0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : run_Leo-III---1.5 %s %d 0.14/0.36 % Computer : n026.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 960 0.14/0.36 % WCLimit : 120 0.14/0.36 % DateTime : Thu Jul 2 06:53:54 EDT 2020 0.14/0.36 % CPUTime : 0.14/0.37 % Leo-III: Strategy 1 (for '60') 24.85/7.42 % [INFO] Running in sequential loop mode. 24.85/7.42 % [CONFIG] Using configuration: timeout(60) with strategy 24.85/7.42 % [INFO] eprover registered as external prover. 24.85/7.42 % [INFO] cvc4 registered as external prover. 24.85/7.42 % [INFO] Parsing finished. Scanning for conjecture ... 24.85/7.42 % [INFO] Found a conjecture and 315 axioms. Running axiom selection ... 24.85/7.42 % [INFO] Axiom selection finished. Selected 296 axioms (removed 19 axioms). 24.85/7.42 % [INFO] Type checking passed. Searching for refutation ... 24.85/7.42 % [INFO] Killing All external provers ... 24.85/7.42 % Time passed: 5586ms 24.85/7.42 % Effective reasoning time: 3581ms 24.85/7.42 % Solved by strategy 24.85/7.42 % Axioms used in derivation (296): fact_173_insert__ident, fact_56_image__constant__conv, fact_184_insert__Collect, fact_296_subsetI, fact_262_insert__subset, fact_231_empty__not__insert, fact_8_finite__Collect__subsets, fact_135_equals0D, fact_238_subset__empty, fact_234_finite__insert, fact_93_finite__surj, fact_224_singletonE, fact_104_emptyE, fact_293_finite__subset__induct, fact_174_insert__code, fact_243_finite__subset, fact_154_empty__Collect__eq, fact_15_finite__imageI, fact_244_finite__subset, fact_260_subset__insert, fact_110_insertCI, help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T, fact_185_insert__Collect, fact_186_insert__compr, fact_124_image__eqI, fact_167_empty__def, fact_91_finite__surj, fact_275_Collect__conv__if2, fact_49_finite__Collect__conjI, fact_29_finite__imageI, fact_106_emptyE, fact_1_asm, fact_155_ex__in__conv, fact_206_set__eq__subset, fact_64_image__constant__conv, fact_25_finite__imageI, fact_32_finite__imageI, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com, fact_188_insert__compr, fact_137_equals0D, fact_277_Collect__conv__if2, fact_142_Collect__empty__eq, fact_274_Collect__conv__if, fact_43_finite_OemptyI, fact_255_Collect__def, conj_3, fact_148_empty__iff, fact_157_ex__in__conv, fact_132_image__eqI, fact_3_thin, fact_281_singleton__conv, fact_249_rev__finite__subset, fact_105_emptyE, fact_67_image__constant, fact_143_Collect__empty__eq, fact_209_subset__refl, fact_103_MGF, fact_168_insert__absorb, fact_0_empty, fact_153_empty__Collect__eq, fact_216_finite__Collect__disjI, fact_146_empty__iff, fact_284_singleton__conv2, fact_152_empty__Collect__eq, fact_264_subset__insertI, fact_204_equalityD1, fact_287_MGF__lemma1, fact_229_insert__not__empty, fact_268_image__mono, fact_195_subset__trans, fact_26_finite__imageI, fact_99_subset__singletonD, fact_240_image__empty, fact_283_singleton__conv2, fact_96_finite__surj, fact_292_finite__subset__induct, fact_159_all__not__in__conv, fact_272_Collect__conv__if, fact_191_insertI1, fact_212_image__iff, fact_233_finite__insert, fact_265_subset__insertI, fact_61_image__constant__conv, fact_130_image__eqI, fact_75_image__constant, fact_76_image__constant, fact_181_insert__absorb2, fact_269_subset__image__iff, fact_237_subset__empty, fact_171_insertI2, fact_179_insert__commute, fact_134_image__eqI, fact_128_image__eqI, fact_172_insert__ident, fact_219_insert__compr__raw, fact_123_subsetD, fact_222_singleton__inject, fact_111_insertCI, fact_248_rev__finite__subset, fact_280_singleton__conv, fact_83_finite__surj, fact_162_all__not__in__conv, fact_35_empty__subsetI, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_41_finite_OinsertI, fact_92_finite__surj, fact_252_mem__def, fact_176_insert__iff, fact_114_insertE, fact_259_subset__insertI2, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com, fact_286_singleton__conv2, fact_246_rev__finite__subset, fact_253_mem__def, help_fequal_1_1_fequal_000tc__Com__Opname_T, fact_57_image__constant__conv, fact_256_Collect__def, fact_9_finite__Collect__subsets, fact_102_subset__singletonD, fact_245_finite__subset, conj_2, fact_250_insert__mono, fact_161_all__not__in__conv, fact_276_Collect__conv__if2, fact_86_finite__surj, fact_20_finite__imageI, fact_119_equalityI, fact_194_subset__trans, fact_145_empty__iff, fact_88_finite__surj, fact_271_Collect__conv__if, fact_169_insert__absorb, fact_66_image__constant, help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T, fact_203_equalityD2, fact_68_image__constant, fact_207_set__eq__subset, fact_109_insertCI, fact_44_finite_OemptyI, fact_131_image__eqI, fact_201_in__mono, fact_273_Collect__conv__if, fact_112_insertE, fact_70_image__constant, fact_97_finite__surj, fact_79_insert__dom, fact_100_subset__singletonD, fact_291_finite__subset__induct, fact_164_empty__def, fact_278_Collect__conv__if2, fact_84_finite__surj, fact_220_insert__compr__raw, fact_214_finite__Collect__disjI, fact_202_equalityD2, fact_217_insert__compr__raw, fact_125_image__eqI, fact_21_finite__imageI, fact_136_equals0D, fact_133_image__eqI, help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It, fact_87_finite__surj, fact_5_hoare__derivs_Oinsert, fact_282_singleton__conv, fact_108_insertCI, fact_215_finite__Collect__disjI, fact_213_finite__Collect__disjI, fact_285_singleton__conv2, fact_6_derivs__insertD, fact_211_imageI, fact_298_finite__dom__body, fact_279_singleton__conv, fact_74_image__constant, fact_200_in__mono, fact_170_insertI2, fact_138_equals0D, fact_299_com_Osimps_I6_J, fact_254_Collect__def, fact_117_equalityI, fact_187_insert__compr, fact_263_insert__subset, fact_16_finite__imageI, fact_225_doubleton__eq__iff, fact_190_insertI1, fact_48_finite_OemptyI, fact_52_finite__Collect__conjI, fact_126_image__eqI, fact_251_insert__mono, fact_158_ex__in__conv, fact_218_insert__compr__raw, fact_258_subset__insertI2, fact_107_emptyE, fact_22_finite__imageI, fact_51_finite__Collect__conjI, fact_13_finite__Collect__subsets, fact_227_singleton__iff, fact_193_equalityE, fact_47_finite_OemptyI, fact_221_singleton__inject, fact_247_rev__finite__subset, fact_85_finite__surj, fact_62_image__constant__conv, fact_261_subset__insert, fact_294_WTs__elim__cases_I7_J, fact_223_singletonE, help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It, fact_198_set__rev__mp, fact_141_Collect__empty__eq, fact_267_image__insert, fact_73_image__constant, fact_101_subset__singletonD, fact_72_image__constant, conj_6, fact_182_insert__Collect, conj_1, fact_82_finite__surj, fact_205_equalityD1, fact_156_ex__in__conv, fact_78_insert__dom, fact_232_empty__not__insert, fact_65_image__constant__conv, fact_199_set__rev__mp, fact_266_insert__image, fact_230_insert__not__empty, fact_122_subsetD, fact_63_image__constant__conv, fact_98_finite__surj, fact_297_finite__subset__image, fact_81_finite__surj, fact_189_insert__compr, fact_50_finite__Collect__conjI, fact_295_subsetI, fact_196_set__mp, fact_288_WT__bodiesD, fact_270_domI, fact_34_empty__subsetI, fact_55_image__constant__conv, fact_113_insertE, fact_165_empty__def, fact_2_weaken, fact_116_equalityI, fact_197_set__mp, fact_226_doubleton__eq__iff, fact_147_empty__iff, fact_241_empty__is__image, fact_69_image__constant, conj_4, fact_210_rev__image__eqI, fact_115_insertE, fact_30_finite__imageI, fact_4_cut, fact_127_image__eqI, fact_192_equalityE, fact_289_imageE, fact_290_finite__subset__induct, fact_175_insert__code, fact_80_finite__surj, fact_31_finite__imageI, fact_129_image__eqI, fact_19_finite__imageI, fact_12_finite__Collect__subsets, fact_71_image__constant, fact_18_finite__imageI, fact_7_MGT__BodyN, fact_239_image__is__empty, conj_5, fact_118_equalityI, fact_53_finite__Collect__conjI, fact_121_subsetD, conj_0, fact_59_image__constant__conv, fact_36_empty__subsetI, fact_120_subsetD, fact_180_insert__absorb2, fact_17_finite__imageI, fact_60_image__constant__conv, fact_235_finite__insert, fact_58_image__constant__conv, fact_54_finite__Collect__conjI, fact_242_finite__subset, fact_236_finite__insert, fact_37_finite_OinsertI, fact_160_all__not__in__conv, fact_183_insert__Collect, fact_178_insert__commute, fact_42_finite_OinsertI, fact_166_empty__def, fact_144_Collect__empty__eq, fact_14_finite__imageI, fact_177_insert__iff, fact_208_subset__refl, fact_33_empty__subsetI, fact_77_insert__dom, fact_38_finite_OinsertI, fact_151_empty__Collect__eq, fact_228_singleton__iff, fact_257_Collect__def 24.85/7.42 % No. of inferences in proof: 596 24.85/7.42 % No. of processed clauses: 1 24.85/7.42 % No. of generated clauses: 0 24.85/7.42 % No. of forward subsumed clauses: 0 24.85/7.42 % No. of backward subsumed clauses: 0 24.85/7.42 % No. of ground rewrite rules in store: 1 24.85/7.42 % No. of non-ground rewrite rules in store: 0 24.85/7.42 % No. of positive (non-rewrite) units in store: 0 24.85/7.42 % No. of negative (non-rewrite) units in store: 0 24.85/7.42 % No. of choice functions detected: 0 24.85/7.42 % No. of choice instantiations: 0 24.85/7.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5586 ms resp. 3581 ms w/o parsing 24.85/7.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 24.85/7.42 thf(com_type, type, com: $tType). 24.85/7.42 thf(pname_type, type, pname: $tType). 24.85/7.42 thf(hoare_1262092251_state_type, type, hoare_1262092251_state: $tType). 24.85/7.42 thf(option_com_type, type, option_com: $tType). 24.85/7.42 thf(wt_type, type, wt: (com > $o)). 24.85/7.42 thf(wT_bodies_type, type, wT_bodies: $o). 24.85/7.42 thf(body_type, type, body: (pname > option_com)). 24.85/7.42 thf(body_1_type, type, body_1: (pname > com)). 24.85/7.42 thf(finite1066544169me_o_o_type, type, finite1066544169me_o_o: ((((pname > $o) > $o) > $o) > $o)). 24.85/7.42 thf(finite1303896758te_o_o_type, type, finite1303896758te_o_o: ((((hoare_1262092251_state > $o) > $o) > $o) > $o)). 24.85/7.42 thf(finite297249702name_o_type, type, finite297249702name_o: (((pname > $o) > $o) > $o)). 24.85/7.42 thf(finite1423311111tate_o_type, type, finite1423311111tate_o: (((hoare_1262092251_state > $o) > $o) > $o)). 24.85/7.42 thf(finite_finite_pname_type, type, finite_finite_pname: ((pname > $o) > $o)). 24.85/7.42 thf(finite1178804552_state_type, type, finite1178804552_state: ((hoare_1262092251_state > $o) > $o)). 24.85/7.42 thf(hoare_Mirabelle_MGT_type, type, hoare_Mirabelle_MGT: (com > hoare_1262092251_state)). 24.85/7.42 thf(hoare_930741239_state_type, type, hoare_930741239_state: ((hoare_1262092251_state > $o) > ((hoare_1262092251_state > $o) > $o))). 24.85/7.42 thf(hoare_1821564147gleton_type, type, hoare_1821564147gleton: $o). 24.85/7.42 thf(dom_pname_o_com_type, type, dom_pname_o_com: (((pname > $o) > option_com) > ((pname > $o) > $o))). 24.85/7.42 thf(dom_Ho1489634536_o_com_type, type, dom_Ho1489634536_o_com: (((hoare_1262092251_state > $o) > option_com) > ((hoare_1262092251_state > $o) > $o))). 24.85/7.42 thf(dom_pname_com_type, type, dom_pname_com: ((pname > option_com) > (pname > $o))). 24.85/7.42 thf(some_com_type, type, some_com: (com > option_com)). 24.85/7.42 thf(the_com_type, type, the_com: (option_com > com)). 24.85/7.42 thf(bot_bot_pname_o_o_type, type, bot_bot_pname_o_o: ((pname > $o) > $o)). 24.85/7.42 thf(bot_bo1962689075te_o_o_type, type, bot_bo1962689075te_o_o: ((hoare_1262092251_state > $o) > $o)). 24.85/7.42 thf(bot_bot_pname_o_type, type, bot_bot_pname_o: (pname > $o)). 24.85/7.42 thf(bot_bo113204042tate_o_type, type, bot_bo113204042tate_o: (hoare_1262092251_state > $o)). 24.85/7.42 thf(ord_le1205211808me_o_o_type, type, ord_le1205211808me_o_o: (((pname > $o) > $o) > (((pname > $o) > $o) > $o))). 24.85/7.42 thf(ord_le2012720639te_o_o_type, type, ord_le2012720639te_o_o: (((hoare_1262092251_state > $o) > $o) > (((hoare_1262092251_state > $o) > $o) > $o))). 24.85/7.42 thf(ord_less_eq_pname_o_type, type, ord_less_eq_pname_o: ((pname > $o) > ((pname > $o) > $o))). 24.85/7.42 thf(ord_le870406270tate_o_type, type, ord_le870406270tate_o: ((hoare_1262092251_state > $o) > ((hoare_1262092251_state > $o) > $o))). 24.85/7.42 thf(collect_pname_o_o_type, type, collect_pname_o_o: ((((pname > $o) > $o) > $o) > (((pname > $o) > $o) > $o))). 24.85/7.42 thf(collec341954548te_o_o_type, type, collec341954548te_o_o: ((((hoare_1262092251_state > $o) > $o) > $o) > (((hoare_1262092251_state > $o) > $o) > $o))). 24.85/7.42 thf(collect_pname_o_type, type, collect_pname_o: (((pname > $o) > $o) > ((pname > $o) > $o))). 24.85/7.42 thf(collec313158217tate_o_type, type, collec313158217tate_o: (((hoare_1262092251_state > $o) > $o) > ((hoare_1262092251_state > $o) > $o))). 24.85/7.42 thf(collect_pname_type, type, collect_pname: ((pname > $o) > (pname > $o))). 24.85/7.42 thf(collec1121927558_state_type, type, collec1121927558_state: ((hoare_1262092251_state > $o) > (hoare_1262092251_state > $o))). 24.85/7.42 thf(image_471733107_pname_type, type, image_471733107_pname: ((((pname > $o) > $o) > pname) > ((((pname > $o) > $o) > $o) > (pname > $o)))). 24.85/7.42 thf(image_1036078444_state_type, type, image_1036078444_state: ((((pname > $o) > $o) > hoare_1262092251_state) > ((((pname > $o) > $o) > $o) > (hoare_1262092251_state > $o)))). 24.85/7.42 thf(image_893364936_pname_type, type, image_893364936_pname: ((((hoare_1262092251_state > $o) > $o) > pname) > ((((hoare_1262092251_state > $o) > $o) > $o) > (pname > $o)))). 24.85/7.42 thf(image_165349207_state_type, type, image_165349207_state: ((((hoare_1262092251_state > $o) > $o) > hoare_1262092251_state) > ((((hoare_1262092251_state > $o) > $o) > $o) > (hoare_1262092251_state > $o)))). 24.85/7.42 thf(image_pname_o_pname_type, type, image_pname_o_pname: (((pname > $o) > pname) > (((pname > $o) > $o) > (pname > $o)))). 24.85/7.42 thf(image_1476171975_state_type, type, image_1476171975_state: (((pname > $o) > hoare_1262092251_state) > (((pname > $o) > $o) > (hoare_1262092251_state > $o)))). 24.85/7.42 thf(image_1820530197_pname_type, type, image_1820530197_pname: (((hoare_1262092251_state > $o) > pname) > (((hoare_1262092251_state > $o) > $o) > (pname > $o)))). 24.85/7.42 thf(image_234589002_state_type, type, image_234589002_state: (((hoare_1262092251_state > $o) > hoare_1262092251_state) > (((hoare_1262092251_state > $o) > $o) > (hoare_1262092251_state > $o)))). 24.85/7.42 thf(image_pname_pname_o_type, type, image_pname_pname_o: ((pname > (pname > $o)) > ((pname > $o) > ((pname > $o) > $o)))). 24.85/7.42 thf(image_518521461tate_o_type, type, image_518521461tate_o: ((pname > (hoare_1262092251_state > $o)) > ((pname > $o) > ((hoare_1262092251_state > $o) > $o)))). 24.85/7.42 thf(image_pname_pname_type, type, image_pname_pname: ((pname > pname) > ((pname > $o) > (pname > $o)))). 24.85/7.42 thf(image_669833818_state_type, type, image_669833818_state: ((pname > hoare_1262092251_state) > ((pname > $o) > (hoare_1262092251_state > $o)))). 24.85/7.42 thf(image_1320925383name_o_type, type, image_1320925383name_o: ((hoare_1262092251_state > (pname > $o)) > ((hoare_1262092251_state > $o) > ((pname > $o) > $o)))). 24.85/7.42 thf(image_1403668518tate_o_type, type, image_1403668518tate_o: ((hoare_1262092251_state > (hoare_1262092251_state > $o)) > ((hoare_1262092251_state > $o) > ((hoare_1262092251_state > $o) > $o)))). 24.85/7.42 thf(image_202231862_pname_type, type, image_202231862_pname: ((hoare_1262092251_state > pname) > ((hoare_1262092251_state > $o) > (pname > $o)))). 24.85/7.42 thf(insert_pname_o_type, type, insert_pname_o: ((pname > $o) > (((pname > $o) > $o) > ((pname > $o) > $o)))). 24.85/7.42 thf(insert1042460334tate_o_type, type, insert1042460334tate_o: ((hoare_1262092251_state > $o) > (((hoare_1262092251_state > $o) > $o) > ((hoare_1262092251_state > $o) > $o)))). 24.85/7.42 thf(insert_pname_type, type, insert_pname: (pname > ((pname > $o) > (pname > $o)))). 24.85/7.42 thf(insert81609953_state_type, type, insert81609953_state: (hoare_1262092251_state > ((hoare_1262092251_state > $o) > (hoare_1262092251_state > $o)))). 24.85/7.42 thf(fequal_pname_o_type, type, fequal_pname_o: ((pname > $o) > ((pname > $o) > $o))). 24.85/7.42 thf(fequal1529404211tate_o_type, type, fequal1529404211tate_o: ((hoare_1262092251_state > $o) > ((hoare_1262092251_state > $o) > $o))). 24.85/7.42 thf(fequal_pname_type, type, fequal_pname: (pname > (pname > $o))). 24.85/7.42 thf(fequal1925511196_state_type, type, fequal1925511196_state: (hoare_1262092251_state > (hoare_1262092251_state > $o))). 24.85/7.42 thf(member_pname_o_type, type, member_pname_o: ((pname > $o) > (((pname > $o) > $o) > $o))). 24.85/7.42 thf(member907417095tate_o_type, type, member907417095tate_o: ((hoare_1262092251_state > $o) > (((hoare_1262092251_state > $o) > $o) > $o))). 24.85/7.42 thf(member_pname_type, type, member_pname: (pname > ((pname > $o) > $o))). 24.85/7.42 thf(member5164104_state_type, type, member5164104_state: (hoare_1262092251_state > ((hoare_1262092251_state > $o) > $o))). 24.85/7.42 thf(fa_type, type, fa: (hoare_1262092251_state > $o)). 24.85/7.42 thf(pn_type, type, pn: pname). 24.85/7.42 thf(y_type, type, y: com). 24.85/7.42 thf(28,axiom,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((insert_pname_o @ A @ (collect_pname_o @ B)) = (collect_pname_o @ (^ [C:(pname > $o)]: ((~ (C = A)) => (B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_insert__Collect)). 24.85/7.42 thf(365,plain,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((insert_pname_o @ A @ (collect_pname_o @ B)) = (collect_pname_o @ (^ [C:(pname > $o)]: ((~ (C = A)) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 24.85/7.42 thf(152,axiom,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > hoare_1262092251_state),C:((hoare_1262092251_state > $o) > $o)]: (((ord_le870406270tate_o @ A @ (image_234589002_state @ B @ C)) => (finite1178804552_state @ A)) <= (finite1423311111tate_o @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite__surj)). 24.85/7.42 thf(760,plain,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > hoare_1262092251_state),C:((hoare_1262092251_state > $o) > $o)]: (((ord_le870406270tate_o @ (A) @ (image_234589002_state @ (B) @ (C))) => (finite1178804552_state @ (A))) | ~ (finite1423311111tate_o @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 24.85/7.42 thf(20,axiom,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((insert1042460334tate_o @ A @ (collec313158217tate_o @ B)) = (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((~ (C = A)) => (B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_insert__Collect)). 24.85/7.42 thf(347,plain,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((insert1042460334tate_o @ A @ (collec313158217tate_o @ B)) = (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((~ (C = A)) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 24.85/7.42 thf(82,axiom,((! [A:(pname > $o),B:pname]: ((((collect_pname @ (^ [C:pname]: ((C = B) & (A @ C)))) = bot_bot_pname_o) <= (~ (A @ B))) & (((collect_pname @ (^ [C:pname]: ((C = B) & (A @ C)))) = (insert_pname @ B @ bot_bot_pname_o)) <= (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_Collect__conv__if)). 24.85/7.42 thf(518,plain,((! [A:(pname > $o),B:pname]: ((((collect_pname @ (^ [C:pname]: ((C = B) & (A @ C)))) = (bot_bot_pname_o)) | (A @ B)) & (((collect_pname @ (^ [C:pname]: ((C = B) & (A @ C)))) = (insert_pname @ B @ bot_bot_pname_o)) | ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 24.85/7.42 thf(202,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > (hoare_1262092251_state > $o)),D:hoare_1262092251_state]: (((member907417095tate_o @ B @ (image_1403668518tate_o @ C @ A)) <= (member5164104_state @ D @ A)) <= (B = (C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_image__eqI)). 24.85/7.42 thf(941,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > (hoare_1262092251_state > $o)),D:hoare_1262092251_state]: ((member907417095tate_o @ (B) @ (image_1403668518tate_o @ C @ A)) | ~ (member5164104_state @ D @ (A)) | ~ ((B) = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 24.85/7.42 thf(91,axiom,((! [A:((pname > $o) > $o),B:(pname > $o)]: (((A = (insert_pname_o @ B @ bot_bot_pname_o_o)) | (A = bot_bot_pname_o_o)) <= (ord_le1205211808me_o_o @ A @ (insert_pname_o @ B @ bot_bot_pname_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_subset__singletonD)). 