @ (produc1909270103_state @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 33.99/12.55 thf(162,axiom,((! [A:list_list_com,B:state,C:list_state,D:set_Pr849496667_state]: ((~ (! [E:list_com,F:list_list_com]: (((~ (member1442949316_state @ (produc1742567891_state @ F @ C) @ (listre1268245261_state @ D))) <= (member64234660_state @ (produc1204172211_state @ E @ B) @ D)) <= (A = (cons_list_com @ E @ F))))) <= (member1442949316_state @ (produc1742567891_state @ A @ (cons_state @ B @ C)) @ (listre1268245261_state @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_listrel__Cons2)). 33.99/12.55 thf(1024,plain,((! [A:list_list_com,B:state,C:list_state,D:set_Pr849496667_state]: (~ (! [E:list_com,F:list_list_com]: (~ (member1442949316_state @ (produc1742567891_state @ F @ C) @ (listre1268245261_state @ D)) | ~ (member64234660_state @ (produc1204172211_state @ E @ B) @ D) | ~ (A = (cons_list_com @ E @ F)))) | ~ (member1442949316_state @ (produc1742567891_state @ A @ (cons_state @ B @ C)) @ (listre1268245261_state @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 33.99/12.55 thf(14,axiom,((! [A:(state > $o),B:state,C:com,D:state,E:com]: (((exec @ B @ C @ D) => (exec @ B @ (cond @ A @ E @ C) @ D)) <= (~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_exec_OIfFalse)). 33.99/12.55 thf(365,plain,((! [A:(state > $o),B:state,C:com,D:state,E:com]: (((exec @ B @ C @ D) => (exec @ B @ (cond @ (A) @ E @ C) @ D)) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 33.99/12.55 thf(213,axiom,((! [A:state,B:com,C:state,D:list_com]: ((exec @ A @ B @ C) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ B @ D) @ A) @ (produc1204172211_state @ D @ C)) @ (transi1302705790_state @ pHoare259243666_exec1))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_exec__impl__execs)). 33.99/12.55 thf(1237,plain,((! [A:state,B:com,C:state,D:list_com]: ((exec @ A @ B @ C) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ B @ D) @ A) @ (produc1204172211_state @ D @ C)) @ (transi1302705790_state @ pHoare259243666_exec1))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 33.99/12.55 thf(138,axiom,(((concat_com @ nil_list_com) = nil_com)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_concat_Osimps_I1_J)). 33.99/12.55 thf(909,plain,(((concat_com @ nil_list_com) = nil_com)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 33.99/12.55 thf(147,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => (? [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ D @ B) @ C) & (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_tranclD2)). 33.99/12.55 thf(962,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => (? [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ D @ B) @ C) & (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 33.99/12.55 thf(201,axiom,((! [A:state,B:list_com,C:state]: ((pHoare259243732_execs @ A @ B @ C) => (((C != A) <= (B = nil_com)) => (~ (! [D:com,E:state,F:list_com]: ((B = (cons_com @ D @ F)) => ((exec @ A @ D @ E) => (~ (pHoare259243732_execs @ E @ F @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_execs_Ocases)). 33.99/12.55 thf(1179,plain,((! [A:state,B:list_com,C:state]: ((pHoare259243732_execs @ A @ B @ C) => ((~ (C = A) | ~ (B = nil_com)) => (~ (! [D:com,E:state,F:list_com]: ((B = (cons_com @ D @ F)) => ((exec @ A @ D @ E) => (~ (pHoare259243732_execs @ E @ F @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 33.99/12.55 thf(283,axiom,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel_com_com @ C)) = (((B = nil_com) & (A = nil_com)) | ? [D:com,E:com,F:list_com,G:list_com]: ((member1333916004om_com @ (product_Pair_com_com @ D @ E) @ C) & (member32358020st_com @ (produc1307105171st_com @ F @ G) @ (listrel_com_com @ C)) & (B = (cons_com @ E @ G)) & (A = (cons_com @ D @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_listrel_Osimps)). 33.99/12.55 thf(1586,plain,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel_com_com @ C)) = (((B = nil_com) & (A = nil_com)) | ? [D:com,E:com,F:list_com,G:list_com]: ((member1333916004om_com @ (product_Pair_com_com @ D @ E) @ C) & (member32358020st_com @ (produc1307105171st_com @ F @ G) @ (listrel_com_com @ C)) & (B = (cons_com @ E @ G)) & (A = (cons_com @ D @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 33.99/12.55 thf(262,axiom,((! [A:list_com]: ((append_com @ A @ nil_com) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_append_Oright__neutral)). 33.99/12.55 thf(1501,plain,((! [A:list_com]: ((append_com @ A @ nil_com) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 33.99/12.55 thf(198,axiom,((! [A:com,B:list_com,C:state,D:list_com,E:state]: ((? [F:list_com]: (D = (append_com @ F @ B))) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ A @ B) @ C) @ (produc1204172211_state @ D @ E)) @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_exec1__only1)). 33.99/12.55 thf(1168,plain,((! [A:com,B:list_com,C:state,D:list_com,E:state]: (? [F:list_com]: (D = (append_com @ F @ B)) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ A @ B) @ C) @ (produc1204172211_state @ D @ E)) @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 33.99/12.55 thf(104,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((n_lists_com @ A @ nil_com) = (cons_list_com @ nil_com @ nil_list_com))) & ((A != zero_zero_nat) => ((n_lists_com @ A @ nil_com) = nil_list_com))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_n__lists__Nil)). 33.99/12.55 thf(760,plain,((! [A:nat]: (((A = zero_zero_nat) => ((n_lists_com @ A @ nil_com) = (cons_list_com @ nil_com @ nil_list_com))) & ((~ (A = zero_zero_nat)) => ((n_lists_com @ A @ nil_com) = nil_list_com))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 33.99/12.55 thf(40,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ D) @ (transi463013610_state @ C)) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rtrancl__trans)). 33.99/12.55 thf(479,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ D) @ (transi463013610_state @ C)) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C))) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 33.99/12.55 thf(183,axiom,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com,E:list_com]: (((member32358020st_com @ (produc1307105171st_com @ D @ E) @ (listrel_com_com @ C)) => (member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ D) @ (cons_com @ B @ E)) @ (listrel_com_com @ C))) <= (member1333916004om_com @ (product_Pair_com_com @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_listrel_OCons)). 33.99/12.55 thf(1105,plain,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com,E:list_com]: (((member32358020st_com @ (produc1307105171st_com @ D @ E) @ (listrel_com_com @ C)) => (member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ D) @ (cons_com @ B @ E)) @ (listrel_com_com @ C))) | ~ (member1333916004om_com @ (product_Pair_com_com @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 33.99/12.55 thf(173,axiom,((! [A:list_com,B:list_com]: (((append_com @ A @ B) = nil_com) = ((B = nil_com) & (A = nil_com))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_append__is__Nil__conv)). 33.99/12.55 thf(1068,plain,((! [A:list_com,B:list_com]: (((append_com @ A @ B) = nil_com) = ((B = nil_com) & (A = nil_com))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 33.99/12.55 thf(329,axiom,((pHoare2126160787le_inf = (^ [A:list_com,B:state]: ? [C:(nat > produc2041926651_state)]: (((C @ zero_zero_nat) = (produc1204172211_state @ A @ B)) & ! [D:nat]: (member1069318160_state @ (produc1909270103_state @ (C @ D) @ (C @ (suc @ D))) @ pHoare259243666_exec1))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_inf__def)). 33.99/12.55 thf(1808,plain,(((pHoare2126160787le_inf) = (^ [A:list_com,B:state]: ? [C:(nat > produc2041926651_state)]: (((C @ zero_zero_nat) = (produc1204172211_state @ A @ B)) & ! [D:nat]: (member1069318160_state @ (produc1909270103_state @ (C @ D) @ (C @ (suc @ D))) @ pHoare259243666_exec1))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 33.99/12.55 thf(289,axiom,((! [A:produc410756839_state,B:(produc410756839_state > $o)]: ((member1069318160_state @ A @ (collec300063826_state @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mem__Collect__eq)). 33.99/12.55 thf(1618,plain,((! [A:produc410756839_state,B:(produc410756839_state > $o)]: ((member1069318160_state @ A @ (collec300063826_state @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 33.99/12.55 thf(273,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => ((~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ C) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ (transi1726587420_state @ C)))))) <= (~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_converse__tranclE)). 33.99/12.55 thf(1544,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => (~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ C) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ (transi1726587420_state @ C))))) | (member1069318160_state @ (produc1909270103_state @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 33.99/12.55 thf(74,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) = ((A = B) | ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) & (A != B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rtrancl__eq__or__trancl)). 33.99/12.55 thf(614,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) = ((A = B) | ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) & ~ (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 33.99/12.55 thf(70,axiom,((! [A:list_com,B:list_com,C:list_com]: (((append_com @ A @ B) = (append_com @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_append__same__eq)). 33.99/12.55 thf(597,plain,((! [A:list_com,B:list_com,C:list_com]: (((append_com @ A @ B) = (append_com @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 33.99/12.55 thf(257,axiom,((! [A:list_com,B:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ nil_com @ A) @ (lexord_com @ B)) = (? [C:com,D:list_com]: (A = (cons_com @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_lexord__Nil__left)). 33.99/12.55 thf(1486,plain,((! [A:list_com,B:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ nil_com @ A) @ (lexord_com @ B)) = (? [C:com,D:list_com]: (A = (cons_com @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 33.99/12.55 thf(50,axiom,((! [A:(state > $o),B:state,C:com,D:state,E:state]: ((((exec @ D @ (while @ A @ C) @ E) => (exec @ B @ (while @ A @ C) @ E)) <= (exec @ B @ C @ D)) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_exec_OWhileTrue)). 33.99/12.55 thf(523,plain,((! [A:(state > $o),B:state,C:com,D:state,E:state]: (((exec @ D @ (while @ (A) @ C) @ E) => (exec @ B @ (while @ (A) @ C) @ E)) | ~ (exec @ B @ C @ D) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 33.99/12.55 thf(196,axiom,((! [A:list_com,B:com,C:list_com]: ((A = (cons_com @ B @ C)) => (A != nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_list_OdiscI)). 33.99/12.55 thf(1158,plain,((! [A:list_com,B:com,C:list_com]: ((A = (cons_com @ B @ C)) => (~ (A = nil_com))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 33.99/12.55 thf(191,axiom,((! [A:set_Pr1165141447_state]: ((transi1726587420_state @ (transi1302705790_state @ A)) = (transi1302705790_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_rtrancl__trancl__absorb)). 33.99/12.55 thf(1142,plain,((! [A:set_Pr1165141447_state]: ((transi1726587420_state @ (transi1302705790_state @ A)) = (transi1302705790_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 33.99/12.55 thf(219,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((B != A) => (~ (! [D:produc2041926651_state]: ((~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ C)) <= (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_rtrancl_Ocases)). 33.99/12.55 thf(1269,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((~ (B = A)) => (~ (! [D:produc2041926651_state]: (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ C) | ~ (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 33.99/12.55 thf(232,axiom,((! [A:list_com,B:state,C:list_com,D:state,E:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (append_com @ A @ E) @ B) @ (produc1204172211_state @ (append_com @ C @ E) @ D)) @ pHoare259243666_exec1) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_app__exec)). 33.99/12.55 thf(1327,plain,((! [A:list_com,B:state,C:list_com,D:state,E:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (append_com @ A @ E) @ B) @ (produc1204172211_state @ (append_com @ C @ E) @ D)) @ pHoare259243666_exec1) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 33.99/12.55 thf(143,axiom,((! [A:list_com,B:state,C:list_com,D:state]: ((~ ((B != D) <= (A = C))) <= ((produc1204172211_state @ A @ B) = (produc1204172211_state @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Pair__inject)). 33.99/12.55 thf(945,plain,((! [A:list_com,B:state,C:list_com,D:state]: (~ (~ (B = D) | ~ (A = C)) | ~ ((produc1204172211_state @ A @ B) = (produc1204172211_state @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 33.99/12.55 thf(6,axiom,((! [A:produc186437863_state,B:(produc186437863_state > $o)]: ((member512523024_state @ A @ (collec489924946_state @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_mem__Collect__eq)). 33.99/12.55 thf(340,plain,((! [A:produc186437863_state,B:(produc186437863_state > $o)]: ((member512523024_state @ A @ (collec489924946_state @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 33.99/12.55 thf(55,axiom,((! [A:(state > $o),B:state,C:com]: ((~ (A @ B)) => (termi @ (while @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_termi_OWhileFalse)). 33.99/12.55 thf(538,plain,((! [A:(state > $o),B:state,C:com]: ((~ (A @ B)) => (termi @ (while @ (A) @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 33.99/12.55 thf(204,axiom,((! [A:list_com,B:state,C:list_com,D:state]: ((! [E:com,F:list_com]: ((? [G:list_com]: (C = (append_com @ G @ F))) <= (A = (cons_com @ E @ F)))) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_exec1__only1__aux)). 33.99/12.55 thf(1196,plain,((! [A:list_com,B:state,C:list_com,D:state]: (! [E:com,F:list_com]: (? [G:list_com]: (C = (append_com @ G @ F)) | ~ (A = (cons_com @ E @ F))) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 33.99/12.55 thf(95,axiom,((! [A:list_com,B:com,C:list_com,D:com]: (((append_com @ A @ (cons_com @ B @ nil_com)) = (append_com @ C @ (cons_com @ D @ nil_com))) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_append1__eq__conv)). 33.99/12.55 thf(709,plain,((! [A:list_com,B:com,C:list_com,D:com]: (((append_com @ A @ (cons_com @ B @ nil_com)) = (append_com @ C @ (cons_com @ D @ nil_com))) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 33.99/12.55 thf(244,axiom,((! [A:list_com,B:list_com,C:com,D:list_com]: (((append_com @ A @ B) = (cons_com @ C @ D)) = (((A = nil_com) & (B = (cons_com @ C @ D))) | ? [E:list_com]: ((A = (cons_com @ C @ E)) & ((append_com @ E @ B) = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_append__eq__Cons__conv)). 33.99/12.55 thf(1386,plain,((! [A:list_com,B:list_com,C:com,D:list_com]: (((append_com @ A @ B) = (cons_com @ C @ D)) = (((A = nil_com) & (B = (cons_com @ C @ D))) | ? [E:list_com]: ((A = (cons_com @ C @ E)) & ((append_com @ E @ B) = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 33.99/12.55 thf(64,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > $o)]: (((D @ A) => ((! [E:produc410756839_state,F:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ E @ F) @ C) => ((D @ E) => (D @ F))) <= (member512523024_state @ (produc2065881943_state @ A @ E) @ (transi463013610_state @ C)))) => (D @ B))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_rtrancl__induct)). 33.99/12.55 thf(565,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > $o)]: (((D @ A) => ((! [E:produc410756839_state,F:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ E @ F) @ C) => ((D @ E) => (D @ F))) | ~ (member512523024_state @ (produc2065881943_state @ A @ E) @ (transi463013610_state @ C)))) => (D @ B))) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 33.99/12.55 thf(33,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > $o)]: ((((D @ A) <= (! [E:produc410756839_state,F:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ F @ B) @ (transi463013610_state @ C)) => ((D @ F) => (D @ E))) <= (member512523024_state @ (produc2065881943_state @ E @ F) @ C)))) <= (D @ B)) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_converse__rtrancl__induct)). 33.99/12.55 thf(436,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > $o)]: ((D @ A) | ~ (! [E:produc410756839_state,F:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ F @ B) @ (transi463013610_state @ C)) => ((D @ F) => (D @ E))) | ~ (member512523024_state @ (produc2065881943_state @ E @ F) @ C))) | ~ (D @ B) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 33.99/12.55 thf(267,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: (((~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)) => (~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ C)))))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_trancl_Ocases)). 33.99/12.55 thf(1518,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: (((~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)) => (~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ C)))))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 33.99/12.55 thf(83,axiom,((! [A:(state > $o),B:com,C:com,D:(state > $o),E:com,F:com]: (((cond @ A @ B @ C) = (cond @ D @ E @ F)) = ((A = D) & (C = F) & (B = E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_com_Oinject_I3_J)). 33.99/12.55 thf(651,plain,((! [A:(state > $o),B:com,C:com,D:(state > $o),E:com,F:com]: (((cond @ (A) @ B @ C) = (cond @ (D) @ E @ F)) = (((A) = (D)) & (C = F) & (B = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 33.99/12.55 thf(188,axiom,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre1738592858_state @ C)) => (~ (! [D:produc2041926651_state,E:produc2041926651_state]: ((! [F:list_P1040014977_state,G:list_P1040014977_state]: ((B != (append982487830_state @ F @ (cons_P465369265_state @ E @ G))) <= (A = (append982487830_state @ F @ (cons_P465369265_state @ D @ G))))) <= (member1069318160_state @ (produc1909270103_state @ D @ E) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_listrel1E)). 33.99/12.55 thf(1127,plain,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre1738592858_state @ C)) => (~ (! [D:produc2041926651_state,E:produc2041926651_state]: (! [F:list_P1040014977_state,G:list_P1040014977_state]: (~ (B = (append982487830_state @ F @ (cons_P465369265_state @ E @ G))) | ~ (A = (append982487830_state @ F @ (cons_P465369265_state @ D @ G)))) | ~ (member1069318160_state @ (produc1909270103_state @ D @ E) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 33.99/12.55 thf(324,axiom,((! [A:list_com,B:com,C:list_com,D:set_Pr1822651163om_com]: (((~ (! [E:list_com]: ((~ (member32358020st_com @ (produc1307105171st_com @ E @ C) @ (listrel1_com @ D))) <= (A = (cons_com @ B @ E))))) <= (! [E:com]: ((A = (cons_com @ E @ C)) => (~ (member1333916004om_com @ (product_Pair_com_com @ E @ B) @ D))))) <= (member32358020st_com @ (produc1307105171st_com @ A @ (cons_com @ B @ C)) @ (listrel1_com @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_Cons__listrel1E2)). 33.99/12.55 thf(1782,plain,((! [A:list_com,B:com,C:list_com,D:set_Pr1822651163om_com]: (~ (! [E:list_com]: (~ (member32358020st_com @ (produc1307105171st_com @ E @ C) @ (listrel1_com @ D)) | ~ (A = (cons_com @ B @ E)))) | ~ (! [E:com]: ((A = (cons_com @ E @ C)) => (~ (member1333916004om_com @ (product_Pair_com_com @ E @ B) @ D)))) | ~ (member32358020st_com @ (produc1307105171st_com @ A @ (cons_com @ B @ C)) @ (listrel1_com @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 33.99/12.55 thf(21,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ D) @ (transi1666849160_state @ C)) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_trancl__trans)). 33.99/12.55 thf(389,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ D) @ (transi1666849160_state @ C)) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C))) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 33.99/12.55 thf(224,axiom,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ B @ (append_com @ B @ A)) @ (lexord_com @ C)) <= (? [D:com,E:list_com]: (A = (cons_com @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_lexord__append__rightI)). 33.99/12.55 thf(1287,plain,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ B @ (append_com @ B @ A)) @ (lexord_com @ C)) | ~ (? [D:com,E:list_com]: (A = (cons_com @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 33.99/12.55 thf(306,axiom,((! [A:com,B:com,C:list_com,D:state]: (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (semi @ A @ B) @ C) @ D) @ (produc1204172211_state @ (cons_com @ A @ (cons_com @ B @ C)) @ D)) @ pHoare259243666_exec1))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_exec1_OSemi)). 33.99/12.55 thf(1709,plain,((! [A:com,B:com,C:list_com,D:state]: (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (semi @ A @ B) @ C) @ D) @ (produc1204172211_state @ (cons_com @ A @ (cons_com @ B @ C)) @ D)) @ pHoare259243666_exec1))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 33.99/12.55 thf(98,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > $o)]: (((D @ B) => ((! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => ((member1069318160_state @ (produc1909270103_state @ F @ B) @ (transi1302705790_state @ C)) => ((D @ F) => (D @ E))))) => (D @ A))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_converse__rtrancl__induct)). 33.99/12.55 thf(719,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > $o)]: (((D @ B) => ((! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => ((member1069318160_state @ (produc1909270103_state @ F @ B) @ (transi1302705790_state @ C)) => ((D @ F) => (D @ E))))) => (D @ A))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 33.99/12.55 thf(280,axiom,((! [A:(list_com > (list_com > $o)),B:list_com,C:list_com]: ((! [D:list_com]: (A @ nil_com @ D)) => ((! [D:com,E:list_com,F:list_com]: ((A @ (cons_com @ D @ E) @ F) <= (A @ F @ E))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_splice_Oinduct)). 33.99/12.55 thf(1577,plain,((! [A:(list_com > (list_com > $o)),B:list_com,C:list_com]: ((! [D:list_com]: (A @ nil_com @ D)) => ((! [D:com,E:list_com,F:list_com]: ((A @ (cons_com @ D @ E) @ F) | ~ (A @ F @ E))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 33.99/12.55 thf(141,axiom,((! [A:produc2041926651_state,B:(nat > produc2041926651_state),C:set_Pr1165141447_state,D:produc2041926651_state]: ((! [E:nat]: ((member1069318160_state @ (produc1909270103_state @ A @ (B @ E)) @ (transi1302705790_state @ C)) & (member1069318160_state @ (produc1909270103_state @ (B @ E) @ (B @ (suc @ E))) @ C))) => ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C)) => ((? [E:(nat > produc2041926651_state)]: (! [F:nat]: (member1069318160_state @ (produc1909270103_state @ (E @ F) @ (E @ (suc @ F))) @ C) & ((E @ zero_zero_nat) = A))) <= (D = (B @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_renumber__aux)). 33.99/12.55 thf(934,plain,((! [A:produc2041926651_state,B:(nat > produc2041926651_state),C:set_Pr1165141447_state,D:produc2041926651_state]: ((! [E:nat]: ((member1069318160_state @ (produc1909270103_state @ A @ (B @ E)) @ (transi1302705790_state @ C)) & (member1069318160_state @ (produc1909270103_state @ (B @ E) @ (B @ (suc @ E))) @ C))) => ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C)) => (? [E:(nat > produc2041926651_state)]: (! [F:nat]: (member1069318160_state @ (produc1909270103_state @ (E @ F) @ (E @ (suc @ F))) @ C) & ((E @ zero_zero_nat) = A)) | ~ (D = (B @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 33.99/12.55 thf(170,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) <= (member1069318160_state @ (produc1909270103_state @ B @ D) @ C)) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_r__r__into__trancl)). 