0.00/0.01 % Leo-III: Strategy 1 (for '60') 23.58/11.09 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 23.58/11.09 % [INFO] Parsing done (539ms). 23.58/11.09 % [INFO] Running in sequential loop mode. 23.58/11.09 % [CONFIG] Using configuration: timeout(60) with strategy 23.58/11.09 % [INFO] eprover registered as external prover. 23.58/11.09 % [INFO] cvc4 registered as external prover. 23.58/11.09 % [INFO] Parsing finished. Scanning for conjecture ... 23.58/11.09 % [INFO] Found a conjecture and 352 axioms. Running axiom selection ... 23.58/11.09 % [INFO] Axiom selection finished. Selected 289 axioms (removed 63 axioms). 23.58/11.09 % [INFO] Problem is higher-order (TPTP THF). 23.58/11.09 % [INFO] Type checking passed. Searching for refutation ... 23.58/11.09 % External prover 'cvc4' found a proof! 23.58/11.09 % [INFO] Killing All external provers ... 23.58/11.09 % Time passed: 8253ms (effective reasoning time: 7177ms) 23.58/11.09 % Solved by strategy 23.58/11.09 % Axioms used in derivation (289): fact_342_suffix__order_Oeq__refl, fact_235_neq__Nil__rev__conv, fact_97_self__append__conv, fact_343_suffix__order_Oantisym, fact_281_old_Opath__snoc, fact_298_subset__code_I1_J, fact_178_list_Oexpand, fact_156_list_Osel_I2_J, fact_306_prefix__order_Oorder__refl, fact_176_in__set__butlast__appendI, fact_12_old_Opath2__hd__in__ns, fact_315_same__prefix__prefix, fact_333_suffix__order_Odual__order_Oeq__iff, fact_241_list__append__eq__Cons__cases, fact_167_Nil__tl, fact_153_in__set__butlastD, fact_227_append_Oleft__neutral, fact_240_list__Cons__eq__append__cases, fact_38_hd__append2, fact_224_Cons__eq__appendI, fact_17_old_Opath2__hd, fact_350_suffix__appendD, fact_87_Nil__is__append__conv, fact_116_list__se__match_I4_J, fact_273_hd__append, fact_137_hd__Cons__tl, fact_271_list_Oset__sel_I1_J, fact_331_not__suffix__induct, fact_189_append__eq__appendI, fact_54_old_Oelem__set__implies__elem__tl__app__cons, fact_280_old_Opath_Osimps, fact_15_old_Opath2__tl__in___092_060alpha_062n, fact_348_Sublist_Osuffix__def, fact_319_snoc__suffix__snoc, fact_85_append__is__Nil__conv, fact_141_ri__props_I4_J, fact_193_revg_Oinduct, fact_311_prefix__Nil, fact_151_list_Osel_I3_J, fact_258_split__list__last__prop, fact_194_list_Oexhaust, fact_79_append_Oright__neutral, fact_318_same__suffix__nil, fact_296_ord__eq__le__eq__trans, fact_198_splice_Oinduct, fact_257_in__set__list__format, fact_133_list_Ocollapse, fact_248_xy__in__set__cases, fact_161_tl__obtain__elem, fact_128_rs__props_I3_J, fact_275__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_286_old_Oempty__path, fact_346_suffixE, fact_30_rs_H__props_I4_J, fact_33_rs__def, fact_205_sorted__wrt_Oinduct, fact_186_not__Cons__self2, fact_107_old_Opath2__rev__induct, fact_267_split__list__first__prop__iff, fact_57_list_Oinject, fact_245_split__list__last, fact_238_rev__nonempty__induct, fact_31_assms_I7_J, fact_208_successively_Oinduct, fact_246_split__list__prop, fact_65_Collect__cong, fact_188_append__eq__append__conv2, fact_122_list__se__match_I2_J, fact_25__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062, fact_120_list__se__match_I3_J, fact_288_old_Opath2__split__first__prop, fact_117_list__se__match_I4_J, fact_321_suffix__tl, fact_74_old_Osuccessor__in___092_060alpha_062n, fact_60_mem__Collect__eq, fact_127_old_Opath2__cases, fact_261_split__list__first__propE, fact_37_hd__append2, fact_61_mem__Collect__eq, fact_293_old_Opath__in___092_060alpha_062n, fact_76_old_Opath2__app, fact_232_rev__exhaust, fact_185_list_Oexhaust__sel, fact_56_list_Oinject, fact_300_tl__subset, fact_314_suffix__Nil, fact_88_Nil__is__append__conv, fact_187_list__tail__coinc, fact_344_suffix__order_Oeq__iff, fact_150_list_Osel_I3_J, fact_102_append__Nil2, fact_266_split__list__last__prop__iff, fact_69_append__assoc, fact_165_tl__Nil, fact_351_suffix__appendI, fact_309_Cons__prefix__Cons, fact_312_prefix__bot_Obot_Oextremum__unique, fact_46_list__ee__eq__leel_I2_J, fact_305_prefix__order_Odual__order_Orefl, fact_168_Nil__tl, fact_251_split__list__propE, fact_233_neq__Nil__revE, fact_162_tl__obtain__elem, fact_75_old_Opath2__app_H, fact_63_Collect__mem__eq, fact_299_set__subset__Cons, fact_142_ms_H__props_I2_J, fact_19__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H__rest_O_Ars_H_A_061_Ari_A_064_Ars_H__rest_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_287_old_Opath__split_I1_J, fact_184_butlast__eq__consE, fact_13_old_Opath2__in___092_060alpha_062n, fact_304_same__prefix__nil, fact_10_old_Opath2__not__Nil2, fact_182_butlast__eq__cons__conv, fact_289_old_Opath2__prefix__ex, fact_126_tl__append2, fact_81_empty__append__eq__id, fact_96_self__append__conv, fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062tmp_O_Ari_A_061_Atmp_A_064_A_091i_093_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_272_longest__common__prefix, fact_214_strict__sorted_Oinduct, fact_349_suffix__append, fact_7_rs_H__rest__prop, fact_228_append__Nil, fact_32_rs__props_I1_J, fact_8_rs_H__props_I3_J, fact_40_append1__eq__conv, fact_170_butlast__append, fact_93_append__self__conv2, fact_212_mergesort__by__rel__merge_Oinduct, fact_145_butlast__tl, fact_325_suffix__ConsD2, fact_136_hd__Cons__tl, fact_337_suffix__order_Oorder_Oantisym, fact_203_list__2pre__induct, fact_341_suffix__order_Oorder_Otrans, fact_292_old_Opath__invar, fact_310_prefix__code_I1_J, fact_278_old_Opath_Ocases, fact_274__092_060open_062old_OpathsConverge_Ag_Am_Ams_H_An_A_Ins_A_064_Atl_Ari_J_Ai_092_060close_062, fact_339_suffix__order_Oantisym__conv, fact_26__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_183_butlast__eq__cons__conv, fact_328_Nil__suffix, fact_2_old_Oinvar, fact_324_suffix__ConsI, fact_11_old_Opath2__hd__in___092_060alpha_062n, fact_263_in__set__conv__decomp__last, fact_130_butlast__snoc, fact_221_set__ConsD, fact_125_tl__append2, fact_206_remdups__adj_Oinduct, fact_316_same__suffix__suffix, fact_47_list__ee__eq__leel_I2_J, fact_171_butlast__append, fact_27_old_Oempty__path2, fact_103_append__Nil2, fact_123_list__se__match_I2_J, fact_100_append__self__conv, fact_28_ms_H__props_I3_J, fact_201_min__list_Oinduct, fact_71_append_Oassoc, fact_106_old_Opath2__split__ex, fact_209_list__all__zip_Oinduct, fact_265_in__set__conv__decomp__first, fact_217_list_Oset__intros_I2_J, fact_322_suffix__Cons, fact_313_suffix__bot_Obot_Oextremum__unique, fact_320_suffix__snoc, fact_43_list__ee__eq__leel_I1_J, fact_41_append1__eq__conv, fact_230_list_Osel_I1_J, fact_323_suffix__ConsD, fact_234_rev__induct2_H, fact_196_neq__Nil__conv, fact_108_old_Opath2__snoc, fact_155_list_Osel_I2_J, fact_49_list__se__match_I1_J, fact_210_list__nonempty__induct, fact_260_split__list__last__propE, fact_336_suffix__order_Oord__eq__le__trans, fact_14_old_Opath2__last__in__ns, fact_347_suffixI, fact_329_set__mono__suffix, fact_301_butlast__subset, fact_111_list__e__eq__lel_I2_J, fact_202_shuffles_Oinduct, fact_243_split__list, fact_131_butlast__snoc, fact_140_in__hd__or__tl__conv, fact_326_suffix__bot_Obot_Oextremum__uniqueI, fact_5_rs_H__props_I1_J, fact_6_ms_H__props_I1_J, fact_276__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_231_rev__induct, fact_67_append__same__eq, fact_114_list__e__eq__lel_I1_J, fact_9_old_Opath2__not__Nil, fact_174_list_Oset__sel_I2_J, fact_94_append__self__conv2, fact_50_list__se__match_I1_J, fact_59_same__append__eq, fact_147_butlast_Osimps_I1_J, fact_158_butlast_Osimps_I2_J, fact_64_Collect__cong, fact_317_old_Opath2__split__last__prop, fact_62_Collect__mem__eq, fact_334_suffix__order_Odual__order_Otrans, fact_78_append_Oright__neutral, fact_308_suffix__order_Oorder__refl, fact_195_list_Oinducts, fact_34_assms_I8_J, fact_148_butlast_Osimps_I1_J, fact_199_induct__list012, fact_338_suffix__order_Oorder_Oeq__iff, fact_143_old_OCons__path2, fact_90_self__append__conv2, fact_73_old_Osuccessor__is__node, fact_335_suffix__order_Oord__le__eq__trans, fact_35_rs_H__loopfree, fact_51_ri__props_I3_J, fact_179_list_Oexpand, fact_24_old_Opath2__split_I1_J, fact_16_old_Opath2__forget__hd, fact_104_old_Opath2__split__ex_H, fact_236_Cons__eq__append__conv, fact_191_neq__NilE, fact_237_append__eq__Cons__conv, fact_181_not__hd__in__tl, fact_82_empty__append__eq__id, fact_327_suffix__bot_Obot_Oextremum, fact_290_old_OCons__path, fact_283_old_Opath__not__Nil, fact_295_subset__Collect__conv, fact_269_hd__in__set, fact_99_append__self__conv, fact_294_old_Opath__by__tail, fact_307_suffix__order_Odual__order_Orefl, fact_1_rs_H__rest__def, fact_211_map__tailrec__rev_Oinduct, fact_113_list__e__eq__lel_I1_J, fact_200_min__list_Ocases, fact_84_append__is__Nil__conv, fact_4_False, fact_207_list__induct__first2, fact_0_m__i__differ_I2_J, fact_285_old_Opath__split_I2_J, fact_225_append__Cons, fact_119_list__se__match_I3_J, fact_134_list_Ocollapse, fact_213_mergesort__by__rel__merge__induct, fact_105_old_Opath2__induct, fact_215_transpose_Ocases, fact_164_tl__Nil, fact_279_old_Opath_Oinducts, fact_21_m__i__differ_I1_J, fact_302_prefix__snoc, fact_3_old_Opath2__split_I2_J, fact_277_old_Opath2__simple__loop, fact_259_split__list__first__prop, fact_226_list__match__lel__lel, fact_110_list__e__eq__lel_I2_J, fact_340_suffix__order_Oorder__trans, fact_250_split__list__first, fact_29_assms_I10_J, fact_303_old_Opath2__split__first__last, fact_282_ri__rs_H__prefix, fact_23_ri__props_I1_J, fact_229_eq__Nil__appendI, fact_159_butlast_Osimps_I2_J, fact_345_suffix__same__cases, fact_330_not__suffix__cases, fact_44_list__ee__eq__leel_I1_J, fact_91_self__append__conv2, fact_219_list_Oset__intros_I1_J, fact_190_list_Odistinct_I1_J, fact_239_rev__nonempty__induct2_H, fact_255_in__set__conv__decomp, fact_332_suffix__order_Odual__order_Oantisym, fact_20_ri__props_I2_J, fact_204_remdups__adj_Ocases, fact_291_old_Opath2__prefix, fact_18__092_060open_062ri_A_061_Atmp_A_064_A_091i_093_092_060close_062, fact_72_old_Opredecessor__is__node, fact_197_list__induct2_H, fact_284_old_Opath__hd, fact_192_list_OdiscI, fact_253_append__Cons__eq__iff, fact_223_list_Oset__cases 23.58/11.09 % No. of inferences in proof: 582 23.58/11.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8253 ms resp. 7177 ms w/o parsing 23.58/11.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 23.58/11.09 thf(list_P561207620_edgeD_type, type, list_P561207620_edgeD: $tType). 23.58/11.09 thf(option_list_val_type, type, option_list_val: $tType). 23.58/11.09 thf(produc1432036078de_val_type, type, produc1432036078de_val: $tType). 23.58/11.09 thf(list_list_node_type, type, list_list_node: $tType). 23.58/11.09 thf(set_list_node_type, type, set_list_node: $tType). 23.58/11.09 thf(list_node_type, type, list_node: $tType). 23.58/11.09 thf(list_val_type, type, list_val: $tType). 23.58/11.09 thf(set_node_type, type, set_node: $tType). 23.58/11.09 thf(set_val_type, type, set_val: $tType). 23.58/11.09 thf(node_type, type, node: $tType). 23.58/11.09 thf(val_type, type, val: $tType). 23.58/11.09 thf(g_type, type, g: $tType). 23.58/11.09 thf(graph_1012773594_edgeD_type, type, graph_1012773594_edgeD: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > (g > (node > (list_node > (node > $o)))))))). 23.58/11.09 thf(graph_435229452_edgeD_type, type, graph_435229452_edgeD: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > (g > (list_node > $o)))))). 23.58/11.09 thf(graph_272749361_edgeD_type, type, graph_272749361_edgeD: ((g > (node > list_P561207620_edgeD)) > (g > (node > list_node)))). 23.58/11.09 thf(append_list_node_type, type, append_list_node: (list_list_node > (list_list_node > list_list_node))). 23.58/11.09 thf(append_node_type, type, append_node: (list_node > (list_node > list_node))). 23.58/11.09 thf(butlast_list_node_type, type, butlast_list_node: (list_list_node > list_list_node)). 23.58/11.09 thf(butlast_node_type, type, butlast_node: (list_node > list_node)). 23.58/11.09 thf(cons_list_node_type, type, cons_list_node: (list_node > (list_list_node > list_list_node))). 23.58/11.09 thf(cons_node_type, type, cons_node: (node > (list_node > list_node))). 23.58/11.09 thf(nil_list_node_type, type, nil_list_node: list_list_node). 23.58/11.09 thf(nil_node_type, type, nil_node: list_node). 23.58/11.09 thf(hd_list_node_type, type, hd_list_node: (list_list_node > list_node)). 23.58/11.09 thf(hd_node_type, type, hd_node: (list_node > node)). 23.58/11.09 thf(set_node2_type, type, set_node2: (list_node > set_node)). 23.58/11.09 thf(tl_list_node_type, type, tl_list_node: (list_list_node > list_list_node)). 23.58/11.09 thf(tl_node_type, type, tl_node: (list_node > list_node)). 23.58/11.09 thf(graph_2009891965_edgeD_type, type, graph_2009891965_edgeD: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > (g > (node > (list_node > (node > (list_node > (node > $o)))))))))). 23.58/11.09 thf(ord_less_eq_set_node_type, type, ord_less_eq_set_node: (set_node > (set_node > $o))). 23.58/11.09 thf(sSA_CF848637139eD_val_type, type, sSA_CF848637139eD_val: ((g > list_node) > ((g > (node > list_P561207620_edgeD)) > ((g > (produc1432036078de_val > option_list_val)) > (g > (node > set_val)))))). 23.58/11.09 thf(sSA_CF551432799de_val_type, type, sSA_CF551432799de_val: ((g > list_node) > ((g > (node > set_val)) > ((g > (produc1432036078de_val > option_list_val)) > (g > (val > node)))))). 23.58/11.09 thf(sSA_CF1252180629de_val_type, type, sSA_CF1252180629de_val: ((g > list_node) > ((g > (node > set_val)) > ((g > (produc1432036078de_val > option_list_val)) > (g > (val > (val > $o))))))). 23.58/11.09 thf(collect_node_type, type, collect_node: ((node > $o) > set_node)). 23.58/11.09 thf(collect_val_type, type, collect_val: ((val > $o) > set_val)). 23.58/11.09 thf(prefix_node_type, type, prefix_node: (list_node > (list_node > $o))). 23.58/11.09 thf(suffix_node_type, type, suffix_node: (list_node > (list_node > $o))). 23.58/11.09 thf(member_node_type, type, member_node: (node > (set_node > $o))). 23.58/11.09 thf(member_val_type, type, member_val: (val > (set_val > $o))). 23.58/11.09 thf(alpha_n_type, type, alpha_n: (g > list_node)). 23.58/11.09 thf(phi_r_type, type, phi_r: val). 23.58/11.09 thf(defs_type, type, defs: (g > (node > set_val))). 23.58/11.09 thf(g2_type, type, g2: g). 23.58/11.09 thf(i_type, type, i: node). 23.58/11.09 thf(inEdges_type, type, inEdges: (g > (node > list_P561207620_edgeD))). 23.58/11.09 thf(invar_type, type, invar: (g > $o)). 23.58/11.09 thf(m_type, type, m: node). 23.58/11.09 thf(ms_type, type, ms: list_node). 23.58/11.09 thf(ms2_type, type, ms2: list_node). 23.58/11.09 thf(n_type, type, n: node). 