24.85/7.42 thf(555,plain,((! [A:((pname > $o) > $o),B:(pname > $o)]: (((A) = (insert_pname_o @ B @ bot_bot_pname_o_o)) | ((A) = (bot_bot_pname_o_o)) | ~ (ord_le1205211808me_o_o @ (A) @ (insert_pname_o @ B @ bot_bot_pname_o_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 24.85/7.42 thf(123,axiom,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((image_1403668518tate_o @ (^ [D:hoare_1262092251_state]: (A)) @ C) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)) <= (member5164104_state @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_image__constant)). 24.85/7.42 thf(666,plain,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((image_1403668518tate_o @ (^ [D:hoare_1262092251_state]: (A)) @ C) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)) | ~ (member5164104_state @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 24.85/7.42 thf(249,axiom,((! [A:hoare_1262092251_state,B:(pname > $o)]: ((((image_669833818_state @ (^ [C:pname]: (A)) @ B) = (insert81609953_state @ A @ bot_bo113204042tate_o)) <= (B != bot_bot_pname_o)) & ((B = bot_bot_pname_o) => ((image_669833818_state @ (^ [C:pname]: (A)) @ B) = bot_bo113204042tate_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_image__constant__conv)). 24.85/7.42 thf(1110,plain,((! [A:hoare_1262092251_state,B:(pname > $o)]: ((((image_669833818_state @ (^ [C:pname]: (A)) @ B) = (insert81609953_state @ A @ bot_bo113204042tate_o)) | ((B) = (bot_bot_pname_o))) & (((B) = (bot_bot_pname_o)) => ((image_669833818_state @ (^ [C:pname]: (A)) @ B) = (bot_bo113204042tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 24.85/7.42 thf(109,axiom,((! [A:(hoare_1262092251_state > (hoare_1262092251_state > $o)),B:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ B) => (finite1423311111tate_o @ (image_1403668518tate_o @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_finite__imageI)). 24.85/7.42 thf(628,plain,((! [A:(hoare_1262092251_state > (hoare_1262092251_state > $o)),B:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ (B)) => (finite1423311111tate_o @ (image_1403668518tate_o @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 24.85/7.42 thf(223,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: (((member5164104_state @ A @ C) & (ord_le870406270tate_o @ B @ C)) = (ord_le870406270tate_o @ (insert81609953_state @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_insert__subset)). 24.85/7.42 thf(1031,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: (((member5164104_state @ A @ (C)) & (ord_le870406270tate_o @ (B) @ (C))) = (ord_le870406270tate_o @ (insert81609953_state @ A @ B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 24.85/7.42 thf(272,axiom,((! [A:hoare_1262092251_state]: ((collec1121927558_state @ (fequal1925511196_state @ A)) = (insert81609953_state @ A @ bot_bo113204042tate_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_singleton__conv2)). 24.85/7.42 thf(1200,plain,((! [A:hoare_1262092251_state]: ((collec1121927558_state @ (fequal1925511196_state @ A)) = (insert81609953_state @ A @ bot_bo113204042tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 24.85/7.42 thf(153,axiom,((! [A:(hoare_1262092251_state > pname),B:(hoare_1262092251_state > $o)]: ((finite_finite_pname @ (image_202231862_pname @ A @ B)) <= (finite1178804552_state @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_finite__imageI)). 24.85/7.42 thf(762,plain,((! [A:(hoare_1262092251_state > pname),B:(hoare_1262092251_state > $o)]: ((finite_finite_pname @ (image_202231862_pname @ A @ B)) | ~ (finite1178804552_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 24.85/7.42 thf(128,axiom,((! [A:(hoare_1262092251_state > $o)]: ((collec313158217tate_o @ (^ [B:(hoare_1262092251_state > $o)]: (B = A))) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_singleton__conv)). 24.85/7.42 thf(683,plain,((! [A:(hoare_1262092251_state > $o)]: ((collec313158217tate_o @ (^ [B:(hoare_1262092251_state > $o)]: (B = A))) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 24.85/7.42 thf(212,axiom,((! [A:(pname > hoare_1262092251_state),B:(pname > $o)]: (((image_669833818_state @ A @ B) = bot_bo113204042tate_o) = (B = bot_bot_pname_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_image__is__empty)). 24.85/7.42 thf(994,plain,((! [A:(pname > hoare_1262092251_state),B:(pname > $o)]: (((image_669833818_state @ A @ B) = (bot_bo113204042tate_o)) = ((B) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 24.85/7.42 thf(146,axiom,((! [A:(pname > $o)]: ~ (member_pname_o @ A @ bot_bot_pname_o_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_empty__iff)). 24.85/7.42 thf(741,plain,((! [A:(pname > $o)]: ~ (member_pname_o @ (A) @ (bot_bot_pname_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 24.85/7.42 thf(60,axiom,((! [A:((pname > $o) > $o)]: ((finite1066544169me_o_o @ (collect_pname_o_o @ (^ [B:((pname > $o) > $o)]: (ord_le1205211808me_o_o @ B @ A)))) <= (finite297249702name_o @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__Collect__subsets)). 24.85/7.42 thf(449,plain,((! [A:((pname > $o) > $o)]: ((finite1066544169me_o_o @ (collect_pname_o_o @ (^ [B:((pname > $o) > $o)]: (ord_le1205211808me_o_o @ B @ A)))) | ~ (finite297249702name_o @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 24.85/7.42 thf(259,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ (insert81609953_state @ A @ B)) = (finite1178804552_state @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_finite__insert)). 24.85/7.42 thf(1142,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ (insert81609953_state @ A @ B)) = (finite1178804552_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 24.85/7.42 thf(57,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ (collect_pname_o @ A)) | (finite297249702name_o @ (collect_pname_o @ B))) => (finite297249702name_o @ (collect_pname_o @ (^ [C:(pname > $o)]: ((B @ C) & (A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_finite__Collect__conjI)). 24.85/7.42 thf(440,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ (collect_pname_o @ A)) | (finite297249702name_o @ (collect_pname_o @ B))) => (finite297249702name_o @ (collect_pname_o @ (^ [C:(pname > $o)]: ((B @ C) & (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 24.85/7.42 thf(227,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ (insert81609953_state @ B @ C)) = (insert81609953_state @ B @ (insert81609953_state @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_insert__commute)). 24.85/7.42 thf(1041,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ (insert81609953_state @ B @ C)) = (insert81609953_state @ B @ (insert81609953_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 24.85/7.42 thf(239,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((member5164104_state @ A @ B) => ((insert81609953_state @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_insert__absorb)). 24.85/7.42 thf(1078,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((member5164104_state @ A @ (B)) => ((insert81609953_state @ A @ B) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 24.85/7.42 thf(36,axiom,((! [A:(((pname > $o) > $o) > pname),B:(((pname > $o) > $o) > $o)]: ((finite_finite_pname @ (image_471733107_pname @ A @ B)) <= (finite1066544169me_o_o @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI)). 24.85/7.42 thf(384,plain,((! [A:(((pname > $o) > $o) > pname),B:(((pname > $o) > $o) > $o)]: ((finite_finite_pname @ (image_471733107_pname @ (A) @ (B))) | ~ (finite1066544169me_o_o @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 24.85/7.42 thf(257,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ B @ C) => (ord_le870406270tate_o @ B @ (insert81609953_state @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_subset__insertI2)). 24.85/7.42 thf(1137,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ (B) @ (C)) => (ord_le870406270tate_o @ (B) @ (insert81609953_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 24.85/7.42 thf(76,axiom,((! [A:((pname > $o) > $o),B:(pname > $o)]: ((((collect_pname_o @ (^ [C:(pname > $o)]: ((C = B) & (A @ C)))) = bot_bot_pname_o_o) <= (~ (A @ B))) & ((A @ B) => ((collect_pname_o @ (^ [C:(pname > $o)]: ((C = B) & (A @ C)))) = (insert_pname_o @ B @ bot_bot_pname_o_o)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_Collect__conv__if)). 24.85/7.42 thf(500,plain,((! [A:((pname > $o) > $o),B:(pname > $o)]: ((((collect_pname_o @ (^ [C:(pname > $o)]: ((C = B) & (A @ C)))) = (bot_bot_pname_o_o)) | (A @ (B))) & ((A @ (B)) => ((collect_pname_o @ (^ [C:(pname > $o)]: ((C = B) & (A @ C)))) = (insert_pname_o @ B @ bot_bot_pname_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 24.85/7.42 thf(293,axiom,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((~ (member5164104_state @ B @ A)) => (((insert81609953_state @ B @ C) = (insert81609953_state @ B @ A)) = (C = A))) <= (~ (member5164104_state @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_insert__ident)). 24.85/7.42 thf(1275,plain,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((~ (member5164104_state @ B @ (A))) => (((insert81609953_state @ B @ C) = (insert81609953_state @ B @ A)) = ((C) = (A)))) | (member5164104_state @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 24.85/7.42 thf(203,axiom,((! [A:(((hoare_1262092251_state > $o) > $o) > $o),B:((hoare_1262092251_state > $o) > $o),C:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ C) => ((((A @ C) <= (! [D:(hoare_1262092251_state > $o),E:((hoare_1262092251_state > $o) > $o)]: (((member907417095tate_o @ D @ B) => ((~ (member907417095tate_o @ D @ E)) => ((A @ E) => (A @ (insert1042460334tate_o @ D @ E))))) <= (finite1423311111tate_o @ E)))) <= (A @ bot_bo1962689075te_o_o)) <= (ord_le2012720639te_o_o @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_finite__subset__induct)). 24.85/7.42 thf(945,plain,((! [A:(((hoare_1262092251_state > $o) > $o) > $o),B:((hoare_1262092251_state > $o) > $o),C:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ (C)) => ((A @ (C)) | ~ (! [D:(hoare_1262092251_state > $o),E:((hoare_1262092251_state > $o) > $o)]: (((member907417095tate_o @ (D) @ (B)) => ((~ (member907417095tate_o @ (D) @ (E))) => ((A @ (E)) => (A @ (insert1042460334tate_o @ D @ E))))) | ~ (finite1423311111tate_o @ (E)))) | ~ (A @ (bot_bo1962689075te_o_o)) | ~ (ord_le2012720639te_o_o @ (C) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 24.85/7.42 thf(86,axiom,((! [A:(pname > $o)]: ((? [B:pname]: (member_pname @ B @ A)) = (A != bot_bot_pname_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_ex__in__conv)). 24.85/7.42 thf(538,plain,((! [A:(pname > $o)]: ((? [B:pname]: (member_pname @ B @ (A))) = (~ ((A) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 24.85/7.42 thf(198,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:pname,C:((hoare_1262092251_state > $o) > pname),D:(hoare_1262092251_state > $o)]: (((member907417095tate_o @ D @ A) => (member_pname @ B @ (image_1820530197_pname @ C @ A))) <= (B = (C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_image__eqI)). 24.85/7.42 thf(930,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:pname,C:((hoare_1262092251_state > $o) > pname),D:(hoare_1262092251_state > $o)]: (((member907417095tate_o @ (D) @ (A)) => (member_pname @ B @ (image_1820530197_pname @ (C) @ (A)))) | ~ (B = (C @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 24.85/7.42 thf(235,axiom,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state]: (ord_le870406270tate_o @ A @ (insert81609953_state @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_subset__insertI)). 24.85/7.42 thf(1063,plain,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state]: (ord_le870406270tate_o @ (A) @ (insert81609953_state @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 24.85/7.42 thf(17,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: ((ord_le2012720639te_o_o @ A @ B) => ((finite1423311111tate_o @ A) <= (finite1423311111tate_o @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_finite__subset)). 24.85/7.42 thf(340,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: ((ord_le2012720639te_o_o @ (A) @ (B)) => ((finite1423311111tate_o @ (A)) | ~ (finite1423311111tate_o @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 24.85/7.42 thf(283,axiom,((! [A:(pname > option_com),B:pname,C:com]: (((A @ B) = (some_com @ C)) => (member_pname @ B @ (dom_pname_com @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_domI)). 24.85/7.42 thf(1243,plain,((! [A:(pname > option_com),B:pname,C:com]: (((A @ B) = (some_com @ C)) => (member_pname @ B @ (dom_pname_com @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 24.85/7.42 thf(160,axiom,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ (insert_pname @ A @ C)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_insertI2)). 24.85/7.42 thf(782,plain,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ (insert_pname @ A @ C)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 24.85/7.42 thf(55,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ B) => (finite297249702name_o @ A)) <= (ord_le1205211808me_o_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_finite__subset)). 24.85/7.42 thf(436,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ (B)) => (finite297249702name_o @ (A))) | ~ (ord_le1205211808me_o_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 24.85/7.42 thf(245,axiom,((! [A:(hoare_1262092251_state > $o),B:(pname > hoare_1262092251_state),C:(pname > $o)]: ((? [D:(pname > $o)]: ((A = (image_669833818_state @ B @ D)) & (ord_less_eq_pname_o @ D @ C))) = (ord_le870406270tate_o @ A @ (image_669833818_state @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_subset__image__iff)). 24.85/7.42 thf(1095,plain,((! [A:(hoare_1262092251_state > $o),B:(pname > hoare_1262092251_state),C:(pname > $o)]: ((? [D:(pname > $o)]: (((A) = (image_669833818_state @ B @ D)) & (ord_less_eq_pname_o @ (D) @ (C)))) = (ord_le870406270tate_o @ (A) @ (image_669833818_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 24.85/7.42 thf(44,axiom,((! [A:(pname > $o)]: ((! [B:pname]: ~ (A @ B)) = ((collect_pname @ A) = bot_bot_pname_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Collect__empty__eq)). 24.85/7.42 thf(404,plain,((! [A:(pname > $o)]: ((! [B:pname]: ~ (A @ B)) = ((collect_pname @ A) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 24.85/7.42 thf(206,axiom,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => ((image_pname_pname @ (^ [D:pname]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_image__constant)). 24.85/7.42 thf(973,plain,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => ((image_pname_pname @ (^ [D:pname]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 24.85/7.42 thf(229,axiom,((! [A:(pname > option_com),B:pname,C:com]: (((A @ B) = (some_com @ C)) => ((insert_pname @ B @ (dom_pname_com @ A)) = (dom_pname_com @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_insert__dom)). 24.85/7.42 thf(1046,plain,((! [A:(pname > option_com),B:pname,C:com]: (((A @ B) = (some_com @ C)) => ((insert_pname @ B @ (dom_pname_com @ A)) = (dom_pname_com @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 24.85/7.42 thf(38,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((B @ C) & (A @ C))))) <= ((finite1423311111tate_o @ (collec313158217tate_o @ B)) | (finite1423311111tate_o @ (collec313158217tate_o @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_finite__Collect__conjI)). 24.85/7.42 thf(389,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((B @ C) & (A @ C))))) | ~ ((finite1423311111tate_o @ (collec313158217tate_o @ B)) | (finite1423311111tate_o @ (collec313158217tate_o @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 24.85/7.42 thf(31,axiom,((! [A:(pname > $o),B:((pname > $o) > $o),C:((pname > $o) > $o)]: ((ord_le1205211808me_o_o @ B @ C) => ((member_pname_o @ A @ B) => (member_pname_o @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_subsetD)). 24.85/7.42 thf(372,plain,((! [A:(pname > $o),B:((pname > $o) > $o),C:((pname > $o) > $o)]: ((ord_le1205211808me_o_o @ (B) @ (C)) => ((member_pname_o @ (A) @ (B)) => (member_pname_o @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 24.85/7.42 thf(288,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ (insert81609953_state @ A @ B)) <= (finite1178804552_state @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_finite_OinsertI)). 24.85/7.42 thf(1264,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ (insert81609953_state @ A @ B)) | ~ (finite1178804552_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 24.85/7.42 thf(171,axiom,((! [A:(pname > $o),B:pname]: (((A @ B) => ((collect_pname @ (^ [C:pname]: ((B = C) & (A @ C)))) = (insert_pname @ B @ bot_bot_pname_o))) & (((collect_pname @ (^ [C:pname]: ((B = C) & (A @ C)))) = bot_bot_pname_o) <= (~ (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_Collect__conv__if2)). 24.85/7.42 thf(838,plain,((! [A:(pname > $o),B:pname]: (((A @ B) => ((collect_pname @ (^ [C:pname]: ((B = C) & (A @ C)))) = (insert_pname @ B @ bot_bot_pname_o))) & (((collect_pname @ (^ [C:pname]: ((B = C) & (A @ C)))) = (bot_bot_pname_o)) | (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 24.85/7.42 thf(135,axiom,((! [A:(pname > $o)]: ~ (member_pname_o @ A @ bot_bot_pname_o_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_emptyE)). 24.85/7.42 thf(702,plain,((! [A:(pname > $o)]: ~ (member_pname_o @ (A) @ (bot_bot_pname_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 24.85/7.42 thf(255,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: (((hoare_930741239_state @ B @ A) <= (ord_le870406270tate_o @ A @ C)) <= (hoare_930741239_state @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_weaken)). 24.85/7.42 thf(1132,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((hoare_930741239_state @ (B) @ (A)) | ~ (ord_le870406270tate_o @ (A) @ (C)) | ~ (hoare_930741239_state @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 24.85/7.42 thf(199,axiom,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((insert1042460334tate_o @ A @ B) = (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((C = A) | (member907417095tate_o @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_insert__compr__raw)). 24.85/7.42 thf(934,plain,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((insert1042460334tate_o @ A @ B) = (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((C = A) | (member907417095tate_o @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 24.85/7.42 thf(270,axiom,(((body @ pn) = (some_com @ y))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5)). 24.85/7.42 thf(1191,plain,(((body @ pn) = (some_com @ y))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 24.85/7.42 thf(242,axiom,((! [A:(pname > hoare_1262092251_state),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => (ord_le870406270tate_o @ (image_669833818_state @ A @ B) @ (image_669833818_state @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_image__mono)). 24.85/7.42 thf(1087,plain,((! [A:(pname > hoare_1262092251_state),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => (ord_le870406270tate_o @ (image_669833818_state @ A @ B) @ (image_669833818_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 24.85/7.42 thf(284,axiom,((! [A:(pname > $o),B:hoare_1262092251_state,C:(pname > hoare_1262092251_state),D:pname]: (((member_pname @ D @ A) => (member5164104_state @ B @ (image_669833818_state @ C @ A))) <= (B = (C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_image__eqI)). 24.85/7.42 thf(1247,plain,((! [A:(pname > $o),B:hoare_1262092251_state,C:(pname > hoare_1262092251_state),D:pname]: (((member_pname @ D @ (A)) => (member5164104_state @ B @ (image_669833818_state @ C @ A))) | ~ (B = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 24.85/7.42 thf(50,axiom,((! [A:(pname > $o)]: ((finite297249702name_o @ (collect_pname_o @ (^ [B:(pname > $o)]: (ord_less_eq_pname_o @ B @ A)))) <= (finite_finite_pname @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets)). 