33.99/12.55 thf(1059,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) | ~ (member1069318160_state @ (produc1909270103_state @ B @ D) @ C) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 33.99/12.55 thf(233,axiom,((! [A:(produc2041926651_state > $o),B:produc2041926651_state]: ((A @ B) <= (! [C:list_com,D:state]: (A @ (produc1204172211_state @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_prod__cases)). 33.99/12.55 thf(1330,plain,((! [A:(produc2041926651_state > $o),B:produc2041926651_state]: ((A @ B) | ~ (! [C:list_com,D:state]: (A @ (produc1204172211_state @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 33.99/12.55 thf(218,axiom,((! [A:list_com,B:list_list_com,C:list_state,D:set_Pr849496667_state]: ((member1442949316_state @ (produc1742567891_state @ (cons_list_com @ A @ B) @ C) @ (listre1268245261_state @ D)) => (~ (! [E:state,F:list_state]: (((~ (member1442949316_state @ (produc1742567891_state @ B @ F) @ (listre1268245261_state @ D))) <= (member64234660_state @ (produc1204172211_state @ A @ E) @ D)) <= (C = (cons_state @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_listrel__Cons1)). 33.99/12.55 thf(1264,plain,((! [A:list_com,B:list_list_com,C:list_state,D:set_Pr849496667_state]: ((member1442949316_state @ (produc1742567891_state @ (cons_list_com @ A @ B) @ C) @ (listre1268245261_state @ D)) => (~ (! [E:state,F:list_state]: (~ (member1442949316_state @ (produc1742567891_state @ B @ F) @ (listre1268245261_state @ D)) | ~ (member64234660_state @ (produc1204172211_state @ A @ E) @ D) | ~ (C = (cons_state @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 33.99/12.55 thf(66,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) <= (member512523024_state @ (produc2065881943_state @ B @ D) @ (transi463013610_state @ C))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_trancl__rtrancl__trancl)). 33.99/12.55 thf(587,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ B @ D) @ (transi463013610_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 33.99/12.55 thf(128,axiom,((! [A:produc2058209240st_com]: ((! [B:(com > (com > $o))]: (A != (produc1914379986st_com @ B @ nil_com))) => ((! [B:(com > (com > $o)),C:com]: (A != (produc1914379986st_com @ B @ (cons_com @ C @ nil_com)))) => (~ (! [B:(com > (com > $o)),C:com,D:com,E:list_com]: (A != (produc1914379986st_com @ B @ (cons_com @ C @ (cons_com @ D @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_successively_Ocases)). 33.99/12.55 thf(838,plain,((! [A:produc2058209240st_com]: ((! [B:(com > (com > $o))]: ~ (A = (produc1914379986st_com @ (B) @ nil_com))) => ((! [B:(com > (com > $o)),C:com]: ~ (A = (produc1914379986st_com @ (B) @ (cons_com @ C @ nil_com)))) => (~ (! [B:(com > (com > $o)),C:com,D:com,E:list_com]: ~ (A = (produc1914379986st_com @ (B) @ (cons_com @ C @ (cons_com @ D @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 33.99/12.55 thf(229,axiom,((! [A:list_com]: ((A != nil_com) => (~ (! [B:com,C:list_com]: (A != (cons_com @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_list_Oexhaust)). 33.99/12.55 thf(1313,plain,((! [A:list_com]: ((~ (A = nil_com)) => (~ (! [B:com,C:list_com]: ~ (A = (cons_com @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 33.99/12.55 thf(222,axiom,((! [A:list_list_com,B:list_state,C:set_Pr849496667_state,D:(list_list_com > (list_state > $o))]: (((D @ nil_list_com @ nil_state) => ((D @ A @ B) <= (! [E:list_com,F:state,G:list_list_com,H:list_state]: ((((D @ G @ H) => (D @ (cons_list_com @ E @ G) @ (cons_state @ F @ H))) <= (member1442949316_state @ (produc1742567891_state @ G @ H) @ (listre1268245261_state @ C))) <= (member64234660_state @ (produc1204172211_state @ E @ F) @ C))))) <= (member1442949316_state @ (produc1742567891_state @ A @ B) @ (listre1268245261_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_listrel_Oinducts)). 33.99/12.55 thf(1279,plain,((! [A:list_list_com,B:list_state,C:set_Pr849496667_state,D:(list_list_com > (list_state > $o))]: (((D @ nil_list_com @ nil_state) => ((D @ A @ B) | ~ (! [E:list_com,F:state,G:list_list_com,H:list_state]: (((D @ G @ H) => (D @ (cons_list_com @ E @ G) @ (cons_state @ F @ H))) | ~ (member1442949316_state @ (produc1742567891_state @ G @ H) @ (listre1268245261_state @ C)) | ~ (member64234660_state @ (produc1204172211_state @ E @ F) @ C))))) | ~ (member1442949316_state @ (produc1742567891_state @ A @ B) @ (listre1268245261_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 33.99/12.55 thf(62,axiom,((! [A:list_com,B:list_com,C:list_com]: ((append_com @ (append_com @ A @ B) @ C) = (append_com @ A @ (append_com @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_append__assoc)). 33.99/12.55 thf(559,plain,((! [A:list_com,B:list_com,C:list_com]: ((append_com @ (append_com @ A @ B) @ C) = (append_com @ A @ (append_com @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 33.99/12.55 thf(326,axiom,((! [A:com,B:state]: ((termi @ A @ B) => (~ (pHoare2126160787le_inf @ (cons_com @ A @ nil_com) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_termi__impl__not__inf)). 33.99/12.55 thf(1800,plain,((! [A:com,B:state]: ((termi @ A @ B) => (~ (pHoare2126160787le_inf @ (cons_com @ A @ nil_com) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 33.99/12.55 thf(178,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E))))) <= (! [D:nat]: (A @ zero_zero_nat @ (suc @ D)))) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_diff__induct)). 33.99/12.55 thf(1087,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) | ~ (! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 33.99/12.55 thf(286,axiom,((! [A:nat]: (member1069318160_state @ (produc1909270103_state @ (f @ A) @ (f @ (suc @ A))) @ (transi1726587420_state @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)). 33.99/12.55 thf(1609,plain,((! [A:nat]: (member1069318160_state @ (produc1909270103_state @ (f @ A) @ (f @ (suc @ A))) @ (transi1726587420_state @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 33.99/12.55 thf(238,axiom,((! [A:list_P1040014977_state,B:produc2041926651_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: ((~ (! [E:produc2041926651_state,F:list_P1040014977_state]: ((A = (cons_P465369265_state @ E @ F)) => ((~ (member1267359376_state @ (produc1298457559_state @ F @ C) @ (listre194873521_state @ D))) <= (member1069318160_state @ (produc1909270103_state @ E @ B) @ D))))) <= (member1267359376_state @ (produc1298457559_state @ A @ (cons_P465369265_state @ B @ C)) @ (listre194873521_state @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_listrel__Cons2)). 33.99/12.55 thf(1347,plain,((! [A:list_P1040014977_state,B:produc2041926651_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: (~ (! [E:produc2041926651_state,F:list_P1040014977_state]: ((A = (cons_P465369265_state @ E @ F)) => (~ (member1267359376_state @ (produc1298457559_state @ F @ C) @ (listre194873521_state @ D)) | ~ (member1069318160_state @ (produc1909270103_state @ E @ B) @ D)))) | ~ (member1267359376_state @ (produc1298457559_state @ A @ (cons_P465369265_state @ B @ C)) @ (listre194873521_state @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 33.99/12.55 thf(241,axiom,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com]: ((member1333916004om_com @ (product_Pair_com_com @ A @ B) @ C) => (member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ D) @ (cons_com @ B @ D)) @ (listrel1_com @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_listrel1I1)). 33.99/12.55 thf(1362,plain,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com]: ((member1333916004om_com @ (product_Pair_com_com @ A @ B) @ C) => (member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ D) @ (cons_com @ B @ D)) @ (listrel1_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 33.99/12.55 thf(323,axiom,((! [A:produc186437863_state]: ~ (! [B:produc410756839_state,C:produc2041926651_state,D:list_com,E:state]: (A != (produc2065881943_state @ B @ (produc1909270103_state @ C @ (produc1204172211_state @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_prod__cases4)). 33.99/12.55 thf(1778,plain,((! [A:produc186437863_state]: ~ (! [B:produc410756839_state,C:produc2041926651_state,D:list_com,E:state]: ~ (A = (produc2065881943_state @ B @ (produc1909270103_state @ C @ (produc1204172211_state @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 33.99/12.55 thf(258,axiom,((! [A:com]: ((insert_com @ A @ nil_com) = (cons_com @ A @ nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_insert__Nil)). 33.99/12.55 thf(1489,plain,((! [A:com]: ((insert_com @ A @ nil_com) = (cons_com @ A @ nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 33.99/12.55 thf(44,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) = (? [D:produc410756839_state,E:produc410756839_state]: ((B = E) & (member512523024_state @ (produc2065881943_state @ D @ E) @ C) & (A = D)) | ? [D:produc410756839_state,E:produc410756839_state,F:produc410756839_state]: ((A = D) & (member512523024_state @ (produc2065881943_state @ E @ F) @ C) & (member512523024_state @ (produc2065881943_state @ D @ E) @ (transi1666849160_state @ C)) & (B = F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_trancl_Osimps)). 33.99/12.55 thf(492,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) = (? [D:produc410756839_state,E:produc410756839_state]: ((B = E) & (member512523024_state @ (produc2065881943_state @ D @ E) @ C) & (A = D)) | ? [D:produc410756839_state,E:produc410756839_state,F:produc410756839_state]: ((A = D) & (member512523024_state @ (produc2065881943_state @ E @ F) @ C) & (member512523024_state @ (produc2065881943_state @ D @ E) @ (transi1666849160_state @ C)) & (B = F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 33.99/12.55 thf(103,axiom,((! [A:produc2058209240st_com]: ((! [B:(com > (com > $o))]: (A != (produc1914379986st_com @ B @ nil_com))) => (~ (! [B:(com > (com > $o)),C:com,D:list_com]: (A != (produc1914379986st_com @ B @ (cons_com @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_sorted__wrt_Ocases)). 33.99/12.55 thf(756,plain,((! [A:produc2058209240st_com]: ((! [B:(com > (com > $o))]: ~ (A = (produc1914379986st_com @ (B) @ nil_com))) => (~ (! [B:(com > (com > $o)),C:com,D:list_com]: ~ (A = (produc1914379986st_com @ (B) @ (cons_com @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 33.99/12.55 thf(111,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_old_Onat_Odistinct_I2_J)). 33.99/12.55 thf(789,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 33.99/12.55 thf(194,axiom,((! [A:produc2041926651_state,B:list_P1040014977_state,C:produc2041926651_state,D:list_P1040014977_state,E:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ B) @ (cons_P465369265_state @ C @ D)) @ (listre1738592858_state @ E)) = (((member1069318160_state @ (produc1909270103_state @ A @ C) @ E) & (B = D)) | ((member1267359376_state @ (produc1298457559_state @ B @ D) @ (listre1738592858_state @ E)) & (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_Cons__listrel1__Cons)). 33.99/12.55 thf(1151,plain,((! [A:produc2041926651_state,B:list_P1040014977_state,C:produc2041926651_state,D:list_P1040014977_state,E:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ B) @ (cons_P465369265_state @ C @ D)) @ (listre1738592858_state @ E)) = (((member1069318160_state @ (produc1909270103_state @ A @ C) @ E) & (B = D)) | ((member1267359376_state @ (produc1298457559_state @ B @ D) @ (listre1738592858_state @ E)) & (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 33.99/12.55 thf(248,axiom,((! [A:(list_com > $o),B:list_com]: ((A @ nil_com) => ((! [C:com]: (A @ (cons_com @ C @ nil_com))) => ((A @ B) <= (! [C:com,D:com,E:list_com]: ((A @ E) => ((A @ (cons_com @ C @ (cons_com @ D @ E))) <= (A @ (cons_com @ D @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_induct__list012)). 33.99/12.55 thf(1418,plain,((! [A:(list_com > $o),B:list_com]: ((A @ nil_com) => ((! [C:com]: (A @ (cons_com @ C @ nil_com))) => ((A @ B) | ~ (! [C:com,D:com,E:list_com]: ((A @ E) => ((A @ (cons_com @ C @ (cons_com @ D @ E))) | ~ (A @ (cons_com @ D @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 33.99/12.55 thf(77,axiom,((! [A:com,B:com,C:(state > $o),D:com]: ((semi @ A @ B) != (while @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_com_Odistinct_I13_J)). 33.99/12.55 thf(623,plain,((! [A:com,B:com,C:(state > $o),D:com]: ~ ((semi @ A @ B) = (while @ (C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 33.99/12.55 thf(42,axiom,((! [A:(state > $o),B:com,C:com,D:(state > $o),E:com]: ((cond @ A @ B @ C) != (while @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_com_Odistinct_I19_J)). 33.99/12.55 thf(485,plain,((! [A:(state > $o),B:com,C:com,D:(state > $o),E:com]: ~ ((cond @ (A) @ B @ C) = (while @ (D) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 33.99/12.55 thf(190,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state,E:set_Pr2096893127_state,F:(produc2041926651_state > (produc2041926651_state > $o))]: (((F @ C @ D) => ((F @ A @ B) <= (! [G:produc2041926651_state,H:produc2041926651_state,I:produc2041926651_state,J:produc2041926651_state]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ G @ H) @ (produc1909270103_state @ I @ J)) @ E) => (((F @ I @ J) => (F @ G @ H)) <= (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ I @ J) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E))))))) <= (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_converse__rtrancl__induct2)). 33.99/12.55 thf(1136,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state,E:set_Pr2096893127_state,F:(produc2041926651_state > (produc2041926651_state > $o))]: (((F @ C @ D) => ((F @ A @ B) | ~ (! [G:produc2041926651_state,H:produc2041926651_state,I:produc2041926651_state,J:produc2041926651_state]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ G @ H) @ (produc1909270103_state @ I @ J)) @ E) => (((F @ I @ J) => (F @ G @ H)) | ~ (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ I @ J) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E))))))) | ~ (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 33.99/12.55 thf(243,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state]: ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ D) @ (cons_P465369265_state @ B @ D)) @ (listre1738592858_state @ C)) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_listrel1I1)). 33.99/12.55 thf(1383,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state]: ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ D) @ (cons_P465369265_state @ B @ D)) @ (listre1738592858_state @ C)) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 33.99/12.55 thf(9,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) => ((~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ C))))) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rtranclE)). 33.99/12.55 thf(348,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) => (~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ C)))) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 33.99/12.55 thf(281,axiom,((! [A:produc410756839_state,B:set_Pr1165141447_state]: ((member1069318160_state @ A @ (transi1726587420_state @ B)) <= (member1069318160_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_r__into__trancl_H)). 33.99/12.55 thf(1581,plain,((! [A:produc410756839_state,B:set_Pr1165141447_state]: ((member1069318160_state @ A @ (transi1726587420_state @ B)) | ~ (member1069318160_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 33.99/12.55 thf(10,axiom,((! [A:set_state]: ((collect_state @ (^ [B:state]: (member_state @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Collect__mem__eq)). 33.99/12.55 thf(353,plain,((! [A:set_state]: ((collect_state @ (^ [B:state]: (member_state @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 33.99/12.55 thf(23,axiom,((! [A:(state > set_state),B:(state > set_state)]: (((do @ A) = (do @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_com_Oinject_I1_J)). 33.99/12.55 thf(396,plain,((! [A:(state > set_state),B:(state > set_state)]: (((do @ (A)) = (do @ (B))) = ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 33.99/12.55 thf(205,axiom,((! [A:com,B:list_com,C:state]: ((pHoare806997636termis @ (cons_com @ A @ B) @ C) = (! [D:state]: ((exec @ C @ A @ D) => (pHoare806997636termis @ B @ D)) & (termi @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_termis_Osimps_I2_J)). 33.99/12.55 thf(1201,plain,((! [A:com,B:list_com,C:state]: ((pHoare806997636termis @ (cons_com @ A @ B) @ C) = (! [D:state]: ((exec @ C @ A @ D) => (pHoare806997636termis @ B @ D)) & (termi @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 33.99/12.55 thf(131,axiom,((! [A:list_com,B:state,C:list_com,D:state,E:set_Pr1165141447_state,F:(list_com > (state > $o))]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1726587420_state @ E)) => ((! [G:list_com,H:state]: ((F @ G @ H) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ G @ H)) @ E))) => ((! [G:list_com,H:state,I:list_com,J:state]: (((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ G @ H) @ (produc1204172211_state @ I @ J)) @ E) => ((F @ G @ H) => (F @ I @ J))) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ G @ H)) @ (transi1726587420_state @ E)))) => (F @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_trancl__induct2)). 33.99/12.55 thf(849,plain,((! [A:list_com,B:state,C:list_com,D:state,E:set_Pr1165141447_state,F:(list_com > (state > $o))]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1726587420_state @ E)) => ((! [G:list_com,H:state]: ((F @ G @ H) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ G @ H)) @ E))) => ((! [G:list_com,H:state,I:list_com,J:state]: (((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ G @ H) @ (produc1204172211_state @ I @ J)) @ E) => ((F @ G @ H) => (F @ I @ J))) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ G @ H)) @ (transi1726587420_state @ E)))) => (F @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 33.99/12.55 thf(268,axiom,((! [A:com,B:list_com,C:state]: ((pHoare2126160787le_inf @ (cons_com @ A @ B) @ C) => (? [D:state]: ((exec @ C @ A @ D) & (pHoare2126160787le_inf @ B @ D)) | (pHoare2126160787le_inf @ (cons_com @ A @ nil_com) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_inf__cases)). 33.99/12.55 thf(1521,plain,((! [A:com,B:list_com,C:state]: ((pHoare2126160787le_inf @ (cons_com @ A @ B) @ C) => (? [D:state]: ((exec @ C @ A @ D) & (pHoare2126160787le_inf @ B @ D)) | (pHoare2126160787le_inf @ (cons_com @ A @ nil_com) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 33.99/12.55 thf(134,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C)) <= (member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1302705790_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rtrancl__trans)). 33.99/12.55 thf(877,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C)) | ~ (member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1302705790_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 33.99/12.55 thf(90,axiom,((! [A:com,B:list_com]: ((cons_com @ A @ B) != B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_not__Cons__self2)). 33.99/12.55 thf(692,plain,((! [A:com,B:list_com]: ~ ((cons_com @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 33.99/12.55 thf(142,axiom,((! [A:nat]: ((? [B:nat]: (A = (suc @ B))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_not0__implies__Suc)). 33.99/12.55 thf(942,plain,((! [A:nat]: (? [B:nat]: (A = (suc @ B)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 33.99/12.55 thf(52,axiom,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:list_com]: ((member32358020st_com @ (produc1307105171st_com @ (append_com @ D @ A) @ (append_com @ D @ B)) @ (lexord_com @ C)) <= (member32358020st_com @ (produc1307105171st_com @ A @ B) @ (lexord_com @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_lexord__append__leftI)). 33.99/12.55 thf(529,plain,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:list_com]: ((member32358020st_com @ (produc1307105171st_com @ (append_com @ D @ A) @ (append_com @ D @ B)) @ (lexord_com @ C)) | ~ (member32358020st_com @ (produc1307105171st_com @ A @ B) @ (lexord_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 33.99/12.55 thf(119,axiom,((! [A:list_com,B:set_Pr1822651163om_com]: ~ (member32358020st_com @ (produc1307105171st_com @ nil_com @ A) @ (listrel1_com @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_not__Nil__listrel1)). 33.99/12.55 thf(810,plain,((! [A:list_com,B:set_Pr1822651163om_com]: ~ (member32358020st_com @ (produc1307105171st_com @ nil_com @ A) @ (listrel1_com @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 33.99/12.55 thf(57,axiom,((! [A:produc186437863_state,B:set_Pr2096893127_state]: ((member512523024_state @ A @ (transi1666849160_state @ B)) <= (member512523024_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_r__into__trancl_H)). 33.99/12.55 thf(546,plain,((! [A:produc186437863_state,B:set_Pr2096893127_state]: ((member512523024_state @ A @ (transi1666849160_state @ B)) | ~ (member512523024_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 33.99/12.55 thf(112,axiom,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ (transi1302705790_state @ C))) <= (member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre1738592858_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_listrel__reflcl__if__listrel1)). 33.99/12.55 thf(793,plain,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ (transi1302705790_state @ C))) | ~ (member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre1738592858_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 33.99/12.55 thf(312,axiom,((! [A:(list_com > (list_com > $o)),B:list_com,C:list_com]: ((A @ nil_com @ nil_com) => ((((! [D:com,E:list_com,F:com,G:list_com]: ((A @ (cons_com @ D @ E) @ (cons_com @ F @ G)) <= (A @ E @ G))) => (A @ B @ C)) <= (! [D:com,E:list_com]: (A @ nil_com @ (cons_com @ D @ E)))) <= (! [D:com,E:list_com]: (A @ (cons_com @ D @ E) @ nil_com)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_list__induct2_H)). 33.99/12.55 thf(1730,plain,((! [A:(list_com > (list_com > $o)),B:list_com,C:list_com]: ((A @ nil_com @ nil_com) => (((! [D:com,E:list_com,F:com,G:list_com]: ((A @ (cons_com @ D @ E) @ (cons_com @ F @ G)) | ~ (A @ E @ G))) => (A @ B @ C)) | ~ (! [D:com,E:list_com]: (A @ nil_com @ (cons_com @ D @ E))) | ~ (! [D:com,E:list_com]: (A @ (cons_com @ D @ E) @ nil_com)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 33.99/12.55 thf(114,axiom,((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ n)) @ (transi1302705790_state @ pHoare259243666_exec1))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3)). 33.99/12.55 thf(798,plain,((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ n)) @ (transi1302705790_state @ pHoare259243666_exec1))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 33.99/12.55 thf(197,axiom,((! [A:com,B:list_com,C:list_com,D:set_Pr1822651163om_com]: ((~ (! [E:com,F:list_com]: ((C = (cons_com @ E @ F)) => ((member1333916004om_com @ (product_Pair_com_com @ A @ E) @ D) => (~ (member32358020st_com @ (produc1307105171st_com @ B @ F) @ (listrel_com_com @ D))))))) <= (member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ B) @ C) @ (listrel_com_com @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_listrel__Cons1)). 33.99/12.55 thf(1163,plain,((! [A:com,B:list_com,C:list_com,D:set_Pr1822651163om_com]: (~ (! [E:com,F:list_com]: ((C = (cons_com @ E @ F)) => ((member1333916004om_com @ (product_Pair_com_com @ A @ E) @ D) => (~ (member32358020st_com @ (produc1307105171st_com @ B @ F) @ (listrel_com_com @ D)))))) | ~ (member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ B) @ C) @ (listrel_com_com @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 33.99/12.55 thf(220,axiom,((! [A:produc410756839_state,B:set_Pr1165141447_state]: ((member1069318160_state @ A @ B) => (member1069318160_state @ A @ (transi1302705790_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_r__into__rtrancl)). 