23.58/11.09 thf(ns_type, type, ns: list_node). 23.58/11.09 thf(phis_type, type, phis: (g > (produc1432036078de_val > option_list_val))). 23.58/11.09 thf(pred_phi_r_type, type, pred_phi_r: node). 23.58/11.09 thf(r_type, type, r: val). 23.58/11.09 thf(ri_type, type, ri: list_node). 23.58/11.09 thf(rs_type, type, rs: list_node). 23.58/11.09 thf(rs_rest_type, type, rs_rest: list_node). 23.58/11.09 thf(rs2_type, type, rs2: list_node). 23.58/11.09 thf(s_type, type, s: val). 23.58/11.09 thf(tmp_type, type, tmp: list_node). 23.58/11.09 thf(222,axiom,((! [A:node,B:g,C:node]: ((member_node @ A @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ B @ C))) => (((invar @ B) => (member_node @ C @ (set_node2 @ (alpha_n @ B)))) <= (member_node @ A @ (set_node2 @ (alpha_n @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_old_Osuccessor__is__node)). 23.58/11.09 thf(1190,plain,((! [A:node,B:g,C:node]: ((member_node @ A @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ B @ C))) => (((invar @ B) => (member_node @ C @ (set_node2 @ (alpha_n @ B)))) | ~ (member_node @ A @ (set_node2 @ (alpha_n @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 23.58/11.09 thf(142,axiom,((! [A:((node > (node > $o)) > (list_node > (list_node > $o))),B:(node > (node > $o)),C:list_node,D:list_node]: (((! [E:(node > (node > $o)),F:list_node]: (A @ E @ F @ nil_node)) => ((! [E:(node > (node > $o)),F:node,G:list_node]: (A @ E @ nil_node @ (cons_node @ F @ G))) => (A @ B @ C @ D))) <= (! [E:(node > (node > $o)),F:node,G:list_node,H:node,I:list_node]: (((E @ F @ H) => (A @ E @ G @ (cons_node @ H @ I))) => (((A @ E @ (cons_node @ F @ G) @ I) <= (~ (E @ F @ H))) => (A @ E @ (cons_node @ F @ G) @ (cons_node @ H @ I)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_mergesort__by__rel__merge_Oinduct)). 23.58/11.09 thf(760,plain,((! [A:((node > (node > $o)) > (list_node > (list_node > $o))),B:(node > (node > $o)),C:list_node,D:list_node]: (((! [E:(node > (node > $o)),F:list_node]: (A @ (E) @ F @ nil_node)) => ((! [E:(node > (node > $o)),F:node,G:list_node]: (A @ (E) @ nil_node @ (cons_node @ F @ G))) => (A @ (B) @ C @ D))) | ~ (! [E:(node > (node > $o)),F:node,G:list_node,H:node,I:list_node]: (((E @ F @ H) => (A @ (E) @ G @ (cons_node @ H @ I))) => (((A @ (E) @ (cons_node @ F @ G) @ I) | (E @ F @ H)) => (A @ (E) @ (cons_node @ F @ G) @ (cons_node @ H @ I)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 23.58/11.09 thf(179,axiom,((! [A:list_node]: ((A != nil_node) => (~ (! [B:node,C:list_node]: (A != (cons_node @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_list_Oexhaust)). 23.58/11.09 thf(962,plain,((! [A:list_node]: ((~ (A = nil_node)) => (~ (! [B:node,C:list_node]: ~ (A = (cons_node @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 23.58/11.09 thf(207,axiom,((! [A:node,B:node,C:list_node]: ((member_node @ A @ (set_node2 @ (cons_node @ B @ C))) => ((member_node @ A @ (set_node2 @ C)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_set__ConsD)). 23.58/11.09 thf(1110,plain,((! [A:node,B:node,C:list_node]: ((member_node @ A @ (set_node2 @ (cons_node @ B @ C))) => ((member_node @ A @ (set_node2 @ C)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 23.58/11.09 thf(62,axiom,((! [A:list_list_node,B:list_node,C:list_list_node]: ((((cons_list_node @ B @ nil_list_node) = (append_list_node @ A @ C)) = ((C = nil_list_node) & (A = (cons_list_node @ B @ nil_list_node)))) <= (A != nil_list_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_list__se__match_I3_J)). 23.58/11.09 thf(481,plain,((! [A:list_list_node,B:list_node,C:list_list_node]: ((((cons_list_node @ B @ nil_list_node) = (append_list_node @ A @ C)) = ((C = nil_list_node) & (A = (cons_list_node @ B @ nil_list_node)))) | (A = nil_list_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 23.58/11.09 thf(190,axiom,((! [A:g,B:list_node,C:node,D:list_node]: ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (cons_node @ C @ D)) <= (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (append_node @ B @ (cons_node @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_old_Opath__split_I2_J)). 23.58/11.09 thf(1024,plain,((! [A:g,B:list_node,C:node,D:list_node]: ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (cons_node @ C @ D)) | ~ (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (append_node @ B @ (cons_node @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 23.58/11.09 thf(287,axiom,((! [A:list_node]: (((cons_node @ (hd_node @ A) @ (tl_node @ A)) = A) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_hd__Cons__tl)). 23.58/11.09 thf(1469,plain,((! [A:list_node]: (((cons_node @ (hd_node @ A) @ (tl_node @ A)) = A) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 23.58/11.09 thf(254,axiom,((! [A:node,B:list_node]: ((? [C:list_node,D:list_node]: (~ (member_node @ A @ (set_node2 @ D)) & (B = (append_node @ C @ (cons_node @ A @ D))))) <= (member_node @ A @ (set_node2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_split__list__last)). 23.58/11.09 thf(1315,plain,((! [A:node,B:list_node]: (? [C:list_node,D:list_node]: (~ (member_node @ A @ (set_node2 @ D)) & (B = (append_node @ C @ (cons_node @ A @ D)))) | ~ (member_node @ A @ (set_node2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 23.58/11.09 thf(72,axiom,((! [A:list_node,B:list_node,C:list_node]: ((append_node @ (append_node @ A @ B) @ C) = (append_node @ A @ (append_node @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_append_Oassoc)). 23.58/11.09 thf(518,plain,((! [A:list_node,B:list_node,C:list_node]: ((append_node @ (append_node @ A @ B) @ C) = (append_node @ A @ (append_node @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 23.58/11.09 thf(115,axiom,((! [A:list_node]: ((butlast_node @ (tl_node @ A)) = (tl_node @ (butlast_node @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_butlast__tl)). 23.58/11.09 thf(666,plain,((! [A:list_node]: ((butlast_node @ (tl_node @ A)) = (tl_node @ (butlast_node @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 23.58/11.09 thf(248,axiom,((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_assms_I7_J)). 23.58/11.09 thf(1295,plain,((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ n @ ns @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 23.58/11.09 thf(275,axiom,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => (B = (hd_node @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_old_Opath2__hd)). 23.58/11.09 thf(1422,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (B = (hd_node @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 23.58/11.09 thf(198,axiom,((! [A:node,B:list_node,C:list_node,D:list_node,E:list_node]: ((((cons_node @ A @ D) = (append_node @ C @ E)) <= (D = (append_node @ B @ E))) <= ((cons_node @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Cons__eq__appendI)). 23.58/11.09 thf(1073,plain,((! [A:node,B:list_node,C:list_node,D:list_node,E:list_node]: (((cons_node @ A @ D) = (append_node @ C @ E)) | ~ (D = (append_node @ B @ E)) | ~ ((cons_node @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 23.58/11.09 thf(243,axiom,((! [A:g,B:node,C:list_node,D:node,E:node]: (((member_node @ E @ (set_node2 @ C)) => (~ (! [F:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E) => (! [G:list_node]: (((C != (append_node @ (butlast_node @ F) @ G)) <= (C = (append_node @ F @ (tl_node @ G)))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D))))))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_old_Opath2__split__ex)). 23.58/11.09 thf(1269,plain,((! [A:g,B:node,C:list_node,D:node,E:node]: (((member_node @ E @ (set_node2 @ C)) => (~ (! [F:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ F @ E) => (! [G:list_node]: (~ (C = (append_node @ (butlast_node @ F) @ G)) | ~ (C = (append_node @ F @ (tl_node @ G))) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ E @ G @ D))))))) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 23.58/11.09 thf(94,axiom,((! [A:list_node,B:list_node]: ((A != nil_node) => ((tl_node @ (append_node @ A @ B)) = (append_node @ (tl_node @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_tl__append2)). 23.58/11.09 thf(597,plain,((! [A:list_node,B:list_node]: ((~ (A = nil_node)) => ((tl_node @ (append_node @ A @ B)) = (append_node @ (tl_node @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 23.58/11.09 thf(280,axiom,((! [A:node,B:list_node,C:node,D:list_node]: (((cons_node @ A @ B) = (cons_node @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_list_Oinject)). 23.58/11.09 thf(1437,plain,((! [A:node,B:list_node,C:node,D:list_node]: (((cons_node @ A @ B) = (cons_node @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 23.58/11.09 thf(219,axiom,((! [A:list_list_node]: (((! [B:list_list_node]: (A != (cons_list_node @ nil_node @ B))) => (~ (! [B:node,C:list_node,D:list_list_node]: (A != (cons_list_node @ (cons_node @ B @ C) @ D))))) <= (A != nil_list_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_transpose_Ocases)). 23.58/11.09 thf(1173,plain,((! [A:list_list_node]: (((! [B:list_list_node]: ~ (A = (cons_list_node @ nil_node @ B))) => (~ (! [B:node,C:list_node,D:list_list_node]: ~ (A = (cons_list_node @ (cons_node @ B @ C) @ D))))) | (A = nil_list_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 23.58/11.09 thf(166,axiom,((! [A:g,B:list_node,C:node]: (((member_node @ C @ (set_node2 @ (alpha_n @ A))) <= (member_node @ C @ (set_node2 @ B))) <= (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_old_Opath__in___092_060alpha_062n)). 23.58/11.09 thf(878,plain,((! [A:g,B:list_node,C:node]: ((member_node @ C @ (set_node2 @ (alpha_n @ A))) | ~ (member_node @ C @ (set_node2 @ B)) | ~ (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 23.58/11.09 thf(47,axiom,((! [A:list_node]: (suffix_node @ nil_node @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_suffix__bot_Obot_Oextremum)). 23.58/11.09 thf(440,plain,((! [A:list_node]: (suffix_node @ nil_node @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 23.58/11.09 thf(99,axiom,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => ((B = A) <= (suffix_node @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_suffix__order_Odual__order_Oantisym)). 23.58/11.09 thf(614,plain,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => ((B = A) | ~ (suffix_node @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 23.58/11.09 thf(119,axiom,((! [A:list_node,B:list_node,C:list_node]: ((append_node @ (append_node @ A @ B) @ C) = (append_node @ A @ (append_node @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_append__assoc)). 23.58/11.09 thf(677,plain,((! [A:list_node,B:list_node,C:list_node]: ((append_node @ (append_node @ A @ B) @ C) = (append_node @ A @ (append_node @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 23.58/11.09 thf(76,axiom,((! [A:list_node,B:list_node]: (((suffix_node @ B @ A) => (A = B)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_suffix__order_Oorder_Oantisym)). 23.58/11.09 thf(533,plain,((! [A:list_node,B:list_node]: (((suffix_node @ B @ A) => (A = B)) | ~ (suffix_node @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 23.58/11.09 thf(80,axiom,((! [A:val,B:(val > $o)]: ((member_val @ A @ (collect_val @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_mem__Collect__eq)). 23.58/11.09 thf(550,plain,((! [A:val,B:(val > $o)]: ((member_val @ A @ (collect_val @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 23.58/11.09 thf(67,axiom,((r != phi_r)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_False)). 23.58/11.09 thf(500,plain,((~ (r = phi_r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 23.58/11.09 thf(241,axiom,((! [A:g,B:node,C:list_node,D:node,E:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => ((~ (! [F:list_node]: ((! [G:list_node]: ((C != (append_node @ (butlast_node @ F) @ G)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E)))) <= (member_node @ E @ (set_node2 @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_old_Opath2__split__ex_H)). 23.58/11.09 thf(1260,plain,((! [A:g,B:node,C:list_node,D:node,E:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (~ (! [F:list_node]: (! [G:list_node]: (~ (C = (append_node @ (butlast_node @ F) @ G)) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ E @ G @ D)) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ F @ E))) | ~ (member_node @ E @ (set_node2 @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 23.58/11.09 thf(17,axiom,((! [A:list_list_node,B:list_list_node]: ((nil_list_node = (append_list_node @ A @ B)) = ((A = nil_list_node) & (B = nil_list_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Nil__is__append__conv)). 23.58/11.09 thf(340,plain,((! [A:list_list_node,B:list_list_node]: ((nil_list_node = (append_list_node @ A @ B)) = ((A = nil_list_node) & (B = nil_list_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 23.58/11.09 thf(78,axiom,((! [A:list_node,B:list_node]: (((A = nil_node) = (B = nil_node)) => (((A != nil_node) => ((((tl_node @ A) = (tl_node @ B)) & ((hd_node @ A) = (hd_node @ B))) <= (B != nil_node))) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_list_Oexpand)). 23.58/11.09 thf(538,plain,((! [A:list_node,B:list_node]: (((A = nil_node) = (B = nil_node)) => (((~ (A = nil_node)) => ((((tl_node @ A) = (tl_node @ B)) & ((hd_node @ A) = (hd_node @ B))) | (B = nil_node))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 23.58/11.09 thf(199,axiom,((! [A:g,B:node,C:list_node,D:node]: ((member_node @ B @ (set_node2 @ C)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_old_Opath2__hd__in__ns)). 23.58/11.09 thf(1078,plain,((! [A:g,B:node,C:list_node,D:node]: ((member_node @ B @ (set_node2 @ C)) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 23.58/11.09 thf(276,axiom,((! [A:list_node,B:node,C:list_node]: (((butlast_node @ A) = (cons_node @ B @ C)) = (? [D:node]: (A = (cons_node @ B @ (append_node @ C @ (cons_node @ D @ nil_node)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_butlast__eq__cons__conv)). 23.58/11.09 thf(1426,plain,((! [A:list_node,B:node,C:list_node]: (((butlast_node @ A) = (cons_node @ B @ C)) = (? [D:node]: (A = (cons_node @ B @ (append_node @ C @ (cons_node @ D @ nil_node)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 23.58/11.09 thf(185,axiom,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) = (? [C:list_node,D:list_node]: (B = (append_node @ C @ (cons_node @ A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_in__set__conv__decomp)). 