24.85/7.42 thf(421,plain,((! [A:(pname > $o)]: ((finite297249702name_o @ (collect_pname_o @ (^ [B:(pname > $o)]: (ord_less_eq_pname_o @ B @ A)))) | ~ (finite_finite_pname @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 24.85/7.42 thf(205,axiom,((! [A:((hoare_1262092251_state > $o) > option_com),B:(hoare_1262092251_state > $o),C:com]: (((insert1042460334tate_o @ B @ (dom_Ho1489634536_o_com @ A)) = (dom_Ho1489634536_o_com @ A)) <= ((A @ B) = (some_com @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_insert__dom)). 24.85/7.42 thf(969,plain,((! [A:((hoare_1262092251_state > $o) > option_com),B:(hoare_1262092251_state > $o),C:com]: (((insert1042460334tate_o @ B @ (dom_Ho1489634536_o_com @ A)) = (dom_Ho1489634536_o_com @ A)) | ~ ((A @ (B)) = (some_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 24.85/7.42 thf(9,axiom,((! [A:(pname > (pname > $o)),B:(pname > $o)]: ((finite297249702name_o @ (image_pname_pname_o @ A @ B)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__imageI)). 24.85/7.42 thf(316,plain,((! [A:(pname > (pname > $o)),B:(pname > $o)]: ((finite297249702name_o @ (image_pname_pname_o @ A @ B)) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 24.85/7.42 thf(247,axiom,((! [A:hoare_1262092251_state,B:((hoare_1262092251_state > $o) > $o)]: (((B != bot_bo1962689075te_o_o) => ((image_234589002_state @ (^ [C:(hoare_1262092251_state > $o)]: (A)) @ B) = (insert81609953_state @ A @ bot_bo113204042tate_o))) & (((image_234589002_state @ (^ [C:(hoare_1262092251_state > $o)]: (A)) @ B) = bot_bo113204042tate_o) <= (B = bot_bo1962689075te_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_image__constant__conv)). 24.85/7.42 thf(1100,plain,((! [A:hoare_1262092251_state,B:((hoare_1262092251_state > $o) > $o)]: (((~ ((B) = (bot_bo1962689075te_o_o))) => ((image_234589002_state @ (^ [C:(hoare_1262092251_state > $o)]: (A)) @ (B)) = (insert81609953_state @ A @ bot_bo113204042tate_o))) & (((image_234589002_state @ (^ [C:(hoare_1262092251_state > $o)]: (A)) @ (B)) = (bot_bo113204042tate_o)) | ~ ((B) = (bot_bo1962689075te_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 24.85/7.42 thf(280,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: ((A = B) = (member5164104_state @ A @ (insert81609953_state @ B @ bot_bo113204042tate_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_singleton__iff)). 24.85/7.42 thf(1232,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: ((A = B) = (member5164104_state @ A @ (insert81609953_state @ B @ bot_bo113204042tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 24.85/7.42 thf(114,axiom,((! [A:(hoare_1262092251_state > $o)]: ((collec313158217tate_o @ (fequal1529404211tate_o @ A)) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_singleton__conv2)). 24.85/7.42 thf(638,plain,((! [A:(hoare_1262092251_state > $o)]: ((collec313158217tate_o @ (fequal1529404211tate_o @ A)) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 24.85/7.42 thf(176,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((member5164104_state @ A @ B) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_mem__def)). 24.85/7.42 thf(853,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((member5164104_state @ A @ (B)) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 24.85/7.42 thf(196,axiom,((! [A:pname,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((member5164104_state @ B @ C) => ((image_202231862_pname @ (^ [D:hoare_1262092251_state]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_image__constant)). 24.85/7.42 thf(924,plain,((! [A:pname,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((member5164104_state @ B @ (C)) => ((image_202231862_pname @ (^ [D:hoare_1262092251_state]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 24.85/7.42 thf(58,axiom,((! [A:pname,B:pname]: ((A != B) | (fequal_pname @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T)). 24.85/7.42 thf(443,plain,((! [A:pname,B:pname]: (~ (A = B) | (fequal_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 24.85/7.42 thf(11,axiom,((! [A:((pname > $o) > $o)]: ((! [B:(pname > $o)]: ~ (A @ B)) = (bot_bot_pname_o_o = (collect_pname_o @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_empty__Collect__eq)). 24.85/7.42 thf(321,plain,((! [A:((pname > $o) > $o)]: ((! [B:(pname > $o)]: ~ (A @ (B))) = ((bot_bot_pname_o_o) = (collect_pname_o @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 24.85/7.42 thf(33,axiom,((! [A:(pname > $o),B:((hoare_1262092251_state > $o) > pname),C:((hoare_1262092251_state > $o) > $o)]: (((ord_less_eq_pname_o @ A @ (image_1820530197_pname @ B @ C)) => (finite_finite_pname @ A)) <= (finite1423311111tate_o @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_finite__surj)). 24.85/7.42 thf(376,plain,((! [A:(pname > $o),B:((hoare_1262092251_state > $o) > pname),C:((hoare_1262092251_state > $o) > $o)]: (((ord_less_eq_pname_o @ (A) @ (image_1820530197_pname @ (B) @ (C))) => (finite_finite_pname @ (A))) | ~ (finite1423311111tate_o @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 24.85/7.42 thf(80,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => ((ord_less_eq_pname_o @ B @ A) <= (ord_less_eq_pname_o @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_subset__trans)). 24.85/7.42 thf(514,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => ((ord_less_eq_pname_o @ (B) @ (A)) | ~ (ord_less_eq_pname_o @ (C) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 24.85/7.42 thf(166,axiom,((! [A:(pname > $o),B:(pname > pname),C:(pname > $o)]: (((finite_finite_pname @ A) <= (ord_less_eq_pname_o @ A @ (image_pname_pname @ B @ C))) <= (finite_finite_pname @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_finite__surj)). 24.85/7.42 thf(806,plain,((! [A:(pname > $o),B:(pname > pname),C:(pname > $o)]: ((finite_finite_pname @ (A)) | ~ (ord_less_eq_pname_o @ (A) @ (image_pname_pname @ B @ C)) | ~ (finite_finite_pname @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 24.85/7.42 thf(68,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ A @ B) => ((A = B) <= (ord_le870406270tate_o @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_equalityI)). 24.85/7.42 thf(480,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ (A) @ (B)) => (((A) = (B)) | ~ (ord_le870406270tate_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 24.85/7.42 thf(262,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ B @ C) => (ord_le870406270tate_o @ (insert81609953_state @ A @ B) @ (insert81609953_state @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_insert__mono)). 24.85/7.42 thf(1151,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ (B) @ (C)) => (ord_le870406270tate_o @ (insert81609953_state @ A @ B) @ (insert81609953_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 24.85/7.42 thf(200,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((ord_less_eq_pname_o @ C @ A) => (member_pname @ B @ A)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_set__rev__mp)). 24.85/7.42 thf(937,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((ord_less_eq_pname_o @ (C) @ (A)) => (member_pname @ B @ (A))) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 24.85/7.42 thf(23,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: ((finite297249702name_o @ B) => ((ord_le1205211808me_o_o @ A @ B) => (finite297249702name_o @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_rev__finite__subset)). 24.85/7.42 thf(353,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: ((finite297249702name_o @ (B)) => ((ord_le1205211808me_o_o @ (A) @ (B)) => (finite297249702name_o @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 24.85/7.42 thf(204,axiom,((! [A:pname,B:(pname > $o)]: ((member_pname @ A @ B) => ((insert_pname @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_insert__absorb)). 24.85/7.42 thf(966,plain,((! [A:pname,B:(pname > $o)]: ((member_pname @ A @ (B)) => ((insert_pname @ A @ B) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 24.85/7.42 thf(183,axiom,((! [A:(pname > $o)]: ((! [B:pname]: ~ (member_pname @ B @ A)) = (A = bot_bot_pname_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_all__not__in__conv)). 24.85/7.42 thf(877,plain,((! [A:(pname > $o)]: ((! [B:pname]: ~ (member_pname @ B @ (A))) = ((A) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 24.85/7.42 thf(237,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ B) = (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((C = A) | (member5164104_state @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_insert__compr)). 24.85/7.42 thf(1072,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ B) = (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((C = A) | (member5164104_state @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 24.85/7.42 thf(41,axiom,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o),C:((hoare_1262092251_state > $o) > $o)]: ((ord_le2012720639te_o_o @ B @ C) => ((member907417095tate_o @ A @ C) <= (member907417095tate_o @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_subsetD)). 24.85/7.42 thf(396,plain,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o),C:((hoare_1262092251_state > $o) > $o)]: ((ord_le2012720639te_o_o @ (B) @ (C)) => ((member907417095tate_o @ (A) @ (C)) | ~ (member907417095tate_o @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 24.85/7.42 thf(121,axiom,((! [A:pname,B:pname,C:(pname > $o)]: ((insert_pname @ A @ (insert_pname @ B @ C)) = (insert_pname @ B @ (insert_pname @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_insert__commute)). 24.85/7.42 thf(660,plain,((! [A:pname,B:pname,C:(pname > $o)]: ((insert_pname @ A @ (insert_pname @ B @ C)) = (insert_pname @ B @ (insert_pname @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 24.85/7.42 thf(210,axiom,((! [A:((pname > $o) > hoare_1262092251_state),B:((pname > $o) > $o)]: ((finite1178804552_state @ (image_1476171975_state @ A @ B)) <= (finite297249702name_o @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI)). 24.85/7.42 thf(988,plain,((! [A:((pname > $o) > hoare_1262092251_state),B:((pname > $o) > $o)]: ((finite1178804552_state @ (image_1476171975_state @ (A) @ (B))) | ~ (finite297249702name_o @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 24.85/7.42 thf(77,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => ((image_pname_pname_o @ (^ [D:pname]: (A)) @ C) = (insert_pname_o @ A @ bot_bot_pname_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_image__constant)). 24.85/7.42 thf(507,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => ((image_pname_pname_o @ (^ [D:pname]: (A)) @ C) = (insert_pname_o @ A @ bot_bot_pname_o_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 24.85/7.42 thf(7,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: (((finite1423311111tate_o @ (collec313158217tate_o @ A)) & (finite1423311111tate_o @ (collec313158217tate_o @ B))) = (finite1423311111tate_o @ (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((A @ C) | (B @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_finite__Collect__disjI)). 24.85/7.42 thf(312,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: (((finite1423311111tate_o @ (collec313158217tate_o @ A)) & (finite1423311111tate_o @ (collec313158217tate_o @ B))) = (finite1423311111tate_o @ (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((A @ C) | (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 24.85/7.42 thf(274,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((member5164104_state @ B @ C) => (member5164104_state @ B @ (insert81609953_state @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_insertI2)). 24.85/7.42 thf(1206,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((member5164104_state @ B @ (C)) => (member5164104_state @ B @ (insert81609953_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 24.85/7.42 thf(79,axiom,((! [A:(hoare_1262092251_state > $o),B:((pname > $o) > hoare_1262092251_state),C:((pname > $o) > $o)]: ((finite297249702name_o @ C) => ((finite1178804552_state @ A) <= (ord_le870406270tate_o @ A @ (image_1476171975_state @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__surj)). 24.85/7.42 thf(512,plain,((! [A:(hoare_1262092251_state > $o),B:((pname > $o) > hoare_1262092251_state),C:((pname > $o) > $o)]: ((finite297249702name_o @ (C)) => ((finite1178804552_state @ (A)) | ~ (ord_le870406270tate_o @ (A) @ (image_1476171975_state @ (B) @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 24.85/7.42 thf(89,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((A = B) => (~ ((ord_less_eq_pname_o @ A @ B) => (~ (ord_less_eq_pname_o @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_equalityE)). 24.85/7.42 thf(546,plain,((! [A:(pname > $o),B:(pname > $o)]: (((A) = (B)) => (~ ((ord_less_eq_pname_o @ (A) @ (B)) => (~ (ord_less_eq_pname_o @ (B) @ (A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 24.85/7.42 thf(263,axiom,((! [A:pname,B:com]: (((wt @ B) <= ((body @ A) = (some_com @ B))) <= (wT_bodies)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_WT__bodiesD)). 24.85/7.42 thf(1153,plain,((! [A:pname,B:com]: ((wt @ B) | ~ ((body @ A) = (some_com @ B)) | ~ (wT_bodies)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 24.85/7.42 thf(35,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((finite_finite_pname @ (collect_pname @ A)) | (finite_finite_pname @ (collect_pname @ B))) => (finite_finite_pname @ (collect_pname @ (^ [C:pname]: ((B @ C) & (A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_finite__Collect__conjI)). 24.85/7.42 thf(381,plain,((! [A:(pname > $o),B:(pname > $o)]: (((finite_finite_pname @ (collect_pname @ A)) | (finite_finite_pname @ (collect_pname @ B))) => (finite_finite_pname @ (collect_pname @ (^ [C:pname]: ((B @ C) & (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 24.85/7.42 thf(233,axiom,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((~ (member5164104_state @ B @ C)) => ((ord_le870406270tate_o @ C @ A) = (ord_le870406270tate_o @ C @ (insert81609953_state @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_subset__insert)). 24.85/7.42 thf(1057,plain,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((~ (member5164104_state @ B @ (C))) => ((ord_le870406270tate_o @ (C) @ (A)) = (ord_le870406270tate_o @ (C) @ (insert81609953_state @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 24.85/7.42 thf(148,axiom,((! [A:(pname > $o),B:pname]: (ord_less_eq_pname_o @ A @ (insert_pname @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_subset__insertI)). 24.85/7.42 thf(746,plain,((! [A:(pname > $o),B:pname]: (ord_less_eq_pname_o @ (A) @ (insert_pname @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 24.85/7.42 thf(179,axiom,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((insert_pname_o @ A @ B) = (collect_pname_o @ (^ [C:(pname > $o)]: ((C = A) | (member_pname_o @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_insert__compr)). 24.85/7.42 thf(862,plain,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((insert_pname_o @ A @ B) = (collect_pname_o @ (^ [C:(pname > $o)]: ((C = A) | (member_pname_o @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 24.85/7.42 thf(98,axiom,((! [A:pname,B:(hoare_1262092251_state > $o),C:((hoare_1262092251_state > $o) > $o)]: (((image_1820530197_pname @ (^ [D:(hoare_1262092251_state > $o)]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o)) <= (member907417095tate_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_image__constant)). 24.85/7.42 thf(598,plain,((! [A:pname,B:(hoare_1262092251_state > $o),C:((hoare_1262092251_state > $o) > $o)]: (((image_1820530197_pname @ (^ [D:(hoare_1262092251_state > $o)]: (A)) @ (C)) = (insert_pname @ A @ bot_bot_pname_o)) | ~ (member907417095tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 24.85/7.42 thf(39,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ B) => ((ord_le2012720639te_o_o @ A @ B) => (finite1423311111tate_o @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_rev__finite__subset)). 24.85/7.42 thf(392,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ (B)) => ((ord_le2012720639te_o_o @ (A) @ (B)) => (finite1423311111tate_o @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 24.85/7.42 thf(53,axiom,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ (insert1042460334tate_o @ A @ B)) = (finite1423311111tate_o @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_finite__insert)). 24.85/7.42 thf(429,plain,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ (insert1042460334tate_o @ A @ B)) = (finite1423311111tate_o @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 24.85/7.42 thf(162,axiom,((! [A:(pname > $o)]: ((collect_pname_o @ (^ [B:(pname > $o)]: (B = A))) = (insert_pname_o @ A @ bot_bot_pname_o_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_singleton__conv)). 24.85/7.42 thf(788,plain,((! [A:(pname > $o)]: ((collect_pname_o @ (^ [B:(pname > $o)]: (B = A))) = (insert_pname_o @ A @ bot_bot_pname_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 24.85/7.42 thf(282,axiom,((! [A:(pname > hoare_1262092251_state),B:(pname > $o),C:(hoare_1262092251_state > $o)]: (((ord_le870406270tate_o @ C @ (image_669833818_state @ A @ B)) => (? [D:(pname > $o)]: ((ord_less_eq_pname_o @ D @ B) & (finite_finite_pname @ D) & (C = (image_669833818_state @ A @ D))))) <= (finite1178804552_state @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_finite__subset__image)). 24.85/7.42 thf(1238,plain,((! [A:(pname > hoare_1262092251_state),B:(pname > $o),C:(hoare_1262092251_state > $o)]: (((ord_le870406270tate_o @ (C) @ (image_669833818_state @ A @ B)) => (? [D:(pname > $o)]: ((ord_less_eq_pname_o @ (D) @ (B)) & (finite_finite_pname @ (D)) & ((C) = (image_669833818_state @ A @ D))))) | ~ (finite1178804552_state @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 24.85/7.42 thf(45,axiom,((! [A:((hoare_1262092251_state > $o) > $o)]: (((collec313158217tate_o @ A) = bot_bo1962689075te_o_o) = (! [B:(hoare_1262092251_state > $o)]: ~ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Collect__empty__eq)). 24.85/7.42 thf(407,plain,((! [A:((hoare_1262092251_state > $o) > $o)]: (((collec313158217tate_o @ A) = (bot_bo1962689075te_o_o)) = (! [B:(hoare_1262092251_state > $o)]: ~ (A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 24.85/7.42 thf(132,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:hoare_1262092251_state,C:((hoare_1262092251_state > $o) > hoare_1262092251_state),D:(hoare_1262092251_state > $o)]: (((member5164104_state @ B @ (image_234589002_state @ C @ A)) <= (member907417095tate_o @ D @ A)) <= (B = (C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_image__eqI)). 24.85/7.42 thf(693,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:hoare_1262092251_state,C:((hoare_1262092251_state > $o) > hoare_1262092251_state),D:(hoare_1262092251_state > $o)]: ((member5164104_state @ B @ (image_234589002_state @ (C) @ (A))) | ~ (member907417095tate_o @ (D) @ (A)) | ~ (B = (C @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 24.85/7.42 thf(110,axiom,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ A @ (insert_pname @ B @ C)) => ((A != B) => (member_pname @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_insertE)). 24.85/7.42 thf(630,plain,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ A @ (insert_pname @ B @ C)) => ((~ (A = B)) => (member_pname @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 24.85/7.42 thf(108,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((! [C:pname]: ((member_pname @ C @ A) <= (member_pname @ C @ B))) => (ord_less_eq_pname_o @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_subsetI)). 24.85/7.42 thf(625,plain,((! [A:(pname > $o),B:(pname > $o)]: ((! [C:pname]: ((member_pname @ C @ (A)) | ~ (member_pname @ C @ (B)))) => (ord_less_eq_pname_o @ (B) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 24.85/7.42 thf(175,axiom,(wT_bodies),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)). 