33.99/12.55 thf(1274,plain,((! [A:produc410756839_state,B:set_Pr1165141447_state]: ((member1069318160_state @ A @ B) => (member1069318160_state @ A @ (transi1302705790_state @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 33.99/12.55 thf(4,axiom,((! [A:produc186437863_state]: ? [B:produc410756839_state,C:produc410756839_state]: (A = (produc2065881943_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_surj__pair)). 33.99/12.55 thf(334,plain,((! [A:produc186437863_state]: ? [B:produc410756839_state,C:produc410756839_state]: (A = (produc2065881943_state @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 33.99/12.55 thf(179,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state,E:list_P1040014977_state,F:list_P1040014977_state,G:list_P1040014977_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ C) => (((G = (append982487830_state @ E @ (cons_P465369265_state @ B @ F))) => (member1267359376_state @ (produc1298457559_state @ D @ G) @ (listre1738592858_state @ C))) <= (D = (append982487830_state @ E @ (cons_P465369265_state @ A @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_listrel1I)). 33.99/12.55 thf(1091,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state,E:list_P1040014977_state,F:list_P1040014977_state,G:list_P1040014977_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ C) => (((G = (append982487830_state @ E @ (cons_P465369265_state @ B @ F))) => (member1267359376_state @ (produc1298457559_state @ D @ G) @ (listre1738592858_state @ C))) | ~ (D = (append982487830_state @ E @ (cons_P465369265_state @ A @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 33.99/12.55 thf(237,axiom,((! [A:((com > (com > $o)) > (list_com > $o)),B:(com > (com > $o)),C:list_com]: ((! [D:(com > (com > $o))]: (A @ D @ nil_com)) => ((A @ B @ C) <= (! [D:(com > (com > $o)),E:com,F:list_com]: ((A @ D @ F) => (A @ D @ (cons_com @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_sorted__wrt_Oinduct)). 33.99/12.55 thf(1343,plain,((! [A:((com > (com > $o)) > (list_com > $o)),B:(com > (com > $o)),C:list_com]: ((! [D:(com > (com > $o))]: (A @ (D) @ nil_com)) => ((A @ (B) @ C) | ~ (! [D:(com > (com > $o)),E:com,F:list_com]: ((A @ (D) @ F) => (A @ (D) @ (cons_com @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 33.99/12.55 thf(161,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) = (((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) & (A != B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rtrancl__eq__or__trancl)). 33.99/12.55 thf(1021,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) = (((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) & ~ (A = B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 33.99/12.55 thf(240,axiom,((! [A:set_nat,B:com]: (((member_nat @ zero_zero_nat @ A) => ((nths_com @ (cons_com @ B @ nil_com) @ A) = (cons_com @ B @ nil_com))) & ((~ (member_nat @ zero_zero_nat @ A)) => ((nths_com @ (cons_com @ B @ nil_com) @ A) = nil_com))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_nths__singleton)). 33.99/12.55 thf(1355,plain,((! [A:set_nat,B:com]: (((member_nat @ zero_zero_nat @ A) => ((nths_com @ (cons_com @ B @ nil_com) @ A) = (cons_com @ B @ nil_com))) & ((~ (member_nat @ zero_zero_nat @ A)) => ((nths_com @ (cons_com @ B @ nil_com) @ A) = nil_com))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 33.99/12.55 thf(22,axiom,((! [A:(state > $o),B:state,C:com]: ((A @ B) => (((termi @ (while @ A @ C) @ B) <= (! [D:state]: ((exec @ B @ C @ D) => (termi @ (while @ A @ C) @ D)))) <= (termi @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_termi_OWhileTrue)). 33.99/12.55 thf(392,plain,((! [A:(state > $o),B:state,C:com]: ((A @ B) => ((termi @ (while @ (A) @ C) @ B) | ~ (! [D:state]: ((exec @ B @ C @ D) => (termi @ (while @ (A) @ C) @ D))) | ~ (termi @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 33.99/12.55 thf(29,axiom,((! [A:(produc186437863_state > $o),B:produc186437863_state]: ((A @ B) <= (! [C:produc410756839_state,D:produc410756839_state]: (A @ (produc2065881943_state @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_old_Oprod_Oinducts)). 33.99/12.55 thf(424,plain,((! [A:(produc186437863_state > $o),B:produc186437863_state]: ((A @ B) | ~ (! [C:produc410756839_state,D:produc410756839_state]: (A @ (produc2065881943_state @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 33.99/12.55 thf(79,axiom,((! [A:(produc186437863_state > $o),B:produc186437863_state]: ((! [C:produc410756839_state,D:produc410756839_state]: (A @ (produc2065881943_state @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_prod__cases)). 33.99/12.55 thf(630,plain,((! [A:(produc186437863_state > $o),B:produc186437863_state]: ((! [C:produc410756839_state,D:produc410756839_state]: (A @ (produc2065881943_state @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 33.99/12.55 thf(165,axiom,((! [A:set_Pr1165141447_state]: ((transi1302705790_state @ (transi1726587420_state @ A)) = (transi1302705790_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_trancl__rtrancl__absorb)). 33.99/12.55 thf(1042,plain,((! [A:set_Pr1165141447_state]: ((transi1302705790_state @ (transi1726587420_state @ A)) = (transi1302705790_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 33.99/12.55 thf(144,axiom,((! [A:(state > $o),B:state,C:com,D:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ A @ C) @ D) @ B) @ (produc1204172211_state @ D @ B)) @ pHoare259243666_exec1) <= (~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_exec1_OWhileFalse)). 33.99/12.55 thf(952,plain,((! [A:(state > $o),B:state,C:com,D:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ (A) @ C) @ D) @ B) @ (produc1204172211_state @ D @ B)) @ pHoare259243666_exec1) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 33.99/12.55 thf(242,axiom,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state,D:(list_P1040014977_state > (list_P1040014977_state > $o))]: ((member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ C)) => (((D @ A @ B) <= (! [E:produc2041926651_state,F:produc2041926651_state,G:list_P1040014977_state,H:list_P1040014977_state]: (((member1267359376_state @ (produc1298457559_state @ G @ H) @ (listre194873521_state @ C)) => ((D @ (cons_P465369265_state @ E @ G) @ (cons_P465369265_state @ F @ H)) <= (D @ G @ H))) <= (member1069318160_state @ (produc1909270103_state @ E @ F) @ C)))) <= (D @ nil_Pr1844458753_state @ nil_Pr1844458753_state))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_listrel_Oinducts)). 33.99/12.55 thf(1365,plain,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state,D:(list_P1040014977_state > (list_P1040014977_state > $o))]: ((member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ C)) => ((D @ A @ B) | ~ (! [E:produc2041926651_state,F:produc2041926651_state,G:list_P1040014977_state,H:list_P1040014977_state]: (((member1267359376_state @ (produc1298457559_state @ G @ H) @ (listre194873521_state @ C)) => ((D @ (cons_P465369265_state @ E @ G) @ (cons_P465369265_state @ F @ H)) | ~ (D @ G @ H))) | ~ (member1069318160_state @ (produc1909270103_state @ E @ F) @ C))) | ~ (D @ nil_Pr1844458753_state @ nil_Pr1844458753_state))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 33.99/12.55 thf(275,axiom,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:com]: ((member32358020st_com @ (produc1307105171st_com @ (cons_com @ D @ A) @ (cons_com @ D @ B)) @ (transi436345274st_com @ (listrel1_com @ C))) <= (member32358020st_com @ (produc1307105171st_com @ A @ B) @ (transi436345274st_com @ (listrel1_com @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_rtrancl__listrel1__ConsI1)). 33.99/12.55 thf(1555,plain,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:com]: ((member32358020st_com @ (produc1307105171st_com @ (cons_com @ D @ A) @ (cons_com @ D @ B)) @ (transi436345274st_com @ (listrel1_com @ C))) | ~ (member32358020st_com @ (produc1307105171st_com @ A @ B) @ (transi436345274st_com @ (listrel1_com @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 33.99/12.55 thf(226,axiom,((! [A:(list_com > (list_com > $o)),B:list_com,C:list_com]: ((! [D:list_com]: (A @ nil_com @ D)) => ((! [D:list_com]: (A @ D @ nil_com)) => ((A @ B @ C) <= (! [D:com,E:list_com,F:com,G:list_com]: ((A @ E @ (cons_com @ F @ G)) => ((A @ (cons_com @ D @ E) @ G) => (A @ (cons_com @ D @ E) @ (cons_com @ F @ G)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_shuffles_Oinduct)). 33.99/12.55 thf(1296,plain,((! [A:(list_com > (list_com > $o)),B:list_com,C:list_com]: ((! [D:list_com]: (A @ nil_com @ D)) => ((! [D:list_com]: (A @ D @ nil_com)) => ((A @ B @ C) | ~ (! [D:com,E:list_com,F:com,G:list_com]: ((A @ E @ (cons_com @ F @ G)) => ((A @ (cons_com @ D @ E) @ G) => (A @ (cons_com @ D @ E) @ (cons_com @ F @ G)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 33.99/12.55 thf(301,axiom,((! [A:set_Pr1165141447_state]: ((transi1302705790_state @ (transi1302705790_state @ A)) = (transi1302705790_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_rtrancl__idemp)). 33.99/12.55 thf(1687,plain,((! [A:set_Pr1165141447_state]: ((transi1302705790_state @ (transi1302705790_state @ A)) = (transi1302705790_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 33.99/12.55 thf(291,axiom,((! [A:(state > $o),B:com,C:com,D:list_com,E:state,F:list_com,G:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (cond @ A @ B @ C) @ D) @ E) @ (produc1204172211_state @ F @ G)) @ pHoare259243666_exec1) => (((F = (cons_com @ B @ D)) => ((G = E) => (~ (A @ E)))) => (~ ((F = (cons_com @ C @ D)) => ((G = E) => (A @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_exec1E_I4_J)). 33.99/12.55 thf(1624,plain,((! [A:(state > $o),B:com,C:com,D:list_com,E:state,F:list_com,G:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (cond @ (A) @ B @ C) @ D) @ E) @ (produc1204172211_state @ F @ G)) @ pHoare259243666_exec1) => (((F = (cons_com @ B @ D)) => ((G = E) => (~ (A @ E)))) => (~ ((F = (cons_com @ C @ D)) => ((G = E) => (A @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 33.99/12.55 thf(295,axiom,((! [A:produc2041926651_state,B:set_Pr1165141447_state]: (member1069318160_state @ (produc1909270103_state @ A @ A) @ (transi1302705790_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_rtrancl_Ortrancl__refl)). 33.99/12.55 thf(1656,plain,((! [A:produc2041926651_state,B:set_Pr1165141447_state]: (member1069318160_state @ (produc1909270103_state @ A @ A) @ (transi1302705790_state @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 33.99/12.55 thf(59,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (((~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ C) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ (transi1666849160_state @ C)))))) <= (~ (member512523024_state @ (produc2065881943_state @ A @ B) @ C))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_converse__tranclE)). 33.99/12.55 thf(551,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ C) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ (transi1666849160_state @ C))))) | (member512523024_state @ (produc2065881943_state @ A @ B) @ C) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 33.99/12.55 thf(278,axiom,(((product_lists_com @ nil_list_com) = (cons_list_com @ nil_com @ nil_list_com))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_product__lists_Osimps_I1_J)). 33.99/12.55 thf(1573,plain,(((product_lists_com @ nil_list_com) = (cons_list_com @ nil_com @ nil_list_com))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 33.99/12.55 thf(65,axiom,((! [A:(state > set_state),B:(state > $o),C:com]: ((do @ A) != (while @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_com_Odistinct_I5_J)). 33.99/12.55 thf(583,plain,((! [A:(state > set_state),B:(state > $o),C:com]: ~ ((do @ (A)) = (while @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 33.99/12.55 thf(125,axiom,((! [A:list_com,B:state,C:list_com,D:state]: (((pHoare806997636termis @ A @ B) => (pHoare806997636termis @ C @ D)) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ pHoare259243666_exec1))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_execs__pres__termis)). 33.99/12.55 thf(830,plain,((! [A:list_com,B:state,C:list_com,D:state]: (((pHoare806997636termis @ A @ B) => (pHoare806997636termis @ C @ D)) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ pHoare259243666_exec1))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 33.99/12.55 thf(88,axiom,((! [A:state,B:(state > $o)]: ((member_state @ A @ (collect_state @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_mem__Collect__eq)). 33.99/12.55 thf(682,plain,((! [A:state,B:(state > $o)]: ((member_state @ A @ (collect_state @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 33.99/12.55 thf(246,axiom,((! [A:(produc186437863_state > $o),B:produc186437863_state]: ((A @ B) <= (! [C:produc410756839_state,D:produc2041926651_state,E:produc2041926651_state]: (A @ (produc2065881943_state @ C @ (produc1909270103_state @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_prod__induct3)). 33.99/12.55 thf(1407,plain,((! [A:(produc186437863_state > $o),B:produc186437863_state]: ((A @ B) | ~ (! [C:produc410756839_state,D:produc2041926651_state,E:produc2041926651_state]: (A @ (produc2065881943_state @ C @ (produc1909270103_state @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 33.99/12.55 thf(313,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state,E:list_P1040014977_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ D) @ (cons_P465369265_state @ B @ E)) @ (transi339813252_state @ (listre1738592858_state @ C))) <= (member1267359376_state @ (produc1298457559_state @ D @ E) @ (transi339813252_state @ (listre1738592858_state @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_rtrancl__listrel1__ConsI2)). 33.99/12.55 thf(1740,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state,E:list_P1040014977_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ D) @ (cons_P465369265_state @ B @ E)) @ (transi339813252_state @ (listre1738592858_state @ C))) | ~ (member1267359376_state @ (produc1298457559_state @ D @ E) @ (transi339813252_state @ (listre1738592858_state @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 33.99/12.55 thf(129,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1726587420_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_trancl__trans)). 33.99/12.55 thf(842,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1726587420_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 33.99/12.55 thf(318,axiom,((! [A:com,B:list_com,C:com,D:list_com,E:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ B) @ (cons_com @ C @ D)) @ (listrel1_com @ E)) = (((member1333916004om_com @ (product_Pair_com_com @ A @ C) @ E) & (B = D)) | ((member32358020st_com @ (produc1307105171st_com @ B @ D) @ (listrel1_com @ E)) & (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Cons__listrel1__Cons)). 33.99/12.55 thf(1762,plain,((! [A:com,B:list_com,C:com,D:list_com,E:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ B) @ (cons_com @ C @ D)) @ (listrel1_com @ E)) = (((member1333916004om_com @ (product_Pair_com_com @ A @ C) @ E) & (B = D)) | ((member32358020st_com @ (produc1307105171st_com @ B @ D) @ (listrel1_com @ E)) & (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 33.99/12.55 thf(185,axiom,((! [A:com,B:list_com,C:com,D:list_com,E:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ B) @ (cons_com @ C @ D)) @ (lexord_com @ E)) = ((member1333916004om_com @ (product_Pair_com_com @ A @ C) @ E) | ((member32358020st_com @ (produc1307105171st_com @ B @ D) @ (lexord_com @ E)) & (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_lexord__cons__cons)). 33.99/12.55 thf(1111,plain,((! [A:com,B:list_com,C:com,D:list_com,E:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ B) @ (cons_com @ C @ D)) @ (lexord_com @ E)) = ((member1333916004om_com @ (product_Pair_com_com @ A @ C) @ E) | ((member32358020st_com @ (produc1307105171st_com @ B @ D) @ (lexord_com @ E)) & (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 33.99/12.55 thf(261,axiom,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (append982487830_state @ A @ B) @ (append982487830_state @ A @ C)) @ (lexord1062073966_state @ D)) => ((member1267359376_state @ (produc1298457559_state @ B @ C) @ (lexord1062073966_state @ D)) <= (! [E:produc2041926651_state]: ~ (member1069318160_state @ (produc1909270103_state @ E @ E) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_lexord__append__leftD)). 33.99/12.55 thf(1498,plain,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (append982487830_state @ A @ B) @ (append982487830_state @ A @ C)) @ (lexord1062073966_state @ D)) => ((member1267359376_state @ (produc1298457559_state @ B @ C) @ (lexord1062073966_state @ D)) | ~ (! [E:produc2041926651_state]: ~ (member1069318160_state @ (produc1909270103_state @ E @ E) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 33.99/12.55 thf(157,axiom,(((f @ zero_zero_nat) = (produc1204172211_state @ (cons_com @ c @ nil_com) @ s))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)). 33.99/12.55 thf(1006,plain,(((f @ zero_zero_nat) = (produc1204172211_state @ (cons_com @ c @ nil_com) @ s))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 33.99/12.55 thf(317,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state]: (((produc1909270103_state @ A @ B) = (produc1909270103_state @ C @ D)) => (~ ((A = C) => (B != D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Pair__inject)). 33.99/12.55 thf(1755,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state]: (((produc1909270103_state @ A @ B) = (produc1909270103_state @ C @ D)) => (~ ((A = C) => (~ (B = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 33.99/12.55 thf(109,axiom,((! [A:state,B:com,C:state,D:list_com,E:state]: (((pHoare259243732_execs @ A @ (cons_com @ B @ D) @ E) <= (pHoare259243732_execs @ C @ D @ E)) <= (exec @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_execs_Ointros_I2_J)). 33.99/12.55 thf(783,plain,((! [A:state,B:com,C:state,D:list_com,E:state]: ((pHoare259243732_execs @ A @ (cons_com @ B @ D) @ E) | ~ (pHoare259243732_execs @ C @ D @ E) | ~ (exec @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 33.99/12.55 thf(152,axiom,((! [A:produc410756839_state]: ~ (! [B:produc2041926651_state,C:list_com,D:state]: (A != (produc1909270103_state @ B @ (produc1204172211_state @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_prod__cases3)). 33.99/12.55 thf(989,plain,((! [A:produc410756839_state]: ~ (! [B:produc2041926651_state,C:list_com,D:state]: ~ (A = (produc1909270103_state @ B @ (produc1204172211_state @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 33.99/12.55 thf(132,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) = (? [D:produc2041926651_state,E:produc2041926651_state]: ((B = E) & (member1069318160_state @ (produc1909270103_state @ D @ E) @ C) & (A = D)) | ? [D:produc2041926651_state,E:produc2041926651_state,F:produc2041926651_state]: ((A = D) & (member1069318160_state @ (produc1909270103_state @ E @ F) @ C) & (member1069318160_state @ (produc1909270103_state @ D @ E) @ (transi1726587420_state @ C)) & (B = F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_trancl_Osimps)). 33.99/12.55 thf(857,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) = (? [D:produc2041926651_state,E:produc2041926651_state]: ((B = E) & (member1069318160_state @ (produc1909270103_state @ D @ E) @ C) & (A = D)) | ? [D:produc2041926651_state,E:produc2041926651_state,F:produc2041926651_state]: ((A = D) & (member1069318160_state @ (produc1909270103_state @ E @ F) @ C) & (member1069318160_state @ (produc1909270103_state @ D @ E) @ (transi1726587420_state @ C)) & (B = F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 33.99/12.55 thf(212,axiom,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state,D:list_P1040014977_state]: (((member1267359376_state @ (produc1298457559_state @ B @ D) @ (listre194873521_state @ (transi1302705790_state @ C))) => (member1267359376_state @ (produc1298457559_state @ A @ D) @ (listre194873521_state @ (transi1302705790_state @ C)))) <= (member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ (transi1302705790_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_listrel__rtrancl__trans)). 33.99/12.55 thf(1234,plain,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state,D:list_P1040014977_state]: (((member1267359376_state @ (produc1298457559_state @ B @ D) @ (listre194873521_state @ (transi1302705790_state @ C))) => (member1267359376_state @ (produc1298457559_state @ A @ D) @ (listre194873521_state @ (transi1302705790_state @ C)))) | ~ (member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ (transi1302705790_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 33.99/12.55 thf(272,axiom,((! [A:set_Pr1165141447_state]: ((listre194873521_state @ (transi1302705790_state @ A)) = (transi339813252_state @ (listre1738592858_state @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_listrel__rtrancl__eq__rtrancl__listrel1)). 33.99/12.55 thf(1541,plain,((! [A:set_Pr1165141447_state]: ((listre194873521_state @ (transi1302705790_state @ A)) = (transi339813252_state @ (listre1738592858_state @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 33.99/12.55 thf(321,axiom,((! [A:(state > $o),B:state,C:com,D:com,E:list_com]: ((A @ B) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (cond @ A @ C @ D) @ E) @ B) @ (produc1204172211_state @ (cons_com @ C @ E) @ B)) @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_exec1_OIfTrue)). 33.99/12.55 thf(1772,plain,((! [A:(state > $o),B:state,C:com,D:com,E:list_com]: ((A @ B) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (cond @ (A) @ C @ D) @ E) @ B) @ (produc1204172211_state @ (cons_com @ C @ E) @ B)) @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 33.99/12.55 thf(217,axiom,((! [A:com,B:list_com,C:list_com,D:list_com,E:list_com]: ((((cons_com @ A @ D) = (append_com @ C @ E)) <= (D = (append_com @ B @ E))) <= ((cons_com @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Cons__eq__appendI)). 33.99/12.55 thf(1259,plain,((! [A:com,B:list_com,C:list_com,D:list_com,E:list_com]: (((cons_com @ A @ D) = (append_com @ C @ E)) | ~ (D = (append_com @ B @ E)) | ~ ((cons_com @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 33.99/12.55 thf(180,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ B @ D) @ C) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_rtrancl_Ortrancl__into__rtrancl)). 33.99/12.55 thf(1096,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ B @ D) @ C) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 33.99/12.55 thf(298,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_trancl__into__rtrancl)). 33.99/12.55 thf(1672,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 33.99/12.55 thf(309,axiom,((! [A:list_com]: ((n_lists_com @ zero_zero_nat @ A) = (cons_list_com @ nil_com @ nil_list_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_n__lists_Osimps_I1_J)). 33.99/12.55 thf(1719,plain,((! [A:list_com]: ((n_lists_com @ zero_zero_nat @ A) = (cons_list_com @ nil_com @ nil_list_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 33.99/12.55 thf(11,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_trancl__into__rtrancl)). 33.99/12.55 thf(356,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 33.99/12.55 thf(225,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Suc__neq__Zero)). 33.99/12.55 thf(1292,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 33.99/12.55 thf(60,axiom,((! [A:(state > $o),B:com,C:state]: ((termi @ (while @ A @ B) @ C) => ((A @ C) => (termi @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_while__termiE)). 33.99/12.55 thf(554,plain,((! [A:(state > $o),B:com,C:state]: ((termi @ (while @ (A) @ B) @ C) => ((A @ C) => (termi @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 33.99/12.55 thf(39,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) = (? [D:produc410756839_state,E:produc410756839_state,F:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ D @ E) @ (transi463013610_state @ C)) & (member512523024_state @ (produc2065881943_state @ E @ F) @ C) & (B = F) & (A = D)) | ? [D:produc410756839_state]: ((B = D) & (A = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_rtrancl_Osimps)). 