23.58/11.09 thf(1001,plain,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) = (? [C:list_node,D:list_node]: (B = (append_node @ C @ (cons_node @ A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 23.58/11.09 thf(144,axiom,((! [A:g,B:node,C:list_node,D:node,E:(node > (list_node > (node > $o)))]: ((((E @ D @ (cons_node @ D @ nil_node) @ D) <= (invar @ A)) => ((! [F:list_node,G:node,H:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ H @ F @ D) => (((member_node @ G @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ H))) => (E @ G @ (cons_node @ G @ F) @ D)) <= (E @ H @ F @ D)))) => (E @ B @ C @ D))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_old_Opath2__induct)). 23.58/11.09 thf(782,plain,((! [A:g,B:node,C:list_node,D:node,E:(node > (list_node > (node > $o)))]: ((((E @ D @ (cons_node @ D @ nil_node) @ D) | ~ (invar @ A)) => ((! [F:list_node,G:node,H:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ H @ F @ D) => (((member_node @ G @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ H))) => (E @ G @ (cons_node @ G @ F) @ D)) | ~ (E @ H @ F @ D)))) => (E @ B @ C @ D))) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 23.58/11.09 thf(39,axiom,((! [A:list_node]: ((prefix_node @ A @ nil_node) = (A = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_prefix__bot_Obot_Oextremum__unique)). 23.58/11.09 thf(417,plain,((! [A:list_node]: ((prefix_node @ A @ nil_node) = (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 23.58/11.09 thf(85,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ (append_node @ B @ C)) = (? [D:list_node]: ((A = (append_node @ D @ C)) & (suffix_node @ D @ B)) | (suffix_node @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_suffix__append)). 23.58/11.09 thf(565,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ (append_node @ B @ C)) = (? [D:list_node]: ((A = (append_node @ D @ C)) & (suffix_node @ D @ B)) | (suffix_node @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 23.58/11.09 thf(46,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ C @ A) <= (A = (append_node @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_suffixI)). 23.58/11.09 thf(436,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ C @ A) | ~ (A = (append_node @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 23.58/11.09 thf(234,axiom,((! [A:list_node,B:(node > $o)]: ((? [C:list_node,D:node]: ((B @ D) & ? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E))))) <= (? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_split__list__prop)). 23.58/11.09 thf(1228,plain,((! [A:list_node,B:(node > $o)]: (? [C:list_node,D:node]: ((B @ D) & ? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))) | ~ (? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 23.58/11.09 thf(133,axiom,((! [A:g,B:node,C:list_node,D:node,E:(node > $o)]: (((~ (! [F:node,G:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ F @ G @ D) => (((~ (suffix_node @ G @ C)) <= (! [H:node]: ((~ (E @ H)) <= (member_node @ H @ (set_node2 @ (tl_node @ G)))))) <= (E @ F))))) <= (? [F:node]: ((E @ F) & (member_node @ F @ (set_node2 @ C))))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_old_Opath2__split__last__prop)). 23.58/11.09 thf(724,plain,((! [A:g,B:node,C:list_node,D:node,E:(node > $o)]: (~ (! [F:node,G:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ F @ G @ D) => (~ (suffix_node @ G @ C) | ~ (! [H:node]: (~ (E @ H) | ~ (member_node @ H @ (set_node2 @ (tl_node @ G))))) | ~ (E @ F)))) | ~ (? [F:node]: ((E @ F) & (member_node @ F @ (set_node2 @ C)))) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 23.58/11.09 thf(87,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => (suffix_node @ A @ (append_node @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_suffix__appendI)). 23.58/11.09 thf(570,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => (suffix_node @ A @ (append_node @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 23.58/11.09 thf(278,axiom,((! [A:g,B:list_node,C:node]: (((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (cons_node @ C @ B)) <= (member_node @ C @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ (hd_node @ B))))) <= (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_old_OCons__path)). 23.58/11.09 thf(1430,plain,((! [A:g,B:list_node,C:node]: ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (cons_node @ C @ B)) | ~ (member_node @ C @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ (hd_node @ B)))) | ~ (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 23.58/11.09 thf(256,axiom,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((A @ nil_node @ nil_node) => ((! [D:node,E:list_node,F:list_node]: ((A @ E @ F) => (A @ (cons_node @ D @ E) @ F))) => ((A @ B @ C) <= (! [D:node,E:list_node,F:list_node]: ((A @ E @ F) => (A @ E @ (cons_node @ D @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_list__2pre__induct)). 23.58/11.09 thf(1323,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((A @ nil_node @ nil_node) => ((! [D:node,E:list_node,F:list_node]: ((A @ E @ F) => (A @ (cons_node @ D @ E) @ F))) => ((A @ B @ C) | ~ (! [D:node,E:list_node,F:list_node]: ((A @ E @ F) => (A @ E @ (cons_node @ D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 23.58/11.09 thf(175,axiom,((! [A:node,B:node,C:list_node,D:node,E:node,F:list_node]: (((cons_node @ A @ (cons_node @ B @ nil_node)) = (append_node @ C @ (cons_node @ D @ (cons_node @ E @ F)))) = ((B = E) & (F = nil_node) & (A = D) & (C = nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_list__ee__eq__leel_I1_J)). 23.58/11.09 thf(949,plain,((! [A:node,B:node,C:list_node,D:node,E:node,F:list_node]: (((cons_node @ A @ (cons_node @ B @ nil_node)) = (append_node @ C @ (cons_node @ D @ (cons_node @ E @ F)))) = ((B = E) & (F = nil_node) & (A = D) & (C = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 23.58/11.09 thf(54,axiom,((! [A:list_node,B:set_node]: ((ord_less_eq_set_node @ (set_node2 @ A) @ B) = (! [C:node]: ((member_node @ C @ B) <= (member_node @ C @ (set_node2 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_subset__code_I1_J)). 23.58/11.09 thf(460,plain,((! [A:list_node,B:set_node]: ((ord_less_eq_set_node @ (set_node2 @ A) @ B) = (! [C:node]: ((member_node @ C @ B) | ~ (member_node @ C @ (set_node2 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 23.58/11.09 thf(285,axiom,((! [A:g,B:list_node]: ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B) = (? [C:node]: ((member_node @ C @ (set_node2 @ (alpha_n @ A))) & (invar @ A) & (B = (cons_node @ C @ nil_node))) | ? [C:list_node,D:node]: ((B = (cons_node @ D @ C)) & (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ C) & (member_node @ D @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ (hd_node @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_old_Opath_Osimps)). 23.58/11.09 thf(1462,plain,((! [A:g,B:list_node]: ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B) = (? [C:node]: ((member_node @ C @ (set_node2 @ (alpha_n @ A))) & (invar @ A) & (B = (cons_node @ C @ nil_node))) | ? [C:list_node,D:node]: ((B = (cons_node @ D @ C)) & (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ C) & (member_node @ D @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ (hd_node @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 23.58/11.09 thf(212,axiom,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A)))) = (? [C:list_node,D:node,E:list_node]: ((A = (append_node @ C @ (cons_node @ D @ E))) & ! [F:node]: ((~ (B @ F)) <= (member_node @ F @ (set_node2 @ E))) & (B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_split__list__last__prop__iff)). 23.58/11.09 thf(1132,plain,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A)))) = (? [C:list_node,D:node,E:list_node]: ((A = (append_node @ C @ (cons_node @ D @ E))) & ! [F:node]: (~ (B @ F) | ~ (member_node @ F @ (set_node2 @ E))) & (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 23.58/11.09 thf(83,axiom,((! [A:list_node]: ((append_node @ nil_node @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_append_Oleft__neutral)). 23.58/11.09 thf(559,plain,((! [A:list_node]: ((append_node @ nil_node @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 23.58/11.09 thf(216,axiom,((! [A:list_node]: ((A = nil_node) <= (! [B:node,C:list_node]: (A != (cons_node @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_min__list_Ocases)). 23.58/11.09 thf(1147,plain,((! [A:list_node]: ((A = nil_node) | ~ (! [B:node,C:list_node]: ~ (A = (cons_node @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 23.58/11.09 thf(255,axiom,((! [A:list_node,B:node,C:list_node]: ((A != nil_node) => (((cons_node @ B @ nil_node) = (append_node @ C @ A)) = ((C = nil_node) & (A = (cons_node @ B @ nil_node))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_list__se__match_I4_J)). 23.58/11.09 thf(1319,plain,((! [A:list_node,B:node,C:list_node]: ((~ (A = nil_node)) => (((cons_node @ B @ nil_node) = (append_node @ C @ A)) = ((C = nil_node) & (A = (cons_node @ B @ nil_node))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 23.58/11.09 thf(96,axiom,((! [A:list_node,B:list_node,C:list_node]: (((append_node @ A @ B) = (append_node @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_append__same__eq)). 23.58/11.09 thf(606,plain,((! [A:list_node,B:list_node,C:list_node]: (((append_node @ A @ B) = (append_node @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 23.58/11.09 thf(167,axiom,((! [A:list_node,B:list_node,C:(list_node > (list_node > $o))]: ((A != nil_node) => (((! [D:node,E:node]: (C @ (cons_node @ D @ nil_node) @ (cons_node @ E @ nil_node))) => ((((C @ A @ B) <= (! [D:node,E:list_node,F:node,G:list_node]: ((C @ E @ G) => ((E != nil_node) => ((G != nil_node) => (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node)))))))) <= (! [D:node,E:node,F:list_node]: ((F != nil_node) => (C @ (cons_node @ D @ nil_node) @ (append_node @ F @ (cons_node @ E @ nil_node)))))) <= (! [D:node,E:list_node,F:node]: ((C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (cons_node @ F @ nil_node)) <= (E != nil_node))))) <= (B != nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_rev__nonempty__induct2_H)). 23.58/11.09 thf(881,plain,((! [A:list_node,B:list_node,C:(list_node > (list_node > $o))]: ((~ (A = nil_node)) => (((! [D:node,E:node]: (C @ (cons_node @ D @ nil_node) @ (cons_node @ E @ nil_node))) => ((C @ A @ B) | ~ (! [D:node,E:list_node,F:node,G:list_node]: ((C @ E @ G) => ((~ (E = nil_node)) => ((~ (G = nil_node)) => (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node))))))) | ~ (! [D:node,E:node,F:list_node]: ((~ (F = nil_node)) => (C @ (cons_node @ D @ nil_node) @ (append_node @ F @ (cons_node @ E @ nil_node))))) | ~ (! [D:node,E:list_node,F:node]: ((C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (cons_node @ F @ nil_node)) | (E = nil_node))))) | (B = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 23.58/11.09 thf(235,axiom,((! [A:list_node]: (((tl_node @ A) = nil_node) = (? [B:node]: (A = (cons_node @ B @ nil_node)) | (A = nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_tl__Nil)). 23.58/11.09 thf(1232,plain,((! [A:list_node]: (((tl_node @ A) = nil_node) = (? [B:node]: (A = (cons_node @ B @ nil_node)) | (A = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 23.58/11.09 thf(106,axiom,((! [A:list_node]: ((A != nil_node) => (member_node @ (hd_node @ A) @ (set_node2 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_list_Oset__sel_I1_J)). 23.58/11.09 thf(638,plain,((! [A:list_node]: ((~ (A = nil_node)) => (member_node @ (hd_node @ A) @ (set_node2 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 23.58/11.09 thf(160,axiom,((! [A:list_node,B:node,C:list_node,D:node]: (((append_node @ A @ (cons_node @ B @ nil_node)) = (append_node @ C @ (cons_node @ D @ nil_node))) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_append1__eq__conv)). 23.58/11.09 thf(853,plain,((! [A:list_node,B:node,C:list_node,D:node]: (((append_node @ A @ (cons_node @ B @ nil_node)) = (append_node @ C @ (cons_node @ D @ nil_node))) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 23.58/11.09 thf(60,axiom,((! [A:node,B:list_node]: ((A != (hd_node @ B)) => ((member_node @ A @ (set_node2 @ B)) => (member_node @ A @ (set_node2 @ (tl_node @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_not__hd__in__tl)). 23.58/11.09 thf(475,plain,((! [A:node,B:list_node]: ((~ (A = (hd_node @ B))) => ((member_node @ A @ (set_node2 @ B)) => (member_node @ A @ (set_node2 @ (tl_node @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 23.58/11.09 thf(286,axiom,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: (((! [D:node,E:list_node,F:list_node]: ((A @ F @ E) => (A @ (cons_node @ D @ E) @ F))) => (A @ B @ C)) <= (! [D:list_node]: (A @ nil_node @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_splice_Oinduct)). 23.58/11.09 thf(1465,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: (((! [D:node,E:list_node,F:list_node]: ((A @ F @ E) => (A @ (cons_node @ D @ E) @ F))) => (A @ B @ C)) | ~ (! [D:list_node]: (A @ nil_node @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 23.58/11.09 thf(265,axiom,((~ (member_node @ i @ (set_node2 @ (butlast_node @ ms2))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_ms_H__props_I3_J)). 23.58/11.09 thf(1373,plain,((~ (member_node @ i @ (set_node2 @ (butlast_node @ ms2))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 23.58/11.09 thf(274,axiom,((! [A:list_node,B:list_node,C:node]: ((A != nil_node) => (((append_node @ B @ A) = (cons_node @ C @ nil_node)) = ((B = nil_node) & (A = (cons_node @ C @ nil_node))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_list__se__match_I2_J)). 23.58/11.09 thf(1418,plain,((! [A:list_node,B:list_node,C:node]: ((~ (A = nil_node)) => (((append_node @ B @ A) = (cons_node @ C @ nil_node)) = ((B = nil_node) & (A = (cons_node @ C @ nil_node))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 23.58/11.09 thf(63,axiom,(((= @ list_node) = (^ [A:list_node,B:list_node]: ((suffix_node @ A @ B) & (suffix_node @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_suffix__order_Oeq__iff)). 23.58/11.09 thf(485,plain,(((= @ list_node) = (^ [A:list_node,B:list_node]: ((suffix_node @ A @ B) & (suffix_node @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 23.58/11.09 thf(217,axiom,((! [A:g,B:list_node]: (((~ (! [C:list_node,D:node]: ((B = (cons_node @ D @ C)) => ((~ (member_node @ D @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ (hd_node @ C))))) <= (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ C))))) <= (! [C:node]: ((B = (cons_node @ C @ nil_node)) => ((member_node @ C @ (set_node2 @ (alpha_n @ A))) => (~ (invar @ A)))))) <= (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_old_Opath_Ocases)). 