24.85/7.42 thf(852,plain,(wT_bodies),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 24.85/7.43 thf(14,axiom,((! [A:(((pname > $o) > $o) > hoare_1262092251_state),B:(((pname > $o) > $o) > $o)]: ((finite1178804552_state @ (image_1036078444_state @ A @ B)) <= (finite1066544169me_o_o @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI)). 24.85/7.43 thf(329,plain,((! [A:(((pname > $o) > $o) > hoare_1262092251_state),B:(((pname > $o) > $o) > $o)]: ((finite1178804552_state @ (image_1036078444_state @ (A) @ (B))) | ~ (finite1066544169me_o_o @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 24.85/7.43 thf(265,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:hoare_1262092251_state,D:hoare_1262092251_state]: ((((A = D) & (B = C)) | ((A = C) & (B = D))) = ((insert81609953_state @ A @ (insert81609953_state @ B @ bot_bo113204042tate_o)) = (insert81609953_state @ C @ (insert81609953_state @ D @ bot_bo113204042tate_o)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_doubleton__eq__iff)). 24.85/7.43 thf(1159,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:hoare_1262092251_state,D:hoare_1262092251_state]: ((((A = D) & (B = C)) | ((A = C) & (B = D))) = ((insert81609953_state @ A @ (insert81609953_state @ B @ bot_bo113204042tate_o)) = (insert81609953_state @ C @ (insert81609953_state @ D @ bot_bo113204042tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 24.85/7.43 thf(73,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: (~ (fequal1925511196_state @ A @ B) | (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com)). 24.85/7.43 thf(493,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: (~ (fequal1925511196_state @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 24.85/7.43 thf(12,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ (collect_pname_o @ B)) & (finite297249702name_o @ (collect_pname_o @ A))) = (finite297249702name_o @ (collect_pname_o @ (^ [C:(pname > $o)]: ((A @ C) | (B @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_finite__Collect__disjI)). 24.85/7.43 thf(324,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((finite297249702name_o @ (collect_pname_o @ B)) & (finite297249702name_o @ (collect_pname_o @ A))) = (finite297249702name_o @ (collect_pname_o @ (^ [C:(pname > $o)]: ((A @ C) | (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 24.85/7.43 thf(216,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: (((insert81609953_state @ A @ bot_bo113204042tate_o) = (insert81609953_state @ B @ bot_bo113204042tate_o)) => (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_singleton__inject)). 24.85/7.43 thf(1012,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: (((insert81609953_state @ A @ bot_bo113204042tate_o) = (insert81609953_state @ B @ bot_bo113204042tate_o)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 24.85/7.43 thf(118,axiom,((! [A:pname,B:pname]: ((A = B) = (member_pname @ A @ (insert_pname @ B @ bot_bot_pname_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_singleton__iff)). 24.85/7.43 thf(650,plain,((! [A:pname,B:pname]: ((A = B) = (member_pname @ A @ (insert_pname @ B @ bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 24.85/7.43 thf(104,axiom,((! [A:pname,B:(pname > $o),C:pname]: ((insert_pname @ A @ B @ C) = ((A = C) | (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_insert__code)). 24.85/7.43 thf(615,plain,((! [A:pname,B:(pname > $o),C:pname]: ((insert_pname @ A @ (B) @ C) = ((A = C) | (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 24.85/7.43 thf(251,axiom,((! [A:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ A @ bot_bo113204042tate_o) = (A = bot_bo113204042tate_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_subset__empty)). 24.85/7.43 thf(1121,plain,((! [A:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ (A) @ (bot_bo113204042tate_o)) = ((A) = (bot_bo113204042tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 24.85/7.43 thf(96,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (collect_pname @ (^ [C:pname]: ((C = A) | (member_pname @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_insert__compr)). 24.85/7.43 thf(593,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (collect_pname @ (^ [C:pname]: ((C = A) | (member_pname @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 24.85/7.43 thf(133,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((member_pname @ A @ C) <= (member_pname @ A @ B)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_set__mp)). 24.85/7.43 thf(697,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (C)) | ~ (member_pname @ A @ (B)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 24.85/7.43 thf(243,axiom,((! [A:hoare_1262092251_state]: ((collec1121927558_state @ (^ [B:hoare_1262092251_state]: (B = A))) = (insert81609953_state @ A @ bot_bo113204042tate_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_singleton__conv)). 24.85/7.43 thf(1089,plain,((! [A:hoare_1262092251_state]: ((collec1121927558_state @ (^ [B:hoare_1262092251_state]: (B = A))) = (insert81609953_state @ A @ bot_bo113204042tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 24.85/7.43 thf(291,axiom,((! [A:(hoare_1262092251_state > $o)]: ((! [B:hoare_1262092251_state]: ~ (A @ B)) = ((collec1121927558_state @ A) = bot_bo113204042tate_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Collect__empty__eq)). 24.85/7.43 thf(1270,plain,((! [A:(hoare_1262092251_state > $o)]: ((! [B:hoare_1262092251_state]: ~ (A @ B)) = ((collec1121927558_state @ A) = (bot_bo113204042tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 24.85/7.43 thf(286,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ A @ B) => (hoare_930741239_state @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_asm)). 24.85/7.43 thf(1259,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ (A) @ (B)) => (hoare_930741239_state @ (B) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 24.85/7.43 thf(186,axiom,((! [A:pname,B:((hoare_1262092251_state > $o) > $o)]: ((((image_1820530197_pname @ (^ [C:(hoare_1262092251_state > $o)]: (A)) @ B) = (insert_pname @ A @ bot_bot_pname_o)) <= (B != bot_bo1962689075te_o_o)) & (((image_1820530197_pname @ (^ [C:(hoare_1262092251_state > $o)]: (A)) @ B) = bot_bot_pname_o) <= (B = bot_bo1962689075te_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_image__constant__conv)). 24.85/7.43 thf(884,plain,((! [A:pname,B:((hoare_1262092251_state > $o) > $o)]: ((((image_1820530197_pname @ (^ [C:(hoare_1262092251_state > $o)]: (A)) @ (B)) = (insert_pname @ A @ bot_bot_pname_o)) | ((B) = (bot_bo1962689075te_o_o))) & (((image_1820530197_pname @ (^ [C:(hoare_1262092251_state > $o)]: (A)) @ (B)) = (bot_bot_pname_o)) | ~ ((B) = (bot_bo1962689075te_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 24.85/7.43 thf(222,axiom,((! [A:(pname > hoare_1262092251_state),B:(pname > $o)]: ((bot_bo113204042tate_o = (image_669833818_state @ A @ B)) = (B = bot_bot_pname_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_empty__is__image)). 24.85/7.43 thf(1028,plain,((! [A:(pname > hoare_1262092251_state),B:(pname > $o)]: (((bot_bo113204042tate_o) = (image_669833818_state @ A @ B)) = ((B) = (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 24.85/7.43 thf(71,axiom,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_subset__refl)). 24.85/7.43 thf(488,plain,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ (A) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 24.85/7.43 thf(124,axiom,((! [A:(pname > $o)]: ((A = bot_bot_pname_o) = (ord_less_eq_pname_o @ A @ bot_bot_pname_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_subset__empty)). 24.85/7.43 thf(669,plain,((! [A:(pname > $o)]: (((A) = (bot_bot_pname_o)) = (ord_less_eq_pname_o @ (A) @ (bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 24.85/7.43 thf(113,axiom,((finite_finite_pname @ bot_bot_pname_o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_finite_OemptyI)). 24.85/7.43 thf(637,plain,((finite_finite_pname @ (bot_bot_pname_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 24.85/7.43 thf(95,axiom,((! [A:(pname > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((image_1320925383name_o @ (^ [D:hoare_1262092251_state]: (A)) @ C) = (insert_pname_o @ A @ bot_bot_pname_o_o)) <= (member5164104_state @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_image__constant)). 24.85/7.43 thf(590,plain,((! [A:(pname > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((image_1320925383name_o @ (^ [D:hoare_1262092251_state]: (A)) @ C) = (insert_pname_o @ A @ bot_bot_pname_o_o)) | ~ (member5164104_state @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 24.85/7.43 thf(129,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ B @ C) => ((member5164104_state @ A @ B) => (member5164104_state @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_set__mp)). 24.85/7.43 thf(686,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ (B) @ (C)) => ((member5164104_state @ A @ (B)) => (member5164104_state @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 24.85/7.43 thf(238,axiom,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((hoare_930741239_state @ A @ (insert81609953_state @ B @ bot_bo113204042tate_o)) & (hoare_930741239_state @ A @ C)) <= (hoare_930741239_state @ A @ (insert81609953_state @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_derivs__insertD)). 24.85/7.43 thf(1075,plain,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((hoare_930741239_state @ (A) @ (insert81609953_state @ B @ bot_bo113204042tate_o)) & (hoare_930741239_state @ (A) @ (C))) | ~ (hoare_930741239_state @ (A) @ (insert81609953_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 24.85/7.43 thf(107,axiom,((! [A:((pname > $o) > $o)]: ((A != bot_bot_pname_o_o) = (? [B:(pname > $o)]: (member_pname_o @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_ex__in__conv)). 24.85/7.43 thf(622,plain,((! [A:((pname > $o) > $o)]: ((~ ((A) = (bot_bot_pname_o_o))) = (? [B:(pname > $o)]: (member_pname_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 24.85/7.43 thf(289,axiom,((hoare_930741239_state @ (image_669833818_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ fa)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6)). 24.85/7.43 thf(1266,plain,((hoare_930741239_state @ (image_669833818_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ (fa))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 24.85/7.43 thf(193,axiom,((! [A:pname,B:((pname > $o) > $o)]: ((((image_pname_o_pname @ (^ [C:(pname > $o)]: (A)) @ B) = (insert_pname @ A @ bot_bot_pname_o)) <= (B != bot_bot_pname_o_o)) & ((B = bot_bot_pname_o_o) => ((image_pname_o_pname @ (^ [C:(pname > $o)]: (A)) @ B) = bot_bot_pname_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_image__constant__conv)). 24.85/7.43 thf(911,plain,((! [A:pname,B:((pname > $o) > $o)]: ((((image_pname_o_pname @ (^ [C:(pname > $o)]: (A)) @ (B)) = (insert_pname @ A @ bot_bot_pname_o)) | ((B) = (bot_bot_pname_o_o))) & (((B) = (bot_bot_pname_o_o)) => ((image_pname_o_pname @ (^ [C:(pname > $o)]: (A)) @ (B)) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 24.85/7.43 thf(159,axiom,((! [A:(pname > $o)]: ((collect_pname_o @ (fequal_pname_o @ A)) = (insert_pname_o @ A @ bot_bot_pname_o_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_singleton__conv2)). 24.85/7.43 thf(779,plain,((! [A:(pname > $o)]: ((collect_pname_o @ (fequal_pname_o @ A)) = (insert_pname_o @ A @ bot_bot_pname_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 24.85/7.43 thf(117,axiom,((! [A:pname,B:(pname > $o)]: ((finite_finite_pname @ B) = (finite_finite_pname @ (insert_pname @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_finite__insert)). 24.85/7.43 thf(647,plain,((! [A:pname,B:(pname > $o)]: ((finite_finite_pname @ (B)) = (finite_finite_pname @ (insert_pname @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 24.85/7.43 thf(213,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((B != bot_bo113204042tate_o) => ((image_1403668518tate_o @ (^ [C:hoare_1262092251_state]: (A)) @ B) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o))) & ((B = bot_bo113204042tate_o) => ((image_1403668518tate_o @ (^ [C:hoare_1262092251_state]: (A)) @ B) = bot_bo1962689075te_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_image__constant__conv)). 24.85/7.43 thf(997,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((~ ((B) = (bot_bo113204042tate_o))) => ((image_1403668518tate_o @ (^ [C:hoare_1262092251_state]: (A)) @ B) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o))) & (((B) = (bot_bo113204042tate_o)) => ((image_1403668518tate_o @ (^ [C:hoare_1262092251_state]: (A)) @ B) = (bot_bo1962689075te_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 24.85/7.43 thf(234,axiom,((! [A:hoare_1262092251_state,B:(pname > $o),C:((pname > $o) > $o)]: ((member_pname_o @ B @ C) => ((image_1476171975_state @ (^ [D:(pname > $o)]: (A)) @ C) = (insert81609953_state @ A @ bot_bo113204042tate_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_image__constant)). 24.85/7.43 thf(1060,plain,((! [A:hoare_1262092251_state,B:(pname > $o),C:((pname > $o) > $o)]: ((member_pname_o @ (B) @ (C)) => ((image_1476171975_state @ (^ [D:(pname > $o)]: (A)) @ (C)) = (insert81609953_state @ A @ bot_bo113204042tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 24.85/7.43 thf(230,axiom,((! [A:hoare_1262092251_state,B:pname,C:(pname > $o)]: (((image_669833818_state @ (^ [D:pname]: (A)) @ C) = (insert81609953_state @ A @ bot_bo113204042tate_o)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_image__constant)). 24.85/7.43 thf(1050,plain,((! [A:hoare_1262092251_state,B:pname,C:(pname > $o)]: (((image_669833818_state @ (^ [D:pname]: (A)) @ C) = (insert81609953_state @ A @ bot_bo113204042tate_o)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 24.85/7.43 thf(195,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((finite1178804552_state @ (collec1121927558_state @ A)) | (finite1178804552_state @ (collec1121927558_state @ B))) => (finite1178804552_state @ (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((B @ C) & (A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_finite__Collect__conjI)). 24.85/7.43 thf(921,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((finite1178804552_state @ (collec1121927558_state @ A)) | (finite1178804552_state @ (collec1121927558_state @ B))) => (finite1178804552_state @ (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((B @ C) & (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 24.85/7.43 thf(87,axiom,((! [A:pname,B:pname,C:(pname > $o)]: (((A = B) | (member_pname @ A @ C)) = (member_pname @ A @ (insert_pname @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_insert__iff)). 24.85/7.43 thf(541,plain,((! [A:pname,B:pname,C:(pname > $o)]: (((A = B) | (member_pname @ A @ (C))) = (member_pname @ A @ (insert_pname @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 24.85/7.43 thf(232,axiom,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state]: (((A = (insert81609953_state @ B @ bot_bo113204042tate_o)) | (A = bot_bo113204042tate_o)) <= (ord_le870406270tate_o @ A @ (insert81609953_state @ B @ bot_bo113204042tate_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_subset__singletonD)). 24.85/7.43 thf(1054,plain,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state]: (((A) = (insert81609953_state @ B @ bot_bo113204042tate_o)) | ((A) = (bot_bo113204042tate_o)) | ~ (ord_le870406270tate_o @ (A) @ (insert81609953_state @ B @ bot_bo113204042tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 24.85/7.43 thf(92,axiom,((! [A:(((pname > $o) > $o) > $o),B:((pname > $o) > $o),C:((pname > $o) > $o)]: (((ord_le1205211808me_o_o @ C @ B) => ((A @ bot_bot_pname_o_o) => ((! [D:(pname > $o),E:((pname > $o) > $o)]: ((((~ (member_pname_o @ D @ E)) => ((A @ E) => (A @ (insert_pname_o @ D @ E)))) <= (member_pname_o @ D @ B)) <= (finite297249702name_o @ E))) => (A @ C)))) <= (finite297249702name_o @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_finite__subset__induct)). 24.85/7.43 thf(558,plain,((! [A:(((pname > $o) > $o) > $o),B:((pname > $o) > $o),C:((pname > $o) > $o)]: (((ord_le1205211808me_o_o @ (C) @ (B)) => ((A @ (bot_bot_pname_o_o)) => ((! [D:(pname > $o),E:((pname > $o) > $o)]: (((~ (member_pname_o @ (D) @ (E))) => ((A @ (E)) => (A @ (insert_pname_o @ D @ E)))) | ~ (member_pname_o @ (D) @ (B)) | ~ (finite297249702name_o @ (E)))) => (A @ (C))))) | ~ (finite297249702name_o @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 24.85/7.43 thf(111,axiom,((! [A:((pname > $o) > $o),B:(hoare_1262092251_state > (pname > $o)),C:(hoare_1262092251_state > $o)]: (((ord_le1205211808me_o_o @ A @ (image_1320925383name_o @ B @ C)) => (finite297249702name_o @ A)) <= (finite1178804552_state @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite__surj)). 24.85/7.43 thf(633,plain,((! [A:((pname > $o) > $o),B:(hoare_1262092251_state > (pname > $o)),C:(hoare_1262092251_state > $o)]: (((ord_le1205211808me_o_o @ (A) @ (image_1320925383name_o @ B @ C)) => (finite297249702name_o @ (A))) | ~ (finite1178804552_state @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 24.85/7.43 thf(26,axiom,((! [A:((hoare_1262092251_state > $o) > $o)]: ((finite1303896758te_o_o @ (collec341954548te_o_o @ (^ [B:((hoare_1262092251_state > $o) > $o)]: (ord_le2012720639te_o_o @ B @ A)))) <= (finite1423311111tate_o @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__Collect__subsets)). 24.85/7.43 thf(360,plain,((! [A:((hoare_1262092251_state > $o) > $o)]: ((finite1303896758te_o_o @ (collec341954548te_o_o @ (^ [B:((hoare_1262092251_state > $o) > $o)]: (ord_le2012720639te_o_o @ B @ A)))) | ~ (finite1423311111tate_o @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 24.85/7.43 thf(297,axiom,((! [A:(pname > hoare_1262092251_state),B:pname,C:(pname > $o)]: ((image_669833818_state @ A @ (insert_pname @ B @ C)) = (insert81609953_state @ (A @ B) @ (image_669833818_state @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_image__insert)). 24.85/7.43 thf(1286,plain,((! [A:(pname > hoare_1262092251_state),B:pname,C:(pname > $o)]: ((image_669833818_state @ A @ (insert_pname @ B @ C)) = (insert81609953_state @ (A @ B) @ (image_669833818_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 24.85/7.43 thf(42,axiom,((! [A:((pname > $o) > $o)]: ((collect_pname_o @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Collect__def)). 24.85/7.43 thf(398,plain,((! [A:((pname > $o) > $o)]: ((collect_pname_o @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 24.85/7.43 thf(157,axiom,((! [A:((hoare_1262092251_state > $o) > $o)]: ((A = bot_bo1962689075te_o_o) = (! [B:(hoare_1262092251_state > $o)]: ~ (member907417095tate_o @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_all__not__in__conv)). 24.85/7.43 thf(773,plain,((! [A:((hoare_1262092251_state > $o) > $o)]: (((A) = (bot_bo1962689075te_o_o)) = (! [B:(hoare_1262092251_state > $o)]: ~ (member907417095tate_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 24.85/7.43 thf(94,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) != bot_bot_pname_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_insert__not__empty)). 24.85/7.43 thf(586,plain,((! [A:pname,B:(pname > $o)]: ~ ((insert_pname @ A @ B) = (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 24.85/7.43 thf(294,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((B = bot_bo113204042tate_o) => (~ (member5164104_state @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_equals0D)). 24.85/7.43 thf(1278,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: (((B) = (bot_bo113204042tate_o)) => (~ (member5164104_state @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 24.85/7.43 thf(277,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((hoare_930741239_state @ B @ C) => ((hoare_930741239_state @ A @ C) <= (hoare_930741239_state @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_cut)). 24.85/7.43 thf(1219,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((hoare_930741239_state @ (B) @ (C)) => ((hoare_930741239_state @ (A) @ (C)) | ~ (hoare_930741239_state @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 24.85/7.43 thf(292,axiom,((! [A:(hoare_1262092251_state > $o)]: (ord_le870406270tate_o @ bot_bo113204042tate_o @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_empty__subsetI)). 