33.99/12.55 thf(476,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) = (? [D:produc410756839_state,E:produc410756839_state,F:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ D @ E) @ (transi463013610_state @ C)) & (member512523024_state @ (produc2065881943_state @ E @ F) @ C) & (B = F) & (A = D)) | ? [D:produc410756839_state]: ((B = D) & (A = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 33.99/12.55 thf(51,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (((~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ C))))) <= (~ (member512523024_state @ (produc2065881943_state @ A @ B) @ C))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_tranclE)). 33.99/12.55 thf(526,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ C)))) | (member512523024_state @ (produc2065881943_state @ A @ B) @ C) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 33.99/12.55 thf(81,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) => (((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) & (A != B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rtranclD)). 33.99/12.55 thf(637,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) => (((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) & ~ (A = B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 33.99/12.55 thf(43,axiom,((! [A:(state > $o),B:state,C:com]: ((exec @ B @ (while @ A @ C) @ B) <= (~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_exec_OWhileFalse)). 33.99/12.55 thf(489,plain,((! [A:(state > $o),B:state,C:com]: ((exec @ B @ (while @ (A) @ C) @ B) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 33.99/12.55 thf(209,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_n__not__Suc__n)). 33.99/12.55 thf(1214,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 33.99/12.55 thf(67,axiom,((! [A:produc186437863_state,B:set_Pr2096893127_state]: ((member512523024_state @ A @ B) => (member512523024_state @ A @ (transi463013610_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_r__into__rtrancl)). 33.99/12.55 thf(590,plain,((! [A:produc186437863_state,B:set_Pr2096893127_state]: ((member512523024_state @ A @ B) => (member512523024_state @ A @ (transi463013610_state @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 33.99/12.55 thf(94,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) <= (member1069318160_state @ (produc1909270103_state @ B @ D) @ C)) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_rtrancl__into__trancl1)). 33.99/12.55 thf(706,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) | ~ (member1069318160_state @ (produc1909270103_state @ B @ D) @ C) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 33.99/12.55 thf(87,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:produc410756839_state,D:produc410756839_state]: (((produc2065881943_state @ A @ B) = (produc2065881943_state @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_old_Oprod_Oinject)). 33.99/12.55 thf(679,plain,((! [A:produc410756839_state,B:produc410756839_state,C:produc410756839_state,D:produc410756839_state]: (((produc2065881943_state @ A @ B) = (produc2065881943_state @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 33.99/12.55 thf(164,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state,E:list_P1040014977_state,F:list_P1040014977_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ C) => (member1267359376_state @ (produc1298457559_state @ (append982487830_state @ D @ (cons_P465369265_state @ A @ E)) @ (append982487830_state @ D @ (cons_P465369265_state @ B @ F))) @ (lexord1062073966_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_lexord__append__left__rightI)). 33.99/12.55 thf(1039,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state,E:list_P1040014977_state,F:list_P1040014977_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ C) => (member1267359376_state @ (produc1298457559_state @ (append982487830_state @ D @ (cons_P465369265_state @ A @ E)) @ (append982487830_state @ D @ (cons_P465369265_state @ B @ F))) @ (lexord1062073966_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 33.99/12.55 thf(186,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((A @ C) => (A @ (suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_nat__induct)). 33.99/12.55 thf(1114,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ C) => (A @ (suc @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 33.99/12.55 thf(181,axiom,((! [A:list_com]: ((A != nil_com) = (? [B:com,C:list_com]: (A = (cons_com @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_neq__Nil__conv)). 33.99/12.55 thf(1099,plain,((! [A:list_com]: ((~ (A = nil_com)) = (? [B:com,C:list_com]: (A = (cons_com @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 33.99/12.55 thf(84,axiom,((! [A:com,B:state,C:com]: (((! [D:state]: ((exec @ B @ A @ D) => (termi @ C @ D))) => (termi @ (semi @ A @ C) @ B)) <= (termi @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_termi_OSemi)). 33.99/12.55 thf(654,plain,((! [A:com,B:state,C:com]: (((! [D:state]: ((exec @ B @ A @ D) => (termi @ C @ D))) => (termi @ (semi @ A @ C) @ B)) | ~ (termi @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 33.99/12.55 thf(297,axiom,((! [A:nat,B:nat]: ((A = B) <= ((suc @ A) = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Suc__inject)). 33.99/12.55 thf(1668,plain,((! [A:nat,B:nat]: ((A = B) | ~ ((suc @ A) = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 33.99/12.55 thf(202,axiom,((! [A:com,B:state,C:com,D:list_com,E:state]: (((termi @ A @ B) => (termi @ C @ E)) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ A @ nil_com) @ B) @ (produc1204172211_state @ (cons_com @ C @ D) @ E)) @ (transi1302705790_state @ pHoare259243666_exec1))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_execs__pres__termi)). 33.99/12.55 thf(1192,plain,((! [A:com,B:state,C:com,D:list_com,E:state]: (((termi @ A @ B) => (termi @ C @ E)) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ A @ nil_com) @ B) @ (produc1204172211_state @ (cons_com @ C @ D) @ E)) @ (transi1302705790_state @ pHoare259243666_exec1))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 33.99/12.55 thf(35,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > (produc410756839_state > $o))]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) => ((! [E:produc410756839_state,F:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ E @ F) @ C) => (D @ E @ F))) => ((! [E:produc410756839_state,F:produc410756839_state,G:produc410756839_state]: ((((D @ E @ G) <= (member512523024_state @ (produc2065881943_state @ F @ G) @ C)) <= (D @ E @ F)) <= (member512523024_state @ (produc2065881943_state @ E @ F) @ (transi1666849160_state @ C)))) => (D @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_trancl_Oinducts)). 33.99/12.55 thf(457,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > (produc410756839_state > $o))]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) => ((! [E:produc410756839_state,F:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ E @ F) @ C) => (D @ E @ F))) => ((! [E:produc410756839_state,F:produc410756839_state,G:produc410756839_state]: ((D @ E @ G) | ~ (member512523024_state @ (produc2065881943_state @ F @ G) @ C) | ~ (D @ E @ F) | ~ (member512523024_state @ (produc2065881943_state @ E @ F) @ (transi1666849160_state @ C)))) => (D @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 33.99/12.55 thf(139,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > (produc2041926651_state > $o))]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => (((! [E:produc2041926651_state,F:produc2041926651_state,G:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ (transi1302705790_state @ C)) => (((D @ E @ G) <= (member1069318160_state @ (produc1909270103_state @ F @ G) @ C)) <= (D @ E @ F)))) => (D @ A @ B)) <= (! [E:produc2041926651_state]: (D @ E @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_rtrancl_Oinducts)). 33.99/12.55 thf(911,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > (produc2041926651_state > $o))]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => (((! [E:produc2041926651_state,F:produc2041926651_state,G:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ (transi1302705790_state @ C)) => ((D @ E @ G) | ~ (member1069318160_state @ (produc1909270103_state @ F @ G) @ C) | ~ (D @ E @ F)))) => (D @ A @ B)) | ~ (! [E:produc2041926651_state]: (D @ E @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 33.99/12.55 thf(156,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Zero__neq__Suc)). 33.99/12.55 thf(1002,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 33.99/12.55 thf(16,axiom,((! [A:(state > set_state),B:com,C:com]: ((do @ A) != (semi @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_com_Odistinct_I1_J)). 33.99/12.55 thf(371,plain,((! [A:(state > set_state),B:com,C:com]: ~ ((do @ (A)) = (semi @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 33.99/12.55 thf(234,axiom,((! [A:(state > $o),B:state,C:com,D:com,E:list_com]: ((~ (A @ B)) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (cond @ A @ C @ D) @ E) @ B) @ (produc1204172211_state @ (cons_com @ D @ E) @ B)) @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_exec1_OIfFalse)). 33.99/12.55 thf(1333,plain,((! [A:(state > $o),B:state,C:com,D:com,E:list_com]: ((~ (A @ B)) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (cond @ (A) @ C @ D) @ E) @ B) @ (produc1204172211_state @ (cons_com @ D @ E) @ B)) @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 33.99/12.55 thf(7,axiom,((! [A:produc410756839_state,B:set_Pr2096893127_state]: (member512523024_state @ (produc2065881943_state @ A @ A) @ (transi463013610_state @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_rtrancl_Ortrancl__refl)). 33.99/12.55 thf(343,plain,((! [A:produc410756839_state,B:set_Pr2096893127_state]: (member512523024_state @ (produc2065881943_state @ A @ A) @ (transi463013610_state @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 33.99/12.55 thf(80,axiom,((! [A:produc186437863_state]: ~ (! [B:produc410756839_state,C:produc410756839_state]: (A != (produc2065881943_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_old_Oprod_Oexhaust)). 33.99/12.55 thf(633,plain,((! [A:produc186437863_state]: ~ (! [B:produc410756839_state,C:produc410756839_state]: ~ (A = (produc2065881943_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 33.99/12.55 thf(48,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (((A != B) => (~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ C) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ (transi463013610_state @ C))))))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_converse__rtranclE)). 33.99/12.55 thf(508,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (((~ (A = B)) => (~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ C) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ (transi463013610_state @ C))))))) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 33.99/12.55 thf(56,axiom,((! [A:list_com,B:list_com,C:list_com,D:list_com,E:list_com]: (((D = (append_com @ B @ E)) => ((append_com @ A @ D) = (append_com @ C @ E))) <= ((append_com @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_append__eq__appendI)). 33.99/12.55 thf(541,plain,((! [A:list_com,B:list_com,C:list_com,D:list_com,E:list_com]: (((D = (append_com @ B @ E)) => ((append_com @ A @ D) = (append_com @ C @ E))) | ~ ((append_com @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 33.99/12.55 thf(174,axiom,((! [A:com,B:state,C:(nat > state),D:nat,E:(state > $o),F:com]: (((! [G:nat]: (exec @ (C @ G) @ F @ (C @ (suc @ G))) & (A = (while @ E @ F)) & (B = (C @ D))) => (? [G:nat]: ~ (E @ (C @ G)))) <= (termi @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_termi__while__lemma)). 33.99/12.55 thf(1071,plain,((! [A:com,B:state,C:(nat > state),D:nat,E:(state > $o),F:com]: (((! [G:nat]: (exec @ (C @ G) @ F @ (C @ (suc @ G))) & (A = (while @ (E) @ F)) & (B = (C @ D))) => (? [G:nat]: ~ (E @ (C @ G)))) | ~ (termi @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 33.99/12.55 thf(266,axiom,((! [A:list_com,B:com,C:list_com,D:com,E:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ (append_com @ A @ (cons_com @ B @ nil_com)) @ (append_com @ C @ (cons_com @ D @ nil_com))) @ (listrel1_com @ E)) = (((member1333916004om_com @ (product_Pair_com_com @ B @ D) @ E) & (A = C)) | ((member32358020st_com @ (produc1307105171st_com @ A @ C) @ (listrel1_com @ E)) & (B = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_snoc__listrel1__snoc__iff)). 33.99/12.55 thf(1515,plain,((! [A:list_com,B:com,C:list_com,D:com,E:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ (append_com @ A @ (cons_com @ B @ nil_com)) @ (append_com @ C @ (cons_com @ D @ nil_com))) @ (listrel1_com @ E)) = (((member1333916004om_com @ (product_Pair_com_com @ B @ D) @ E) & (A = C)) | ((member32358020st_com @ (produc1307105171st_com @ A @ C) @ (listrel1_com @ E)) & (B = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 33.99/12.55 thf(28,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > (produc410756839_state > $o))]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) => ((! [E:produc410756839_state,F:produc410756839_state]: ((D @ E @ F) <= (member512523024_state @ (produc2065881943_state @ E @ F) @ C))) => ((! [E:produc410756839_state,F:produc410756839_state,G:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ E @ F) @ (transi1666849160_state @ C)) => ((D @ E @ F) => (((D @ E @ G) <= (D @ F @ G)) <= (member512523024_state @ (produc2065881943_state @ F @ G) @ (transi1666849160_state @ C)))))) => (D @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_trancl__trans__induct)). 33.99/12.55 thf(412,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > (produc410756839_state > $o))]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) => ((! [E:produc410756839_state,F:produc410756839_state]: ((D @ E @ F) | ~ (member512523024_state @ (produc2065881943_state @ E @ F) @ C))) => ((! [E:produc410756839_state,F:produc410756839_state,G:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ E @ F) @ (transi1666849160_state @ C)) => ((D @ E @ F) => ((D @ E @ G) | ~ (D @ F @ G) | ~ (member512523024_state @ (produc2065881943_state @ F @ G) @ (transi1666849160_state @ C)))))) => (D @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 33.99/12.55 thf(304,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > $o)]: ((((! [E:produc2041926651_state,F:produc2041926651_state]: ((((D @ E) <= (D @ F)) <= (member1069318160_state @ (produc1909270103_state @ F @ B) @ (transi1726587420_state @ C))) <= (member1069318160_state @ (produc1909270103_state @ E @ F) @ C))) => (D @ A)) <= (! [E:produc2041926651_state]: ((D @ E) <= (member1069318160_state @ (produc1909270103_state @ E @ B) @ C)))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_converse__trancl__induct)). 33.99/12.55 thf(1698,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > $o)]: (((! [E:produc2041926651_state,F:produc2041926651_state]: ((D @ E) | ~ (D @ F) | ~ (member1069318160_state @ (produc1909270103_state @ F @ B) @ (transi1726587420_state @ C)) | ~ (member1069318160_state @ (produc1909270103_state @ E @ F) @ C))) => (D @ A)) | ~ (! [E:produc2041926651_state]: ((D @ E) | ~ (member1069318160_state @ (produc1909270103_state @ E @ B) @ C))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 33.99/12.55 thf(123,axiom,((! [A:list_com]: ((append_com @ nil_com @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_append_Oleft__neutral)). 33.99/12.55 thf(824,plain,((! [A:list_com]: ((append_com @ nil_com @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 33.99/12.55 thf(227,axiom,((! [A:com,B:list_com,C:list_com,D:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ B) @ C) @ (listrel1_com @ D)) => ((~ (! [E:list_com]: ((C = (cons_com @ A @ E)) => (~ (member32358020st_com @ (produc1307105171st_com @ B @ E) @ (listrel1_com @ D)))))) <= (! [E:com]: ((~ (member1333916004om_com @ (product_Pair_com_com @ A @ E) @ D)) <= (C = (cons_com @ E @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_Cons__listrel1E1)). 33.99/12.55 thf(1301,plain,((! [A:com,B:list_com,C:list_com,D:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ B) @ C) @ (listrel1_com @ D)) => (~ (! [E:list_com]: ((C = (cons_com @ A @ E)) => (~ (member32358020st_com @ (produc1307105171st_com @ B @ E) @ (listrel1_com @ D))))) | ~ (! [E:com]: (~ (member1333916004om_com @ (product_Pair_com_com @ A @ E) @ D) | ~ (C = (cons_com @ E @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 33.99/12.55 thf(17,axiom,((! [A:set_Pr2096893127_state]: ((transi1666849160_state @ (transi463013610_state @ A)) = (transi463013610_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_rtrancl__trancl__absorb)). 33.99/12.55 thf(375,plain,((! [A:set_Pr2096893127_state]: ((transi1666849160_state @ (transi463013610_state @ A)) = (transi463013610_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 33.99/12.55 thf(148,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_old_Onat_Oinject)). 33.99/12.55 thf(965,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 33.99/12.55 thf(311,axiom,((! [A:list_com,B:list_com]: (((append_com @ A @ B) = A) = (B = nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_append__self__conv)). 33.99/12.55 thf(1727,plain,((! [A:list_com,B:list_com]: (((append_com @ A @ B) = A) = (B = nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 33.99/12.55 thf(264,axiom,((! [A:com,B:state,C:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ A @ nil_com) @ B) @ (produc1204172211_state @ nil_com @ C)) @ (transi1302705790_state @ pHoare259243666_exec1)) => (exec @ B @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_exec1s__impl__exec)). 33.99/12.55 thf(1510,plain,((! [A:com,B:state,C:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ A @ nil_com) @ B) @ (produc1204172211_state @ nil_com @ C)) @ (transi1302705790_state @ pHoare259243666_exec1)) => (exec @ B @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 33.99/12.55 thf(49,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > $o)]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) => (((D @ B) <= (! [E:produc410756839_state,F:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ E) @ (transi1666849160_state @ C)) => (((D @ E) => (D @ F)) <= (member512523024_state @ (produc2065881943_state @ E @ F) @ C))))) <= (! [E:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ E) @ C) => (D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_trancl__induct)). 33.99/12.55 thf(513,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > $o)]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) => ((D @ B) | ~ (! [E:produc410756839_state,F:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ E) @ (transi1666849160_state @ C)) => (((D @ E) => (D @ F)) | ~ (member512523024_state @ (produc2065881943_state @ E @ F) @ C)))) | ~ (! [E:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ E) @ C) => (D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 33.99/12.55 thf(31,axiom,((! [A:state,B:(state > set_state),C:state]: ((exec @ C @ (do @ B) @ A) <= (member_state @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_exec_ODo)). 33.99/12.55 thf(430,plain,((! [A:state,B:(state > set_state),C:state]: ((exec @ C @ (do @ (B)) @ A) | ~ (member_state @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 33.99/12.55 thf(195,axiom,((! [A:((com > (com > $o)) > (list_com > $o)),B:(com > (com > $o)),C:list_com]: (((! [D:(com > (com > $o)),E:com]: (A @ D @ (cons_com @ E @ nil_com))) => ((A @ B @ C) <= (! [D:(com > (com > $o)),E:com,F:com,G:list_com]: ((A @ D @ (cons_com @ E @ (cons_com @ F @ G))) <= (A @ D @ (cons_com @ F @ G)))))) <= (! [D:(com > (com > $o))]: (A @ D @ nil_com))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_successively_Oinduct)). 33.99/12.55 thf(1154,plain,((! [A:((com > (com > $o)) > (list_com > $o)),B:(com > (com > $o)),C:list_com]: (((! [D:(com > (com > $o)),E:com]: (A @ (D) @ (cons_com @ E @ nil_com))) => ((A @ (B) @ C) | ~ (! [D:(com > (com > $o)),E:com,F:com,G:list_com]: ((A @ (D) @ (cons_com @ E @ (cons_com @ F @ G))) | ~ (A @ (D) @ (cons_com @ F @ G)))))) | ~ (! [D:(com > (com > $o))]: (A @ (D) @ nil_com))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 33.99/12.55 thf(63,axiom,((! [A:list_com,B:list_com,C:list_com,D:set_Pr1822651163om_com]: (((member32358020st_com @ (produc1307105171st_com @ B @ C) @ (lexord_com @ D)) <= (! [E:com]: ~ (member1333916004om_com @ (product_Pair_com_com @ E @ E) @ D))) <= (member32358020st_com @ (produc1307105171st_com @ (append_com @ A @ B) @ (append_com @ A @ C)) @ (lexord_com @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_lexord__append__leftD)). 33.99/12.55 thf(562,plain,((! [A:list_com,B:list_com,C:list_com,D:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ B @ C) @ (lexord_com @ D)) | ~ (! [E:com]: ~ (member1333916004om_com @ (product_Pair_com_com @ E @ E) @ D)) | ~ (member32358020st_com @ (produc1307105171st_com @ (append_com @ A @ B) @ (append_com @ A @ C)) @ (lexord_com @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 33.99/12.55 thf(25,axiom,((! [A:set_Pr1822651163om_com,B:list_com,C:list_com,D:list_com]: ((irrefl_com @ A) => ((member32358020st_com @ (produc1307105171st_com @ (append_com @ B @ C) @ (append_com @ B @ D)) @ (lexord_com @ A)) = (member32358020st_com @ (produc1307105171st_com @ C @ D) @ (lexord_com @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_lexord__same__pref__if__irrefl)). 33.99/12.55 thf(402,plain,((! [A:set_Pr1822651163om_com,B:list_com,C:list_com,D:list_com]: ((irrefl_com @ A) => ((member32358020st_com @ (produc1307105171st_com @ (append_com @ B @ C) @ (append_com @ B @ D)) @ (lexord_com @ A)) = (member32358020st_com @ (produc1307105171st_com @ C @ D) @ (lexord_com @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 33.99/12.55 thf(245,axiom,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:(list_com > (list_com > $o))]: ((((! [E:com,F:com,G:list_com,H:list_com]: ((((D @ (cons_com @ E @ G) @ (cons_com @ F @ H)) <= (D @ G @ H)) <= (member32358020st_com @ (produc1307105171st_com @ G @ H) @ (listrel_com_com @ C))) <= (member1333916004om_com @ (product_Pair_com_com @ E @ F) @ C))) => (D @ A @ B)) <= (D @ nil_com @ nil_com)) <= (member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel_com_com @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_listrel_Oinducts)). 33.99/12.55 thf(1389,plain,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:(list_com > (list_com > $o))]: (((! [E:com,F:com,G:list_com,H:list_com]: ((D @ (cons_com @ E @ G) @ (cons_com @ F @ H)) | ~ (D @ G @ H) | ~ (member32358020st_com @ (produc1307105171st_com @ G @ H) @ (listrel_com_com @ C)) | ~ (member1333916004om_com @ (product_Pair_com_com @ E @ F) @ C))) => (D @ A @ B)) | ~ (D @ nil_com @ nil_com) | ~ (member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel_com_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 33.99/12.55 thf(316,axiom,((! [A:list_com,B:list_com]: ((nil_com = (append_com @ A @ B)) = ((A = nil_com) & (B = nil_com))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_Nil__is__append__conv)). 33.99/12.55 thf(1752,plain,((! [A:list_com,B:list_com]: ((nil_com = (append_com @ A @ B)) = ((A = nil_com) & (B = nil_com))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 33.99/12.55 thf(294,axiom,((! [A:produc2041926651_state]: ~ (! [B:list_com,C:state]: (A != (produc1204172211_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_old_Oprod_Oexhaust)). 