23.58/11.09 thf(1151,plain,((! [A:g,B:list_node]: (~ (! [C:list_node,D:node]: ((B = (cons_node @ D @ C)) => (~ (member_node @ D @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ (hd_node @ C)))) | ~ (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ C)))) | ~ (! [C:node]: ((B = (cons_node @ C @ nil_node)) => ((member_node @ C @ (set_node2 @ (alpha_n @ A))) => (~ (invar @ A))))) | ~ (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 23.58/11.09 thf(189,axiom,((! [A:list_node,B:list_node,C:node]: ((((append_node @ A @ B) = (cons_node @ C @ nil_node)) = ((B = nil_node) & (A = (cons_node @ C @ nil_node)))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_list__se__match_I1_J)). 23.58/11.09 thf(1020,plain,((! [A:list_node,B:list_node,C:node]: ((((append_node @ A @ B) = (cons_node @ C @ nil_node)) = ((B = nil_node) & (A = (cons_node @ C @ nil_node)))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 23.58/11.09 thf(146,axiom,((! [A:list_node,B:(node > $o)]: ((~ (! [C:list_node,D:node]: ((~ (B @ D)) <= (? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E))))))) <= (? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_split__list__propE)). 23.58/11.09 thf(806,plain,((! [A:list_node,B:(node > $o)]: (~ (! [C:list_node,D:node]: (~ (B @ D) | ~ (? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))))) | ~ (? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 23.58/11.09 thf(169,axiom,((! [A:list_node,B:node,C:list_node]: ((suffix_node @ A @ (cons_node @ B @ C)) = ((A = (cons_node @ B @ C)) | (suffix_node @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_suffix__Cons)). 23.58/11.09 thf(905,plain,((! [A:list_node,B:node,C:list_node]: ((suffix_node @ A @ (cons_node @ B @ C)) = ((A = (cons_node @ B @ C)) | (suffix_node @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 23.58/11.09 thf(251,axiom,((! [A:node,B:list_node]: (nil_node != (cons_node @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_list_Odistinct_I1_J)). 23.58/11.09 thf(1302,plain,((! [A:node,B:list_node]: ~ (nil_node = (cons_node @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 23.58/11.09 thf(140,axiom,((member_val @ r @ (sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_rs_H__props_I3_J)). 23.58/11.09 thf(756,plain,((member_val @ r @ (sSA_CF848637139eD_val @ (alpha_n) @ (inEdges) @ (phis) @ g2 @ pred_phi_r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 23.58/11.09 thf(206,axiom,((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rs__props_I1_J)). 23.58/11.09 thf(1109,plain,((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ r) @ rs2 @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 23.58/11.09 thf(10,axiom,((! [A:list_list_node]: ((A != nil_list_node) => ((cons_list_node @ (hd_list_node @ A) @ (tl_list_node @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_hd__Cons__tl)). 23.58/11.09 thf(321,plain,((! [A:list_list_node]: ((~ (A = nil_list_node)) => ((cons_list_node @ (hd_list_node @ A) @ (tl_list_node @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 23.58/11.09 thf(21,axiom,((! [A:list_list_node,B:list_node]: ((butlast_list_node @ (append_list_node @ A @ (cons_list_node @ B @ nil_list_node))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_butlast__snoc)). 23.58/11.09 thf(353,plain,((! [A:list_list_node,B:list_node]: ((butlast_list_node @ (append_list_node @ A @ (cons_list_node @ B @ nil_list_node))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 23.58/11.09 thf(180,axiom,((! [A:list_node,B:list_node,C:(list_node > (list_node > $o))]: ((~ (suffix_node @ A @ B)) => ((((C @ A @ B) <= (! [D:node,E:list_node,F:node,G:list_node]: ((((C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node))) <= (C @ E @ G)) <= (~ (suffix_node @ E @ G))) <= (D = F)))) <= (! [D:node,E:list_node,F:node,G:list_node]: ((C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node))) <= (D != F)))) <= (! [D:node,E:list_node]: (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ nil_node)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_not__suffix__induct)). 23.58/11.09 thf(966,plain,((! [A:list_node,B:list_node,C:(list_node > (list_node > $o))]: ((~ (suffix_node @ A @ B)) => ((C @ A @ B) | ~ (! [D:node,E:list_node,F:node,G:list_node]: ((C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node))) | ~ (C @ E @ G) | (suffix_node @ E @ G) | ~ (D = F))) | ~ (! [D:node,E:list_node,F:node,G:list_node]: ((C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node))) | (D = F))) | ~ (! [D:node,E:list_node]: (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 23.58/11.09 thf(267,axiom,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: (((prefix_node @ (append_node @ E @ (cons_node @ F @ nil_node)) @ C) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ E @ (cons_node @ F @ nil_node)) @ F)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_old_Opath2__prefix)). 23.58/11.09 thf(1377,plain,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: (((prefix_node @ (append_node @ E @ (cons_node @ F @ nil_node)) @ C) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ (append_node @ E @ (cons_node @ F @ nil_node)) @ F)) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 23.58/11.09 thf(229,axiom,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ C @ (cons_node @ D @ E)) @ F) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ (cons_node @ D @ E) @ F)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_old_Opath2__split_I2_J)). 23.58/11.09 thf(1215,plain,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ (append_node @ C @ (cons_node @ D @ E)) @ F) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ D @ (cons_node @ D @ E) @ F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 23.58/11.09 thf(125,axiom,((! [A:list_node,B:node]: ((((B = (hd_node @ A)) | (member_node @ B @ (set_node2 @ (tl_node @ A)))) = (member_node @ B @ (set_node2 @ A))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_in__hd__or__tl__conv)). 23.58/11.09 thf(692,plain,((! [A:list_node,B:node]: ((((B = (hd_node @ A)) | (member_node @ B @ (set_node2 @ (tl_node @ A)))) = (member_node @ B @ (set_node2 @ A))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 23.58/11.09 thf(164,axiom,((! [A:list_node,B:(list_node > $o)]: (((! [C:node]: (B @ (cons_node @ C @ nil_node))) => ((B @ A) <= (! [C:node,D:list_node]: (((B @ D) => (B @ (cons_node @ C @ D))) <= (D != nil_node))))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_list__nonempty__induct)). 23.58/11.09 thf(866,plain,((! [A:list_node,B:(list_node > $o)]: (((! [C:node]: (B @ (cons_node @ C @ nil_node))) => ((B @ A) | ~ (! [C:node,D:list_node]: (((B @ D) => (B @ (cons_node @ C @ D))) | (D = nil_node))))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 23.58/11.09 thf(52,axiom,((! [A:list_node]: ((prefix_node @ A @ nil_node) = (A = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_prefix__Nil)). 23.58/11.09 thf(453,plain,((! [A:list_node]: ((prefix_node @ A @ nil_node) = (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 23.58/11.09 thf(271,axiom,((! [A:(list_node > $o),B:list_node]: ((((A @ B) <= (! [C:node,D:node,E:list_node]: ((A @ (cons_node @ C @ (cons_node @ D @ E))) <= (A @ E)))) <= (! [C:node]: (A @ (cons_node @ C @ nil_node)))) <= (A @ nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_list__induct__first2)). 23.58/11.09 thf(1394,plain,((! [A:(list_node > $o),B:list_node]: ((A @ B) | ~ (! [C:node,D:node,E:list_node]: ((A @ (cons_node @ C @ (cons_node @ D @ E))) | ~ (A @ E))) | ~ (! [C:node]: (A @ (cons_node @ C @ nil_node))) | ~ (A @ nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 23.58/11.09 thf(258,axiom,((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_assms_I8_J)). 23.58/11.09 thf(1351,plain,((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ m @ ms @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ s))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 23.58/11.09 thf(279,axiom,((! [A:list_node]: ((((tl_node @ A) = nil_node) => (~ (! [B:node]: (A != (cons_node @ B @ nil_node))))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_tl__obtain__elem)). 23.58/11.09 thf(1433,plain,((! [A:list_node]: ((((tl_node @ A) = nil_node) => (~ (! [B:node]: ~ (A = (cons_node @ B @ nil_node))))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 23.58/11.09 thf(7,axiom,((! [A:list_list_node,B:list_list_node]: (((append_list_node @ A @ B) = nil_list_node) = ((A = nil_list_node) & (B = nil_list_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_append__is__Nil__conv)). 23.58/11.09 thf(312,plain,((! [A:list_list_node,B:list_list_node]: (((append_list_node @ A @ B) = nil_list_node) = ((A = nil_list_node) & (B = nil_list_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 23.58/11.09 thf(3,axiom,((! [A:list_list_node,B:list_list_node]: (((A = nil_list_node) = (B = nil_list_node)) => ((((((tl_list_node @ A) = (tl_list_node @ B)) & ((hd_list_node @ A) = (hd_list_node @ B))) <= (B != nil_list_node)) <= (A != nil_list_node)) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_list_Oexpand)). 23.58/11.09 thf(293,plain,((! [A:list_list_node,B:list_list_node]: (((A = nil_list_node) = (B = nil_list_node)) => (((((tl_list_node @ A) = (tl_list_node @ B)) & ((hd_list_node @ A) = (hd_list_node @ B))) | (B = nil_list_node) | (A = nil_list_node)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 23.58/11.09 thf(177,axiom,((! [A:list_node,B:list_node,C:node,D:list_node]: (((append_node @ A @ B) = (cons_node @ C @ D)) = (? [E:list_node]: ((A = (cons_node @ C @ E)) & ((append_node @ E @ B) = D)) | ((B = (cons_node @ C @ D)) & (A = nil_node)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_append__eq__Cons__conv)). 23.58/11.09 thf(956,plain,((! [A:list_node,B:list_node,C:node,D:list_node]: (((append_node @ A @ B) = (cons_node @ C @ D)) = (? [E:list_node]: ((A = (cons_node @ C @ E)) & ((append_node @ E @ B) = D)) | ((B = (cons_node @ C @ D)) & (A = nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 23.58/11.09 thf(43,axiom,((! [A:list_node,B:list_node]: ((prefix_node @ (append_node @ A @ B) @ A) = (B = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_same__prefix__nil)). 23.58/11.09 thf(428,plain,((! [A:list_node,B:list_node]: ((prefix_node @ (append_node @ A @ B) @ A) = (B = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 23.58/11.09 thf(226,axiom,((! [A:list_node,B:(list_node > $o)]: ((((B @ A) <= (! [C:node,D:list_node]: (((B @ (append_node @ D @ (cons_node @ C @ nil_node))) <= (B @ D)) <= (D != nil_node)))) <= (! [C:node]: (B @ (cons_node @ C @ nil_node)))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_rev__nonempty__induct)). 23.58/11.09 thf(1201,plain,((! [A:list_node,B:(list_node > $o)]: ((B @ A) | ~ (! [C:node,D:list_node]: ((B @ (append_node @ D @ (cons_node @ C @ nil_node))) | ~ (B @ D) | (D = nil_node))) | ~ (! [C:node]: (B @ (cons_node @ C @ nil_node))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 23.58/11.09 thf(1,conjecture,((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 23.58/11.09 thf(2,negated_conjecture,((~ (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r))),inference(neg_conjecture,[status(cth)],[1])). 23.58/11.09 thf(292,plain,((~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ i @ (cons_node @ i @ rs_rest) @ pred_phi_r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 23.58/11.09 thf(28,axiom,((! [A:node,B:(node > $o)]: ((member_node @ A @ (collect_node @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_mem__Collect__eq)). 23.58/11.09 thf(380,plain,((! [A:node,B:(node > $o)]: ((member_node @ A @ (collect_node @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 23.58/11.09 thf(70,axiom,((! [A:list_node,B:list_node]: (((suffix_node @ B @ A) = (B = A)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_suffix__order_Oantisym__conv)). 23.58/11.09 thf(512,plain,((! [A:list_node,B:list_node]: (((suffix_node @ B @ A) = (B = A)) | ~ (suffix_node @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 23.58/11.09 thf(75,axiom,((! [A:list_node,B:set_node]: ((A != nil_node) => ((ord_less_eq_set_node @ (set_node2 @ (tl_node @ A)) @ B) <= (ord_less_eq_set_node @ (set_node2 @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_tl__subset)). 23.58/11.09 thf(529,plain,((! [A:list_node,B:set_node]: ((~ (A = nil_node)) => ((ord_less_eq_set_node @ (set_node2 @ (tl_node @ A)) @ B) | ~ (ord_less_eq_set_node @ (set_node2 @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 23.58/11.09 thf(252,axiom,((rs = (append_node @ tmp @ (cons_node @ i @ rs_rest)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_rs_H__rest__def)). 23.58/11.09 thf(1306,plain,((rs = (append_node @ tmp @ (cons_node @ i @ rs_rest)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 23.58/11.09 thf(147,axiom,((! [A:node,B:list_node]: (member_node @ A @ (set_node2 @ (cons_node @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_list_Oset__intros_I1_J)). 23.58/11.09 thf(810,plain,((! [A:node,B:list_node]: (member_node @ A @ (set_node2 @ (cons_node @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 23.58/11.09 thf(15,axiom,((! [A:list_list_node,B:list_list_node]: ((A = (append_list_node @ B @ A)) = (B = nil_list_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_self__append__conv2)). 23.58/11.09 thf(334,plain,((! [A:list_list_node,B:list_list_node]: ((A = (append_list_node @ B @ A)) = (B = nil_list_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 23.58/11.09 thf(176,axiom,((! [A:list_node,B:node,C:list_node]: ((((cons_node @ B @ nil_node) = (append_node @ A @ C)) = ((C = nil_node) & (A = (cons_node @ B @ nil_node)))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_list__se__match_I3_J)). 23.58/11.09 thf(952,plain,((! [A:list_node,B:node,C:list_node]: ((((cons_node @ B @ nil_node) = (append_node @ A @ C)) = ((C = nil_node) & (A = (cons_node @ B @ nil_node)))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 23.58/11.09 thf(20,axiom,((! [A:list_list_node,B:list_list_node]: (((tl_list_node @ (append_list_node @ A @ B)) = (append_list_node @ (tl_list_node @ A) @ B)) <= (A != nil_list_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_tl__append2)). 