24.85/7.43 thf(1273,plain,((! [A:(hoare_1262092251_state > $o)]: (ord_le870406270tate_o @ (bot_bo113204042tate_o) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 24.85/7.43 thf(177,axiom,((! [A:(hoare_1262092251_state > $o),B:(pname > $o),C:(hoare_1262092251_state > (pname > $o)),D:hoare_1262092251_state]: ((B = (C @ D)) => ((member_pname_o @ B @ (image_1320925383name_o @ C @ A)) <= (member5164104_state @ D @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_image__eqI)). 24.85/7.43 thf(856,plain,((! [A:(hoare_1262092251_state > $o),B:(pname > $o),C:(hoare_1262092251_state > (pname > $o)),D:hoare_1262092251_state]: (((B) = (C @ D)) => ((member_pname_o @ (B) @ (image_1320925383name_o @ C @ A)) | ~ (member5164104_state @ D @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 24.85/7.43 thf(144,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((member_pname @ A @ C) & (ord_less_eq_pname_o @ B @ C)) = (ord_less_eq_pname_o @ (insert_pname @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_insert__subset)). 24.85/7.43 thf(733,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((member_pname @ A @ (C)) & (ord_less_eq_pname_o @ (B) @ (C))) = (ord_less_eq_pname_o @ (insert_pname @ A @ B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 24.85/7.43 thf(99,axiom,((! [A:pname]: ((collect_pname @ (fequal_pname @ A)) = (insert_pname @ A @ bot_bot_pname_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_singleton__conv2)). 24.85/7.43 thf(601,plain,((! [A:pname]: ((collect_pname @ (fequal_pname @ A)) = (insert_pname @ A @ bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 24.85/7.43 thf(285,axiom,((! [A:hoare_1262092251_state,B:((pname > $o) > $o)]: (((B = bot_bot_pname_o_o) => ((image_1476171975_state @ (^ [C:(pname > $o)]: (A)) @ B) = bot_bo113204042tate_o)) & (((image_1476171975_state @ (^ [C:(pname > $o)]: (A)) @ B) = (insert81609953_state @ A @ bot_bo113204042tate_o)) <= (B != bot_bot_pname_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_image__constant__conv)). 24.85/7.43 thf(1251,plain,((! [A:hoare_1262092251_state,B:((pname > $o) > $o)]: ((((B) = (bot_bot_pname_o_o)) => ((image_1476171975_state @ (^ [C:(pname > $o)]: (A)) @ (B)) = (bot_bo113204042tate_o))) & (((image_1476171975_state @ (^ [C:(pname > $o)]: (A)) @ (B)) = (insert81609953_state @ A @ bot_bo113204042tate_o)) | ((B) = (bot_bot_pname_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 24.85/7.43 thf(105,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((finite_finite_pname @ A) <= (finite_finite_pname @ B)) <= (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_finite__subset)). 24.85/7.43 thf(618,plain,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (A)) | ~ (finite_finite_pname @ (B)) | ~ (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 24.85/7.43 thf(190,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((! [C:hoare_1262092251_state]: ((member5164104_state @ C @ A) <= (member5164104_state @ C @ B))) => (ord_le870406270tate_o @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_subsetI)). 24.85/7.43 thf(904,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((! [C:hoare_1262092251_state]: ((member5164104_state @ C @ (A)) | ~ (member5164104_state @ C @ (B)))) => (ord_le870406270tate_o @ (B) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 24.85/7.43 thf(51,axiom,((! [A:((hoare_1262092251_state > $o) > $o)]: ((collec313158217tate_o @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Collect__def)). 24.85/7.43 thf(423,plain,((! [A:((hoare_1262092251_state > $o) > $o)]: ((collec313158217tate_o @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 24.85/7.43 thf(93,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((((image_pname_pname_o @ (^ [C:pname]: (A)) @ B) = (insert_pname_o @ A @ bot_bot_pname_o_o)) <= (B != bot_bot_pname_o)) & (((image_pname_pname_o @ (^ [C:pname]: (A)) @ B) = bot_bot_pname_o_o) <= (B = bot_bot_pname_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_image__constant__conv)). 24.85/7.43 thf(579,plain,((! [A:(pname > $o),B:(pname > $o)]: ((((image_pname_pname_o @ (^ [C:pname]: (A)) @ B) = (insert_pname_o @ A @ bot_bot_pname_o_o)) | ((B) = (bot_bot_pname_o))) & (((image_pname_pname_o @ (^ [C:pname]: (A)) @ B) = (bot_bot_pname_o_o)) | ~ ((B) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 24.85/7.43 thf(252,axiom,((! [A:(pname > hoare_1262092251_state),B:(pname > $o)]: ((finite_finite_pname @ B) => (finite1178804552_state @ (image_669833818_state @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI)). 24.85/7.43 thf(1124,plain,((! [A:(pname > hoare_1262092251_state),B:(pname > $o)]: ((finite_finite_pname @ (B)) => (finite1178804552_state @ (image_669833818_state @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 24.85/7.43 thf(47,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:(pname > (hoare_1262092251_state > $o)),C:(pname > $o)]: ((finite_finite_pname @ C) => ((ord_le2012720639te_o_o @ A @ (image_518521461tate_o @ B @ C)) => (finite1423311111tate_o @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__surj)). 24.85/7.43 thf(413,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:(pname > (hoare_1262092251_state > $o)),C:(pname > $o)]: ((finite_finite_pname @ (C)) => ((ord_le2012720639te_o_o @ (A) @ (image_518521461tate_o @ B @ C)) => (finite1423311111tate_o @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 24.85/7.43 thf(182,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((ord_less_eq_pname_o @ A @ B) => (finite_finite_pname @ A)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_rev__finite__subset)). 24.85/7.43 thf(875,plain,((! [A:(pname > $o),B:(pname > $o)]: (((ord_less_eq_pname_o @ (A) @ (B)) => (finite_finite_pname @ (A))) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 24.85/7.43 thf(138,axiom,((! [A:(hoare_1262092251_state > (pname > $o)),B:(hoare_1262092251_state > $o)]: ((finite297249702name_o @ (image_1320925383name_o @ A @ B)) <= (finite1178804552_state @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_finite__imageI)). 24.85/7.43 thf(711,plain,((! [A:(hoare_1262092251_state > (pname > $o)),B:(hoare_1262092251_state > $o)]: ((finite297249702name_o @ (image_1320925383name_o @ A @ B)) | ~ (finite1178804552_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 24.85/7.43 thf(115,axiom,((! [A:pname,B:pname,C:pname,D:pname]: (((insert_pname @ A @ (insert_pname @ B @ bot_bot_pname_o)) = (insert_pname @ C @ (insert_pname @ D @ bot_bot_pname_o))) = (((B = D) & (A = C)) | ((A = D) & (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_doubleton__eq__iff)). 24.85/7.43 thf(641,plain,((! [A:pname,B:pname,C:pname,D:pname]: (((insert_pname @ A @ (insert_pname @ B @ bot_bot_pname_o)) = (insert_pname @ C @ (insert_pname @ D @ bot_bot_pname_o))) = (((B = D) & (A = C)) | ((A = D) & (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 24.85/7.43 thf(258,axiom,((! [A:hoare_1262092251_state,B:(pname > hoare_1262092251_state),C:(pname > $o)]: ((member5164104_state @ A @ (image_669833818_state @ B @ C)) = (? [D:pname]: ((A = (B @ D)) & (member_pname @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_image__iff)). 24.85/7.43 thf(1139,plain,((! [A:hoare_1262092251_state,B:(pname > hoare_1262092251_state),C:(pname > $o)]: ((member5164104_state @ A @ (image_669833818_state @ B @ C)) = (? [D:pname]: ((A = (B @ D)) & (member_pname @ D @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 24.85/7.43 thf(102,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: (((member5164104_state @ A @ B) => (member5164104_state @ A @ C)) <= (ord_le870406270tate_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_subsetD)). 24.85/7.43 thf(611,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: (((member5164104_state @ A @ (B)) => (member5164104_state @ A @ (C))) | ~ (ord_le870406270tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 24.85/7.43 thf(248,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:hoare_1262092251_state]: (((B @ C) | (A = C)) = (insert81609953_state @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_insert__code)). 24.85/7.43 thf(1107,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:hoare_1262092251_state]: (((B @ C) | (A = C)) = (insert81609953_state @ A @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 24.85/7.43 thf(244,axiom,((! [A:(hoare_1262092251_state > $o)]: ((! [B:hoare_1262092251_state]: ~ (member5164104_state @ B @ A)) = (A = bot_bo113204042tate_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_all__not__in__conv)). 24.85/7.43 thf(1092,plain,((! [A:(hoare_1262092251_state > $o)]: ((! [B:hoare_1262092251_state]: ~ (member5164104_state @ B @ (A))) = ((A) = (bot_bo113204042tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 24.85/7.43 thf(21,axiom,((finite1423311111tate_o @ bot_bo1962689075te_o_o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite_OemptyI)). 24.85/7.43 thf(350,plain,((finite1423311111tate_o @ (bot_bo1962689075te_o_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 24.85/7.43 thf(125,axiom,((! [A:pname,B:(pname > $o)]: (bot_bot_pname_o != (insert_pname @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_empty__not__insert)). 24.85/7.43 thf(672,plain,((! [A:pname,B:(pname > $o)]: ~ ((bot_bot_pname_o) = (insert_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 24.85/7.43 thf(139,axiom,((! [A:(hoare_1262092251_state > $o)]: ~ (member907417095tate_o @ A @ bot_bo1962689075te_o_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_empty__iff)). 24.85/7.43 thf(713,plain,((! [A:(hoare_1262092251_state > $o)]: ~ (member907417095tate_o @ (A) @ (bot_bo1962689075te_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 24.85/7.43 thf(75,axiom,((! [A:(hoare_1262092251_state > $o),B:(((pname > $o) > $o) > hoare_1262092251_state),C:(((pname > $o) > $o) > $o)]: (((finite1178804552_state @ A) <= (ord_le870406270tate_o @ A @ (image_1036078444_state @ B @ C))) <= (finite1066544169me_o_o @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__surj)). 24.85/7.43 thf(498,plain,((! [A:(hoare_1262092251_state > $o),B:(((pname > $o) > $o) > hoare_1262092251_state),C:(((pname > $o) > $o) > $o)]: ((finite1178804552_state @ (A)) | ~ (ord_le870406270tate_o @ (A) @ (image_1036078444_state @ (B) @ (C))) | ~ (finite1066544169me_o_o @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 24.85/7.43 thf(295,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: (((ord_le870406270tate_o @ B @ A) => (hoare_930741239_state @ A @ C)) <= (hoare_930741239_state @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_thin)). 24.85/7.43 thf(1282,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: (((ord_le870406270tate_o @ (B) @ (A)) => (hoare_930741239_state @ (A) @ (C))) | ~ (hoare_930741239_state @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 24.85/7.43 thf(49,axiom,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((finite297249702name_o @ B) => (finite297249702name_o @ (insert_pname_o @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_finite_OinsertI)). 24.85/7.43 thf(419,plain,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((finite297249702name_o @ (B)) => (finite297249702name_o @ (insert_pname_o @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 24.85/7.43 thf(145,axiom,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ (insert_pname @ A @ C)) <= ((B = A) <= (~ (member_pname @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_insertCI)). 24.85/7.43 thf(736,plain,((! [A:pname,B:pname,C:(pname > $o)]: ((member_pname @ B @ (insert_pname @ A @ C)) | ~ ((B = A) | (member_pname @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 24.85/7.43 thf(211,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: ((fequal1925511196_state @ A @ B) | (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com)). 24.85/7.43 thf(990,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: ((fequal1925511196_state @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 24.85/7.43 thf(10,axiom,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((finite297249702name_o @ (insert_pname_o @ A @ B)) = (finite297249702name_o @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite__insert)). 24.85/7.43 thf(318,plain,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((finite297249702name_o @ (insert_pname_o @ A @ B)) = (finite297249702name_o @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 24.85/7.43 thf(184,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((member_pname @ A @ C) <= (member_pname @ A @ B)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_subsetD)). 24.85/7.43 thf(880,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (C)) | ~ (member_pname @ A @ (B)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 24.85/7.43 thf(4,axiom,((! [A:(((pname > $o) > $o) > $o),B:(((pname > $o) > $o) > $o)]: ((finite1066544169me_o_o @ (collect_pname_o_o @ (^ [C:((pname > $o) > $o)]: ((B @ C) & (A @ C))))) <= ((finite1066544169me_o_o @ (collect_pname_o_o @ A)) | (finite1066544169me_o_o @ (collect_pname_o_o @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_finite__Collect__conjI)). 24.85/7.43 thf(303,plain,((! [A:(((pname > $o) > $o) > $o),B:(((pname > $o) > $o) > $o)]: ((finite1066544169me_o_o @ (collect_pname_o_o @ (^ [C:((pname > $o) > $o)]: ((B @ C) & (A @ C))))) | ~ ((finite1066544169me_o_o @ (collect_pname_o_o @ A)) | (finite1066544169me_o_o @ (collect_pname_o_o @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 24.85/7.43 thf(154,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((A = B) => (ord_less_eq_pname_o @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_equalityD2)). 24.85/7.43 thf(764,plain,((! [A:(pname > $o),B:(pname > $o)]: (((A) = (B)) => (ord_less_eq_pname_o @ (B) @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 24.85/7.43 thf(100,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((A = B) = ((ord_le870406270tate_o @ B @ A) & (ord_le870406270tate_o @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_set__eq__subset)). 24.85/7.43 thf(604,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((A) = (B)) = ((ord_le870406270tate_o @ (B) @ (A)) & (ord_le870406270tate_o @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 24.85/7.43 thf(161,axiom,((! [A:(pname > $o),B:pname,C:(pname > pname),D:pname]: ((B = (C @ D)) => ((member_pname @ B @ (image_pname_pname @ C @ A)) <= (member_pname @ D @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_image__eqI)). 24.85/7.43 thf(784,plain,((! [A:(pname > $o),B:pname,C:(pname > pname),D:pname]: ((B = (C @ D)) => ((member_pname @ B @ (image_pname_pname @ C @ A)) | ~ (member_pname @ D @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 24.85/7.43 thf(250,axiom,((! [A:pname]: ((~ (! [B:com]: ((body @ A) != (some_com @ B)))) <= (wt @ (body_1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_WTs__elim__cases_I7_J)). 24.85/7.43 thf(1117,plain,((! [A:pname]: (~ (! [B:com]: ~ ((body @ A) = (some_com @ B))) | ~ (wt @ (body_1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 24.85/7.43 thf(27,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (~ (fequal1529404211tate_o @ A @ B) | (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It)). 24.85/7.43 thf(362,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (~ (fequal1529404211tate_o @ (A) @ (B)) | ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 24.85/7.43 thf(61,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((A = B) => (ord_le870406270tate_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_equalityD1)). 24.85/7.43 thf(451,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((A) = (B)) => (ord_le870406270tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 24.85/7.43 thf(19,axiom,((! [A:(((hoare_1262092251_state > $o) > $o) > hoare_1262092251_state),B:(((hoare_1262092251_state > $o) > $o) > $o)]: ((finite1303896758te_o_o @ B) => (finite1178804552_state @ (image_165349207_state @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI)). 24.85/7.43 thf(345,plain,((! [A:(((hoare_1262092251_state > $o) > $o) > hoare_1262092251_state),B:(((hoare_1262092251_state > $o) > $o) > $o)]: ((finite1303896758te_o_o @ (B)) => (finite1178804552_state @ (image_165349207_state @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 24.85/7.43 thf(85,axiom,((! [A:(hoare_1262092251_state > $o)]: ~ (member907417095tate_o @ A @ bot_bo1962689075te_o_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_emptyE)). 24.85/7.43 thf(535,plain,((! [A:(hoare_1262092251_state > $o)]: ~ (member907417095tate_o @ (A) @ (bot_bo1962689075te_o_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 24.85/7.43 thf(69,axiom,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((insert_pname_o @ A @ B) = (collect_pname_o @ (^ [C:(pname > $o)]: ((C = A) | (member_pname_o @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_insert__compr__raw)). 24.85/7.43 thf(483,plain,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((insert_pname_o @ A @ B) = (collect_pname_o @ (^ [C:(pname > $o)]: ((C = A) | (member_pname_o @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 24.85/7.43 thf(173,axiom,((! [A:(pname > pname),B:(pname > $o)]: ((finite_finite_pname @ (image_pname_pname @ A @ B)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite__imageI)). 24.85/7.43 thf(848,plain,((! [A:(pname > pname),B:(pname > $o)]: ((finite_finite_pname @ (image_pname_pname @ A @ B)) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 24.85/7.43 thf(188,axiom,((bot_bot_pname_o = (collect_pname @ (^ [A:pname]: ($false))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_empty__def)). 24.85/7.43 thf(895,plain,(((bot_bot_pname_o) = (collect_pname @ (^ [A:pname]: ($false))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 24.85/7.43 thf(261,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: (member5164104_state @ A @ (insert81609953_state @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_insertI1)). 24.85/7.43 thf(1149,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: (member5164104_state @ A @ (insert81609953_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 24.85/7.43 thf(156,axiom,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > $o)),D:pname]: (((member_pname @ D @ A) => (member_pname_o @ B @ (image_pname_pname_o @ C @ A))) <= (B = (C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_image__eqI)). 24.85/7.43 thf(769,plain,((! [A:(pname > $o),B:(pname > $o),C:(pname > (pname > $o)),D:pname]: (((member_pname @ D @ (A)) => (member_pname_o @ (B) @ (image_pname_pname_o @ C @ A))) | ~ ((B) = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 24.85/7.43 thf(219,axiom,((finite1178804552_state @ bot_bo113204042tate_o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_finite_OemptyI)). 24.85/7.43 thf(1022,plain,((finite1178804552_state @ (bot_bo113204042tate_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 24.85/7.43 thf(64,axiom,((! [A:((hoare_1262092251_state > $o) > $o)]: ((A != bot_bo1962689075te_o_o) = (? [B:(hoare_1262092251_state > $o)]: (member907417095tate_o @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_ex__in__conv)). 24.85/7.43 thf(462,plain,((! [A:((hoare_1262092251_state > $o) > $o)]: ((~ ((A) = (bot_bo1962689075te_o_o))) = (? [B:(hoare_1262092251_state > $o)]: (member907417095tate_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 24.85/7.43 thf(164,axiom,((! [A:(hoare_1262092251_state > $o),B:pname,C:(hoare_1262092251_state > pname),D:hoare_1262092251_state]: (((member_pname @ B @ (image_202231862_pname @ C @ A)) <= (member5164104_state @ D @ A)) <= (B = (C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_image__eqI)). 24.85/7.43 thf(799,plain,((! [A:(hoare_1262092251_state > $o),B:pname,C:(hoare_1262092251_state > pname),D:hoare_1262092251_state]: ((member_pname @ B @ (image_202231862_pname @ C @ A)) | ~ (member5164104_state @ D @ (A)) | ~ (B = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 24.85/7.43 thf(266,axiom,((! [A:com]: (((wT_bodies) => ((wt @ A) => (hoare_930741239_state @ bot_bo113204042tate_o @ (insert81609953_state @ (hoare_Mirabelle_MGT @ A) @ bot_bo113204042tate_o)))) <= (hoare_1821564147gleton)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_MGF)). 