33.99/12.55 thf(1652,plain,((! [A:produc2041926651_state]: ~ (! [B:list_com,C:state]: ~ (A = (produc1204172211_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 33.99/12.55 thf(101,axiom,((! [A:list_com,B:com,C:list_com,D:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ (cons_com @ B @ C)) @ (listrel_com_com @ D)) => (~ (! [E:com,F:list_com]: (((member1333916004om_com @ (product_Pair_com_com @ E @ B) @ D) => (~ (member32358020st_com @ (produc1307105171st_com @ F @ C) @ (listrel_com_com @ D)))) <= (A = (cons_com @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_listrel__Cons2)). 33.99/12.55 thf(743,plain,((! [A:list_com,B:com,C:list_com,D:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ (cons_com @ B @ C)) @ (listrel_com_com @ D)) => (~ (! [E:com,F:list_com]: (((member1333916004om_com @ (product_Pair_com_com @ E @ B) @ D) => (~ (member32358020st_com @ (produc1307105171st_com @ F @ C) @ (listrel_com_com @ D)))) | ~ (A = (cons_com @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 33.99/12.55 thf(187,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state,E:list_P1040014977_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ C) => ((member1267359376_state @ (produc1298457559_state @ D @ E) @ (listre194873521_state @ C)) => (member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ D) @ (cons_P465369265_state @ B @ E)) @ (listre194873521_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_listrel_OCons)). 33.99/12.55 thf(1124,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:list_P1040014977_state,E:list_P1040014977_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ C) => ((member1267359376_state @ (produc1298457559_state @ D @ E) @ (listre194873521_state @ C)) => (member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ D) @ (cons_P465369265_state @ B @ E)) @ (listre194873521_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 33.99/12.55 thf(216,axiom,((! [A:nat,B:com,C:list_com]: ((gen_length_com @ A @ (cons_com @ B @ C)) = (gen_length_com @ (suc @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_gen__length__code_I2_J)). 33.99/12.55 thf(1256,plain,((! [A:nat,B:com,C:list_com]: ((gen_length_com @ A @ (cons_com @ B @ C)) = (gen_length_com @ (suc @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 33.99/12.55 thf(211,axiom,((! [A:produc2041926651_state,B:list_P1040014977_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ B) @ C) @ (listre1738592858_state @ D)) => ((! [E:produc2041926651_state]: ((~ (member1069318160_state @ (produc1909270103_state @ A @ E) @ D)) <= (C = (cons_P465369265_state @ E @ B)))) => (~ (! [E:list_P1040014977_state]: ((C = (cons_P465369265_state @ A @ E)) => (~ (member1267359376_state @ (produc1298457559_state @ B @ E) @ (listre1738592858_state @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_Cons__listrel1E1)). 33.99/12.55 thf(1226,plain,((! [A:produc2041926651_state,B:list_P1040014977_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ B) @ C) @ (listre1738592858_state @ D)) => ((! [E:produc2041926651_state]: (~ (member1069318160_state @ (produc1909270103_state @ A @ E) @ D) | ~ (C = (cons_P465369265_state @ E @ B)))) => (~ (! [E:list_P1040014977_state]: ((C = (cons_P465369265_state @ A @ E)) => (~ (member1267359376_state @ (produc1298457559_state @ B @ E) @ (listre1738592858_state @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 33.99/12.55 thf(73,axiom,((! [A:list_com,B:list_com,C:list_com,D:list_com]: (((append_com @ A @ B) = (append_com @ C @ D)) = (? [E:list_com]: (((B = (append_com @ E @ D)) & ((append_com @ A @ E) = C)) | ((A = (append_com @ C @ E)) & ((append_com @ E @ B) = D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_append__eq__append__conv2)). 33.99/12.55 thf(611,plain,((! [A:list_com,B:list_com,C:list_com,D:list_com]: (((append_com @ A @ B) = (append_com @ C @ D)) = (? [E:list_com]: (((B = (append_com @ E @ D)) & ((append_com @ A @ E) = C)) | ((A = (append_com @ C @ E)) & ((append_com @ E @ B) = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 33.99/12.55 thf(319,axiom,((! [A:com,B:list_com]: (nil_com != (cons_com @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_list_Odistinct_I1_J)). 33.99/12.55 thf(1765,plain,((! [A:com,B:list_com]: ~ (nil_com = (cons_com @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 33.99/12.55 thf(117,axiom,((! [A:state,B:(state > set_state),C:state,D:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (do @ B) @ D) @ C) @ (produc1204172211_state @ D @ A)) @ pHoare259243666_exec1) <= (member_state @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_exec1_ODo)). 33.99/12.55 thf(804,plain,((! [A:state,B:(state > set_state),C:state,D:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (do @ (B)) @ D) @ C) @ (produc1204172211_state @ D @ A)) @ pHoare259243666_exec1) | ~ (member_state @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 33.99/12.55 thf(254,axiom,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state]: (((~ (! [D:produc2041926651_state,E:produc2041926651_state,F:list_P1040014977_state]: ((A = (cons_P465369265_state @ D @ F)) => (! [G:list_P1040014977_state]: ((B = (cons_P465369265_state @ E @ G)) => ((member1069318160_state @ (produc1909270103_state @ D @ E) @ C) => (~ (member1267359376_state @ (produc1298457559_state @ F @ G) @ (listre194873521_state @ C))))))))) <= ((B != nil_Pr1844458753_state) <= (A = nil_Pr1844458753_state))) <= (member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_listrel_Ocases)). 33.99/12.55 thf(1464,plain,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state]: (~ (! [D:produc2041926651_state,E:produc2041926651_state,F:list_P1040014977_state]: ((A = (cons_P465369265_state @ D @ F)) => (! [G:list_P1040014977_state]: ((B = (cons_P465369265_state @ E @ G)) => ((member1069318160_state @ (produc1909270103_state @ D @ E) @ C) => (~ (member1267359376_state @ (produc1298457559_state @ F @ G) @ (listre194873521_state @ C)))))))) | ~ (~ (B = nil_Pr1844458753_state) | ~ (A = nil_Pr1844458753_state)) | ~ (member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 33.99/12.55 thf(203,axiom,((! [A:list_P1040014977_state,B:set_Pr1165141447_state]: (member1267359376_state @ (produc1298457559_state @ A @ A) @ (listre194873521_state @ (transi1302705790_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_listrel__rtrancl__refl)). 33.99/12.55 thf(1194,plain,((! [A:list_P1040014977_state,B:set_Pr1165141447_state]: (member1267359376_state @ (produc1298457559_state @ A @ A) @ (listre194873521_state @ (transi1302705790_state @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 33.99/12.55 thf(207,axiom,((! [A:produc2041926651_state,B:list_P1040014977_state,C:produc2041926651_state,D:list_P1040014977_state,E:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ B) @ (cons_P465369265_state @ C @ D)) @ (lexord1062073966_state @ E)) = ((member1069318160_state @ (produc1909270103_state @ A @ C) @ E) | ((A = C) & (member1267359376_state @ (produc1298457559_state @ B @ D) @ (lexord1062073966_state @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_lexord__cons__cons)). 33.99/12.55 thf(1209,plain,((! [A:produc2041926651_state,B:list_P1040014977_state,C:produc2041926651_state,D:list_P1040014977_state,E:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ B) @ (cons_P465369265_state @ C @ D)) @ (lexord1062073966_state @ E)) = ((member1069318160_state @ (produc1909270103_state @ A @ C) @ E) | ((A = C) & (member1267359376_state @ (produc1298457559_state @ B @ D) @ (lexord1062073966_state @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 33.99/12.55 thf(26,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (((~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ C))))) <= (~ (member512523024_state @ (produc2065881943_state @ A @ B) @ C))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_trancl_Ocases)). 33.99/12.55 thf(406,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ C)))) | (member512523024_state @ (produc2065881943_state @ A @ B) @ C) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 33.99/12.55 thf(159,axiom,((! [A:list_com]: ((A != nil_com) => (~ (! [B:list_com,C:com]: (A != (append_com @ B @ (cons_com @ C @ nil_com)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_rev__exhaust)). 33.99/12.55 thf(1011,plain,((! [A:list_com]: ((~ (A = nil_com)) => (~ (! [B:list_com,C:com]: ~ (A = (append_com @ B @ (cons_com @ C @ nil_com)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 33.99/12.55 thf(269,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_old_Onat_Odistinct_I1_J)). 33.99/12.55 thf(1524,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 33.99/12.55 thf(259,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1302705790_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_converse__rtrancl__into__rtrancl)). 33.99/12.55 thf(1492,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1302705790_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 33.99/12.55 thf(13,axiom,((! [A:set_Pr2096893127_state]: ((transi463013610_state @ (transi1666849160_state @ A)) = (transi463013610_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_trancl__rtrancl__absorb)). 33.99/12.55 thf(362,plain,((! [A:set_Pr2096893127_state]: ((transi463013610_state @ (transi1666849160_state @ A)) = (transi463013610_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 33.99/12.55 thf(310,axiom,((! [A:produc2041926651_state,B:list_P1040014977_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: ((~ (! [E:produc2041926651_state,F:list_P1040014977_state]: ((C = (cons_P465369265_state @ E @ F)) => ((~ (member1267359376_state @ (produc1298457559_state @ B @ F) @ (listre194873521_state @ D))) <= (member1069318160_state @ (produc1909270103_state @ A @ E) @ D))))) <= (member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ B) @ C) @ (listre194873521_state @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_listrel__Cons1)). 33.99/12.55 thf(1722,plain,((! [A:produc2041926651_state,B:list_P1040014977_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: (~ (! [E:produc2041926651_state,F:list_P1040014977_state]: ((C = (cons_P465369265_state @ E @ F)) => (~ (member1267359376_state @ (produc1298457559_state @ B @ F) @ (listre194873521_state @ D)) | ~ (member1069318160_state @ (produc1909270103_state @ A @ E) @ D)))) | ~ (member1267359376_state @ (produc1298457559_state @ (cons_P465369265_state @ A @ B) @ C) @ (listre194873521_state @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 33.99/12.55 thf(99,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: (((~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)) => (~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ C)))))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_tranclE)). 33.99/12.55 thf(737,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: (((~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)) => (~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ C)))))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 33.99/12.55 thf(135,axiom,((! [A:(com > list_com)]: ((bind_com_com @ nil_com @ A) = nil_com))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_bind__simps_I1_J)). 33.99/12.55 thf(880,plain,((! [A:(com > list_com)]: ((bind_com_com @ nil_com @ (A)) = nil_com))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 33.99/12.55 thf(302,axiom,((! [A:produc410756839_state]: ~ (! [B:produc2041926651_state,C:produc2041926651_state]: (A != (produc1909270103_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_old_Oprod_Oexhaust)). 33.99/12.55 thf(1690,plain,((! [A:produc410756839_state]: ~ (! [B:produc2041926651_state,C:produc2041926651_state]: ~ (A = (produc1909270103_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 33.99/12.55 thf(251,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((((A != B) & (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))) | (A = B)) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rtranclD)). 33.99/12.55 thf(1439,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((~ (A = B) & (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))) | (A = B) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 33.99/12.55 thf(284,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > $o)]: ((((D @ B) <= (! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ E) @ (transi1302705790_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => ((D @ F) <= (D @ E)))))) <= (D @ A)) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rtrancl__induct)). 33.99/12.55 thf(1589,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > $o)]: ((D @ B) | ~ (! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ E) @ (transi1302705790_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => ((D @ F) | ~ (D @ E))))) | ~ (D @ A) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 33.99/12.55 thf(154,axiom,((! [A:list_list_com,B:list_state,C:set_Pr849496667_state]: ((member1442949316_state @ (produc1742567891_state @ A @ B) @ (listre1268245261_state @ C)) = (? [D:list_com,E:state,F:list_list_com,G:list_state]: ((A = (cons_list_com @ D @ F)) & (member64234660_state @ (produc1204172211_state @ D @ E) @ C) & (member1442949316_state @ (produc1742567891_state @ F @ G) @ (listre1268245261_state @ C)) & (B = (cons_state @ E @ G))) | ((A = nil_list_com) & (B = nil_state)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_listrel_Osimps)). 33.99/12.55 thf(996,plain,((! [A:list_list_com,B:list_state,C:set_Pr849496667_state]: ((member1442949316_state @ (produc1742567891_state @ A @ B) @ (listre1268245261_state @ C)) = (? [D:list_com,E:state,F:list_list_com,G:list_state]: ((A = (cons_list_com @ D @ F)) & (member64234660_state @ (produc1204172211_state @ D @ E) @ C) & (member1442949316_state @ (produc1742567891_state @ F @ G) @ (listre1268245261_state @ C)) & (B = (cons_state @ E @ G))) | ((A = nil_list_com) & (B = nil_state)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 33.99/12.55 thf(236,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_old_Onat_Oexhaust)). 33.99/12.55 thf(1339,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 33.99/12.55 thf(8,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_zero__reorient)). 33.99/12.55 thf(345,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 33.99/12.55 thf(54,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) <= (member512523024_state @ (produc2065881943_state @ B @ D) @ C)) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_rtrancl_Ortrancl__into__rtrancl)). 33.99/12.55 thf(535,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ B @ D) @ C) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 33.99/12.55 thf(121,axiom,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel1_com @ C)) => (~ (! [D:com,E:com]: ((member1333916004om_com @ (product_Pair_com_com @ D @ E) @ C) => (! [F:list_com,G:list_com]: ((B != (append_com @ F @ (cons_com @ E @ G))) <= (A = (append_com @ F @ (cons_com @ D @ G))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_listrel1E)). 33.99/12.55 thf(816,plain,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel1_com @ C)) => (~ (! [D:com,E:com]: ((member1333916004om_com @ (product_Pair_com_com @ D @ E) @ C) => (! [F:list_com,G:list_com]: (~ (B = (append_com @ F @ (cons_com @ E @ G))) | ~ (A = (append_com @ F @ (cons_com @ D @ G))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 33.99/12.55 thf(115,axiom,((termi @ c @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 33.99/12.55 thf(799,plain,((termi @ c @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 33.99/12.55 thf(92,axiom,((! [A:produc410756839_state]: ? [B:produc2041926651_state,C:produc2041926651_state]: (A = (produc1909270103_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_surj__pair)). 33.99/12.55 thf(700,plain,((! [A:produc410756839_state]: ? [B:produc2041926651_state,C:produc2041926651_state]: (A = (produc1909270103_state @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 33.99/12.55 thf(163,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state,E:set_Pr2096893127_state,F:(produc2041926651_state > (produc2041926651_state > $o))]: (((! [G:produc2041926651_state,H:produc2041926651_state]: ((F @ G @ H) <= (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ G @ H)) @ E))) => ((! [G:produc2041926651_state,H:produc2041926651_state,I:produc2041926651_state,J:produc2041926651_state]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ G @ H)) @ (transi1666849160_state @ E)) => ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ G @ H) @ (produc1909270103_state @ I @ J)) @ E) => ((F @ I @ J) <= (F @ G @ H))))) => (F @ C @ D))) <= (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ C @ D)) @ (transi1666849160_state @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_trancl__induct2)). 33.99/12.55 thf(1029,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state,E:set_Pr2096893127_state,F:(produc2041926651_state > (produc2041926651_state > $o))]: (((! [G:produc2041926651_state,H:produc2041926651_state]: ((F @ G @ H) | ~ (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ G @ H)) @ E))) => ((! [G:produc2041926651_state,H:produc2041926651_state,I:produc2041926651_state,J:produc2041926651_state]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ G @ H)) @ (transi1666849160_state @ E)) => ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ G @ H) @ (produc1909270103_state @ I @ J)) @ E) => ((F @ I @ J) | ~ (F @ G @ H))))) => (F @ C @ D))) | ~ (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ C @ D)) @ (transi1666849160_state @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 33.99/12.55 thf(1,conjecture,((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4)). 33.99/12.55 thf(2,negated_conjecture,((~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1)))),inference(neg_conjecture,[status(cth)],[1])). 33.99/12.55 thf(330,plain,((~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ c @ nil_com) @ s) @ (f @ (suc @ n))) @ (transi1302705790_state @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 33.99/12.55 thf(89,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:produc410756839_state,D:produc410756839_state]: ((~ ((B != D) <= (A = C))) <= ((produc2065881943_state @ A @ B) = (produc2065881943_state @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_Pair__inject)). 33.99/12.55 thf(685,plain,((! [A:produc410756839_state,B:produc410756839_state,C:produc410756839_state,D:produc410756839_state]: (~ (~ (B = D) | ~ (A = C)) | ~ ((produc2065881943_state @ A @ B) = (produc2065881943_state @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 33.99/12.55 thf(24,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ D) @ C) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_trancl_Otrancl__into__trancl)). 33.99/12.55 thf(399,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ D) @ C) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C))) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 33.99/12.55 thf(108,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state]: (((produc1909270103_state @ A @ B) = (produc1909270103_state @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_prod_Oinject)). 33.99/12.55 thf(780,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state]: (((produc1909270103_state @ A @ B) = (produc1909270103_state @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 33.99/12.55 thf(136,axiom,((! [A:(list_com > $o),B:list_com]: (((! [C:com]: (A @ (cons_com @ C @ nil_com))) => ((! [C:com,D:com,E:list_com]: (((A @ (cons_com @ C @ E)) <= (C = D)) => (((C != D) => (A @ (cons_com @ D @ E))) => (A @ (cons_com @ C @ (cons_com @ D @ E)))))) => (A @ B))) <= (A @ nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_remdups__adj_Oinduct)). 33.99/12.55 thf(883,plain,((! [A:(list_com > $o),B:list_com]: (((! [C:com]: (A @ (cons_com @ C @ nil_com))) => ((! [C:com,D:com,E:list_com]: (((A @ (cons_com @ C @ E)) | ~ (C = D)) => (((~ (C = D)) => (A @ (cons_com @ D @ E))) => (A @ (cons_com @ C @ (cons_com @ D @ E)))))) => (A @ B))) | ~ (A @ nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 33.99/12.55 thf(160,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state,E:set_Pr2096893127_state,F:(produc2041926651_state > (produc2041926651_state > $o))]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E)) => ((F @ A @ B) => ((! [G:produc2041926651_state,H:produc2041926651_state,I:produc2041926651_state,J:produc2041926651_state]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ G @ H)) @ (transi463013610_state @ E)) => (((F @ I @ J) <= (F @ G @ H)) <= (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ G @ H) @ (produc1909270103_state @ I @ J)) @ E)))) => (F @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rtrancl__induct2)). 33.99/12.55 thf(1015,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state,E:set_Pr2096893127_state,F:(produc2041926651_state > (produc2041926651_state > $o))]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E)) => ((F @ A @ B) => ((! [G:produc2041926651_state,H:produc2041926651_state,I:produc2041926651_state,J:produc2041926651_state]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ G @ H)) @ (transi463013610_state @ E)) => ((F @ I @ J) | ~ (F @ G @ H) | ~ (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ G @ H) @ (produc1909270103_state @ I @ J)) @ E)))) => (F @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 33.99/12.55 thf(200,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) = (? [D:produc2041926651_state,E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) & (member1069318160_state @ (produc1909270103_state @ D @ E) @ (transi1302705790_state @ C)) & (B = F) & (A = D)) | ? [D:produc2041926651_state]: ((B = D) & (A = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rtrancl_Osimps)). 33.99/12.55 thf(1176,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) = (? [D:produc2041926651_state,E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) & (member1069318160_state @ (produc1909270103_state @ D @ E) @ (transi1302705790_state @ C)) & (B = F) & (A = D)) | ? [D:produc2041926651_state]: ((B = D) & (A = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 33.99/12.55 thf(322,axiom,((! [A:produc2041926651_state]: ? [B:list_com,C:state]: (A = (produc1204172211_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_surj__pair)). 33.99/12.55 thf(1775,plain,((! [A:produc2041926651_state]: ? [B:list_com,C:state]: (A = (produc1204172211_state @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 33.99/12.55 thf(215,axiom,((! [A:state,B:list_com,C:state,D:(state > (list_com > (state > $o)))]: ((((! [E:state,F:com,G:state,H:list_com,I:state]: (((pHoare259243732_execs @ G @ H @ I) => ((D @ E @ (cons_com @ F @ H) @ I) <= (D @ G @ H @ I))) <= (exec @ E @ F @ G))) => (D @ A @ B @ C)) <= (! [E:state]: (D @ E @ nil_com @ E))) <= (pHoare259243732_execs @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_execs_Oinducts)). 33.99/12.55 thf(1250,plain,((! [A:state,B:list_com,C:state,D:(state > (list_com > (state > $o)))]: (((! [E:state,F:com,G:state,H:list_com,I:state]: (((pHoare259243732_execs @ G @ H @ I) => ((D @ E @ (cons_com @ F @ H) @ I) | ~ (D @ G @ H @ I))) | ~ (exec @ E @ F @ G))) => (D @ A @ B @ C)) | ~ (! [E:state]: (D @ E @ nil_com @ E)) | ~ (pHoare259243732_execs @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 33.99/12.55 thf(182,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) <= (member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1726587420_state @ C))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_trancl__into__trancl2)). 33.99/12.55 thf(1102,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) | ~ (member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1726587420_state @ C)) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 33.99/12.55 thf(47,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) => ((member512523024_state @ (produc2065881943_state @ B @ D) @ (transi1666849160_state @ C)) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_rtrancl__trancl__trancl)). 33.99/12.55 thf(505,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) => ((member512523024_state @ (produc2065881943_state @ B @ D) @ (transi1666849160_state @ C)) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 33.99/12.55 thf(303,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Zero__not__Suc)). 