23.58/11.09 thf(349,plain,((! [A:list_list_node,B:list_list_node]: (((tl_list_node @ (append_list_node @ A @ B)) = (append_list_node @ (tl_list_node @ A) @ B)) | (A = nil_list_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 23.58/11.09 thf(230,axiom,((! [A:list_node,B:node,C:list_node,D:node]: ((suffix_node @ (append_node @ A @ (cons_node @ B @ nil_node)) @ (append_node @ C @ (cons_node @ D @ nil_node))) = ((suffix_node @ A @ C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_snoc__suffix__snoc)). 23.58/11.09 thf(1217,plain,((! [A:list_node,B:node,C:list_node,D:node]: ((suffix_node @ (append_node @ A @ (cons_node @ B @ nil_node)) @ (append_node @ C @ (cons_node @ D @ nil_node))) = ((suffix_node @ A @ C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 23.58/11.09 thf(264,axiom,((! [A:g,B:node]: (((member_node @ B @ (set_node2 @ (alpha_n @ A))) <= (invar @ A)) <= ((graph_272749361_edgeD @ inEdges @ A @ B) != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_old_Osuccessor__in___092_060alpha_062n)). 23.58/11.09 thf(1370,plain,((! [A:g,B:node]: ((member_node @ B @ (set_node2 @ (alpha_n @ A))) | ~ (invar @ A) | ((graph_272749361_edgeD @ (inEdges) @ A @ B) = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 23.58/11.09 thf(137,axiom,((! [A:node,B:list_node]: (((~ (! [C:node,D:list_node]: ((B = (cons_node @ C @ D)) => (~ (member_node @ A @ (set_node2 @ D)))))) <= (! [C:list_node]: (B != (cons_node @ A @ C)))) <= (member_node @ A @ (set_node2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_list_Oset__cases)). 23.58/11.09 thf(746,plain,((! [A:node,B:list_node]: (~ (! [C:node,D:list_node]: ((B = (cons_node @ C @ D)) => (~ (member_node @ A @ (set_node2 @ D))))) | ~ (! [C:list_node]: ~ (B = (cons_node @ A @ C))) | ~ (member_node @ A @ (set_node2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 23.58/11.09 thf(203,axiom,((! [A:(list_node > (list_node > $o)),B:(node > (node > $o)),C:list_node,D:list_node]: (((! [E:list_node]: (A @ nil_node @ E)) => ((! [E:node,F:list_node,G:node,H:list_node]: ((B @ E @ G) => ((A @ F @ (cons_node @ G @ H)) => (A @ (cons_node @ E @ F) @ (cons_node @ G @ H))))) => ((! [E:node,F:list_node,G:node,H:list_node]: ((~ (B @ E @ G)) => ((A @ (cons_node @ E @ F) @ (cons_node @ G @ H)) <= (A @ (cons_node @ E @ F) @ H)))) => (A @ C @ D)))) <= (! [E:list_node]: (A @ E @ nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_mergesort__by__rel__merge__induct)). 23.58/11.09 thf(1091,plain,((! [A:(list_node > (list_node > $o)),B:(node > (node > $o)),C:list_node,D:list_node]: (((! [E:list_node]: (A @ nil_node @ E)) => ((! [E:node,F:list_node,G:node,H:list_node]: ((B @ E @ G) => ((A @ F @ (cons_node @ G @ H)) => (A @ (cons_node @ E @ F) @ (cons_node @ G @ H))))) => ((! [E:node,F:list_node,G:node,H:list_node]: ((~ (B @ E @ G)) => ((A @ (cons_node @ E @ F) @ (cons_node @ G @ H)) | ~ (A @ (cons_node @ E @ F) @ H)))) => (A @ C @ D)))) | ~ (! [E:list_node]: (A @ E @ nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 23.58/11.09 thf(240,axiom,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A)))) => (~ (! [C:list_node,D:node]: ((? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))) => ((B @ D) => (~ (! [E:node]: ((~ (B @ E)) <= (member_node @ E @ (set_node2 @ C)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_split__list__first__propE)). 23.58/11.09 thf(1255,plain,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A)))) => (~ (! [C:list_node,D:node]: ((? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))) => ((B @ D) => (~ (! [E:node]: (~ (B @ E) | ~ (member_node @ E @ (set_node2 @ C)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 23.58/11.09 thf(4,axiom,((! [A:list_list_node,B:list_list_node]: ((A != nil_list_node) => ((hd_list_node @ (append_list_node @ A @ B)) = (hd_list_node @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_hd__append2)). 23.58/11.09 thf(302,plain,((! [A:list_list_node,B:list_list_node]: ((~ (A = nil_list_node)) => ((hd_list_node @ (append_list_node @ A @ B)) = (hd_list_node @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 23.58/11.09 thf(102,axiom,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => (ord_less_eq_set_node @ (set_node2 @ A) @ (set_node2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_set__mono__suffix)). 23.58/11.09 thf(625,plain,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => (ord_less_eq_set_node @ (set_node2 @ A) @ (set_node2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 23.58/11.09 thf(159,axiom,((member_node @ i @ (set_node2 @ ms))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_ri__props_I2_J)). 23.58/11.09 thf(852,plain,((member_node @ i @ (set_node2 @ ms))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 23.58/11.09 thf(13,axiom,(((tl_list_node @ nil_list_node) = nil_list_node)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_list_Osel_I2_J)). 23.58/11.09 thf(329,plain,(((tl_list_node @ nil_list_node) = nil_list_node)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 23.58/11.09 thf(249,axiom,((! [A:g,B:list_node]: ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B) => (invar @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_old_Opath__invar)). 23.58/11.09 thf(1296,plain,((! [A:g,B:list_node]: ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B) => (invar @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 23.58/11.09 thf(141,axiom,((! [A:node,B:list_node]: ((tl_node @ (cons_node @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_list_Osel_I3_J)). 23.58/11.09 thf(757,plain,((! [A:node,B:list_node]: ((tl_node @ (cons_node @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 23.58/11.09 thf(245,axiom,((! [A:list_node,B:(node > $o)]: ((? [C:list_node,D:node]: (! [E:node]: ((~ (B @ E)) <= (member_node @ E @ (set_node2 @ C))) & (B @ D) & ? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E))))) <= (? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_split__list__first__prop)). 23.58/11.09 thf(1281,plain,((! [A:list_node,B:(node > $o)]: (? [C:list_node,D:node]: (! [E:node]: (~ (B @ E) | ~ (member_node @ E @ (set_node2 @ C))) & (B @ D) & ? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))) | ~ (? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 23.58/11.09 thf(53,axiom,((! [A:list_node,B:list_node]: ((A != nil_node) => ((hd_node @ (append_node @ A @ B)) = (hd_node @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_hd__append2)). 23.58/11.09 thf(456,plain,((! [A:list_node,B:list_node]: ((~ (A = nil_node)) => ((hd_node @ (append_node @ A @ B)) = (hd_node @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 23.58/11.09 thf(11,axiom,((! [A:(val > $o),B:(val > $o)]: (((collect_val @ A) = (collect_val @ B)) <= (! [C:val]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Collect__cong)). 23.58/11.09 thf(324,plain,((! [A:(val > $o),B:(val > $o)]: (((collect_val @ (A)) = (collect_val @ (B))) | ~ (! [C:val]: ((A @ C) = (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 23.58/11.09 thf(173,axiom,((! [A:g,B:node,C:list_node,D:node,E:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => ((member_node @ E @ (set_node2 @ (alpha_n @ A))) <= (member_node @ E @ (set_node2 @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_old_Opath2__in___092_060alpha_062n)). 23.58/11.09 thf(916,plain,((! [A:g,B:node,C:list_node,D:node,E:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => ((member_node @ E @ (set_node2 @ (alpha_n @ A))) | ~ (member_node @ E @ (set_node2 @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 23.58/11.09 thf(57,axiom,((! [A:list_node,B:set_node]: (((ord_less_eq_set_node @ (set_node2 @ (butlast_node @ A)) @ B) <= (ord_less_eq_set_node @ (set_node2 @ A) @ B)) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_butlast__subset)). 23.58/11.09 thf(467,plain,((! [A:list_node,B:set_node]: ((ord_less_eq_set_node @ (set_node2 @ (butlast_node @ A)) @ B) | ~ (ord_less_eq_set_node @ (set_node2 @ A) @ B) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 23.58/11.09 thf(90,axiom,((! [A:list_node]: (suffix_node @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_suffix__order_Oorder__refl)). 23.58/11.09 thf(583,plain,((! [A:list_node]: (suffix_node @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 23.58/11.09 thf(152,axiom,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C))) => (? [C:list_node,D:node,E:list_node]: (! [F:node]: ((member_node @ F @ (set_node2 @ E)) => (~ (B @ F))) & (B @ D) & (A = (append_node @ C @ (cons_node @ D @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_split__list__last__prop)). 23.58/11.09 thf(830,plain,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C))) => (? [C:list_node,D:node,E:list_node]: (! [F:node]: ((member_node @ F @ (set_node2 @ E)) => (~ (B @ F))) & (B @ D) & (A = (append_node @ C @ (cons_node @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 23.58/11.09 thf(121,axiom,((suffix_node = (^ [A:list_node,B:list_node]: ? [C:list_node]: (B = (append_node @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_Sublist_Osuffix__def)). 23.58/11.09 thf(682,plain,(((suffix_node) = (^ [A:list_node,B:list_node]: ? [C:list_node]: (B = (append_node @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 23.58/11.09 thf(224,axiom,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C))) = (? [C:list_node,D:node]: (! [E:node]: ((member_node @ E @ (set_node2 @ C)) => (~ (B @ E))) & (B @ D) & ? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_split__list__first__prop__iff)). 23.58/11.09 thf(1195,plain,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C))) = (? [C:list_node,D:node]: (! [E:node]: ((member_node @ E @ (set_node2 @ C)) => (~ (B @ E))) & (B @ D) & ? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 23.58/11.09 thf(247,axiom,((! [A:list_node,B:node,C:list_node]: ((~ (! [D:node]: (A != (cons_node @ B @ (append_node @ C @ (cons_node @ D @ nil_node)))))) <= ((butlast_node @ A) = (cons_node @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_butlast__eq__consE)). 23.58/11.09 thf(1291,plain,((! [A:list_node,B:node,C:list_node]: (~ (! [D:node]: ~ (A = (cons_node @ B @ (append_node @ C @ (cons_node @ D @ nil_node))))) | ~ ((butlast_node @ A) = (cons_node @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 23.58/11.09 thf(129,axiom,((! [A:list_node]: ((nil_node = (tl_node @ A)) = (? [B:node]: (A = (cons_node @ B @ nil_node)) | (A = nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Nil__tl)). 23.58/11.09 thf(710,plain,((! [A:list_node]: ((nil_node = (tl_node @ A)) = (? [B:node]: (A = (cons_node @ B @ nil_node)) | (A = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 23.58/11.09 thf(136,axiom,((! [A:list_node]: (((~ (! [B:node,C:node,D:list_node]: (A != (cons_node @ B @ (cons_node @ C @ D))))) <= (! [B:node]: (A != (cons_node @ B @ nil_node)))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_remdups__adj_Ocases)). 23.58/11.09 thf(742,plain,((! [A:list_node]: (~ (! [B:node,C:node,D:list_node]: ~ (A = (cons_node @ B @ (cons_node @ C @ D)))) | ~ (! [B:node]: ~ (A = (cons_node @ B @ nil_node))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 23.58/11.09 thf(165,axiom,((! [A:node,B:list_node]: ((cons_node @ A @ B) != B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_not__Cons__self2)). 23.58/11.09 thf(874,plain,((! [A:node,B:list_node]: ~ ((cons_node @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 23.58/11.09 thf(110,axiom,((! [A:list_node]: (suffix_node @ (tl_node @ A) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_suffix__tl)). 23.58/11.09 thf(650,plain,((! [A:list_node]: (suffix_node @ (tl_node @ A) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 23.58/11.09 thf(266,axiom,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ B @ (cons_node @ A @ nil_node)) <= (invar @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_old_Oempty__path)). 23.58/11.09 thf(1375,plain,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ B @ (cons_node @ A @ nil_node)) | ~ (invar @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 23.58/11.09 thf(34,axiom,((! [A:list_list_node]: ((nil_list_node = (tl_list_node @ A)) = (? [B:list_node]: (A = (cons_list_node @ B @ nil_list_node)) | (A = nil_list_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Nil__tl)). 23.58/11.09 thf(403,plain,((! [A:list_list_node]: ((nil_list_node = (tl_list_node @ A)) = (? [B:list_node]: (A = (cons_list_node @ B @ nil_list_node)) | (A = nil_list_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 23.58/11.09 thf(22,axiom,((! [A:list_node,B:list_list_node]: ((tl_list_node @ (cons_list_node @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_list_Osel_I3_J)). 23.58/11.09 thf(356,plain,((! [A:list_node,B:list_list_node]: ((tl_list_node @ (cons_list_node @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 23.58/11.09 thf(93,axiom,((! [A:list_list_node,B:list_node,C:list_list_node]: ((((cons_list_node @ B @ nil_list_node) = (append_list_node @ C @ A)) = ((A = (cons_list_node @ B @ nil_list_node)) & (C = nil_list_node))) <= (A != nil_list_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_list__se__match_I4_J)). 23.58/11.09 thf(593,plain,((! [A:list_list_node,B:list_node,C:list_list_node]: ((((cons_list_node @ B @ nil_list_node) = (append_list_node @ C @ A)) = ((A = (cons_list_node @ B @ nil_list_node)) & (C = nil_list_node))) | (A = nil_list_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 23.58/11.09 thf(40,axiom,(((tl_node @ nil_node) = nil_node)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_list_Osel_I2_J)). 23.58/11.09 thf(420,plain,(((tl_node @ nil_node) = nil_node)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 23.58/11.09 thf(58,axiom,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => ((A = B) <= (suffix_node @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_suffix__order_Oantisym)). 23.58/11.09 thf(471,plain,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => ((A = B) | ~ (suffix_node @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 23.58/11.09 thf(261,axiom,((! [A:node,B:list_node]: ((hd_node @ (cons_node @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_list_Osel_I1_J)). 23.58/11.09 thf(1361,plain,((! [A:node,B:list_node]: ((hd_node @ (cons_node @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 23.58/11.09 thf(284,axiom,((graph_2009891965_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ n @ (append_node @ ns @ (tl_node @ ri)) @ i)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274__092_060open_062old_OpathsConverge_Ag_Am_Ams_H_An_A_Ins_A_064_Atl_Ari_J_Ai_092_060close_062)). 