24.85/7.43 thf(1162,plain,((! [A:com]: (((wT_bodies) => ((wt @ A) => (hoare_930741239_state @ (bot_bo113204042tate_o) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ A) @ bot_bo113204042tate_o)))) | ~ (hoare_1821564147gleton)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 24.85/7.43 thf(208,axiom,((! [A:pname,B:(pname > $o)]: ((B @ A) = (member_pname @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_mem__def)). 24.85/7.43 thf(983,plain,((! [A:pname,B:(pname > $o)]: ((B @ A) = (member_pname @ A @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 24.85/7.43 thf(155,axiom,(hoare_1821564147gleton),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)). 24.85/7.43 thf(768,plain,(hoare_1821564147gleton),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 24.85/7.43 thf(228,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:hoare_1262092251_state]: (((hoare_930741239_state @ B @ A) => (hoare_930741239_state @ B @ (insert81609953_state @ C @ A))) <= (hoare_930741239_state @ B @ (insert81609953_state @ C @ bot_bo113204042tate_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert)). 24.85/7.43 thf(1044,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:hoare_1262092251_state]: (((hoare_930741239_state @ (B) @ (A)) => (hoare_930741239_state @ (B) @ (insert81609953_state @ C @ A))) | ~ (hoare_930741239_state @ (B) @ (insert81609953_state @ C @ bot_bo113204042tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 24.85/7.43 thf(181,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > $o)]: (((A @ B) => ((collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((C = B) & (A @ C)))) = (insert1042460334tate_o @ B @ bot_bo1962689075te_o_o))) & ((~ (A @ B)) => ((collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((C = B) & (A @ C)))) = bot_bo1962689075te_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_Collect__conv__if)). 24.85/7.43 thf(868,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > $o)]: (((A @ (B)) => ((collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((C = B) & (A @ C)))) = (insert1042460334tate_o @ B @ bot_bo1962689075te_o_o))) & ((~ (A @ (B))) => ((collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((C = B) & (A @ C)))) = (bot_bo1962689075te_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 24.85/7.43 thf(62,axiom,((! [A:(hoare_1262092251_state > $o)]: ((collec1121927558_state @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Collect__def)). 24.85/7.43 thf(455,plain,((! [A:(hoare_1262092251_state > $o)]: ((collec1121927558_state @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 24.85/7.43 thf(217,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((member5164104_state @ A @ C) <= (A != B)) <= (member5164104_state @ A @ (insert81609953_state @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_insertE)). 24.85/7.43 thf(1015,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((member5164104_state @ A @ (C)) | (A = B) | ~ (member5164104_state @ A @ (insert81609953_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 24.85/7.43 thf(1,conjecture,((hoare_930741239_state @ (image_669833818_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_7)). 24.85/7.43 thf(2,negated_conjecture,((~ (hoare_930741239_state @ (image_669833818_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o)))),inference(neg_conjecture,[status(cth)],[1])). 24.85/7.43 thf(299,plain,((~ (hoare_930741239_state @ (image_669833818_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (body_1 @ A))) @ (dom_pname_com @ body)) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo113204042tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 24.85/7.43 thf(56,axiom,((! [A:((pname > $o) > $o)]: (ord_le1205211808me_o_o @ bot_bot_pname_o_o @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_empty__subsetI)). 24.85/7.43 thf(438,plain,((! [A:((pname > $o) > $o)]: (ord_le1205211808me_o_o @ (bot_bot_pname_o_o) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 24.85/7.43 thf(119,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((ord_less_eq_pname_o @ A @ B) & (ord_less_eq_pname_o @ B @ A)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_set__eq__subset)). 24.85/7.43 thf(653,plain,((! [A:(pname > $o),B:(pname > $o)]: (((ord_less_eq_pname_o @ (A) @ (B)) & (ord_less_eq_pname_o @ (B) @ (A))) = ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 24.85/7.43 thf(40,axiom,((! [A:(hoare_1262092251_state > $o)]: ((finite1423311111tate_o @ (collec313158217tate_o @ (^ [B:(hoare_1262092251_state > $o)]: (ord_le870406270tate_o @ B @ A)))) <= (finite1178804552_state @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets)). 24.85/7.43 thf(394,plain,((! [A:(hoare_1262092251_state > $o)]: ((finite1423311111tate_o @ (collec313158217tate_o @ (^ [B:(hoare_1262092251_state > $o)]: (ord_le870406270tate_o @ B @ A)))) | ~ (finite1178804552_state @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 24.85/7.43 thf(209,axiom,((! [A:pname,B:(pname > $o)]: (member_pname @ A @ (insert_pname @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_insertI1)). 24.85/7.43 thf(986,plain,((! [A:pname,B:(pname > $o)]: (member_pname @ A @ (insert_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 24.85/7.43 thf(5,axiom,((! [A:pname,B:pname]: ((A = B) | ~ (fequal_pname @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T)). 24.85/7.43 thf(306,plain,((! [A:pname,B:pname]: ((A = B) | ~ (fequal_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 24.85/7.43 thf(224,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ B) = (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((C = A) | (member5164104_state @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_insert__compr__raw)). 24.85/7.43 thf(1034,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ B) = (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((C = A) | (member5164104_state @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 24.85/7.43 thf(72,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((~ (member_pname @ B @ A)) => (((insert_pname @ B @ C) = (insert_pname @ B @ A)) = (C = A))) <= (~ (member_pname @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_insert__ident)). 24.85/7.43 thf(490,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: (((~ (member_pname @ B @ (A))) => (((insert_pname @ B @ C) = (insert_pname @ B @ A)) = ((C) = (A)))) | (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 24.85/7.43 thf(52,axiom,((! [A:(pname > $o)]: ((! [B:pname]: ~ (A @ B)) = (bot_bot_pname_o = (collect_pname @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_empty__Collect__eq)). 24.85/7.43 thf(426,plain,((! [A:(pname > $o)]: ((! [B:pname]: ~ (A @ B)) = ((bot_bot_pname_o) = (collect_pname @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 24.85/7.43 thf(127,axiom,((! [A:((pname > $o) > $o)]: ((! [B:(pname > $o)]: ~ (member_pname_o @ B @ A)) = (A = bot_bot_pname_o_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_all__not__in__conv)). 24.85/7.43 thf(680,plain,((! [A:((pname > $o) > $o)]: ((! [B:(pname > $o)]: ~ (member_pname_o @ (B) @ (A))) = ((A) = (bot_bot_pname_o_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 24.85/7.43 thf(122,axiom,((! [A:pname]: ~ (member_pname @ A @ bot_bot_pname_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_emptyE)). 24.85/7.43 thf(663,plain,((! [A:pname]: ~ (member_pname @ A @ (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 24.85/7.43 thf(256,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:((hoare_1262092251_state > $o) > $o)]: (((image_234589002_state @ (^ [D:(hoare_1262092251_state > $o)]: (A)) @ C) = (insert81609953_state @ A @ bot_bo113204042tate_o)) <= (member907417095tate_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_image__constant)). 24.85/7.43 thf(1134,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:((hoare_1262092251_state > $o) > $o)]: (((image_234589002_state @ (^ [D:(hoare_1262092251_state > $o)]: (A)) @ (C)) = (insert81609953_state @ A @ bot_bo113204042tate_o)) | ~ (member907417095tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 24.85/7.43 thf(168,axiom,((! [A:((pname > $o) > $o),B:(pname > $o),C:(pname > $o)]: ((((A @ bot_bot_pname_o) => ((A @ C) <= (! [D:pname,E:(pname > $o)]: (((member_pname @ D @ B) => ((~ (member_pname @ D @ E)) => ((A @ E) => (A @ (insert_pname @ D @ E))))) <= (finite_finite_pname @ E))))) <= (ord_less_eq_pname_o @ C @ B)) <= (finite_finite_pname @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_finite__subset__induct)). 24.85/7.43 thf(812,plain,((! [A:((pname > $o) > $o),B:(pname > $o),C:(pname > $o)]: (((A @ (bot_bot_pname_o)) => ((A @ (C)) | ~ (! [D:pname,E:(pname > $o)]: (((member_pname @ D @ (B)) => ((~ (member_pname @ D @ (E))) => ((A @ (E)) => (A @ (insert_pname @ D @ E))))) | ~ (finite_finite_pname @ (E)))))) | ~ (ord_less_eq_pname_o @ (C) @ (B)) | ~ (finite_finite_pname @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 24.85/7.43 thf(240,axiom,((! [A:hoare_1262092251_state,B:(pname > hoare_1262092251_state),C:(pname > $o)]: ((~ (! [D:pname]: ((A = (B @ D)) => (~ (member_pname @ D @ C))))) <= (member5164104_state @ A @ (image_669833818_state @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_imageE)). 24.85/7.43 thf(1081,plain,((! [A:hoare_1262092251_state,B:(pname > hoare_1262092251_state),C:(pname > $o)]: (~ (! [D:pname]: ((A = (B @ D)) => (~ (member_pname @ D @ (C))))) | ~ (member5164104_state @ A @ (image_669833818_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 24.85/7.43 thf(81,axiom,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((member5164104_state @ B @ C) => ((ord_le870406270tate_o @ C @ A) => (member5164104_state @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_set__rev__mp)). 24.85/7.43 thf(516,plain,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((member5164104_state @ B @ (C)) => ((ord_le870406270tate_o @ (C) @ (A)) => (member5164104_state @ B @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 24.85/7.43 thf(201,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > (hoare_1262092251_state > $o)),C:(hoare_1262092251_state > $o)]: (((finite1423311111tate_o @ A) <= (ord_le2012720639te_o_o @ A @ (image_1403668518tate_o @ B @ C))) <= (finite1178804552_state @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_finite__surj)). 24.85/7.43 thf(939,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > (hoare_1262092251_state > $o)),C:(hoare_1262092251_state > $o)]: ((finite1423311111tate_o @ (A)) | ~ (ord_le2012720639te_o_o @ (A) @ (image_1403668518tate_o @ B @ C)) | ~ (finite1178804552_state @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 24.85/7.43 thf(18,axiom,((! [A:(pname > $o)]: ((collect_pname @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Collect__def)). 24.85/7.43 thf(342,plain,((! [A:(pname > $o)]: ((collect_pname @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 24.85/7.43 thf(24,axiom,((! [A:((hoare_1262092251_state > $o) > $o)]: ((! [B:(hoare_1262092251_state > $o)]: ~ (A @ B)) = (bot_bo1962689075te_o_o = (collec313158217tate_o @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_empty__Collect__eq)). 24.85/7.43 thf(355,plain,((! [A:((hoare_1262092251_state > $o) > $o)]: ((! [B:(hoare_1262092251_state > $o)]: ~ (A @ (B))) = ((bot_bo1962689075te_o_o) = (collec313158217tate_o @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 24.85/7.43 thf(90,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((ord_le870406270tate_o @ A @ B) => (finite1178804552_state @ A)) <= (finite1178804552_state @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_rev__finite__subset)). 24.85/7.43 thf(553,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((ord_le870406270tate_o @ (A) @ (B)) => (finite1178804552_state @ (A))) | ~ (finite1178804552_state @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 24.85/7.43 thf(63,axiom,((! [A:((pname > $o) > $o),B:pname,C:((pname > $o) > pname),D:(pname > $o)]: (((member_pname_o @ D @ A) => (member_pname @ B @ (image_pname_o_pname @ C @ A))) <= (B = (C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_image__eqI)). 24.85/7.43 thf(458,plain,((! [A:((pname > $o) > $o),B:pname,C:((pname > $o) > pname),D:(pname > $o)]: (((member_pname_o @ (D) @ (A)) => (member_pname @ B @ (image_pname_o_pname @ (C) @ (A)))) | ~ (B = (C @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 24.85/7.43 thf(170,axiom,((bot_bo1962689075te_o_o = (collec313158217tate_o @ (^ [A:(hoare_1262092251_state > $o)]: ($false))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_empty__def)). 24.85/7.43 thf(836,plain,(((bot_bo1962689075te_o_o) = (collec313158217tate_o @ (^ [A:(hoare_1262092251_state > $o)]: ($false))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 24.85/7.43 thf(273,axiom,((! [A:pname,B:pname]: (((body_1 @ A) = (body_1 @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_com_Osimps_I6_J)). 24.85/7.43 thf(1203,plain,((! [A:pname,B:pname]: (((body_1 @ A) = (body_1 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 24.85/7.43 thf(275,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ B) != bot_bo113204042tate_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_insert__not__empty)). 24.85/7.43 thf(1208,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ~ ((insert81609953_state @ A @ B) = (bot_bo113204042tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 24.85/7.43 thf(197,axiom,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((~ (member_pname @ B @ C)) => ((ord_less_eq_pname_o @ C @ A) = (ord_less_eq_pname_o @ C @ (insert_pname @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_subset__insert)). 24.85/7.43 thf(927,plain,((! [A:(pname > $o),B:pname,C:(pname > $o)]: ((~ (member_pname @ B @ (C))) => ((ord_less_eq_pname_o @ (C) @ (A)) = (ord_less_eq_pname_o @ (C) @ (insert_pname @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 24.85/7.43 thf(32,axiom,((! [A:(pname > (hoare_1262092251_state > $o)),B:(pname > $o)]: ((finite1423311111tate_o @ (image_518521461tate_o @ A @ B)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finite__imageI)). 24.85/7.43 thf(374,plain,((! [A:(pname > (hoare_1262092251_state > $o)),B:(pname > $o)]: ((finite1423311111tate_o @ (image_518521461tate_o @ A @ B)) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 24.85/7.43 thf(260,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: (bot_bo113204042tate_o != (insert81609953_state @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_empty__not__insert)). 24.85/7.43 thf(1145,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ~ ((bot_bo113204042tate_o) = (insert81609953_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 24.85/7.43 thf(218,axiom,((! [A:com,B:(hoare_1262092251_state > $o)]: ((((wt @ A) => (hoare_930741239_state @ B @ (insert81609953_state @ (hoare_Mirabelle_MGT @ A) @ bot_bo113204042tate_o))) <= (! [C:pname]: ((hoare_930741239_state @ B @ (insert81609953_state @ (hoare_Mirabelle_MGT @ (body_1 @ C)) @ bot_bo113204042tate_o)) <= (member_pname @ C @ (dom_pname_com @ body))))) <= (hoare_1821564147gleton)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_MGF__lemma1)). 24.85/7.43 thf(1018,plain,((! [A:com,B:(hoare_1262092251_state > $o)]: (((wt @ A) => (hoare_930741239_state @ (B) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ A) @ bot_bo113204042tate_o))) | ~ (! [C:pname]: ((hoare_930741239_state @ (B) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ (body_1 @ C)) @ bot_bo113204042tate_o)) | ~ (member_pname @ C @ (dom_pname_com @ body)))) | ~ (hoare_1821564147gleton)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 24.85/7.43 thf(158,axiom,((! [A:pname,B:pname]: ((member_pname @ A @ (insert_pname @ B @ bot_bot_pname_o)) => (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_singletonE)). 24.85/7.43 thf(776,plain,((! [A:pname,B:pname]: ((member_pname @ A @ (insert_pname @ B @ bot_bot_pname_o)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 24.85/7.43 thf(83,axiom,((! [A:pname,B:pname]: (((insert_pname @ A @ bot_bot_pname_o) = (insert_pname @ B @ bot_bot_pname_o)) => (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_singleton__inject)). 24.85/7.43 thf(525,plain,((! [A:pname,B:pname]: (((insert_pname @ A @ bot_bot_pname_o) = (insert_pname @ B @ bot_bot_pname_o)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 24.85/7.43 thf(131,axiom,((! [A:pname,B:(pname > $o),C:((pname > $o) > $o)]: ((member_pname_o @ B @ C) => ((image_pname_o_pname @ (^ [D:(pname > $o)]: (A)) @ C) = (insert_pname @ A @ bot_bot_pname_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_image__constant)). 24.85/7.43 thf(690,plain,((! [A:pname,B:(pname > $o),C:((pname > $o) > $o)]: ((member_pname_o @ (B) @ (C)) => ((image_pname_o_pname @ (^ [D:(pname > $o)]: (A)) @ (C)) = (insert_pname @ A @ bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 24.85/7.43 thf(221,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((A = B) | (member5164104_state @ A @ C)) = (member5164104_state @ A @ (insert81609953_state @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_insert__iff)). 24.85/7.43 thf(1025,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: (((A = B) | (member5164104_state @ A @ (C))) = (member5164104_state @ A @ (insert81609953_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 24.85/7.43 thf(136,axiom,((! [A:(pname > $o),B:(pname > $o)]: (((A = B) <= (ord_less_eq_pname_o @ B @ A)) <= (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_equalityI)). 24.85/7.43 thf(705,plain,((! [A:(pname > $o),B:(pname > $o)]: (((A) = (B)) | ~ (ord_less_eq_pname_o @ (B) @ (A)) | ~ (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 24.85/7.43 thf(279,axiom,((! [A:(pname > $o),B:(hoare_1262092251_state > $o)]: (((B != bot_bo113204042tate_o) => ((image_1320925383name_o @ (^ [C:hoare_1262092251_state]: (A)) @ B) = (insert_pname_o @ A @ bot_bot_pname_o_o))) & ((B = bot_bo113204042tate_o) => ((image_1320925383name_o @ (^ [C:hoare_1262092251_state]: (A)) @ B) = bot_bot_pname_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_image__constant__conv)). 24.85/7.43 thf(1225,plain,((! [A:(pname > $o),B:(hoare_1262092251_state > $o)]: (((~ ((B) = (bot_bo113204042tate_o))) => ((image_1320925383name_o @ (^ [C:hoare_1262092251_state]: (A)) @ B) = (insert_pname_o @ A @ bot_bot_pname_o_o))) & (((B) = (bot_bo113204042tate_o)) => ((image_1320925383name_o @ (^ [C:hoare_1262092251_state]: (A)) @ B) = (bot_bot_pname_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 24.85/7.43 thf(13,axiom,((! [A:(((hoare_1262092251_state > $o) > $o) > pname),B:(((hoare_1262092251_state > $o) > $o) > $o)]: ((finite1303896758te_o_o @ B) => (finite_finite_pname @ (image_893364936_pname @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI)). 24.85/7.43 thf(327,plain,((! [A:(((hoare_1262092251_state > $o) > $o) > pname),B:(((hoare_1262092251_state > $o) > $o) > $o)]: ((finite1303896758te_o_o @ (B)) => (finite_finite_pname @ (image_893364936_pname @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 24.85/7.43 thf(290,axiom,((! [A:hoare_1262092251_state]: ~ (member5164104_state @ A @ bot_bo113204042tate_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_empty__iff)). 24.85/7.43 thf(1267,plain,((! [A:hoare_1262092251_state]: ~ (member5164104_state @ A @ (bot_bo113204042tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 24.85/7.43 thf(246,axiom,((~ (member5164104_state @ (hoare_Mirabelle_MGT @ y) @ fa))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3)). 24.85/7.43 thf(1098,plain,((~ (member5164104_state @ (hoare_Mirabelle_MGT @ y) @ (fa)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 24.85/7.43 thf(231,axiom,((ord_le870406270tate_o @ fa @ (image_669833818_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ A)))) @ (dom_pname_com @ body)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4)). 