33.99/12.55 thf(1694,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 33.99/12.55 thf(328,axiom,((! [A:list_P1040014977_state,B:produc2041926651_state,C:list_P1040014977_state,D:produc2041926651_state,E:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (append982487830_state @ A @ (cons_P465369265_state @ B @ nil_Pr1844458753_state)) @ (append982487830_state @ C @ (cons_P465369265_state @ D @ nil_Pr1844458753_state))) @ (listre1738592858_state @ E)) = (((B = D) & (member1267359376_state @ (produc1298457559_state @ A @ C) @ (listre1738592858_state @ E))) | ((member1069318160_state @ (produc1909270103_state @ B @ D) @ E) & (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_snoc__listrel1__snoc__iff)). 33.99/12.55 thf(1805,plain,((! [A:list_P1040014977_state,B:produc2041926651_state,C:list_P1040014977_state,D:produc2041926651_state,E:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ (append982487830_state @ A @ (cons_P465369265_state @ B @ nil_Pr1844458753_state)) @ (append982487830_state @ C @ (cons_P465369265_state @ D @ nil_Pr1844458753_state))) @ (listre1738592858_state @ E)) = (((B = D) & (member1267359376_state @ (produc1298457559_state @ A @ C) @ (listre1738592858_state @ E))) | ((member1069318160_state @ (produc1909270103_state @ B @ D) @ E) & (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 33.99/12.55 thf(85,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > (produc410756839_state > $o))]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) => ((! [E:produc410756839_state]: (D @ E @ E)) => ((D @ A @ B) <= (! [E:produc410756839_state,F:produc410756839_state,G:produc410756839_state]: ((((member512523024_state @ (produc2065881943_state @ F @ G) @ C) => (D @ E @ G)) <= (D @ E @ F)) <= (member512523024_state @ (produc2065881943_state @ E @ F) @ (transi463013610_state @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_rtrancl_Oinducts)). 33.99/12.55 thf(658,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > (produc410756839_state > $o))]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C)) => ((! [E:produc410756839_state]: (D @ E @ E)) => ((D @ A @ B) | ~ (! [E:produc410756839_state,F:produc410756839_state,G:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ F @ G) @ C) => (D @ E @ G)) | ~ (D @ E @ F) | ~ (member512523024_state @ (produc2065881943_state @ E @ F) @ (transi463013610_state @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 33.99/12.55 thf(105,axiom,((! [A:list_com,B:state,C:set_Pr849496667_state,D:list_list_com,E:list_state]: ((member64234660_state @ (produc1204172211_state @ A @ B) @ C) => ((member1442949316_state @ (produc1742567891_state @ D @ E) @ (listre1268245261_state @ C)) => (member1442949316_state @ (produc1742567891_state @ (cons_list_com @ A @ D) @ (cons_state @ B @ E)) @ (listre1268245261_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_listrel_OCons)). 33.99/12.55 thf(768,plain,((! [A:list_com,B:state,C:set_Pr849496667_state,D:list_list_com,E:list_state]: ((member64234660_state @ (produc1204172211_state @ A @ B) @ C) => ((member1442949316_state @ (produc1742567891_state @ D @ E) @ (listre1268245261_state @ C)) => (member1442949316_state @ (produc1742567891_state @ (cons_list_com @ A @ D) @ (cons_state @ B @ E)) @ (listre1268245261_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 33.99/12.55 thf(124,axiom,((! [A:nat]: ((gen_length_com @ A @ nil_com) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_gen__length__code_I1_J)). 33.99/12.55 thf(827,plain,((! [A:nat]: ((gen_length_com @ A @ nil_com) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 33.99/12.55 thf(252,axiom,((! [A:list_com,B:(list_com > $o)]: (((! [C:com]: (B @ (cons_com @ C @ nil_com))) => ((B @ A) <= (! [C:com,D:list_com]: ((D != nil_com) => ((B @ D) => (B @ (append_com @ D @ (cons_com @ C @ nil_com)))))))) <= (A != nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_rev__nonempty__induct)). 33.99/12.55 thf(1445,plain,((! [A:list_com,B:(list_com > $o)]: (((! [C:com]: (B @ (cons_com @ C @ nil_com))) => ((B @ A) | ~ (! [C:com,D:list_com]: ((~ (D = nil_com)) => ((B @ D) => (B @ (append_com @ D @ (cons_com @ C @ nil_com)))))))) | (A = nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 33.99/12.55 thf(270,axiom,((! [A:(produc410756839_state > $o),B:produc410756839_state]: ((A @ B) <= (! [C:produc2041926651_state,D:produc2041926651_state]: (A @ (produc1909270103_state @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_prod__cases)). 33.99/12.55 thf(1528,plain,((! [A:(produc410756839_state > $o),B:produc410756839_state]: ((A @ B) | ~ (! [C:produc2041926651_state,D:produc2041926651_state]: (A @ (produc1909270103_state @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 33.99/12.55 thf(282,axiom,((! [A:com,B:list_com,C:com,D:list_com]: (((cons_com @ A @ B) = (cons_com @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_list_Oinject)). 33.99/12.55 thf(1583,plain,((! [A:com,B:list_com,C:com,D:list_com]: (((cons_com @ A @ B) = (cons_com @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 33.99/12.55 thf(113,axiom,((! [A:list_com]: ((append_com @ nil_com @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_append__Nil)). 33.99/12.55 thf(795,plain,((! [A:list_com]: ((append_com @ nil_com @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 33.99/12.55 thf(58,axiom,((! [A:(state > $o),B:com,C:state,D:state]: ((((exec @ C @ B @ D) => (termi @ (while @ A @ B) @ D)) <= (A @ C)) <= (termi @ (while @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_while__termiE2)). 33.99/12.55 thf(548,plain,((! [A:(state > $o),B:com,C:state,D:state]: (((exec @ C @ B @ D) => (termi @ (while @ (A) @ B) @ D)) | ~ (A @ C) | ~ (termi @ (while @ (A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 33.99/12.55 thf(300,axiom,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ C)) = (((A = nil_Pr1844458753_state) & (B = nil_Pr1844458753_state)) | ? [D:produc2041926651_state,E:produc2041926651_state,F:list_P1040014977_state,G:list_P1040014977_state]: ((B = (cons_P465369265_state @ E @ G)) & (member1069318160_state @ (produc1909270103_state @ D @ E) @ C) & (member1267359376_state @ (produc1298457559_state @ F @ G) @ (listre194873521_state @ C)) & (A = (cons_P465369265_state @ D @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_listrel_Osimps)). 33.99/12.55 thf(1684,plain,((! [A:list_P1040014977_state,B:list_P1040014977_state,C:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ A @ B) @ (listre194873521_state @ C)) = (((A = nil_Pr1844458753_state) & (B = nil_Pr1844458753_state)) | ? [D:produc2041926651_state,E:produc2041926651_state,F:list_P1040014977_state,G:list_P1040014977_state]: ((B = (cons_P465369265_state @ E @ G)) & (member1069318160_state @ (produc1909270103_state @ D @ E) @ C) & (member1267359376_state @ (produc1298457559_state @ F @ G) @ (listre194873521_state @ C)) & (A = (cons_P465369265_state @ D @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 33.99/12.55 thf(176,axiom,((! [A:set_Pr1165141447_state]: ((collec300063826_state @ (^ [B:produc410756839_state]: (member1069318160_state @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Collect__mem__eq)). 33.99/12.55 thf(1081,plain,((! [A:set_Pr1165141447_state]: ((collec300063826_state @ (^ [B:produc410756839_state]: (member1069318160_state @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 33.99/12.55 thf(75,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:produc410756839_state,D:produc410756839_state]: (((produc2065881943_state @ A @ B) = (produc2065881943_state @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_prod_Oinject)). 33.99/12.55 thf(617,plain,((! [A:produc410756839_state,B:produc410756839_state,C:produc410756839_state,D:produc410756839_state]: (((produc2065881943_state @ A @ B) = (produc2065881943_state @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 33.99/12.55 thf(192,axiom,((! [A:list_com,B:state,C:list_com,D:state]: (((produc1204172211_state @ A @ B) = (produc1204172211_state @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_prod_Oinject)). 33.99/12.55 thf(1145,plain,((! [A:list_com,B:state,C:list_com,D:state]: (((produc1204172211_state @ A @ B) = (produc1204172211_state @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 33.99/12.55 thf(149,axiom,((! [A:list_com]: (((! [B:com]: (A != (cons_com @ B @ nil_com))) => (~ (! [B:com,C:com,D:list_com]: (A != (cons_com @ B @ (cons_com @ C @ D)))))) <= (A != nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_remdups__adj_Ocases)). 33.99/12.55 thf(968,plain,((! [A:list_com]: (((! [B:com]: ~ (A = (cons_com @ B @ nil_com))) => (~ (! [B:com,C:com,D:list_com]: ~ (A = (cons_com @ B @ (cons_com @ C @ D)))))) | (A = nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 33.99/12.55 thf(167,axiom,((! [A:list_com,B:list_com]: ((A = B) => (A = (append_com @ nil_com @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_eq__Nil__appendI)). 33.99/12.55 thf(1049,plain,((! [A:list_com,B:list_com]: ((A = B) => (A = (append_com @ nil_com @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 33.99/12.55 thf(38,axiom,((! [A:set_Pr2096893127_state]: ((collec489924946_state @ (^ [B:produc186437863_state]: (member512523024_state @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Collect__mem__eq)). 33.99/12.55 thf(473,plain,((! [A:set_Pr2096893127_state]: ((collec489924946_state @ (^ [B:produc186437863_state]: (member512523024_state @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 33.99/12.55 thf(175,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) <= (A = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_nat_OdiscI)). 33.99/12.55 thf(1076,plain,((! [A:nat,B:nat]: (~ (A = zero_zero_nat) | ~ (A = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 33.99/12.55 thf(96,axiom,((! [A:produc2041926651_state,B:(nat > produc2041926651_state),C:set_Pr1165141447_state]: ((? [D:(nat > produc2041926651_state)]: (! [E:nat]: (member1069318160_state @ (produc1909270103_state @ (D @ E) @ (D @ (suc @ E))) @ C) & ((D @ zero_zero_nat) = A))) <= (! [D:nat]: ((member1069318160_state @ (produc1909270103_state @ A @ (B @ D)) @ (transi1302705790_state @ C)) & (member1069318160_state @ (produc1909270103_state @ (B @ D) @ (B @ (suc @ D))) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_renumber)). 33.99/12.55 thf(712,plain,((! [A:produc2041926651_state,B:(nat > produc2041926651_state),C:set_Pr1165141447_state]: (? [D:(nat > produc2041926651_state)]: (! [E:nat]: (member1069318160_state @ (produc1909270103_state @ (D @ E) @ (D @ (suc @ E))) @ C) & ((D @ zero_zero_nat) = A)) | ~ (! [D:nat]: ((member1069318160_state @ (produc1909270103_state @ A @ (B @ D)) @ (transi1302705790_state @ C)) & (member1069318160_state @ (produc1909270103_state @ (B @ D) @ (B @ (suc @ D))) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 33.99/12.55 thf(287,axiom,((! [A:list_com,B:set_Pr1822651163om_com]: ~ (member32358020st_com @ (produc1307105171st_com @ A @ nil_com) @ (listrel1_com @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_not__listrel1__Nil)). 33.99/12.55 thf(1611,plain,((! [A:list_com,B:set_Pr1822651163om_com]: ~ (member32358020st_com @ (produc1307105171st_com @ A @ nil_com) @ (listrel1_com @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 33.99/12.55 thf(314,axiom,((! [A:produc410756839_state,B:(nat > produc410756839_state),C:set_Pr2096893127_state]: ((! [D:nat]: ((member512523024_state @ (produc2065881943_state @ A @ (B @ D)) @ (transi463013610_state @ C)) & (member512523024_state @ (produc2065881943_state @ (B @ D) @ (B @ (suc @ D))) @ C))) => (? [D:(nat > produc410756839_state)]: (! [E:nat]: (member512523024_state @ (produc2065881943_state @ (D @ E) @ (D @ (suc @ E))) @ C) & ((D @ zero_zero_nat) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_renumber)). 33.99/12.55 thf(1743,plain,((! [A:produc410756839_state,B:(nat > produc410756839_state),C:set_Pr2096893127_state]: ((! [D:nat]: ((member512523024_state @ (produc2065881943_state @ A @ (B @ D)) @ (transi463013610_state @ C)) & (member512523024_state @ (produc2065881943_state @ (B @ D) @ (B @ (suc @ D))) @ C))) => (? [D:(nat > produc410756839_state)]: (! [E:nat]: (member512523024_state @ (produc2065881943_state @ (D @ E) @ (D @ (suc @ E))) @ C) & ((D @ zero_zero_nat) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 33.99/12.55 thf(271,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ (suc @ C)) <= (A @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_old_Onat_Oinducts)). 33.99/12.55 thf(1531,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ (suc @ C)) | ~ (A @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 33.99/12.55 thf(153,axiom,((! [A:(state > $o),B:state,C:com,D:list_com]: ((A @ B) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ A @ C) @ D) @ B) @ (produc1204172211_state @ (cons_com @ C @ (cons_com @ (while @ A @ C) @ D)) @ B)) @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_exec1_OWhileTrue)). 33.99/12.55 thf(993,plain,((! [A:(state > $o),B:state,C:com,D:list_com]: ((A @ B) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ (A) @ C) @ D) @ B) @ (produc1204172211_state @ (cons_com @ C @ (cons_com @ (while @ (A) @ C) @ D)) @ B)) @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 33.99/12.55 thf(274,axiom,((! [A:list_P1040014977_state,B:produc2041926651_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ A @ (cons_P465369265_state @ B @ C)) @ (listre1738592858_state @ D)) => ((~ (! [E:list_P1040014977_state]: ((~ (member1267359376_state @ (produc1298457559_state @ E @ C) @ (listre1738592858_state @ D))) <= (A = (cons_P465369265_state @ B @ E))))) <= (! [E:produc2041926651_state]: ((~ (member1069318160_state @ (produc1909270103_state @ E @ B) @ D)) <= (A = (cons_P465369265_state @ E @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_Cons__listrel1E2)). 33.99/12.55 thf(1547,plain,((! [A:list_P1040014977_state,B:produc2041926651_state,C:list_P1040014977_state,D:set_Pr1165141447_state]: ((member1267359376_state @ (produc1298457559_state @ A @ (cons_P465369265_state @ B @ C)) @ (listre1738592858_state @ D)) => (~ (! [E:list_P1040014977_state]: (~ (member1267359376_state @ (produc1298457559_state @ E @ C) @ (listre1738592858_state @ D)) | ~ (A = (cons_P465369265_state @ B @ E)))) | ~ (! [E:produc2041926651_state]: (~ (member1069318160_state @ (produc1909270103_state @ E @ B) @ D) | ~ (A = (cons_P465369265_state @ E @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 33.99/12.55 thf(315,axiom,((! [A:list_com,B:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ nil_com @ A) @ (listrel_com_com @ B)) => (A = nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_listrel__Nil1)). 33.99/12.55 thf(1748,plain,((! [A:list_com,B:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ nil_com @ A) @ (listrel_com_com @ B)) => (A = nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 33.99/12.55 thf(27,axiom,((! [A:list_list_com,B:list_list_com]: ((concat_com @ (append_list_com @ A @ B)) = (append_com @ (concat_com @ A) @ (concat_com @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_concat__append)). 33.99/12.55 thf(409,plain,((! [A:list_list_com,B:list_list_com]: ((concat_com @ (append_list_com @ A @ B)) = (append_com @ (concat_com @ A) @ (concat_com @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 33.99/12.55 thf(256,axiom,((! [A:state]: (pHoare259243732_execs @ A @ nil_com @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_execs_Ointros_I1_J)). 33.99/12.55 thf(1484,plain,((! [A:state]: (pHoare259243732_execs @ A @ nil_com @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 33.99/12.55 thf(249,axiom,((! [A:(state > set_state),B:list_com,C:state,D:list_com,E:state]: ((~ ((D = B) => (~ (member_state @ E @ (A @ C))))) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (do @ A) @ B) @ C) @ (produc1204172211_state @ D @ E)) @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_exec1E_I2_J)). 33.99/12.55 thf(1432,plain,((! [A:(state > set_state),B:list_com,C:state,D:list_com,E:state]: (~ ((D = B) => (~ (member_state @ E @ (A @ C)))) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (do @ (A)) @ B) @ C) @ (produc1204172211_state @ D @ E)) @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 33.99/12.55 thf(3,axiom,((! [A:list_com,B:list_com,C:list_com]: ((append_com @ (append_com @ A @ B) @ C) = (append_com @ A @ (append_com @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_append_Oassoc)). 33.99/12.55 thf(331,plain,((! [A:list_com,B:list_com,C:list_com]: ((append_com @ (append_com @ A @ B) @ C) = (append_com @ A @ (append_com @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 33.99/12.55 thf(97,axiom,((! [A:state]: (pHoare806997636termis @ nil_com @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_termis_Osimps_I1_J)). 33.99/12.55 thf(717,plain,((! [A:state]: (pHoare806997636termis @ nil_com @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 33.99/12.55 thf(46,axiom,((! [A:list_com,B:list_com,C:list_com]: (((append_com @ A @ B) = (append_com @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_same__append__eq)). 33.99/12.55 thf(502,plain,((! [A:list_com,B:list_com,C:list_com]: (((append_com @ A @ B) = (append_com @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 33.99/12.55 thf(230,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((A != B) => (~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ C) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ (transi1302705790_state @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_converse__rtranclE)). 33.99/12.55 thf(1317,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((~ (A = B)) => (~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ C) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ (transi1302705790_state @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 33.99/12.55 thf(307,axiom,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com,E:list_com,F:list_com,G:list_com]: ((((member32358020st_com @ (produc1307105171st_com @ D @ G) @ (listrel1_com @ C)) <= (G = (append_com @ E @ (cons_com @ B @ F)))) <= (D = (append_com @ E @ (cons_com @ A @ F)))) <= (member1333916004om_com @ (product_Pair_com_com @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_listrel1I)). 33.99/12.55 thf(1711,plain,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com,E:list_com,F:list_com,G:list_com]: ((member32358020st_com @ (produc1307105171st_com @ D @ G) @ (listrel1_com @ C)) | ~ (G = (append_com @ E @ (cons_com @ B @ F))) | ~ (D = (append_com @ E @ (cons_com @ A @ F))) | ~ (member1333916004om_com @ (product_Pair_com_com @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 33.99/12.55 thf(168,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) <= (member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1726587420_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_rtrancl__trancl__trancl)). 33.99/12.55 thf(1053,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) | ~ (member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1726587420_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 33.99/12.55 thf(325,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > (produc2041926651_state > $o))]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => (((! [E:produc2041926651_state,F:produc2041926651_state,G:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ (transi1726587420_state @ C)) => ((D @ E @ F) => ((member1069318160_state @ (produc1909270103_state @ F @ G) @ C) => (D @ E @ G))))) => (D @ A @ B)) <= (! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => (D @ E @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_trancl_Oinducts)). 33.99/12.55 thf(1790,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > (produc2041926651_state > $o))]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => (((! [E:produc2041926651_state,F:produc2041926651_state,G:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ (transi1726587420_state @ C)) => ((D @ E @ F) => ((member1069318160_state @ (produc1909270103_state @ F @ G) @ C) => (D @ E @ G))))) => (D @ A @ B)) | ~ (! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => (D @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 33.99/12.55 thf(308,axiom,((! [A:com,B:list_com,C:list_com,D:list_com]: (((cons_com @ A @ B) = (append_com @ C @ D)) = (? [E:list_com]: (((cons_com @ A @ E) = C) & (B = (append_com @ E @ D))) | (((cons_com @ A @ B) = D) & (C = nil_com)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Cons__eq__append__conv)). 33.99/12.55 thf(1716,plain,((! [A:com,B:list_com,C:list_com,D:list_com]: (((cons_com @ A @ B) = (append_com @ C @ D)) = (? [E:list_com]: (((cons_com @ A @ E) = C) & (B = (append_com @ E @ D))) | (((cons_com @ A @ B) = D) & (C = nil_com)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 33.99/12.55 thf(37,axiom,((! [A:(state > $o),B:state,C:com,D:com]: ((A @ B) => ((termi @ (cond @ A @ C @ D) @ B) <= (termi @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_termi_OIfTrue)). 33.99/12.55 thf(470,plain,((! [A:(state > $o),B:state,C:com,D:com]: ((A @ B) => ((termi @ (cond @ (A) @ C @ D) @ B) | ~ (termi @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 33.99/12.55 thf(296,axiom,((! [A:(nat > $o),B:nat]: (((! [C:nat]: ((A @ C) <= (A @ (suc @ C)))) => (A @ zero_zero_nat)) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_zero__induct)). 33.99/12.55 thf(1658,plain,((! [A:(nat > $o),B:nat]: (((! [C:nat]: ((A @ C) | ~ (A @ (suc @ C)))) => (A @ zero_zero_nat)) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 33.99/12.55 thf(223,axiom,((! [A:list_com,B:state,C:list_com,D:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ pHoare259243666_exec1) => ((pHoare806997636termis @ A @ B) => (pHoare806997636termis @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_exec1__pres__termis)). 33.99/12.55 thf(1285,plain,((! [A:list_com,B:state,C:list_com,D:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ pHoare259243666_exec1) => ((pHoare806997636termis @ A @ B) => (pHoare806997636termis @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 33.99/12.55 thf(210,axiom,((! [A:list_com,B:(list_com > $o)]: ((A != nil_com) => ((! [C:com]: (B @ (cons_com @ C @ nil_com))) => ((! [C:com,D:list_com]: ((D != nil_com) => ((B @ D) => (B @ (cons_com @ C @ D))))) => (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_list__nonempty__induct)). 33.99/12.55 thf(1218,plain,((! [A:list_com,B:(list_com > $o)]: ((~ (A = nil_com)) => ((! [C:com]: (B @ (cons_com @ C @ nil_com))) => ((! [C:com,D:list_com]: ((~ (D = nil_com)) => ((B @ D) => (B @ (cons_com @ C @ D))))) => (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 33.99/12.55 thf(235,axiom,((! [A:(produc410756839_state > $o),B:produc410756839_state]: ((A @ B) <= (! [C:produc2041926651_state,D:list_com,E:state]: (A @ (produc1909270103_state @ C @ (produc1204172211_state @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_prod__induct3)). 33.99/12.55 thf(1336,plain,((! [A:(produc410756839_state > $o),B:produc410756839_state]: ((A @ B) | ~ (! [C:produc2041926651_state,D:list_com,E:state]: (A @ (produc1909270103_state @ C @ (produc1204172211_state @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 33.99/12.55 thf(82,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > $o)]: ((((! [E:produc410756839_state,F:produc410756839_state]: ((((D @ F) => (D @ E)) <= (member512523024_state @ (produc2065881943_state @ F @ B) @ (transi1666849160_state @ C))) <= (member512523024_state @ (produc2065881943_state @ E @ F) @ C))) => (D @ A)) <= (! [E:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ E @ B) @ C) => (D @ E)))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_converse__trancl__induct)). 