23.58/11.09 thf(1461,plain,((graph_2009891965_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ m @ ms2 @ n @ (append_node @ ns @ (tl_node @ ri)) @ i)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 23.58/11.09 thf(116,axiom,((! [A:list_node]: (suffix_node @ nil_node @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_Nil__suffix)). 23.58/11.09 thf(669,plain,((! [A:list_node]: (suffix_node @ nil_node @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 23.58/11.09 thf(273,axiom,((! [A:list_node]: ((A != nil_node) => (~ (! [B:node,C:list_node]: (A != (cons_node @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_neq__NilE)). 23.58/11.09 thf(1414,plain,((! [A:list_node]: ((~ (A = nil_node)) => (~ (! [B:node,C:list_node]: ~ (A = (cons_node @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 23.58/11.09 thf(92,axiom,((! [A:list_node,B:list_node,C:list_node]: ((prefix_node @ (append_node @ A @ B) @ (append_node @ A @ C)) = (prefix_node @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_same__prefix__prefix)). 23.58/11.09 thf(590,plain,((! [A:list_node,B:list_node,C:list_node]: ((prefix_node @ (append_node @ A @ B) @ (append_node @ A @ C)) = (prefix_node @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 23.58/11.09 thf(193,axiom,((! [A:(list_node > $o),B:list_node]: ((A @ nil_node) => ((! [C:node,D:list_node]: ((A @ D) => (A @ (cons_node @ C @ D)))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_strict__sorted_Oinduct)). 23.58/11.09 thf(1039,plain,((! [A:(list_node > $o),B:list_node]: ((A @ nil_node) => ((! [C:node,D:list_node]: ((A @ D) => (A @ (cons_node @ C @ D)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 23.58/11.09 thf(79,axiom,((! [A:list_node]: ((append_node @ A @ nil_node) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_append_Oright__neutral)). 23.58/11.09 thf(547,plain,((! [A:list_node]: ((append_node @ A @ nil_node) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 23.58/11.09 thf(127,axiom,((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ ri @ i)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_ri__props_I1_J)). 23.58/11.09 thf(706,plain,((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ r) @ ri @ i)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 23.58/11.09 thf(109,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ (append_node @ A @ B) @ (append_node @ C @ B)) = (suffix_node @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_same__suffix__suffix)). 23.58/11.09 thf(647,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ (append_node @ A @ B) @ (append_node @ C @ B)) = (suffix_node @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 23.58/11.09 thf(283,axiom,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((A @ nil_node @ nil_node) => ((((A @ B @ C) <= (! [D:node,E:list_node,F:node,G:list_node]: ((A @ (cons_node @ D @ E) @ (cons_node @ F @ G)) <= (A @ E @ G)))) <= (! [D:node,E:list_node]: (A @ nil_node @ (cons_node @ D @ E)))) <= (! [D:node,E:list_node]: (A @ (cons_node @ D @ E) @ nil_node)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_list__induct2_H)). 23.58/11.09 thf(1451,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((A @ nil_node @ nil_node) => ((A @ B @ C) | ~ (! [D:node,E:list_node,F:node,G:list_node]: ((A @ (cons_node @ D @ E) @ (cons_node @ F @ G)) | ~ (A @ E @ G))) | ~ (! [D:node,E:list_node]: (A @ nil_node @ (cons_node @ D @ E))) | ~ (! [D:node,E:list_node]: (A @ (cons_node @ D @ E) @ nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 23.58/11.09 thf(242,axiom,((! [A:g,B:list_node,C:node,D:node]: ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (append_node @ B @ (cons_node @ C @ nil_node))) => ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (append_node @ B @ (cons_node @ C @ (cons_node @ D @ nil_node)))) <= (member_node @ C @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_old_Opath__snoc)). 23.58/11.09 thf(1266,plain,((! [A:g,B:list_node,C:node,D:node]: ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (append_node @ B @ (cons_node @ C @ nil_node))) => ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (append_node @ B @ (cons_node @ C @ (cons_node @ D @ nil_node)))) | ~ (member_node @ C @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 23.58/11.09 thf(112,axiom,((! [A:list_node,B:list_node]: ((A = B) => (suffix_node @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_suffix__order_Oeq__refl)). 23.58/11.09 thf(654,plain,((! [A:list_node,B:list_node]: ((A = B) => (suffix_node @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 23.58/11.09 thf(223,axiom,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: (((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ (butlast_node @ C) @ E) @ F) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_old_Opath2__app_H)). 23.58/11.09 thf(1192,plain,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ (append_node @ (butlast_node @ C) @ E) @ F) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ D @ E @ F) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 23.58/11.09 thf(195,axiom,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ C @ (cons_node @ D @ E)) @ F) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ C @ (cons_node @ D @ nil_node)) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_old_Opath2__split_I1_J)). 23.58/11.09 thf(1050,plain,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ (append_node @ C @ (cons_node @ D @ E)) @ F) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ (append_node @ C @ (cons_node @ D @ nil_node)) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 23.58/11.09 thf(171,axiom,((! [A:node,B:list_node,C:list_node]: ((append_node @ (cons_node @ A @ B) @ C) = (cons_node @ A @ (append_node @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_append__Cons)). 23.58/11.09 thf(911,plain,((! [A:node,B:list_node,C:list_node]: ((append_node @ (cons_node @ A @ B) @ C) = (cons_node @ A @ (append_node @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 23.58/11.09 thf(132,axiom,((m != i)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_m__i__differ_I2_J)). 23.58/11.09 thf(721,plain,((~ (m = i))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 23.58/11.09 thf(277,axiom,((member_node @ pred_phi_r @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rs_H__props_I4_J)). 23.58/11.09 thf(1429,plain,((member_node @ pred_phi_r @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ g2 @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 23.58/11.09 thf(25,axiom,((! [A:list_list_node,B:list_node,C:list_list_node,D:list_node]: (((append_list_node @ A @ (cons_list_node @ B @ nil_list_node)) = (append_list_node @ C @ (cons_list_node @ D @ nil_list_node))) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_append1__eq__conv)). 23.58/11.09 thf(371,plain,((! [A:list_list_node,B:list_node,C:list_list_node,D:list_node]: (((append_list_node @ A @ (cons_list_node @ B @ nil_list_node)) = (append_list_node @ C @ (cons_list_node @ D @ nil_list_node))) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 23.58/11.09 thf(68,axiom,((~ (! [A:list_node]: (rs != (append_node @ ri @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H__rest_O_Ars_H_A_061_Ari_A_064_Ars_H__rest_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 23.58/11.09 thf(503,plain,((~ (! [A:list_node]: ~ (rs = (append_node @ ri @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 23.58/11.09 thf(71,axiom,((! [A:list_list_node,B:list_node,C:list_node,D:list_list_node,E:list_node,F:list_node]: (((append_list_node @ A @ (cons_list_node @ B @ (cons_list_node @ C @ D))) = (cons_list_node @ E @ (cons_list_node @ F @ nil_list_node))) = ((A = nil_list_node) & (E = B) & (F = C) & (D = nil_list_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_list__ee__eq__leel_I2_J)). 23.58/11.09 thf(515,plain,((! [A:list_list_node,B:list_node,C:list_node,D:list_list_node,E:list_node,F:list_node]: (((append_list_node @ A @ (cons_list_node @ B @ (cons_list_node @ C @ D))) = (cons_list_node @ E @ (cons_list_node @ F @ nil_list_node))) = ((A = nil_list_node) & (E = B) & (F = C) & (D = nil_list_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 23.58/11.09 thf(238,axiom,((! [A:list_node]: ((A != nil_node) = (? [B:node,C:list_node]: (A = (cons_node @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_neq__Nil__conv)). 23.58/11.09 thf(1249,plain,((! [A:list_node]: ((~ (A = nil_node)) = (? [B:node,C:list_node]: (A = (cons_node @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 23.58/11.09 thf(18,axiom,((! [A:list_list_node,B:list_list_node]: (((append_list_node @ A @ B) = A) = (B = nil_list_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_append__self__conv)). 23.58/11.09 thf(343,plain,((! [A:list_list_node,B:list_list_node]: (((append_list_node @ A @ B) = A) = (B = nil_list_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 23.58/11.09 thf(145,axiom,((! [A:(list_node > $o),B:list_node]: (((! [C:node]: (A @ (cons_node @ C @ nil_node))) => ((! [C:node,D:node,E:list_node]: (((A @ (cons_node @ D @ E)) => (A @ (cons_node @ C @ (cons_node @ D @ E)))) <= (A @ E))) => (A @ B))) <= (A @ nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_induct__list012)). 23.58/11.09 thf(792,plain,((! [A:(list_node > $o),B:list_node]: (((! [C:node]: (A @ (cons_node @ C @ nil_node))) => ((! [C:node,D:node,E:list_node]: (((A @ (cons_node @ D @ E)) => (A @ (cons_node @ C @ (cons_node @ D @ E)))) | ~ (A @ E))) => (A @ B))) | ~ (A @ nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 23.58/11.09 thf(69,axiom,((! [A:list_node,B:node]: (((member_node @ B @ (set_node2 @ A)) <= (member_node @ B @ (set_node2 @ (tl_node @ A)))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_list_Oset__sel_I2_J)). 23.58/11.09 thf(508,plain,((! [A:list_node,B:node]: ((member_node @ B @ (set_node2 @ A)) | ~ (member_node @ B @ (set_node2 @ (tl_node @ A))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 23.58/11.09 thf(143,axiom,((! [A:list_node,B:node,C:list_node,D:list_node,E:node,F:list_node]: (((((D = A) => ((F != C) <= (E = B))) => (~ (! [G:list_node]: ((C != (append_node @ G @ (cons_node @ E @ F))) <= (D = (append_node @ A @ (cons_node @ B @ G))))))) <= (! [G:list_node]: ((F != (append_node @ G @ (cons_node @ B @ C))) <= (A = (append_node @ D @ (cons_node @ E @ G)))))) <= ((append_node @ A @ (cons_node @ B @ C)) = (append_node @ D @ (cons_node @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_list__match__lel__lel)). 23.58/11.09 thf(765,plain,((! [A:list_node,B:node,C:list_node,D:list_node,E:node,F:list_node]: ((((D = A) => (~ (F = C) | ~ (E = B))) => (~ (! [G:list_node]: (~ (C = (append_node @ G @ (cons_node @ E @ F))) | ~ (D = (append_node @ A @ (cons_node @ B @ G))))))) | ~ (! [G:list_node]: (~ (F = (append_node @ G @ (cons_node @ B @ C))) | ~ (A = (append_node @ D @ (cons_node @ E @ G))))) | ~ ((append_node @ A @ (cons_node @ B @ C)) = (append_node @ D @ (cons_node @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 23.58/11.09 thf(118,axiom,((! [A:list_node]: ((append_node @ A @ nil_node) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_append__Nil2)). 23.58/11.09 thf(674,plain,((! [A:list_node]: ((append_node @ A @ nil_node) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 23.58/11.09 thf(191,axiom,((! [A:list_node,B:list_node,C:node,D:list_node]: (((~ (! [E:list_node]: ((A = (cons_node @ C @ E)) => ((append_node @ E @ B) != D)))) <= ((B != (cons_node @ C @ D)) <= (A = nil_node))) <= ((append_node @ A @ B) = (cons_node @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_list__append__eq__Cons__cases)). 23.58/11.09 thf(1026,plain,((! [A:list_node,B:list_node,C:node,D:list_node]: (~ (! [E:list_node]: ((A = (cons_node @ C @ E)) => (~ ((append_node @ E @ B) = D)))) | ~ (~ (B = (cons_node @ C @ D)) | ~ (A = nil_node)) | ~ ((append_node @ A @ B) = (cons_node @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 23.58/11.09 thf(32,axiom,(((append_node @ nil_node) = (^ [A:list_node]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_empty__append__eq__id)). 23.58/11.09 thf(398,plain,(((append_node @ nil_node) = (^ [A:list_node]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 23.58/11.09 thf(192,axiom,((! [A:((node > (node > $o)) > (list_node > $o)),B:(node > (node > $o)),C:list_node]: ((((A @ B @ C) <= (! [D:(node > (node > $o)),E:node,F:node,G:list_node]: ((A @ D @ (cons_node @ E @ (cons_node @ F @ G))) <= (A @ D @ (cons_node @ F @ G))))) <= (! [D:(node > (node > $o)),E:node]: (A @ D @ (cons_node @ E @ nil_node)))) <= (! [D:(node > (node > $o))]: (A @ D @ nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_successively_Oinduct)). 23.58/11.09 thf(1035,plain,((! [A:((node > (node > $o)) > (list_node > $o)),B:(node > (node > $o)),C:list_node]: ((A @ (B) @ C) | ~ (! [D:(node > (node > $o)),E:node,F:node,G:list_node]: ((A @ (D) @ (cons_node @ E @ (cons_node @ F @ G))) | ~ (A @ (D) @ (cons_node @ F @ G)))) | ~ (! [D:(node > (node > $o)),E:node]: (A @ (D) @ (cons_node @ E @ nil_node))) | ~ (! [D:(node > (node > $o))]: (A @ (D) @ nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 23.58/11.09 thf(42,axiom,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = B) = (A = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_append__self__conv2)). 23.58/11.09 thf(425,plain,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = B) = (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 23.58/11.09 thf(161,axiom,((! [A:list_node,B:list_node,C:node]: ((suffix_node @ A @ B) => (suffix_node @ A @ (cons_node @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_suffix__ConsI)). 23.58/11.09 thf(856,plain,((! [A:list_node,B:list_node,C:node]: ((suffix_node @ A @ B) => (suffix_node @ A @ (cons_node @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 23.58/11.09 thf(88,axiom,(((= @ list_node) = (^ [A:list_node,B:list_node]: ((suffix_node @ A @ B) & (suffix_node @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_suffix__order_Oorder_Oeq__iff)). 23.58/11.09 thf(573,plain,(((= @ list_node) = (^ [A:list_node,B:list_node]: ((suffix_node @ A @ B) & (suffix_node @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 23.58/11.09 thf(49,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ A @ C) <= (suffix_node @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_suffix__order_Oorder__trans)). 