24.85/7.43 thf(1053,plain,((ord_le870406270tate_o @ (fa) @ (image_669833818_state @ (^ [A:pname]: (hoare_Mirabelle_MGT @ (the_com @ (body @ A)))) @ (dom_pname_com @ body)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 24.85/7.43 thf(163,axiom,((! [A:pname,B:(pname > $o)]: (((B = bot_bot_pname_o) => ((image_pname_pname @ (^ [C:pname]: (A)) @ B) = bot_bot_pname_o)) & (((image_pname_pname @ (^ [C:pname]: (A)) @ B) = (insert_pname @ A @ bot_bot_pname_o)) <= (B != bot_bot_pname_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_image__constant__conv)). 24.85/7.43 thf(791,plain,((! [A:pname,B:(pname > $o)]: ((((B) = (bot_bot_pname_o)) => ((image_pname_pname @ (^ [C:pname]: (A)) @ B) = (bot_bot_pname_o))) & (((image_pname_pname @ (^ [C:pname]: (A)) @ B) = (insert_pname @ A @ bot_bot_pname_o)) | ((B) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 24.85/7.43 thf(281,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ (insert81609953_state @ A @ B)) = (insert81609953_state @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_insert__absorb2)). 24.85/7.43 thf(1235,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ (insert81609953_state @ A @ B)) = (insert81609953_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 24.85/7.43 thf(241,axiom,((! [A:(hoare_1262092251_state > $o)]: (hoare_930741239_state @ A @ bot_bo113204042tate_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty)). 24.85/7.43 thf(1085,plain,((! [A:(hoare_1262092251_state > $o)]: (hoare_930741239_state @ (A) @ (bot_bo113204042tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 24.85/7.43 thf(167,axiom,((! [A:((pname > $o) > $o),B:hoare_1262092251_state,C:((pname > $o) > hoare_1262092251_state),D:(pname > $o)]: ((B = (C @ D)) => ((member_pname_o @ D @ A) => (member5164104_state @ B @ (image_1476171975_state @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_image__eqI)). 24.85/7.43 thf(808,plain,((! [A:((pname > $o) > $o),B:hoare_1262092251_state,C:((pname > $o) > hoare_1262092251_state),D:(pname > $o)]: ((B = (C @ (D))) => ((member_pname_o @ (D) @ (A)) => (member5164104_state @ B @ (image_1476171975_state @ (C) @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 24.85/7.43 thf(15,axiom,((! [A:((pname > $o) > pname),B:((pname > $o) > $o)]: ((finite297249702name_o @ B) => (finite_finite_pname @ (image_pname_o_pname @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI)). 24.85/7.43 thf(331,plain,((! [A:((pname > $o) > pname),B:((pname > $o) > $o)]: ((finite297249702name_o @ (B)) => (finite_finite_pname @ (image_pname_o_pname @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 24.85/7.43 thf(269,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ (collec1121927558_state @ B)) = (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((~ (C = A)) => (B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_insert__Collect)). 24.85/7.43 thf(1188,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o)]: ((insert81609953_state @ A @ (collec1121927558_state @ B)) = (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((~ (C = A)) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 24.85/7.43 thf(268,axiom,((bot_bo113204042tate_o = (collec1121927558_state @ (^ [A:hoare_1262092251_state]: ($false))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_empty__def)). 24.85/7.43 thf(1186,plain,(((bot_bo113204042tate_o) = (collec1121927558_state @ (^ [A:hoare_1262092251_state]: ($false))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 24.85/7.43 thf(226,axiom,((! [A:(hoare_1262092251_state > $o)]: ((bot_bo113204042tate_o = (collec1121927558_state @ A)) = (! [B:hoare_1262092251_state]: ~ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_empty__Collect__eq)). 24.85/7.43 thf(1038,plain,((! [A:(hoare_1262092251_state > $o)]: (((bot_bo113204042tate_o) = (collec1121927558_state @ A)) = (! [B:hoare_1262092251_state]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 24.85/7.43 thf(30,axiom,((! [A:((pname > $o) > $o),B:(pname > (pname > $o)),C:(pname > $o)]: ((finite_finite_pname @ C) => ((ord_le1205211808me_o_o @ A @ (image_pname_pname_o @ B @ C)) => (finite297249702name_o @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_finite__surj)). 24.85/7.43 thf(370,plain,((! [A:((pname > $o) > $o),B:(pname > (pname > $o)),C:(pname > $o)]: ((finite_finite_pname @ (C)) => ((ord_le1205211808me_o_o @ (A) @ (image_pname_pname_o @ B @ C)) => (finite297249702name_o @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 24.85/7.43 thf(88,axiom,((bot_bot_pname_o_o = (collect_pname_o @ (^ [A:(pname > $o)]: ($false))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_empty__def)). 24.85/7.43 thf(544,plain,(((bot_bot_pname_o_o) = (collect_pname_o @ (^ [A:(pname > $o)]: ($false))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 24.85/7.43 thf(191,axiom,((finite1178804552_state @ fa)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)). 24.85/7.43 thf(907,plain,((finite1178804552_state @ (fa))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 24.85/7.43 thf(147,axiom,((! [A:(hoare_1262092251_state > $o)]: (ord_le870406270tate_o @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_subset__refl)). 24.85/7.43 thf(744,plain,((! [A:(hoare_1262092251_state > $o)]: (ord_le870406270tate_o @ (A) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 24.85/7.43 thf(103,axiom,((! [A:(pname > $o),B:(((hoare_1262092251_state > $o) > $o) > pname),C:(((hoare_1262092251_state > $o) > $o) > $o)]: ((finite1303896758te_o_o @ C) => ((ord_less_eq_pname_o @ A @ (image_893364936_pname @ B @ C)) => (finite_finite_pname @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_finite__surj)). 24.85/7.43 thf(613,plain,((! [A:(pname > $o),B:(((hoare_1262092251_state > $o) > $o) > pname),C:(((hoare_1262092251_state > $o) > $o) > $o)]: ((finite1303896758te_o_o @ (C)) => ((ord_less_eq_pname_o @ (A) @ (image_893364936_pname @ (B) @ (C))) => (finite_finite_pname @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 24.85/7.43 thf(37,axiom,((! [A:(pname > $o),B:(pname > $o)]: (~ (fequal_pname_o @ A @ B) | (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T)). 24.85/7.43 thf(386,plain,((! [A:(pname > $o),B:(pname > $o)]: (~ (fequal_pname_o @ (A) @ (B)) | ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 24.85/7.43 thf(120,axiom,((! [A:(pname > $o),B:(hoare_1262092251_state > $o),C:(pname > (hoare_1262092251_state > $o)),D:pname]: ((B = (C @ D)) => ((member_pname @ D @ A) => (member907417095tate_o @ B @ (image_518521461tate_o @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_image__eqI)). 24.85/7.43 thf(656,plain,((! [A:(pname > $o),B:(hoare_1262092251_state > $o),C:(pname > (hoare_1262092251_state > $o)),D:pname]: (((B) = (C @ D)) => ((member_pname @ D @ (A)) => (member907417095tate_o @ (B) @ (image_518521461tate_o @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 24.85/7.43 thf(220,axiom,((! [A:pname,B:(hoare_1262092251_state > $o)]: ((hoare_930741239_state @ (insert81609953_state @ (hoare_Mirabelle_MGT @ (body_1 @ A)) @ B) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ (the_com @ (body @ A))) @ bot_bo113204042tate_o)) => (hoare_930741239_state @ B @ (insert81609953_state @ (hoare_Mirabelle_MGT @ (body_1 @ A)) @ bot_bo113204042tate_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MGT__BodyN)). 24.85/7.43 thf(1023,plain,((! [A:pname,B:(hoare_1262092251_state > $o)]: ((hoare_930741239_state @ (insert81609953_state @ (hoare_Mirabelle_MGT @ (body_1 @ A)) @ B) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ (the_com @ (body @ A))) @ bot_bo113204042tate_o)) => (hoare_930741239_state @ (B) @ (insert81609953_state @ (hoare_Mirabelle_MGT @ (body_1 @ A)) @ bot_bo113204042tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 24.85/7.43 thf(278,axiom,((! [A:hoare_1262092251_state,B:(pname > hoare_1262092251_state),C:pname,D:(pname > $o)]: ((member_pname @ C @ D) => ((member5164104_state @ A @ (image_669833818_state @ B @ D)) <= (A = (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_rev__image__eqI)). 24.85/7.43 thf(1221,plain,((! [A:hoare_1262092251_state,B:(pname > hoare_1262092251_state),C:pname,D:(pname > $o)]: ((member_pname @ C @ (D)) => ((member5164104_state @ A @ (image_669833818_state @ B @ D)) | ~ (A = (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 24.85/7.43 thf(296,axiom,((! [A:(hoare_1262092251_state > $o),B:(pname > hoare_1262092251_state),C:(pname > $o)]: (((finite1178804552_state @ A) <= (ord_le870406270tate_o @ A @ (image_669833818_state @ B @ C))) <= (finite_finite_pname @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_finite__surj)). 24.85/7.43 thf(1284,plain,((! [A:(hoare_1262092251_state > $o),B:(pname > hoare_1262092251_state),C:(pname > $o)]: ((finite1178804552_state @ (A)) | ~ (ord_le870406270tate_o @ (A) @ (image_669833818_state @ B @ C)) | ~ (finite_finite_pname @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 24.85/7.43 thf(172,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:((hoare_1262092251_state > $o) > $o)]: (((member907417095tate_o @ A @ C) <= (A != B)) <= (member907417095tate_o @ A @ (insert1042460334tate_o @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_insertE)). 24.85/7.43 thf(845,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:((hoare_1262092251_state > $o) > $o)]: ((member907417095tate_o @ (A) @ (C)) | ((A) = (B)) | ~ (member907417095tate_o @ (A) @ (insert1042460334tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 24.85/7.43 thf(65,axiom,((! [A:(pname > $o),B:((pname > $o) > $o)]: ((B = bot_bot_pname_o_o) => (~ (member_pname_o @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_equals0D)). 24.85/7.43 thf(465,plain,((! [A:(pname > $o),B:((pname > $o) > $o)]: (((B) = (bot_bot_pname_o_o)) => (~ (member_pname_o @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 24.85/7.43 thf(264,axiom,((! [A:(pname > hoare_1262092251_state),B:pname,C:(pname > $o)]: ((member_pname @ B @ C) => (member5164104_state @ (A @ B) @ (image_669833818_state @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_imageI)). 24.85/7.43 thf(1157,plain,((! [A:(pname > hoare_1262092251_state),B:pname,C:(pname > $o)]: ((member_pname @ B @ (C)) => (member5164104_state @ (A @ B) @ (image_669833818_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 24.85/7.43 thf(187,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((A = B) => (ord_less_eq_pname_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_equalityD1)). 24.85/7.43 thf(891,plain,((! [A:(pname > $o),B:(pname > $o)]: (((A) = (B)) => (ord_less_eq_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 24.85/7.43 thf(253,axiom,((! [A:(hoare_1262092251_state > $o)]: ((? [B:hoare_1262092251_state]: (member5164104_state @ B @ A)) = (A != bot_bo113204042tate_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_ex__in__conv)). 24.85/7.43 thf(1126,plain,((! [A:(hoare_1262092251_state > $o)]: ((? [B:hoare_1262092251_state]: (member5164104_state @ B @ (A))) = (~ ((A) = (bot_bo113204042tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 24.85/7.43 thf(207,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((A = B) => (~ ((ord_le870406270tate_o @ A @ B) => (~ (ord_le870406270tate_o @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_equalityE)). 24.85/7.43 thf(976,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((A) = (B)) => (~ ((ord_le870406270tate_o @ (A) @ (B)) => (~ (ord_le870406270tate_o @ (B) @ (A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 24.85/7.43 thf(130,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: (((ord_le870406270tate_o @ C @ A) => (ord_le870406270tate_o @ B @ A)) <= (ord_le870406270tate_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_subset__trans)). 24.85/7.43 thf(688,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: (((ord_le870406270tate_o @ (C) @ (A)) => (ord_le870406270tate_o @ (B) @ (A))) | ~ (ord_le870406270tate_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 24.85/7.43 thf(298,axiom,((! [A:(pname > hoare_1262092251_state),B:pname,C:(pname > $o)]: (((insert81609953_state @ (A @ B) @ (image_669833818_state @ A @ C)) = (image_669833818_state @ A @ C)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_insert__image)). 24.85/7.43 thf(1289,plain,((! [A:(pname > hoare_1262092251_state),B:pname,C:(pname > $o)]: (((insert81609953_state @ (A @ B) @ (image_669833818_state @ A @ C)) = (image_669833818_state @ A @ C)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 24.85/7.43 thf(29,axiom,((! [A:((hoare_1262092251_state > $o) > $o)]: (ord_le2012720639te_o_o @ bot_bo1962689075te_o_o @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_empty__subsetI)). 24.85/7.43 thf(368,plain,((! [A:((hoare_1262092251_state > $o) > $o)]: (ord_le2012720639te_o_o @ (bot_bo1962689075te_o_o) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 24.85/7.43 thf(134,axiom,((! [A:pname]: ~ (member_pname @ A @ bot_bot_pname_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_empty__iff)). 24.85/7.43 thf(699,plain,((! [A:pname]: ~ (member_pname @ A @ (bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 24.85/7.43 thf(149,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ B @ A) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_equalityD2)). 24.85/7.43 thf(748,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ (B) @ (A)) | ~ ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 24.85/7.43 thf(22,axiom,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ B) => (finite1423311111tate_o @ (insert1042460334tate_o @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_finite_OinsertI)). 24.85/7.43 thf(351,plain,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ (B)) => (finite1423311111tate_o @ (insert1042460334tate_o @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 24.85/7.43 thf(43,axiom,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((ord_le1205211808me_o_o @ B @ A) => (A = B)) <= (ord_le1205211808me_o_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_equalityI)). 24.85/7.43 thf(401,plain,((! [A:((pname > $o) > $o),B:((pname > $o) > $o)]: (((ord_le1205211808me_o_o @ (B) @ (A)) => ((A) = (B))) | ~ (ord_le1205211808me_o_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 24.85/7.43 thf(143,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((finite1178804552_state @ B) => (finite1178804552_state @ A)) <= (ord_le870406270tate_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_finite__subset)). 24.85/7.43 thf(731,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((finite1178804552_state @ (B)) => (finite1178804552_state @ (A))) | ~ (ord_le870406270tate_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 24.85/7.43 thf(34,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (collect_pname @ (^ [C:pname]: ((A @ C) | (B @ C))))) = ((finite_finite_pname @ (collect_pname @ A)) & (finite_finite_pname @ (collect_pname @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_finite__Collect__disjI)). 24.85/7.43 thf(378,plain,((! [A:(pname > $o),B:(pname > $o)]: ((finite_finite_pname @ (collect_pname @ (^ [C:pname]: ((A @ C) | (B @ C))))) = ((finite_finite_pname @ (collect_pname @ A)) & (finite_finite_pname @ (collect_pname @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 24.85/7.43 thf(78,axiom,((! [A:(pname > $o),B:(hoare_1262092251_state > pname),C:(hoare_1262092251_state > $o)]: (((ord_less_eq_pname_o @ A @ (image_202231862_pname @ B @ C)) => (finite_finite_pname @ A)) <= (finite1178804552_state @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_finite__surj)). 24.85/7.43 thf(510,plain,((! [A:(pname > $o),B:(hoare_1262092251_state > pname),C:(hoare_1262092251_state > $o)]: (((ord_less_eq_pname_o @ (A) @ (image_202231862_pname @ B @ C)) => (finite_finite_pname @ (A))) | ~ (finite1178804552_state @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 24.85/7.43 thf(271,axiom,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state]: (((~ (A @ B)) => ((collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((C = B) & (A @ C)))) = bot_bo113204042tate_o)) & (((collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((C = B) & (A @ C)))) = (insert81609953_state @ B @ bot_bo113204042tate_o)) <= (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_Collect__conv__if)). 24.85/7.43 thf(1193,plain,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state]: (((~ (A @ B)) => ((collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((C = B) & (A @ C)))) = (bot_bo113204042tate_o))) & (((collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((C = B) & (A @ C)))) = (insert81609953_state @ B @ bot_bo113204042tate_o)) | ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 24.85/7.43 thf(276,axiom,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state]: ((((collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((B = C) & (A @ C)))) = bot_bo113204042tate_o) <= (~ (A @ B))) & (((collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((B = C) & (A @ C)))) = (insert81609953_state @ B @ bot_bo113204042tate_o)) <= (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_Collect__conv__if2)). 24.85/7.43 thf(1212,plain,((! [A:(hoare_1262092251_state > $o),B:hoare_1262092251_state]: ((((collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((B = C) & (A @ C)))) = (bot_bo113204042tate_o)) | (A @ B)) & (((collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((B = C) & (A @ C)))) = (insert81609953_state @ B @ bot_bo113204042tate_o)) | ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 24.85/7.43 thf(140,axiom,((! [A:pname,B:(pname > $o)]: ((B = bot_bot_pname_o) => (~ (member_pname @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_equals0D)). 24.85/7.43 thf(716,plain,((! [A:pname,B:(pname > $o)]: (((B) = (bot_bot_pname_o)) => (~ (member_pname @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 24.85/7.43 thf(3,axiom,((! [A:(((hoare_1262092251_state > $o) > $o) > $o),B:(((hoare_1262092251_state > $o) > $o) > $o)]: (((finite1303896758te_o_o @ (collec341954548te_o_o @ B)) | (finite1303896758te_o_o @ (collec341954548te_o_o @ A))) => (finite1303896758te_o_o @ (collec341954548te_o_o @ (^ [C:((hoare_1262092251_state > $o) > $o)]: ((B @ C) & (A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite__Collect__conjI)). 24.85/7.43 thf(300,plain,((! [A:(((hoare_1262092251_state > $o) > $o) > $o),B:(((hoare_1262092251_state > $o) > $o) > $o)]: (((finite1303896758te_o_o @ (collec341954548te_o_o @ B)) | (finite1303896758te_o_o @ (collec341954548te_o_o @ A))) => (finite1303896758te_o_o @ (collec341954548te_o_o @ (^ [C:((hoare_1262092251_state > $o) > $o)]: ((B @ C) & (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 24.85/7.43 thf(106,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: (((member_pname @ A @ C) <= (member_pname @ A @ B)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_in__mono)). 24.85/7.43 thf(620,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((member_pname @ A @ (C)) | ~ (member_pname @ A @ (B)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 24.85/7.43 thf(150,axiom,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((insert1042460334tate_o @ A @ B) = (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((C = A) | (member907417095tate_o @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_insert__compr)). 24.85/7.43 thf(752,plain,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((insert1042460334tate_o @ A @ B) = (collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((C = A) | (member907417095tate_o @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 24.85/7.43 thf(59,axiom,((! [A:(pname > $o),B:((pname > $o) > pname),C:((pname > $o) > $o)]: ((finite297249702name_o @ C) => ((finite_finite_pname @ A) <= (ord_less_eq_pname_o @ A @ (image_pname_o_pname @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_finite__surj)). 24.85/7.43 thf(447,plain,((! [A:(pname > $o),B:((pname > $o) > pname),C:((pname > $o) > $o)]: ((finite297249702name_o @ (C)) => ((finite_finite_pname @ (A)) | ~ (ord_less_eq_pname_o @ (A) @ (image_pname_o_pname @ (B) @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 24.85/7.43 thf(8,axiom,((finite297249702name_o @ bot_bot_pname_o_o)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_finite_OemptyI)). 