33.99/12.55 thf(643,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:(produc410756839_state > $o)]: (((! [E:produc410756839_state,F:produc410756839_state]: (((D @ F) => (D @ E)) | ~ (member512523024_state @ (produc2065881943_state @ F @ B) @ (transi1666849160_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ E @ F) @ C))) => (D @ A)) | ~ (! [E:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ E @ B) @ C) => (D @ E))) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 33.99/12.55 thf(93,axiom,((! [A:list_com,B:list_com]: (((append_com @ A @ B) = B) = (A = nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_append__self__conv2)). 33.99/12.55 thf(703,plain,((! [A:list_com,B:list_com]: (((append_com @ A @ B) = B) = (A = nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 33.99/12.55 thf(327,axiom,((! [A:list_com,B:set_Pr1822651163om_com]: ~ (member32358020st_com @ (produc1307105171st_com @ A @ nil_com) @ (lexord_com @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_lexord__Nil__right)). 33.99/12.55 thf(1802,plain,((! [A:list_com,B:set_Pr1822651163om_com]: ~ (member32358020st_com @ (produc1307105171st_com @ A @ nil_com) @ (lexord_com @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 33.99/12.55 thf(71,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ C) => ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) <= (member512523024_state @ (produc2065881943_state @ B @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_r__r__into__trancl)). 33.99/12.55 thf(600,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ C) => ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ B @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 33.99/12.55 thf(263,axiom,((! [A:list_com,B:state,C:list_com,D:state,E:set_Pr1165141447_state,F:(list_com > (state > $o))]: ((((! [G:list_com,H:state,I:list_com,J:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ G @ H) @ (produc1204172211_state @ I @ J)) @ E) => (((F @ G @ H) <= (F @ I @ J)) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ I @ J) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E))))) => (F @ A @ B)) <= (F @ C @ D)) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_converse__rtrancl__induct2)). 33.99/12.55 thf(1504,plain,((! [A:list_com,B:state,C:list_com,D:state,E:set_Pr1165141447_state,F:(list_com > (state > $o))]: (((! [G:list_com,H:state,I:list_com,J:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ G @ H) @ (produc1204172211_state @ I @ J)) @ E) => ((F @ G @ H) | ~ (F @ I @ J) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ I @ J) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E))))) => (F @ A @ B)) | ~ (F @ C @ D) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 33.99/12.55 thf(158,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) <= (member1069318160_state @ (produc1909270103_state @ B @ D) @ C)) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_trancl_Otrancl__into__trancl)). 33.99/12.55 thf(1008,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C)) | ~ (member1069318160_state @ (produc1909270103_state @ B @ D) @ C) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 33.99/12.55 thf(69,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ C) => (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_trancl_Or__into__trancl)). 33.99/12.55 thf(595,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ C) => (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 33.99/12.55 thf(214,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > $o)]: (((! [E:produc2041926651_state]: ((D @ E) <= (member1069318160_state @ (produc1909270103_state @ A @ E) @ C))) => ((! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ E) @ (transi1726587420_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => ((D @ E) => (D @ F))))) => (D @ B))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_trancl__induct)). 33.99/12.55 thf(1240,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > $o)]: (((! [E:produc2041926651_state]: ((D @ E) | ~ (member1069318160_state @ (produc1909270103_state @ A @ E) @ C))) => ((! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ E) @ (transi1726587420_state @ C)) => ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => ((D @ E) => (D @ F))))) => (D @ B))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 33.99/12.55 thf(151,axiom,((! [A:list_list_com,B:list_state,C:set_Pr849496667_state]: ((((A = nil_list_com) => (B != nil_state)) => (~ (! [D:list_com,E:state,F:list_list_com]: ((! [G:list_state]: (((member64234660_state @ (produc1204172211_state @ D @ E) @ C) => (~ (member1442949316_state @ (produc1742567891_state @ F @ G) @ (listre1268245261_state @ C)))) <= (B = (cons_state @ E @ G)))) <= (A = (cons_list_com @ D @ F)))))) <= (member1442949316_state @ (produc1742567891_state @ A @ B) @ (listre1268245261_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_listrel_Ocases)). 33.99/12.55 thf(978,plain,((! [A:list_list_com,B:list_state,C:set_Pr849496667_state]: ((((A = nil_list_com) => (~ (B = nil_state))) => (~ (! [D:list_com,E:state,F:list_list_com]: (! [G:list_state]: (((member64234660_state @ (produc1204172211_state @ D @ E) @ C) => (~ (member1442949316_state @ (produc1742567891_state @ F @ G) @ (listre1268245261_state @ C)))) | ~ (B = (cons_state @ E @ G))) | ~ (A = (cons_list_com @ D @ F)))))) | ~ (member1442949316_state @ (produc1742567891_state @ A @ B) @ (listre1268245261_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 33.99/12.55 thf(20,axiom,((! [A:state,B:com,C:state,D:com,E:state]: ((exec @ A @ B @ C) => ((exec @ A @ (semi @ B @ D) @ E) <= (exec @ C @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_exec_OSemi)). 33.99/12.55 thf(386,plain,((! [A:state,B:com,C:state,D:com,E:state]: ((exec @ A @ B @ C) => ((exec @ A @ (semi @ B @ D) @ E) | ~ (exec @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 33.99/12.55 thf(130,axiom,((! [A:produc258871771st_com]: ((~ (! [B:com,C:list_com,D:list_com]: (A != (produc1307105171st_com @ (cons_com @ B @ C) @ D)))) <= (! [B:list_com]: (A != (produc1307105171st_com @ nil_com @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_splice_Ocases)). 33.99/12.55 thf(845,plain,((! [A:produc258871771st_com]: (~ (! [B:com,C:list_com,D:list_com]: ~ (A = (produc1307105171st_com @ (cons_com @ B @ C) @ D))) | ~ (! [B:list_com]: ~ (A = (produc1307105171st_com @ nil_com @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 33.99/12.55 thf(36,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (((B != A) => (~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ C)))))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rtrancl_Ocases)). 33.99/12.55 thf(465,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (((~ (B = A)) => (~ (! [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) => (~ (member512523024_state @ (produc2065881943_state @ D @ B) @ C)))))) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 33.99/12.55 thf(78,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ C) => ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) <= (member512523024_state @ (produc2065881943_state @ B @ D) @ (transi463013610_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_rtrancl__into__trancl2)). 33.99/12.55 thf(627,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ C) => ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ B @ D) @ (transi463013610_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 33.99/12.55 thf(61,axiom,((! [A:list_com,B:list_list_com]: ((concat_com @ (cons_list_com @ A @ B)) = (append_com @ A @ (concat_com @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_concat_Osimps_I2_J)). 33.99/12.55 thf(556,plain,((! [A:list_com,B:list_list_com]: ((concat_com @ (cons_list_com @ A @ B)) = (append_com @ A @ (concat_com @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 33.99/12.55 thf(41,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ D) @ C) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_rtrancl__into__trancl1)). 33.99/12.55 thf(482,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ D) @ C) => (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C))) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi463013610_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 33.99/12.55 thf(45,axiom,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:list_com,E:list_com]: ((((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel1_com @ C)) & (D = E)) | ((member32358020st_com @ (produc1307105171st_com @ D @ E) @ (listrel1_com @ C)) & (A = B))) => (member32358020st_com @ (produc1307105171st_com @ (append_com @ A @ D) @ (append_com @ B @ E)) @ (listrel1_com @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_append__listrel1I)). 33.99/12.55 thf(495,plain,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:list_com,E:list_com]: ((((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel1_com @ C)) & (D = E)) | ((member32358020st_com @ (produc1307105171st_com @ D @ E) @ (listrel1_com @ C)) & (A = B))) => (member32358020st_com @ (produc1307105171st_com @ (append_com @ A @ D) @ (append_com @ B @ E)) @ (listrel1_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 33.99/12.55 thf(279,axiom,((pHoare259243732_execs = (^ [A:state,B:list_com,C:state]: (? [D:state]: ((A = D) & (B = nil_com) & (C = D)) | ? [D:state,E:com,F:state,G:list_com,H:state]: ((A = D) & (B = (cons_com @ E @ G)) & (pHoare259243732_execs @ F @ G @ H) & (exec @ D @ E @ F) & (C = H)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_execs_Osimps)). 33.99/12.55 thf(1575,plain,(((pHoare259243732_execs) = (^ [A:state,B:list_com,C:state]: (? [D:state]: ((A = D) & (B = nil_com) & (C = D)) | ? [D:state,E:com,F:state,G:list_com,H:state]: ((A = D) & (B = (cons_com @ E @ G)) & (pHoare259243732_execs @ F @ G @ H) & (exec @ D @ E @ F) & (C = H)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 33.99/12.55 thf(106,axiom,((! [A:((com > com) > (list_com > (list_com > $o))),B:(com > com),C:list_com,D:list_com]: (((! [E:(com > com),F:com,G:list_com,H:list_com]: ((A @ E @ G @ (cons_com @ (E @ F) @ H)) => (A @ E @ (cons_com @ F @ G) @ H))) => (A @ B @ C @ D)) <= (! [E:(com > com),F:list_com]: (A @ E @ nil_com @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_map__tailrec__rev_Oinduct)). 33.99/12.55 thf(771,plain,((! [A:((com > com) > (list_com > (list_com > $o))),B:(com > com),C:list_com,D:list_com]: (((! [E:(com > com),F:com,G:list_com,H:list_com]: ((A @ (E) @ G @ (cons_com @ (E @ F) @ H)) => (A @ (E) @ (cons_com @ F @ G) @ H))) => (A @ (B) @ C @ D)) | ~ (! [E:(com > com),F:list_com]: (A @ (E) @ nil_com @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 33.99/12.55 thf(184,axiom,((! [A:(produc186437863_state > $o),B:produc186437863_state]: ((! [C:produc410756839_state,D:produc2041926651_state,E:list_com,F:state]: (A @ (produc2065881943_state @ C @ (produc1909270103_state @ D @ (produc1204172211_state @ E @ F))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_prod__induct4)). 33.99/12.55 thf(1108,plain,((! [A:(produc186437863_state > $o),B:produc186437863_state]: ((! [C:produc410756839_state,D:produc2041926651_state,E:list_com,F:state]: (A @ (produc2065881943_state @ C @ (produc1909270103_state @ D @ (produc1204172211_state @ E @ F))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 33.99/12.55 thf(293,axiom,((! [A:com,B:list_com,C:list_com]: ((append_com @ (cons_com @ A @ B) @ C) = (cons_com @ A @ (append_com @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_append__Cons)). 33.99/12.55 thf(1649,plain,((! [A:com,B:list_com,C:list_com]: ((append_com @ (cons_com @ A @ B) @ C) = (cons_com @ A @ (append_com @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 33.99/12.55 thf(177,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => (? [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ C) & (member1069318160_state @ (produc1909270103_state @ D @ B) @ (transi1302705790_state @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_tranclD)). 33.99/12.55 thf(1084,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C)) => (? [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ C) & (member1069318160_state @ (produc1909270103_state @ D @ B) @ (transi1302705790_state @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 33.99/12.55 thf(15,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) => (? [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ D @ B) @ (transi463013610_state @ C)) & (member512523024_state @ (produc2065881943_state @ A @ D) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_tranclD)). 33.99/12.55 thf(368,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C)) => (? [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ D @ B) @ (transi463013610_state @ C)) & (member512523024_state @ (produc2065881943_state @ A @ D) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 33.99/12.55 thf(253,axiom,((! [A:(state > $o),B:com,C:list_com,D:state,E:list_com,F:state]: ((((E = C) => ((F = D) => (A @ D))) => (~ (((~ (A @ D)) <= (F = D)) <= (E = (cons_com @ B @ (cons_com @ (while @ A @ B) @ C)))))) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ A @ B) @ C) @ D) @ (produc1204172211_state @ E @ F)) @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_exec1E_I5_J)). 33.99/12.55 thf(1453,plain,((! [A:(state > $o),B:com,C:list_com,D:state,E:list_com,F:state]: ((((E = C) => ((F = D) => (A @ D))) => (~ (~ (A @ D) | ~ (F = D) | ~ (E = (cons_com @ B @ (cons_com @ (while @ (A) @ B) @ C)))))) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (while @ (A) @ B) @ C) @ D) @ (produc1204172211_state @ E @ F)) @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 33.99/12.55 thf(221,axiom,((! [A:(produc2041926651_state > $o),B:produc2041926651_state]: ((! [C:list_com,D:state]: (A @ (produc1204172211_state @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_old_Oprod_Oinducts)). 33.99/12.55 thf(1276,plain,((! [A:(produc2041926651_state > $o),B:produc2041926651_state]: ((! [C:list_com,D:state]: (A @ (produc1204172211_state @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 33.99/12.55 thf(292,axiom,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com,E:list_com]: (((member32358020st_com @ (produc1307105171st_com @ D @ E) @ (transi436345274st_com @ (listrel1_com @ C))) => (member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ D) @ (cons_com @ B @ E)) @ (transi436345274st_com @ (listrel1_com @ C)))) <= (member1333916004om_com @ (product_Pair_com_com @ A @ B) @ (transi863150634cl_com @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_rtrancl__listrel1__ConsI2)). 33.99/12.55 thf(1646,plain,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com,E:list_com]: (((member32358020st_com @ (produc1307105171st_com @ D @ E) @ (transi436345274st_com @ (listrel1_com @ C))) => (member32358020st_com @ (produc1307105171st_com @ (cons_com @ A @ D) @ (cons_com @ B @ E)) @ (transi436345274st_com @ (listrel1_com @ C)))) | ~ (member1333916004om_com @ (product_Pair_com_com @ A @ B) @ (transi863150634cl_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 33.99/12.55 thf(120,axiom,((! [A:list_com,B:list_com]: ((A = (append_com @ B @ A)) = (B = nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_self__append__conv2)). 33.99/12.55 thf(813,plain,((! [A:list_com,B:list_com]: ((A = (append_com @ B @ A)) = (B = nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 33.99/12.55 thf(102,axiom,((! [A:set_Pr1165141447_state,B:list_P1040014977_state,C:list_P1040014977_state]: ((! [D:produc2041926651_state,E:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ D) @ A) | (D = E) | (member1069318160_state @ (produc1909270103_state @ D @ E) @ A))) => ((B = C) | (member1267359376_state @ (produc1298457559_state @ C @ B) @ (lexord1062073966_state @ A)) | (member1267359376_state @ (produc1298457559_state @ B @ C) @ (lexord1062073966_state @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_lexord__linear)). 33.99/12.55 thf(748,plain,((! [A:set_Pr1165141447_state,B:list_P1040014977_state,C:list_P1040014977_state]: ((! [D:produc2041926651_state,E:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ D) @ A) | (D = E) | (member1069318160_state @ (produc1909270103_state @ D @ E) @ A))) => ((B = C) | (member1267359376_state @ (produc1298457559_state @ C @ B) @ (lexord1062073966_state @ A)) | (member1267359376_state @ (produc1298457559_state @ B @ C) @ (lexord1062073966_state @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 33.99/12.55 thf(299,axiom,((! [A:(list_com > $o),B:list_com]: (((A @ B) <= (! [C:com,D:list_com]: ((A @ D) => (A @ (cons_com @ C @ D))))) <= (A @ nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_list_Oinducts)). 33.99/12.55 thf(1674,plain,((! [A:(list_com > $o),B:list_com]: ((A @ B) | ~ (! [C:com,D:list_com]: ((A @ D) => (A @ (cons_com @ C @ D)))) | ~ (A @ nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 33.99/12.55 thf(171,axiom,((! [A:(produc410756839_state > $o),B:produc410756839_state]: ((A @ B) <= (! [C:produc2041926651_state,D:produc2041926651_state]: (A @ (produc1909270103_state @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_old_Oprod_Oinducts)). 33.99/12.55 thf(1062,plain,((! [A:(produc410756839_state > $o),B:produc410756839_state]: ((A @ B) | ~ (! [C:produc2041926651_state,D:produc2041926651_state]: (A @ (produc1909270103_state @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 33.99/12.55 thf(255,axiom,((! [A:(com > list_com)]: ((maps_com_com @ A @ nil_com) = nil_com))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_maps__simps_I2_J)). 33.99/12.55 thf(1481,plain,((! [A:(com > list_com)]: ((maps_com_com @ (A) @ nil_com) = nil_com))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 33.99/12.55 thf(110,axiom,((! [A:list_com,B:list_com,C:state,D:list_com,E:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (append_com @ A @ B) @ C) @ (produc1204172211_state @ (append_com @ D @ B) @ E)) @ pHoare259243666_exec1) => ((A != nil_com) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ C) @ (produc1204172211_state @ D @ E)) @ pHoare259243666_exec1))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_exec1__drop__suffix)). 33.99/12.55 thf(786,plain,((! [A:list_com,B:list_com,C:state,D:list_com,E:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (append_com @ A @ B) @ C) @ (produc1204172211_state @ (append_com @ D @ B) @ E)) @ pHoare259243666_exec1) => ((~ (A = nil_com)) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ C) @ (produc1204172211_state @ D @ E)) @ pHoare259243666_exec1))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 33.99/12.55 thf(276,axiom,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:com]: ((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel1_com @ C)) => (member32358020st_com @ (produc1307105171st_com @ (cons_com @ D @ A) @ (cons_com @ D @ B)) @ (listrel1_com @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_listrel1I2)). 33.99/12.55 thf(1558,plain,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com,D:com]: ((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel1_com @ C)) => (member32358020st_com @ (produc1307105171st_com @ (cons_com @ D @ A) @ (cons_com @ D @ B)) @ (listrel1_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 33.99/12.55 thf(18,axiom,((! [A:set_Pr2096893127_state,B:produc410756839_state,C:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ C) @ A) => (B != C)) <= (! [D:produc410756839_state]: ~ (member512523024_state @ (produc2065881943_state @ D @ D) @ (transi1666849160_state @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_irrefl__trancl__rD)). 33.99/12.55 thf(378,plain,((! [A:set_Pr2096893127_state,B:produc410756839_state,C:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ B @ C) @ A) => (~ (B = C))) | ~ (! [D:produc410756839_state]: ~ (member512523024_state @ (produc2065881943_state @ D @ D) @ (transi1666849160_state @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 33.99/12.55 thf(140,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((A != B) => (~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C)) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rtranclE)). 33.99/12.55 thf(929,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1302705790_state @ C)) => ((~ (A = B)) => (~ (! [D:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1302705790_state @ C)) => (~ (member1069318160_state @ (produc1909270103_state @ D @ B) @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 33.99/12.55 thf(305,axiom,((! [A:list_list_com,B:list_com,C:list_com]: (((concat_com @ A) = (append_com @ B @ C)) = (((? [D:list_list_com,E:list_com,F:list_com,G:list_list_com]: ((C = (append_com @ F @ (concat_com @ G))) & (B = (append_com @ (concat_com @ D) @ E)) & (A = (append_list_com @ D @ (cons_list_com @ (append_com @ E @ F) @ G))))) <= (A != nil_list_com)) & (((C = nil_com) & (B = nil_com)) <= (A = nil_list_com)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_concat__eq__append__conv)). 33.99/12.55 thf(1706,plain,((! [A:list_list_com,B:list_com,C:list_com]: (((concat_com @ A) = (append_com @ B @ C)) = ((? [D:list_list_com,E:list_com,F:list_com,G:list_list_com]: ((C = (append_com @ F @ (concat_com @ G))) & (B = (append_com @ (concat_com @ D) @ E)) & (A = (append_list_com @ D @ (cons_list_com @ (append_com @ E @ F) @ G)))) | (A = nil_list_com)) & (((C = nil_com) & (B = nil_com)) | ~ (A = nil_list_com)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 33.99/12.55 thf(208,axiom,(((subseqs_com @ nil_com) = (cons_list_com @ nil_com @ nil_list_com))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_subseqs_Osimps_I1_J)). 33.99/12.55 thf(1212,plain,(((subseqs_com @ nil_com) = (cons_list_com @ nil_com @ nil_list_com))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 33.99/12.55 thf(285,axiom,((! [A:set_Pr1822651163om_com]: (member32358020st_com @ (produc1307105171st_com @ nil_com @ nil_com) @ (listrel_com_com @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_listrel_ONil)). 33.99/12.55 thf(1607,plain,((! [A:set_Pr1822651163om_com]: (member32358020st_com @ (produc1307105171st_com @ nil_com @ nil_com) @ (listrel_com_com @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 33.99/12.55 thf(19,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: ((? [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ D @ B) @ C) & (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_tranclD2)). 33.99/12.55 thf(383,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state]: (? [D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ D @ B) @ C) & (member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C))) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ (transi1666849160_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 33.99/12.55 thf(137,axiom,((! [A:(list_com > $o),B:list_com]: (((! [C:com,D:list_com]: ((A @ (append_com @ D @ (cons_com @ C @ nil_com))) <= (A @ D))) => (A @ B)) <= (A @ nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_rev__induct)). 33.99/12.55 thf(899,plain,((! [A:(list_com > $o),B:list_com]: (((! [C:com,D:list_com]: ((A @ (append_com @ D @ (cons_com @ C @ nil_com))) | ~ (A @ D))) => (A @ B)) | ~ (A @ nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 33.99/12.55 thf(126,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_nat_Oinject)). 33.99/12.55 thf(832,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 33.99/12.55 thf(228,axiom,((! [A:list_com,B:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ nil_com) @ (listrel_com_com @ B)) => (A = nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_listrel__Nil2)). 33.99/12.55 thf(1309,plain,((! [A:list_com,B:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ nil_com) @ (listrel_com_com @ B)) => (A = nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 33.99/12.55 thf(166,axiom,((! [A:produc258871771st_com]: ((! [B:list_com]: (A != (produc1307105171st_com @ nil_com @ B))) => ((! [B:list_com]: (A != (produc1307105171st_com @ B @ nil_com))) => (~ (! [B:com,C:list_com,D:com,E:list_com]: (A != (produc1307105171st_com @ (cons_com @ B @ C) @ (cons_com @ D @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_shuffles_Ocases)). 