23.58/11.09 thf(444,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ A @ C) | ~ (suffix_node @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 23.58/11.09 thf(134,axiom,((~ (! [A:node,B:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ B @ A) => ((member_node @ A @ (set_node2 @ ms)) => ((~ (prefix_node @ B @ rs2)) <= (! [C:node]: ((member_node @ C @ (set_node2 @ (butlast_node @ B))) => (~ (member_node @ C @ (set_node2 @ ms))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 23.58/11.09 thf(733,plain,((~ (! [A:node,B:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ r) @ B @ A) => ((member_node @ A @ (set_node2 @ ms)) => (~ (prefix_node @ B @ rs2) | ~ (! [C:node]: ((member_node @ C @ (set_node2 @ (butlast_node @ B))) => (~ (member_node @ C @ (set_node2 @ ms))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 23.58/11.09 thf(95,axiom,((! [A:set_node,B:set_node,C:set_node,D:set_node]: ((A = B) => (((ord_less_eq_set_node @ A @ D) <= (C = D)) <= (ord_less_eq_set_node @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_ord__eq__le__eq__trans)). 23.58/11.09 thf(601,plain,((! [A:set_node,B:set_node,C:set_node,D:set_node]: ((A = B) => ((ord_less_eq_set_node @ A @ D) | ~ (C = D) | ~ (ord_less_eq_set_node @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 23.58/11.09 thf(213,axiom,((! [A:g,B:node,C:list_node,D:node]: (((~ (! [E:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ B) => ((member_node @ D @ (set_node2 @ E)) => ((~ (ord_less_eq_set_node @ (set_node2 @ E) @ (set_node2 @ C))) <= (~ (member_node @ B @ (set_node2 @ (tl_node @ (butlast_node @ E)))))))))) <= (member_node @ D @ (set_node2 @ C))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_old_Opath2__simple__loop)). 23.58/11.09 thf(1135,plain,((! [A:g,B:node,C:list_node,D:node]: (~ (! [E:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ E @ B) => ((member_node @ D @ (set_node2 @ E)) => (~ (ord_less_eq_set_node @ (set_node2 @ E) @ (set_node2 @ C)) | (member_node @ B @ (set_node2 @ (tl_node @ (butlast_node @ E)))))))) | ~ (member_node @ D @ (set_node2 @ C)) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 23.58/11.09 thf(37,axiom,((! [A:list_node,B:list_node,C:list_node]: ((((suffix_node @ C @ A) | (suffix_node @ A @ C)) <= (suffix_node @ C @ B)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_suffix__same__cases)). 23.58/11.09 thf(412,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ C @ A) | (suffix_node @ A @ C) | ~ (suffix_node @ C @ B) | ~ (suffix_node @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 23.58/11.09 thf(84,axiom,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = nil_node) = ((A = nil_node) & (B = nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_append__is__Nil__conv)). 23.58/11.09 thf(562,plain,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = nil_node) = ((A = nil_node) & (B = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 23.58/11.09 thf(187,axiom,((! [A:g,B:node,C:list_node,D:node,E:node]: (((~ (! [F:list_node,G:list_node,H:list_node]: ((C = (append_node @ F @ (append_node @ G @ H))) => (((suffix_node @ (cons_node @ E @ H) @ C) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ F @ (cons_node @ E @ nil_node)) @ E) => ((~ (member_node @ E @ (set_node2 @ F))) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ E) => ((member_node @ E @ (set_node2 @ H)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ (cons_node @ E @ H) @ D)))))) <= (prefix_node @ (append_node @ F @ (cons_node @ E @ nil_node)) @ C))))) <= (member_node @ E @ (set_node2 @ C))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_old_Opath2__split__first__last)). 23.58/11.09 thf(1007,plain,((! [A:g,B:node,C:list_node,D:node,E:node]: (~ (! [F:list_node,G:list_node,H:list_node]: ((C = (append_node @ F @ (append_node @ G @ H))) => (((suffix_node @ (cons_node @ E @ H) @ C) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ (append_node @ F @ (cons_node @ E @ nil_node)) @ E) => ((~ (member_node @ E @ (set_node2 @ F))) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ E @ G @ E) => ((member_node @ E @ (set_node2 @ H)) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ E @ (cons_node @ E @ H) @ D)))))) | ~ (prefix_node @ (append_node @ F @ (cons_node @ E @ nil_node)) @ C)))) | ~ (member_node @ E @ (set_node2 @ C)) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 23.58/11.09 thf(270,axiom,((! [A:list_node,B:node,C:list_node]: ((A != nil_node) <= (A = (cons_node @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_list_OdiscI)). 23.58/11.09 thf(1389,plain,((! [A:list_node,B:node,C:list_node]: (~ (A = nil_node) | ~ (A = (cons_node @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 23.58/11.09 thf(155,axiom,((! [A:g]: (invar @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_old_Oinvar)). 23.58/11.09 thf(843,plain,((! [A:g]: (invar @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 23.58/11.09 thf(233,axiom,((! [A:list_node,B:node]: (ord_less_eq_set_node @ (set_node2 @ A) @ (set_node2 @ (cons_node @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_set__subset__Cons)). 23.58/11.09 thf(1226,plain,((! [A:list_node,B:node]: (ord_less_eq_set_node @ (set_node2 @ A) @ (set_node2 @ (cons_node @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 23.58/11.09 thf(107,axiom,((! [A:set_node,B:(node > $o)]: ((ord_less_eq_set_node @ A @ (collect_node @ B)) = (! [C:node]: ((B @ C) <= (member_node @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_subset__Collect__conv)). 23.58/11.09 thf(641,plain,((! [A:set_node,B:(node > $o)]: ((ord_less_eq_set_node @ A @ (collect_node @ (B))) = (! [C:node]: ((B @ C) | ~ (member_node @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 23.58/11.09 thf(30,axiom,((! [A:list_node,B:list_node]: ((suffix_node @ (append_node @ A @ B) @ B) = (A = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_same__suffix__nil)). 23.58/11.09 thf(391,plain,((! [A:list_node,B:list_node]: ((suffix_node @ (append_node @ A @ B) @ B) = (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 23.58/11.09 thf(130,axiom,((i != (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_m__i__differ_I1_J)). 23.58/11.09 thf(713,plain,((~ (i = (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 23.58/11.09 thf(205,axiom,((rs2 = (append_node @ rs @ (cons_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r) @ nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_rs__def)). 23.58/11.09 thf(1107,plain,((rs2 = (append_node @ rs @ (cons_node @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r) @ nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 23.58/11.09 thf(174,axiom,((! [A:list_node,B:list_node]: ((((B != nil_node) <= (A != nil_node)) => ((! [C:node,D:list_node]: ((A = (append_node @ D @ (cons_node @ C @ nil_node))) => (! [E:node,F:list_node]: ((B = (append_node @ F @ (cons_node @ E @ nil_node))) => ((E = C) => (suffix_node @ D @ F)))))) => (~ (! [C:node]: ((? [D:list_node]: (A = (append_node @ D @ (cons_node @ C @ nil_node)))) => (! [D:node]: ((D = C) <= (? [E:list_node]: (B = (append_node @ E @ (cons_node @ D @ nil_node))))))))))) <= (~ (suffix_node @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_not__suffix__cases)). 23.58/11.09 thf(919,plain,((! [A:list_node,B:list_node]: (((~ (B = nil_node) | (A = nil_node)) => ((! [C:node,D:list_node]: ((A = (append_node @ D @ (cons_node @ C @ nil_node))) => (! [E:node,F:list_node]: ((B = (append_node @ F @ (cons_node @ E @ nil_node))) => ((E = C) => (suffix_node @ D @ F)))))) => (~ (! [C:node]: ((? [D:list_node]: (A = (append_node @ D @ (cons_node @ C @ nil_node)))) => (! [D:node]: ((D = C) | ~ (? [E:list_node]: (B = (append_node @ E @ (cons_node @ D @ nil_node))))))))))) | (suffix_node @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 23.58/11.09 thf(232,axiom,((~ (member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs2))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_rs__props_I3_J)). 23.58/11.09 thf(1224,plain,((~ (member_node @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ r) @ (set_node2 @ (tl_node @ rs2))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 23.58/11.09 thf(260,axiom,((~ (! [A:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ A @ i) => ((prefix_node @ A @ ms) => (member_node @ i @ (set_node2 @ (butlast_node @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 23.58/11.09 thf(1356,plain,((~ (! [A:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ m @ A @ i) => ((prefix_node @ A @ ms) => (member_node @ i @ (set_node2 @ (butlast_node @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 23.58/11.09 thf(182,axiom,((! [A:((node > (node > $o)) > (list_node > (list_node > $o))),B:(node > (node > $o)),C:list_node,D:list_node]: (((! [E:(node > (node > $o)),F:node,G:list_node,H:node,I:list_node]: ((A @ E @ (cons_node @ F @ G) @ (cons_node @ H @ I)) <= (A @ E @ G @ I))) => (((! [E:(node > (node > $o)),F:node,G:list_node]: (A @ E @ nil_node @ (cons_node @ F @ G))) => (A @ B @ C @ D)) <= (! [E:(node > (node > $o)),F:node,G:list_node]: (A @ E @ (cons_node @ F @ G) @ nil_node)))) <= (! [E:(node > (node > $o))]: (A @ E @ nil_node @ nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_list__all__zip_Oinduct)). 23.58/11.09 thf(979,plain,((! [A:((node > (node > $o)) > (list_node > (list_node > $o))),B:(node > (node > $o)),C:list_node,D:list_node]: (((! [E:(node > (node > $o)),F:node,G:list_node,H:node,I:list_node]: ((A @ (E) @ (cons_node @ F @ G) @ (cons_node @ H @ I)) | ~ (A @ (E) @ G @ I))) => (((! [E:(node > (node > $o)),F:node,G:list_node]: (A @ (E) @ nil_node @ (cons_node @ F @ G))) => (A @ (B) @ C @ D)) | ~ (! [E:(node > (node > $o)),F:node,G:list_node]: (A @ (E) @ (cons_node @ F @ G) @ nil_node)))) | ~ (! [E:(node > (node > $o))]: (A @ (E) @ nil_node @ nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 23.58/11.09 thf(227,axiom,((! [A:g,B:node,C:list_node,D:node]: ((member_node @ B @ (set_node2 @ (alpha_n @ A))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_old_Opath2__hd__in___092_060alpha_062n)). 23.58/11.09 thf(1209,plain,((! [A:g,B:node,C:list_node,D:node]: ((member_node @ B @ (set_node2 @ (alpha_n @ A))) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 23.58/11.09 thf(35,axiom,((! [A:list_node,B:list_node]: ((nil_node = (append_node @ A @ B)) = ((B = nil_node) & (A = nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Nil__is__append__conv)). 23.58/11.09 thf(406,plain,((! [A:list_node,B:list_node]: ((nil_node = (append_node @ A @ B)) = ((B = nil_node) & (A = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 23.58/11.09 thf(209,axiom,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) = (? [C:list_node,D:list_node]: (~ (member_node @ A @ (set_node2 @ D)) & (B = (append_node @ C @ (cons_node @ A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_in__set__conv__decomp__last)). 23.58/11.09 thf(1117,plain,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) = (? [C:list_node,D:list_node]: (~ (member_node @ A @ (set_node2 @ D)) & (B = (append_node @ C @ (cons_node @ A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 23.58/11.09 thf(27,axiom,((! [A:list_list_node,B:list_node,C:list_list_node,D:list_node]: (((append_list_node @ A @ (cons_list_node @ B @ C)) = (cons_list_node @ D @ nil_list_node)) = ((A = nil_list_node) & (C = nil_list_node) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_list__e__eq__lel_I2_J)). 23.58/11.09 thf(377,plain,((! [A:list_list_node,B:list_node,C:list_list_node,D:list_node]: (((append_list_node @ A @ (cons_list_node @ B @ C)) = (cons_list_node @ D @ nil_list_node)) = ((A = nil_list_node) & (C = nil_list_node) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 23.58/11.09 thf(291,axiom,((! [A:(list_node > $o),B:list_node]: (((A @ B) <= (A @ nil_node)) <= (! [C:node,D:list_node]: ((! [E:node,F:list_node]: ((D = (cons_node @ E @ F)) => (A @ D))) => (A @ (cons_node @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_min__list_Oinduct)). 23.58/11.09 thf(1492,plain,((! [A:(list_node > $o),B:list_node]: ((A @ B) | ~ (A @ nil_node) | ~ (! [C:node,D:list_node]: ((! [E:node,F:list_node]: ((D = (cons_node @ E @ F)) => (A @ D))) => (A @ (cons_node @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 23.58/11.09 thf(215,axiom,((! [A:list_node]: ((A != nil_node) => (A = (cons_node @ (hd_node @ A) @ (tl_node @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_list_Oexhaust__sel)). 23.58/11.09 thf(1144,plain,((! [A:list_node]: ((~ (A = nil_node)) => (A = (cons_node @ (hd_node @ A) @ (tl_node @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 23.58/11.09 thf(9,axiom,((! [A:list_list_node,B:list_list_node]: (((append_list_node @ A @ B) = B) = (A = nil_list_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_append__self__conv2)). 23.58/11.09 thf(318,plain,((! [A:list_list_node,B:list_list_node]: (((append_list_node @ A @ B) = B) = (A = nil_list_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 23.58/11.09 thf(211,axiom,((! [A:g,B:node,C:list_node,D:node,E:(node > (list_node > (node > $o)))]: ((((E @ B @ (cons_node @ B @ nil_node) @ B) <= (member_node @ B @ (set_node2 @ (alpha_n @ A)))) => ((E @ B @ C @ D) <= (! [F:list_node,G:node,H:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ G) => ((E @ B @ F @ G) => ((E @ B @ (append_node @ F @ (cons_node @ H @ nil_node)) @ H) <= (member_node @ G @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ H))))))))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_old_Opath2__rev__induct)). 23.58/11.09 thf(1122,plain,((! [A:g,B:node,C:list_node,D:node,E:(node > (list_node > (node > $o)))]: ((((E @ B @ (cons_node @ B @ nil_node) @ B) | ~ (member_node @ B @ (set_node2 @ (alpha_n @ A)))) => ((E @ B @ C @ D) | ~ (! [F:list_node,G:node,H:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ F @ G) => ((E @ B @ F @ G) => ((E @ B @ (append_node @ F @ (cons_node @ H @ nil_node)) @ H) | ~ (member_node @ G @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ H))))))))) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 23.58/11.09 thf(163,axiom,((! [A:list_node,B:node]: ((butlast_node @ (append_node @ A @ (cons_node @ B @ nil_node))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_butlast__snoc)). 23.58/11.09 thf(863,plain,((! [A:list_node,B:node]: ((butlast_node @ (append_node @ A @ (cons_node @ B @ nil_node))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 23.58/11.09 thf(65,axiom,((! [A:list_node]: ((A != nil_node) => (member_node @ (hd_node @ A) @ (set_node2 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_hd__in__set)). 