24.85/7.43 thf(315,plain,((finite297249702name_o @ (bot_bot_pname_o_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 24.85/7.43 thf(54,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((fequal1529404211tate_o @ A @ B) | (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It)). 24.85/7.43 thf(432,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: ((fequal1529404211tate_o @ (A) @ (B)) | ~ ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 24.85/7.43 thf(180,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((finite1178804552_state @ (collec1121927558_state @ B)) & (finite1178804552_state @ (collec1121927558_state @ A))) = (finite1178804552_state @ (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((A @ C) | (B @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_finite__Collect__disjI)). 24.85/7.43 thf(865,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o)]: (((finite1178804552_state @ (collec1121927558_state @ B)) & (finite1178804552_state @ (collec1121927558_state @ A))) = (finite1178804552_state @ (collec1121927558_state @ (^ [C:hoare_1262092251_state]: ((A @ C) | (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 24.85/7.43 thf(169,axiom,((! [A:(hoare_1262092251_state > $o),B:pname,C:(pname > $o)]: (((image_518521461tate_o @ (^ [D:pname]: (A)) @ C) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)) <= (member_pname @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_image__constant)). 24.85/7.43 thf(833,plain,((! [A:(hoare_1262092251_state > $o),B:pname,C:(pname > $o)]: (((image_518521461tate_o @ (^ [D:pname]: (A)) @ C) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)) | ~ (member_pname @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 24.85/7.43 thf(46,axiom,((! [A:((pname > $o) > $o)]: ((! [B:(pname > $o)]: ~ (A @ B)) = ((collect_pname_o @ A) = bot_bot_pname_o_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Collect__empty__eq)). 24.85/7.43 thf(410,plain,((! [A:((pname > $o) > $o)]: ((! [B:(pname > $o)]: ~ (A @ (B))) = ((collect_pname_o @ A) = (bot_bot_pname_o_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 24.85/7.43 thf(194,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (collect_pname @ (^ [C:pname]: ((C = A) | (member_pname @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_insert__compr__raw)). 24.85/7.43 thf(918,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ B) = (collect_pname @ (^ [C:pname]: ((C = A) | (member_pname @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 24.85/7.43 thf(25,axiom,((! [A:((hoare_1262092251_state > $o) > pname),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ B) => (finite_finite_pname @ (image_1820530197_pname @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI)). 24.85/7.43 thf(358,plain,((! [A:((hoare_1262092251_state > $o) > pname),B:((hoare_1262092251_state > $o) > $o)]: ((finite1423311111tate_o @ (B)) => (finite_finite_pname @ (image_1820530197_pname @ (A) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 24.85/7.43 thf(112,axiom,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ bot_bot_pname_o @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_empty__subsetI)). 24.85/7.43 thf(635,plain,((! [A:(pname > $o)]: (ord_less_eq_pname_o @ (bot_bot_pname_o) @ (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 24.85/7.43 thf(236,axiom,((! [A:pname,B:(hoare_1262092251_state > $o)]: ((((image_202231862_pname @ (^ [C:hoare_1262092251_state]: (A)) @ B) = (insert_pname @ A @ bot_bot_pname_o)) <= (B != bot_bo113204042tate_o)) & ((B = bot_bo113204042tate_o) => ((image_202231862_pname @ (^ [C:hoare_1262092251_state]: (A)) @ B) = bot_bot_pname_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_image__constant__conv)). 24.85/7.43 thf(1065,plain,((! [A:pname,B:(hoare_1262092251_state > $o)]: ((((image_202231862_pname @ (^ [C:hoare_1262092251_state]: (A)) @ B) = (insert_pname @ A @ bot_bot_pname_o)) | ((B) = (bot_bo113204042tate_o))) & (((B) = (bot_bo113204042tate_o)) => ((image_202231862_pname @ (^ [C:hoare_1262092251_state]: (A)) @ B) = (bot_bot_pname_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 24.85/7.43 thf(48,axiom,((! [A:(pname > $o),B:(pname > $o)]: ((A != B) | (fequal_pname_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T)). 24.85/7.43 thf(415,plain,((! [A:(pname > $o),B:(pname > $o)]: (~ ((A) = (B)) | (fequal_pname_o @ (A) @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 24.85/7.43 thf(189,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > $o)]: ((((collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((B = C) & (A @ C)))) = (insert1042460334tate_o @ B @ bot_bo1962689075te_o_o)) <= (A @ B)) & ((~ (A @ B)) => ((collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((B = C) & (A @ C)))) = bot_bo1962689075te_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_Collect__conv__if2)). 24.85/7.43 thf(897,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > $o)]: ((((collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((B = C) & (A @ C)))) = (insert1042460334tate_o @ B @ bot_bo1962689075te_o_o)) | ~ (A @ (B))) & ((~ (A @ (B))) => ((collec313158217tate_o @ (^ [C:(hoare_1262092251_state > $o)]: ((B = C) & (A @ C)))) = (bot_bo1962689075te_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 24.85/7.43 thf(67,axiom,((! [A:((hoare_1262092251_state > $o) > hoare_1262092251_state),B:((hoare_1262092251_state > $o) > $o)]: ((finite1178804552_state @ (image_234589002_state @ A @ B)) <= (finite1423311111tate_o @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI)). 24.85/7.43 thf(474,plain,((! [A:((hoare_1262092251_state > $o) > hoare_1262092251_state),B:((hoare_1262092251_state > $o) > $o)]: ((finite1178804552_state @ (image_234589002_state @ (A) @ (B))) | ~ (finite1423311111tate_o @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 24.85/7.43 thf(141,axiom,((! [A:pname]: ((collect_pname @ (^ [B:pname]: (B = A))) = (insert_pname @ A @ bot_bot_pname_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_singleton__conv)). 24.85/7.43 thf(720,plain,((! [A:pname]: ((collect_pname @ (^ [B:pname]: (B = A))) = (insert_pname @ A @ bot_bot_pname_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 24.85/7.43 thf(267,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ C) => (((A @ bot_bo113204042tate_o) => ((A @ C) <= (! [D:hoare_1262092251_state,E:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ E) => (((~ (member5164104_state @ D @ E)) => ((A @ (insert81609953_state @ D @ E)) <= (A @ E))) <= (member5164104_state @ D @ B)))))) <= (ord_le870406270tate_o @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_finite__subset__induct)). 24.85/7.43 thf(1165,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ (C)) => (((A @ (bot_bo113204042tate_o)) => ((A @ (C)) | ~ (! [D:hoare_1262092251_state,E:(hoare_1262092251_state > $o)]: ((finite1178804552_state @ (E)) => (((~ (member5164104_state @ D @ (E))) => ((A @ (insert81609953_state @ D @ E)) | ~ (A @ (E)))) | ~ (member5164104_state @ D @ (B))))))) | ~ (ord_le870406270tate_o @ (C) @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 24.85/7.43 thf(254,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: ((A = B) <= (member5164104_state @ A @ (insert81609953_state @ B @ bot_bo113204042tate_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_singletonE)). 24.85/7.43 thf(1129,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state]: ((A = B) | ~ (member5164104_state @ A @ (insert81609953_state @ B @ bot_bo113204042tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 24.85/7.43 thf(287,axiom,((! [A:hoare_1262092251_state]: ~ (member5164104_state @ A @ bot_bo113204042tate_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_emptyE)). 24.85/7.43 thf(1261,plain,((! [A:hoare_1262092251_state]: ~ (member5164104_state @ A @ (bot_bo113204042tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 24.85/7.43 thf(178,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ (insert_pname @ A @ C)) <= (ord_less_eq_pname_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_subset__insertI2)). 24.85/7.43 thf(860,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (insert_pname @ A @ C)) | ~ (ord_less_eq_pname_o @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 24.85/7.43 thf(97,axiom,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ B @ C) => (ord_less_eq_pname_o @ (insert_pname @ A @ B) @ (insert_pname @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_insert__mono)). 24.85/7.43 thf(596,plain,((! [A:pname,B:(pname > $o),C:(pname > $o)]: ((ord_less_eq_pname_o @ (B) @ (C)) => (ord_less_eq_pname_o @ (insert_pname @ A @ B) @ (insert_pname @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 24.85/7.43 thf(84,axiom,((! [A:((pname > $o) > $o),B:(pname > $o)]: ((((collect_pname_o @ (^ [C:(pname > $o)]: ((B = C) & (A @ C)))) = bot_bot_pname_o_o) <= (~ (A @ B))) & ((A @ B) => ((collect_pname_o @ (^ [C:(pname > $o)]: ((B = C) & (A @ C)))) = (insert_pname_o @ B @ bot_bot_pname_o_o)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_Collect__conv__if2)). 24.85/7.43 thf(528,plain,((! [A:((pname > $o) > $o),B:(pname > $o)]: ((((collect_pname_o @ (^ [C:(pname > $o)]: ((B = C) & (A @ C)))) = (bot_bot_pname_o_o)) | (A @ (B))) & ((A @ (B)) => ((collect_pname_o @ (^ [C:(pname > $o)]: ((B = C) & (A @ C)))) = (insert_pname_o @ B @ bot_bot_pname_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 24.85/7.43 thf(116,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > $o)]: (((A = (insert1042460334tate_o @ B @ bot_bo1962689075te_o_o)) | (A = bot_bo1962689075te_o_o)) <= (ord_le2012720639te_o_o @ A @ (insert1042460334tate_o @ B @ bot_bo1962689075te_o_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_subset__singletonD)). 24.85/7.43 thf(644,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:(hoare_1262092251_state > $o)]: (((A) = (insert1042460334tate_o @ B @ bot_bo1962689075te_o_o)) | ((A) = (bot_bo1962689075te_o_o)) | ~ (ord_le2012720639te_o_o @ (A) @ (insert1042460334tate_o @ B @ bot_bo1962689075te_o_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 24.85/7.43 thf(192,axiom,((! [A:(pname > $o),B:(pname > $o),C:((pname > $o) > $o)]: ((member_pname_o @ A @ (insert_pname_o @ B @ C)) => ((A != B) => (member_pname_o @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_insertE)). 24.85/7.43 thf(908,plain,((! [A:(pname > $o),B:(pname > $o),C:((pname > $o) > $o)]: ((member_pname_o @ (A) @ (insert_pname_o @ B @ C)) => ((~ ((A) = (B))) => (member_pname_o @ (A) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 24.85/7.43 thf(142,axiom,((! [A:(hoare_1262092251_state > $o),B:(pname > $o)]: (((B = bot_bot_pname_o) => ((image_518521461tate_o @ (^ [C:pname]: (A)) @ B) = bot_bo1962689075te_o_o)) & ((B != bot_bot_pname_o) => ((image_518521461tate_o @ (^ [C:pname]: (A)) @ B) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_image__constant__conv)). 24.85/7.43 thf(723,plain,((! [A:(hoare_1262092251_state > $o),B:(pname > $o)]: ((((B) = (bot_bot_pname_o)) => ((image_518521461tate_o @ (^ [C:pname]: (A)) @ B) = (bot_bo1962689075te_o_o))) & ((~ ((B) = (bot_bot_pname_o))) => ((image_518521461tate_o @ (^ [C:pname]: (A)) @ B) = (insert1042460334tate_o @ A @ bot_bo1962689075te_o_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 24.85/7.43 thf(174,axiom,((! [A:(pname > $o),B:(((pname > $o) > $o) > pname),C:(((pname > $o) > $o) > $o)]: ((finite1066544169me_o_o @ C) => ((ord_less_eq_pname_o @ A @ (image_471733107_pname @ B @ C)) => (finite_finite_pname @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_finite__surj)). 24.85/7.43 thf(850,plain,((! [A:(pname > $o),B:(((pname > $o) > $o) > pname),C:(((pname > $o) > $o) > $o)]: ((finite1066544169me_o_o @ (C)) => ((ord_less_eq_pname_o @ (A) @ (image_471733107_pname @ (B) @ (C))) => (finite_finite_pname @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 24.85/7.43 thf(214,axiom,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((member5164104_state @ B @ (insert81609953_state @ A @ C)) <= ((B = A) <= (~ (member5164104_state @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_insertCI)). 24.85/7.43 thf(1004,plain,((! [A:hoare_1262092251_state,B:hoare_1262092251_state,C:(hoare_1262092251_state > $o)]: ((member5164104_state @ B @ (insert81609953_state @ A @ C)) | ~ ((B = A) | (member5164104_state @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 24.85/7.43 thf(101,axiom,((! [A:((pname > $o) > option_com),B:(pname > $o),C:com]: (((insert_pname_o @ B @ (dom_pname_o_com @ A)) = (dom_pname_o_com @ A)) <= ((A @ B) = (some_com @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_insert__dom)). 24.85/7.43 thf(607,plain,((! [A:((pname > $o) > option_com),B:(pname > $o),C:com]: (((insert_pname_o @ B @ (dom_pname_o_com @ A)) = (dom_pname_o_com @ A)) | ~ ((A @ (B)) = (some_com @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 24.85/7.43 thf(70,axiom,((! [A:pname,B:(pname > $o)]: ((finite_finite_pname @ (insert_pname @ A @ B)) <= (finite_finite_pname @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_finite_OinsertI)). 24.85/7.43 thf(486,plain,((! [A:pname,B:(pname > $o)]: ((finite_finite_pname @ (insert_pname @ A @ B)) | ~ (finite_finite_pname @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 24.85/7.43 thf(165,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (insert_pname @ A @ B)) = (insert_pname @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_insert__absorb2)). 24.85/7.43 thf(803,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (insert_pname @ A @ B)) = (insert_pname @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 24.85/7.43 thf(16,axiom,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: ((ord_le2012720639te_o_o @ A @ B) => ((A = B) <= (ord_le2012720639te_o_o @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_equalityI)). 24.85/7.43 thf(337,plain,((! [A:((hoare_1262092251_state > $o) > $o),B:((hoare_1262092251_state > $o) > $o)]: ((ord_le2012720639te_o_o @ (A) @ (B)) => (((A) = (B)) | ~ (ord_le2012720639te_o_o @ (B) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 24.85/7.43 thf(66,axiom,((! [A:(pname > $o),B:(pname > $o),C:((pname > $o) > $o)]: (((~ (member_pname_o @ B @ C)) => (B = A)) => (member_pname_o @ B @ (insert_pname_o @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_insertCI)). 24.85/7.43 thf(469,plain,((! [A:(pname > $o),B:(pname > $o),C:((pname > $o) > $o)]: (((~ (member_pname_o @ (B) @ (C))) => ((B) = (A))) => (member_pname_o @ (B) @ (insert_pname_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 24.85/7.43 thf(215,axiom,((! [A:(pname > hoare_1262092251_state)]: ((image_669833818_state @ A @ bot_bot_pname_o) = bot_bo113204042tate_o))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_image__empty)). 24.85/7.43 thf(1009,plain,((! [A:(pname > hoare_1262092251_state)]: ((image_669833818_state @ A @ bot_bot_pname_o) = (bot_bo113204042tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 24.85/7.43 thf(6,axiom,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (collect_pname @ B)) = (collect_pname @ (^ [C:pname]: ((~ (C = A)) => (B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_insert__Collect)). 24.85/7.43 thf(309,plain,((! [A:pname,B:(pname > $o)]: ((insert_pname @ A @ (collect_pname @ B)) = (collect_pname @ (^ [C:pname]: ((~ (C = A)) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 24.85/7.43 thf(225,axiom,((finite_finite_pname @ (dom_pname_com @ body))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_finite__dom__body)). 24.85/7.43 thf(1037,plain,((finite_finite_pname @ (dom_pname_com @ body))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 24.85/7.43 thf(74,axiom,((! [A:(hoare_1262092251_state > $o),B:(((hoare_1262092251_state > $o) > $o) > hoare_1262092251_state),C:(((hoare_1262092251_state > $o) > $o) > $o)]: (((ord_le870406270tate_o @ A @ (image_165349207_state @ B @ C)) => (finite1178804552_state @ A)) <= (finite1303896758te_o_o @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite__surj)). 24.85/7.43 thf(496,plain,((! [A:(hoare_1262092251_state > $o),B:(((hoare_1262092251_state > $o) > $o) > hoare_1262092251_state),C:(((hoare_1262092251_state > $o) > $o) > $o)]: (((ord_le870406270tate_o @ (A) @ (image_165349207_state @ (B) @ (C))) => (finite1178804552_state @ (A))) | ~ (finite1303896758te_o_o @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 24.85/7.43 thf(137,axiom,((! [A:(pname > $o),B:pname]: (((A = (insert_pname @ B @ bot_bot_pname_o)) | (A = bot_bot_pname_o)) <= (ord_less_eq_pname_o @ A @ (insert_pname @ B @ bot_bot_pname_o))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_subset__singletonD)). 24.85/7.43 thf(708,plain,((! [A:(pname > $o),B:pname]: (((A) = (insert_pname @ B @ bot_bot_pname_o)) | ((A) = (bot_bot_pname_o)) | ~ (ord_less_eq_pname_o @ (A) @ (insert_pname @ B @ bot_bot_pname_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 24.85/7.43 thf(185,axiom,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ B @ C) => ((member5164104_state @ A @ B) => (member5164104_state @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_in__mono)). 24.85/7.43 thf(882,plain,((! [A:hoare_1262092251_state,B:(hoare_1262092251_state > $o),C:(hoare_1262092251_state > $o)]: ((ord_le870406270tate_o @ (B) @ (C)) => ((member5164104_state @ A @ (B)) => (member5164104_state @ A @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 24.85/7.43 thf(151,axiom,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:((hoare_1262092251_state > $o) > $o)]: (((B = A) <= (~ (member907417095tate_o @ B @ C))) => (member907417095tate_o @ B @ (insert1042460334tate_o @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_insertCI)). 24.85/7.43 thf(755,plain,((! [A:(hoare_1262092251_state > $o),B:(hoare_1262092251_state > $o),C:((hoare_1262092251_state > $o) > $o)]: ((((B) = (A)) | (member907417095tate_o @ (B) @ (C))) => (member907417095tate_o @ (B) @ (insert1042460334tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 24.85/7.43 thf(126,axiom,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: ((~ (member907417095tate_o @ A @ B)) <= (B = bot_bo1962689075te_o_o)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_equals0D)). 24.85/7.43 thf(676,plain,((! [A:(hoare_1262092251_state > $o),B:((hoare_1262092251_state > $o) > $o)]: (~ (member907417095tate_o @ (A) @ (B)) | ~ ((B) = (bot_bo1962689075te_o_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 24.85/7.43 thf(1292,plain,($false),inference(e,[status(thm)],[365,760,347,518,941,555,666,1110,628,1031,1200,762,683,994,741,449,1142,440,1041,1078,384,1137,500,1275,945,538,930,1063,340,1243,782,436,1095,404,973,1046,389,372,1264,838,702,1132,934,1191,1087,1247,421,969,316,1100,1232,638,853,924,443,321,376,514,806,480,1151,937,353,966,877,1072,396,660,988,507,312,1206,512,546,1153,381,1057,746,862,598,392,429,788,1238,407,693,630,625,852,329,1159,493,324,1012,650,615,1121,593,697,1089,1270,1259,884,1028,488,669,637,590,686,1075,622,1266,911,779,647,997,1060,1050,921,541,1054,558,633,360,1286,398,773,586,1278,1219,1273,856,733,601,1251,618,904,423,579,1124,413,875,711,641,1139,611,1107,1092,350,672,713,498,1282,419,736,990,318,880,303,764,604,784,1117,362,451,345,535,483,848,895,1149,769,1022,462,799,1162,983,768,1044,868,455,1015,299,438,653,394,986,306,1034,490,426,680,663,1134,812,1081,516,939,342,355,553,458,836,1203,1208,927,374,1145,1018,776,525,690,1025,705,1225,327,1267,1098,1053,791,1235,1085,808,331,1188,1186,1038,370,544,907,744,613,386,656,1023,1221,1284,845,465,1157,891,1126,976,688,1289,368,699,748,351,401,731,378,510,1193,1212,716,300,620,752,447,315,432,865,833,410,918,358,635,1065,415,897,474,720,1165,1129,1261,860,596,528,644,908,723,850,1004,607,486,803,337,469,1009,309,1037,496,708,882,755,676])). 24.85/7.43 % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 24.85/7.43 % [INFO] Killing All external provers ... 24.85/7.43 FINAL WATCH: 24.6 CPU 6.0 WC 24.85/7.43 Killed 1 orphans 24.85/7.43 EOF