33.99/12.55 thf(1045,plain,((! [A:produc258871771st_com]: ((! [B:list_com]: ~ (A = (produc1307105171st_com @ nil_com @ B))) => ((! [B:list_com]: ~ (A = (produc1307105171st_com @ B @ nil_com))) => (~ (! [B:com,C:list_com,D:com,E:list_com]: ~ (A = (produc1307105171st_com @ (cons_com @ B @ C) @ (cons_com @ D @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 33.99/12.55 thf(288,axiom,((! [A:produc186437863_state]: ~ (! [B:produc410756839_state,C:produc2041926651_state,D:produc2041926651_state]: (A != (produc2065881943_state @ B @ (produc1909270103_state @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_prod__cases3)). 33.99/12.55 thf(1614,plain,((! [A:produc186437863_state]: ~ (! [B:produc410756839_state,C:produc2041926651_state,D:produc2041926651_state]: ~ (A = (produc2065881943_state @ B @ (produc1909270103_state @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 33.99/12.55 thf(116,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_nat_Odistinct_I1_J)). 33.99/12.55 thf(800,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 33.99/12.55 thf(189,axiom,((! [A:state,B:list_com,C:state]: ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ nil_com @ A) @ (produc1204172211_state @ B @ C)) @ pHoare259243666_exec1))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_exec1E_I1_J)). 33.99/12.55 thf(1133,plain,((! [A:state,B:list_com,C:state]: ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ nil_com @ A) @ (produc1204172211_state @ B @ C)) @ pHoare259243666_exec1))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 33.99/12.55 thf(265,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state]: (((produc1909270103_state @ A @ B) = (produc1909270103_state @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_old_Oprod_Oinject)). 33.99/12.55 thf(1512,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state]: (((produc1909270103_state @ A @ B) = (produc1909270103_state @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 33.99/12.55 thf(32,axiom,((! [A:com,B:com,C:(state > $o),D:com,E:com]: ((semi @ A @ B) != (cond @ C @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_com_Odistinct_I11_J)). 33.99/12.55 thf(432,plain,((! [A:com,B:com,C:(state > $o),D:com,E:com]: ~ ((semi @ A @ B) = (cond @ (C) @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 33.99/12.55 thf(127,axiom,((! [A:list_com,B:state,C:list_com,D:state]: (((produc1204172211_state @ A @ B) = (produc1204172211_state @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_old_Oprod_Oinject)). 33.99/12.55 thf(835,plain,((! [A:list_com,B:state,C:list_com,D:state]: (((produc1204172211_state @ A @ B) = (produc1204172211_state @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 33.99/12.55 thf(193,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1302705790_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_rtrancl__into__trancl2)). 33.99/12.55 thf(1148,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1302705790_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 33.99/12.55 thf(72,axiom,((! [A:list_list_com,B:list_com,C:list_com]: (((concat_com @ A) = (append_com @ B @ C)) => ((? [D:list_list_com,E:list_com,F:list_com,G:list_list_com]: ((B = (append_com @ (concat_com @ D) @ E)) & (C = (append_com @ F @ (concat_com @ G))) & (A = (append_list_com @ D @ (cons_list_com @ (append_com @ E @ F) @ G))))) <= (A != nil_list_com))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_concat__eq__appendD)). 33.99/12.55 thf(603,plain,((! [A:list_list_com,B:list_com,C:list_com]: (((concat_com @ A) = (append_com @ B @ C)) => (? [D:list_list_com,E:list_com,F:list_com,G:list_list_com]: ((B = (append_com @ (concat_com @ D) @ E)) & (C = (append_com @ F @ (concat_com @ G))) & (A = (append_list_com @ D @ (cons_list_com @ (append_com @ E @ F) @ G)))) | (A = nil_list_com))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 33.99/12.55 thf(155,axiom,((! [A:(com > list_com),B:com,C:list_com]: ((maps_com_com @ A @ (cons_com @ B @ C)) = (append_com @ (A @ B) @ (maps_com_com @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_maps__simps_I1_J)). 33.99/12.55 thf(999,plain,((! [A:(com > list_com),B:com,C:list_com]: ((maps_com_com @ (A) @ (cons_com @ B @ C)) = (append_com @ (A @ B) @ (maps_com_com @ (A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 33.99/12.55 thf(76,axiom,((! [A:set_Pr2096893127_state]: ((transi463013610_state @ (transi463013610_state @ A)) = (transi463013610_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rtrancl__idemp)). 33.99/12.55 thf(620,plain,((! [A:set_Pr2096893127_state]: ((transi463013610_state @ (transi463013610_state @ A)) = (transi463013610_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 33.99/12.55 thf(250,axiom,((! [A:list_com]: ((append_com @ A @ nil_com) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_append__Nil2)). 33.99/12.55 thf(1436,plain,((! [A:list_com]: ((append_com @ A @ nil_com) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 33.99/12.55 thf(260,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1302705790_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_trancl__rtrancl__trancl)). 33.99/12.55 thf(1495,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:produc2041926651_state]: (((member1069318160_state @ (produc1909270103_state @ B @ D) @ (transi1302705790_state @ C)) => (member1069318160_state @ (produc1909270103_state @ A @ D) @ (transi1726587420_state @ C))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 33.99/12.55 thf(277,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > (produc2041926651_state > $o))]: (((! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => (D @ E @ F))) => ((D @ A @ B) <= (! [E:produc2041926651_state,F:produc2041926651_state,G:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ (transi1726587420_state @ C)) => ((D @ E @ F) => ((member1069318160_state @ (produc1909270103_state @ F @ G) @ (transi1726587420_state @ C)) => ((D @ E @ G) <= (D @ F @ G)))))))) <= (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_trancl__trans__induct)). 33.99/12.55 thf(1561,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state,D:(produc2041926651_state > (produc2041926651_state > $o))]: (((! [E:produc2041926651_state,F:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ C) => (D @ E @ F))) => ((D @ A @ B) | ~ (! [E:produc2041926651_state,F:produc2041926651_state,G:produc2041926651_state]: ((member1069318160_state @ (produc1909270103_state @ E @ F) @ (transi1726587420_state @ C)) => ((D @ E @ F) => ((member1069318160_state @ (produc1909270103_state @ F @ G) @ (transi1726587420_state @ C)) => ((D @ E @ G) | ~ (D @ F @ G)))))))) | ~ (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 33.99/12.55 thf(169,axiom,((! [A:list_com,B:state,C:list_com,D:state,E:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ pHoare259243666_exec1)) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (append_com @ A @ E) @ B) @ (produc1204172211_state @ (append_com @ C @ E) @ D)) @ (transi1302705790_state @ pHoare259243666_exec1))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_app__execs)). 33.99/12.55 thf(1056,plain,((! [A:list_com,B:state,C:list_com,D:state,E:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ pHoare259243666_exec1)) => (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (append_com @ A @ E) @ B) @ (produc1204172211_state @ (append_com @ C @ E) @ D)) @ (transi1302705790_state @ pHoare259243666_exec1))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 33.99/12.55 thf(146,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ C) => (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_trancl_Or__into__trancl)). 33.99/12.55 thf(960,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:set_Pr1165141447_state]: ((member1069318160_state @ (produc1909270103_state @ A @ B) @ C) => (member1069318160_state @ (produc1909270103_state @ A @ B) @ (transi1726587420_state @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 33.99/12.55 thf(91,axiom,((! [A:list_com,B:state,C:list_com,D:state]: ((! [E:list_com,F:list_com,G:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ E @ B) @ (produc1204172211_state @ G @ D)) @ pHoare259243666_exec1) <= ((E != nil_com) & (C = (append_com @ G @ F)) & (A = (append_com @ E @ F))))) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ pHoare259243666_exec1)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_exec1__drop__suffix__aux)). 33.99/12.55 thf(696,plain,((! [A:list_com,B:state,C:list_com,D:state]: (! [E:list_com,F:list_com,G:list_com]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ E @ B) @ (produc1204172211_state @ G @ D)) @ pHoare259243666_exec1) | ~ (~ (E = nil_com) & (C = (append_com @ G @ F)) & (A = (append_com @ E @ F)))) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ pHoare259243666_exec1)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 33.99/12.55 thf(145,axiom,((! [A:com,B:com,C:list_com,D:state,E:list_com,F:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (semi @ A @ B) @ C) @ D) @ (produc1204172211_state @ E @ F)) @ pHoare259243666_exec1) => (~ ((E = (cons_com @ A @ (cons_com @ B @ C))) => (F != D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_exec1E_I3_J)). 33.99/12.55 thf(955,plain,((! [A:com,B:com,C:list_com,D:state,E:list_com,F:state]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ (cons_com @ (semi @ A @ B) @ C) @ D) @ (produc1204172211_state @ E @ F)) @ pHoare259243666_exec1) => (~ ((E = (cons_com @ A @ (cons_com @ B @ C))) => (~ (F = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 33.99/12.55 thf(12,axiom,((! [A:(state > set_state),B:(state > $o),C:com,D:com]: ((do @ A) != (cond @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_com_Odistinct_I3_J)). 33.99/12.55 thf(358,plain,((! [A:(state > set_state),B:(state > $o),C:com,D:com]: ~ ((do @ (A)) = (cond @ (B) @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 33.99/12.55 thf(118,axiom,((! [A:com,B:list_com,C:(com > list_com)]: ((bind_com_com @ (cons_com @ A @ B) @ C) = (append_com @ (C @ A) @ (bind_com_com @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_bind__simps_I2_J)). 33.99/12.55 thf(807,plain,((! [A:com,B:list_com,C:(com > list_com)]: ((bind_com_com @ (cons_com @ A @ B) @ (C)) = (append_com @ (C @ A) @ (bind_com_com @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 33.99/12.55 thf(199,axiom,((! [A:list_list_com]: (((! [B:list_list_com]: (A != (cons_list_com @ nil_com @ B))) => (~ (! [B:com,C:list_com,D:list_list_com]: (A != (cons_list_com @ (cons_com @ B @ C) @ D))))) <= (A != nil_list_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_transpose_Ocases)). 33.99/12.55 thf(1172,plain,((! [A:list_list_com]: (((! [B:list_list_com]: ~ (A = (cons_list_com @ nil_com @ B))) => (~ (! [B:com,C:list_com,D:list_list_com]: ~ (A = (cons_list_com @ (cons_com @ B @ C) @ D))))) | (A = nil_list_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 33.99/12.55 thf(247,axiom,((! [A:produc410756839_state,B:(nat > produc410756839_state),C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) => ((D = (B @ zero_zero_nat)) => (? [E:(nat > produc410756839_state)]: (! [F:nat]: (member512523024_state @ (produc2065881943_state @ (E @ F) @ (E @ (suc @ F))) @ C) & ((E @ zero_zero_nat) = A))))) <= (! [E:nat]: ((member512523024_state @ (produc2065881943_state @ A @ (B @ E)) @ (transi463013610_state @ C)) & (member512523024_state @ (produc2065881943_state @ (B @ E) @ (B @ (suc @ E))) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_renumber__aux)). 33.99/12.55 thf(1410,plain,((! [A:produc410756839_state,B:(nat > produc410756839_state),C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) => ((D = (B @ zero_zero_nat)) => (? [E:(nat > produc410756839_state)]: (! [F:nat]: (member512523024_state @ (produc2065881943_state @ (E @ F) @ (E @ (suc @ F))) @ C) & ((E @ zero_zero_nat) = A))))) | ~ (! [E:nat]: ((member512523024_state @ (produc2065881943_state @ A @ (B @ E)) @ (transi463013610_state @ C)) & (member512523024_state @ (produc2065881943_state @ (B @ E) @ (B @ (suc @ E))) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 33.99/12.55 thf(53,axiom,((! [A:com,B:com,C:com,D:com]: (((semi @ A @ B) = (semi @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_com_Oinject_I2_J)). 33.99/12.55 thf(532,plain,((! [A:com,B:com,C:com,D:com]: (((semi @ A @ B) = (semi @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 33.99/12.55 thf(172,axiom,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com,E:list_com,F:list_com]: ((member32358020st_com @ (produc1307105171st_com @ (append_com @ D @ (cons_com @ A @ E)) @ (append_com @ D @ (cons_com @ B @ F))) @ (lexord_com @ C)) <= (member1333916004om_com @ (product_Pair_com_com @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_lexord__append__left__rightI)). 33.99/12.55 thf(1065,plain,((! [A:com,B:com,C:set_Pr1822651163om_com,D:list_com,E:list_com,F:list_com]: ((member32358020st_com @ (produc1307105171st_com @ (append_com @ D @ (cons_com @ A @ E)) @ (append_com @ D @ (cons_com @ B @ F))) @ (lexord_com @ C)) | ~ (member1333916004om_com @ (product_Pair_com_com @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 33.99/12.55 thf(100,axiom,((! [A:set_nat]: ((nths_com @ nil_com @ A) = nil_com))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_nths__nil)). 33.99/12.55 thf(740,plain,((! [A:set_nat]: ((nths_com @ nil_com @ A) = nil_com))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 33.99/12.55 thf(239,axiom,((! [A:set_Pr1165141447_state,B:list_P1040014977_state]: ((! [C:produc2041926651_state]: ~ (member1069318160_state @ (produc1909270103_state @ C @ C) @ A)) => (~ (member1267359376_state @ (produc1298457559_state @ B @ B) @ (lexord1062073966_state @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_lexord__irreflexive)). 33.99/12.55 thf(1352,plain,((! [A:set_Pr1165141447_state,B:list_P1040014977_state]: ((! [C:produc2041926651_state]: ~ (member1069318160_state @ (produc1909270103_state @ C @ C) @ A)) => (~ (member1267359376_state @ (produc1298457559_state @ B @ B) @ (lexord1062073966_state @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 33.99/12.55 thf(30,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ C) => ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) <= (member512523024_state @ (produc2065881943_state @ B @ D) @ (transi463013610_state @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_converse__rtrancl__into__rtrancl)). 33.99/12.55 thf(427,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ B) @ C) => ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi463013610_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ B @ D) @ (transi463013610_state @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 33.99/12.55 thf(133,axiom,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel_com_com @ C)) => (((A = nil_com) => (B != nil_com)) => (~ (! [D:com,E:com,F:list_com]: ((A = (cons_com @ D @ F)) => (! [G:list_com]: ((B = (cons_com @ E @ G)) => ((member1333916004om_com @ (product_Pair_com_com @ D @ E) @ C) => (~ (member32358020st_com @ (produc1307105171st_com @ F @ G) @ (listrel_com_com @ C))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_listrel_Ocases)). 33.99/12.55 thf(860,plain,((! [A:list_com,B:list_com,C:set_Pr1822651163om_com]: ((member32358020st_com @ (produc1307105171st_com @ A @ B) @ (listrel_com_com @ C)) => (((A = nil_com) => (~ (B = nil_com))) => (~ (! [D:com,E:com,F:list_com]: ((A = (cons_com @ D @ F)) => (! [G:list_com]: ((B = (cons_com @ E @ G)) => ((member1333916004om_com @ (product_Pair_com_com @ D @ E) @ C) => (~ (member32358020st_com @ (produc1307105171st_com @ F @ G) @ (listrel_com_com @ C))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 33.99/12.55 thf(122,axiom,((! [A:list_com,B:state,C:state]: ((pHoare259243732_execs @ B @ A @ C) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ nil_com @ C)) @ (transi1302705790_state @ pHoare259243666_exec1))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_exec1s__impl__execs)). 33.99/12.55 thf(822,plain,((! [A:list_com,B:state,C:state]: ((pHoare259243732_execs @ B @ A @ C) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ nil_com @ C)) @ (transi1302705790_state @ pHoare259243666_exec1))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 33.99/12.55 thf(290,axiom,((! [A:(state > $o),B:com,C:(nat > state),D:nat]: ((termi @ (while @ A @ B) @ (C @ D)) => ((? [E:nat]: ~ (A @ (C @ E))) <= (! [E:nat]: (exec @ (C @ E) @ B @ (C @ (suc @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_termi__while)). 33.99/12.55 thf(1621,plain,((! [A:(state > $o),B:com,C:(nat > state),D:nat]: ((termi @ (while @ (A) @ B) @ (C @ D)) => (? [E:nat]: ~ (A @ (C @ E)) | ~ (! [E:nat]: (exec @ (C @ E) @ B @ (C @ (suc @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 33.99/12.55 thf(5,axiom,((! [A:(state > $o),B:state,C:com,D:com]: (((termi @ (cond @ A @ D @ C) @ B) <= (termi @ C @ B)) <= (~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_termi_OIfFalse)). 33.99/12.55 thf(337,plain,((! [A:(state > $o),B:state,C:com,D:com]: ((termi @ (cond @ (A) @ D @ C) @ B) | ~ (termi @ C @ B) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 33.99/12.55 thf(107,axiom,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state,E:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E)) => (((produc1909270103_state @ A @ B) != (produc1909270103_state @ C @ D)) => (~ (! [F:produc2041926651_state,G:produc2041926651_state]: ((~ (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ F @ G) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E))) <= (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ F @ G)) @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_converse__rtranclE2)). 33.99/12.55 thf(775,plain,((! [A:produc2041926651_state,B:produc2041926651_state,C:produc2041926651_state,D:produc2041926651_state,E:set_Pr2096893127_state]: ((member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E)) => ((~ ((produc1909270103_state @ A @ B) = (produc1909270103_state @ C @ D))) => (~ (! [F:produc2041926651_state,G:produc2041926651_state]: (~ (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ F @ G) @ (produc1909270103_state @ C @ D)) @ (transi463013610_state @ E)) | ~ (member512523024_state @ (produc2065881943_state @ (produc1909270103_state @ A @ B) @ (produc1909270103_state @ F @ G)) @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 33.99/12.55 thf(206,axiom,((! [A:list_com,B:state,C:list_com,D:state,E:set_Pr1165141447_state]: ((((produc1204172211_state @ A @ B) != (produc1204172211_state @ C @ D)) => (~ (! [F:list_com,G:state]: ((~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ F @ G) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E))) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ F @ G)) @ E))))) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_converse__rtranclE2)). 33.99/12.55 thf(1204,plain,((! [A:list_com,B:state,C:list_com,D:state,E:set_Pr1165141447_state]: (((~ ((produc1204172211_state @ A @ B) = (produc1204172211_state @ C @ D))) => (~ (! [F:list_com,G:state]: (~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ F @ G) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E)) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ F @ G)) @ E))))) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 33.99/12.55 thf(68,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_211_com_Oinject_I4_J)). 33.99/12.55 thf(592,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)],[68])). 33.99/12.55 thf(34,axiom,((! [A:(state > $o),B:state,C:com,D:state,E:com]: ((A @ B) => ((exec @ B @ (cond @ A @ C @ E) @ D) <= (exec @ B @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_exec_OIfTrue)). 33.99/12.55 thf(454,plain,((! [A:(state > $o),B:state,C:com,D:state,E:com]: ((A @ B) => ((exec @ B @ (cond @ (A) @ C @ E) @ D) | ~ (exec @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 33.99/12.55 thf(150,axiom,((! [A:list_com,B:state,C:list_com,D:state,E:set_Pr1165141447_state,F:(list_com > (state > $o))]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E)) => ((F @ A @ B) => ((F @ C @ D) <= (! [G:list_com,H:state,I:list_com,J:state]: ((((F @ G @ H) => (F @ I @ J)) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ G @ H) @ (produc1204172211_state @ I @ J)) @ E)) <= (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ G @ H)) @ (transi1302705790_state @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rtrancl__induct2)). 33.99/12.55 thf(972,plain,((! [A:list_com,B:state,C:list_com,D:state,E:set_Pr1165141447_state,F:(list_com > (state > $o))]: ((member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ C @ D)) @ (transi1302705790_state @ E)) => ((F @ A @ B) => ((F @ C @ D) | ~ (! [G:list_com,H:state,I:list_com,J:state]: (((F @ G @ H) => (F @ I @ J)) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ G @ H) @ (produc1204172211_state @ I @ J)) @ E) | ~ (member1069318160_state @ (produc1909270103_state @ (produc1204172211_state @ A @ B) @ (produc1204172211_state @ G @ H)) @ (transi1302705790_state @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 33.99/12.55 thf(320,axiom,((! [A:list_com,B:list_com]: ((A = (append_com @ A @ B)) = (B = nil_com)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_self__append__conv)). 33.99/12.55 thf(1769,plain,((! [A:list_com,B:list_com]: ((A = (append_com @ A @ B)) = (B = nil_com)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 33.99/12.55 thf(86,axiom,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: (((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) <= (member512523024_state @ (produc2065881943_state @ B @ D) @ (transi1666849160_state @ C))) <= (member512523024_state @ (produc2065881943_state @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_trancl__into__trancl2)). 33.99/12.55 thf(676,plain,((! [A:produc410756839_state,B:produc410756839_state,C:set_Pr2096893127_state,D:produc410756839_state]: ((member512523024_state @ (produc2065881943_state @ A @ D) @ (transi1666849160_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ B @ D) @ (transi1666849160_state @ C)) | ~ (member512523024_state @ (produc2065881943_state @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 33.99/12.55 thf(1994,plain,($false),inference(cvc4,[status(thm)],[1322,1024,365,1237,909,962,1179,1586,1501,1168,760,479,1105,1068,1808,1618,1544,614,597,1486,523,1158,1142,1269,1327,945,340,538,1196,709,1386,565,436,1518,651,1127,1782,389,1287,1709,719,1577,934,1059,1330,1264,587,838,1313,1279,559,1800,1087,1609,1347,1362,1778,1489,492,756,789,1151,1418,623,485,1136,1383,348,1581,353,396,1201,849,1521,877,692,942,529,810,546,793,1730,798,1163,1274,334,1091,1343,1021,1355,392,424,630,1042,952,1365,1555,1296,1687,1624,1656,551,1573,583,830,682,1407,1740,842,1762,1111,1498,1006,1755,783,989,857,1234,1541,1772,1259,1096,1672,1719,356,1292,554,476,526,637,489,1214,590,706,679,1039,1114,1099,654,1668,1192,457,911,1002,371,1333,343,633,508,541,1071,1515,412,1698,824,1301,375,965,1727,1510,513,430,1154,562,402,1389,1752,1652,743,1124,1256,1226,611,1765,804,1464,1194,1209,406,1011,1524,1492,362,1722,737,880,1690,1439,1589,996,1339,345,535,816,799,700,1029,330,685,399,780,883,1015,1176,1775,1250,1102,505,1694,1805,658,768,827,1445,1528,1583,795,548,1684,1081,617,1145,968,1049,473,1076,712,1611,1743,1531,993,1547,1748,409,1484,1432,331,717,502,1317,1711,1053,1790,1716,470,1658,1285,1218,1336,643,703,1802,600,1504,1008,595,1240,978,386,845,465,627,556,482,495,1575,771,1108,1649,1084,368,1453,1276,1646,813,748,1674,1062,1481,786,1558,378,929,1706,1212,1607,383,899,832,1309,1045,1614,800,1133,1512,432,835,1148,603,999,620,1436,1495,1561,1056,960,696,955,358,807,1172,1410,532,1065,740,1352,427,860,822,1621,337,775,1204,592,454,972,1769,676])). 33.99/12.55 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 33.99/12.55 % [INFO] Killing All external provers ... 33.99/12.55 FINAL WATCH: 32.1 CPU 9.5 WC 33.99/12.55 Killed 1 orphans 33.99/12.55 Killed 1 orphans 33.99/12.55 Killed 1 orphans 33.99/12.55 EOF