23.58/11.09 thf(494,plain,((! [A:list_node]: ((~ (A = nil_node)) => (member_node @ (hd_node @ A) @ (set_node2 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 23.58/11.09 thf(24,axiom,((! [A:list_list_node,B:list_list_node,C:list_node]: ((A != nil_list_node) => (((append_list_node @ A @ B) = (cons_list_node @ C @ nil_list_node)) = ((A = (cons_list_node @ C @ nil_list_node)) & (B = nil_list_node)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_list__se__match_I1_J)). 23.58/11.09 thf(367,plain,((! [A:list_list_node,B:list_list_node,C:list_node]: ((~ (A = nil_list_node)) => (((append_list_node @ A @ B) = (cons_list_node @ C @ nil_list_node)) = ((A = (cons_list_node @ C @ nil_list_node)) & (B = nil_list_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 23.58/11.09 thf(97,axiom,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = A) = (B = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_append__self__conv)). 23.58/11.09 thf(609,plain,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = A) = (B = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 23.58/11.09 thf(157,axiom,((! [A:node,B:list_node,C:list_node]: ((suffix_node @ (cons_node @ A @ B) @ C) => (suffix_node @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_suffix__ConsD)). 23.58/11.09 thf(848,plain,((! [A:node,B:list_node,C:list_node]: ((suffix_node @ (cons_node @ A @ B) @ C) => (suffix_node @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 23.58/11.09 thf(220,axiom,((! [A:node,B:list_node]: ((~ (! [C:list_node,D:list_node]: (B != (append_node @ C @ (cons_node @ A @ D))))) <= (member_node @ A @ (set_node2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_in__set__list__format)). 23.58/11.09 thf(1177,plain,((! [A:node,B:list_node]: (~ (! [C:list_node,D:list_node]: ~ (B = (append_node @ C @ (cons_node @ A @ D)))) | ~ (member_node @ A @ (set_node2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 23.58/11.09 thf(73,axiom,((! [A:list_list_node,B:list_list_node,C:list_node]: ((A != nil_list_node) => (((append_list_node @ B @ A) = (cons_list_node @ C @ nil_list_node)) = ((A = (cons_list_node @ C @ nil_list_node)) & (B = nil_list_node)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_list__se__match_I2_J)). 23.58/11.09 thf(521,plain,((! [A:list_list_node,B:list_list_node,C:list_node]: ((~ (A = nil_list_node)) => (((append_list_node @ B @ A) = (cons_list_node @ C @ nil_list_node)) = ((A = (cons_list_node @ C @ nil_list_node)) & (B = nil_list_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 23.58/11.09 thf(183,axiom,((! [A:(list_node > $o),B:list_node]: (((! [C:node]: (A @ (cons_node @ C @ nil_node))) => ((! [C:node,D:node,E:list_node]: (((A @ (cons_node @ C @ E)) <= (C = D)) => (((A @ (cons_node @ D @ E)) <= (C != D)) => (A @ (cons_node @ C @ (cons_node @ D @ E)))))) => (A @ B))) <= (A @ nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_remdups__adj_Oinduct)). 23.58/11.09 thf(983,plain,((! [A:(list_node > $o),B:list_node]: (((! [C:node]: (A @ (cons_node @ C @ nil_node))) => ((! [C:node,D:node,E:list_node]: (((A @ (cons_node @ C @ E)) | ~ (C = D)) => (((A @ (cons_node @ D @ E)) | (C = D)) => (A @ (cons_node @ C @ (cons_node @ D @ E)))))) => (A @ B))) | ~ (A @ nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 23.58/11.09 thf(225,axiom,((! [A:list_node]: (((cons_node @ (hd_node @ A) @ (tl_node @ A)) = A) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_list_Ocollapse)). 23.58/11.09 thf(1198,plain,((! [A:list_node]: (((cons_node @ (hd_node @ A) @ (tl_node @ A)) = A) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 23.58/11.09 thf(178,axiom,((! [A:list_node,B:list_node,C:node]: ((prefix_node @ A @ (append_node @ B @ (cons_node @ C @ nil_node))) = ((prefix_node @ A @ B) | (A = (append_node @ B @ (cons_node @ C @ nil_node))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_prefix__snoc)). 23.58/11.09 thf(959,plain,((! [A:list_node,B:list_node,C:node]: ((prefix_node @ A @ (append_node @ B @ (cons_node @ C @ nil_node))) = ((prefix_node @ A @ B) | (A = (append_node @ B @ (cons_node @ C @ nil_node))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 23.58/11.09 thf(151,axiom,((! [A:node,B:list_node,C:list_node,D:node]: ((member_node @ A @ (set_node2 @ B)) => (member_node @ A @ (set_node2 @ (tl_node @ (append_node @ C @ (cons_node @ D @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_old_Oelem__set__implies__elem__tl__app__cons)). 23.58/11.09 thf(827,plain,((! [A:node,B:list_node,C:list_node,D:node]: ((member_node @ A @ (set_node2 @ B)) => (member_node @ A @ (set_node2 @ (tl_node @ (append_node @ C @ (cons_node @ D @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 23.58/11.09 thf(208,axiom,((! [A:g,B:node,C:node,D:list_node,E:list_node]: ((((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (cons_node @ C @ E)) <= (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (cons_node @ C @ D))) => (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (cons_node @ B @ (cons_node @ C @ E)))) <= (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (cons_node @ B @ (cons_node @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_old_Opath__by__tail)). 23.58/11.09 thf(1113,plain,((! [A:g,B:node,C:node,D:list_node,E:list_node]: ((((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (cons_node @ C @ E)) | ~ (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (cons_node @ C @ D))) => (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (cons_node @ B @ (cons_node @ C @ E)))) | ~ (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (cons_node @ B @ (cons_node @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 23.58/11.09 thf(262,axiom,((! [A:list_node,B:node,C:list_node,D:node]: (((append_node @ A @ (cons_node @ B @ C)) = (cons_node @ D @ nil_node)) = ((A = nil_node) & (B = D) & (C = nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_list__e__eq__lel_I2_J)). 23.58/11.09 thf(1364,plain,((! [A:list_node,B:node,C:list_node,D:node]: (((append_node @ A @ (cons_node @ B @ C)) = (cons_node @ D @ nil_node)) = ((A = nil_node) & (B = D) & (C = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 23.58/11.09 thf(204,axiom,((! [A:g,B:node,C:list_node,D:node,E:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => ((member_node @ E @ (set_node2 @ C)) => (~ (! [F:list_node]: (((prefix_node @ F @ C) => (member_node @ E @ (set_node2 @ (butlast_node @ F)))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_old_Opath2__prefix__ex)). 23.58/11.09 thf(1102,plain,((! [A:g,B:node,C:list_node,D:node,E:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => ((member_node @ E @ (set_node2 @ C)) => (~ (! [F:list_node]: (((prefix_node @ F @ C) => (member_node @ E @ (set_node2 @ (butlast_node @ F)))) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ F @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 23.58/11.09 thf(44,axiom,((! [A:node]: ((member_node @ A @ (set_node2 @ (butlast_node @ ri))) => (~ (member_node @ A @ (set_node2 @ ms)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_ri__props_I3_J)). 23.58/11.09 thf(431,plain,((! [A:node]: ((member_node @ A @ (set_node2 @ (butlast_node @ ri))) => (~ (member_node @ A @ (set_node2 @ ms)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 23.58/11.09 thf(113,axiom,((prefix_node @ ri @ rs)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_ri__rs_H__prefix)). 23.58/11.09 thf(658,plain,((prefix_node @ ri @ rs)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 23.58/11.09 thf(31,axiom,((! [A:list_node,B:list_node]: ((A = (append_node @ nil_node @ B)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_eq__Nil__appendI)). 23.58/11.09 thf(394,plain,((! [A:list_node,B:list_node]: ((A = (append_node @ nil_node @ B)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 23.58/11.09 thf(5,axiom,((! [A:(node > $o),B:(node > $o)]: ((! [C:node]: ((A @ C) = (B @ C))) => ((collect_node @ A) = (collect_node @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Collect__cong)). 23.58/11.09 thf(306,plain,((! [A:(node > $o),B:(node > $o)]: ((! [C:node]: ((A @ C) = (B @ C))) => ((collect_node @ (A)) = (collect_node @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 23.58/11.09 thf(218,axiom,((! [A:node,B:list_node,C:node,D:list_node]: (((cons_node @ A @ B) = (cons_node @ C @ D)) => ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_list__tail__coinc)). 23.58/11.09 thf(1166,plain,((! [A:node,B:list_node,C:node,D:list_node]: (((cons_node @ A @ B) = (cons_node @ C @ D)) => ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 23.58/11.09 thf(120,axiom,((! [A:list_node]: (suffix_node @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_suffix__order_Odual__order_Orefl)). 23.58/11.09 thf(680,plain,((! [A:list_node]: (suffix_node @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 23.58/11.09 thf(26,axiom,((! [A:list_node,B:list_node,C:list_node]: (((append_node @ A @ B) = (append_node @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_same__append__eq)). 23.58/11.09 thf(374,plain,((! [A:list_node,B:list_node,C:list_node]: (((append_node @ A @ B) = (append_node @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 23.58/11.09 thf(244,axiom,((! [A:list_node]: ((~ (! [B:list_node,C:node]: (A != (append_node @ B @ (cons_node @ C @ nil_node))))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_rev__exhaust)). 23.58/11.09 thf(1277,plain,((! [A:list_node]: (~ (! [B:list_node,C:node]: ~ (A = (append_node @ B @ (cons_node @ C @ nil_node)))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 23.58/11.09 thf(64,axiom,((! [A:list_node,B:list_node]: ((((butlast_node @ (append_node @ B @ A)) = (append_node @ B @ (butlast_node @ A))) <= (A != nil_node)) & ((A = nil_node) => ((butlast_node @ (append_node @ B @ A)) = (butlast_node @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_butlast__append)). 23.58/11.09 thf(487,plain,((! [A:list_node,B:list_node]: ((((butlast_node @ (append_node @ B @ A)) = (append_node @ B @ (butlast_node @ A))) | (A = nil_node)) & ((A = nil_node) => ((butlast_node @ (append_node @ B @ A)) = (butlast_node @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 23.58/11.09 thf(148,axiom,((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ms_H__props_I1_J)). 23.58/11.09 thf(812,plain,((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ m @ ms2 @ i)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 23.58/11.09 thf(200,axiom,((! [A:g,B:node,C:list_node]: ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (cons_node @ B @ C)) => (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (cons_node @ B @ nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_old_Opath__hd)). 23.58/11.09 thf(1081,plain,((! [A:g,B:node,C:list_node]: ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (cons_node @ B @ C)) => (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (cons_node @ B @ nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 23.58/11.09 thf(100,axiom,((! [A:list_node,B:list_node,C:list_node,D:list_node]: (((append_node @ A @ B) = (append_node @ C @ D)) = (? [E:list_node]: (((B = (append_node @ E @ D)) & ((append_node @ A @ E) = C)) | (((append_node @ E @ B) = D) & (A = (append_node @ C @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_append__eq__append__conv2)). 23.58/11.09 thf(617,plain,((! [A:list_node,B:list_node,C:list_node,D:list_node]: (((append_node @ A @ B) = (append_node @ C @ D)) = (? [E:list_node]: (((B = (append_node @ E @ D)) & ((append_node @ A @ E) = C)) | (((append_node @ E @ B) = D) & (A = (append_node @ C @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 23.58/11.09 thf(288,axiom,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => (((D != B) <= (C = (cons_node @ B @ nil_node))) => (~ ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (hd_node @ (tl_node @ C)) @ (tl_node @ C) @ D) => (~ (member_node @ B @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ (hd_node @ (tl_node @ C)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_old_Opath2__cases)). 23.58/11.09 thf(1472,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => ((~ (D = B) | ~ (C = (cons_node @ B @ nil_node))) => (~ ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (hd_node @ (tl_node @ C)) @ (tl_node @ C) @ D) => (~ (member_node @ B @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ (hd_node @ (tl_node @ C)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 23.58/11.09 thf(188,axiom,((rs = (append_node @ ri @ rs_rest))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_rs_H__rest__prop)). 23.58/11.09 thf(1018,plain,((rs = (append_node @ ri @ rs_rest))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 23.58/11.09 thf(81,axiom,((! [A:list_node]: ((suffix_node @ A @ nil_node) => (A = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_suffix__bot_Obot_Oextremum__uniqueI)). 23.58/11.09 thf(553,plain,((! [A:list_node]: ((suffix_node @ A @ nil_node) => (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 23.58/11.09 thf(194,axiom,((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_assms_I10_J)). 23.58/11.09 thf(1049,plain,((sSA_CF1252180629de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r @ r)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 23.58/11.09 thf(221,axiom,((! [A:node,B:list_node,C:list_node,D:list_node]: (((cons_node @ A @ B) = (append_node @ C @ D)) => ((~ (! [E:list_node]: ((C = (cons_node @ A @ E)) => ((append_node @ E @ D) != B)))) <= ((D != (cons_node @ A @ B)) <= (C = nil_node)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_list__Cons__eq__append__cases)). 23.58/11.09 thf(1181,plain,((! [A:node,B:list_node,C:list_node,D:list_node]: (((cons_node @ A @ B) = (append_node @ C @ D)) => (~ (! [E:list_node]: ((C = (cons_node @ A @ E)) => (~ ((append_node @ E @ D) = B)))) | ~ (~ (D = (cons_node @ A @ B)) | ~ (C = nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 23.58/11.09 thf(150,axiom,((! [A:g,B:list_node]: ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B) => (B != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_old_Opath__not__Nil)). 23.58/11.09 thf(823,plain,((! [A:g,B:list_node]: ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B) => (~ (B = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 23.58/11.09 thf(74,axiom,((! [A:list_list_node]: ((A != nil_list_node) => (((tl_list_node @ A) = nil_list_node) => (~ (! [B:list_node]: (A != (cons_list_node @ B @ nil_list_node)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_tl__obtain__elem)). 23.58/11.09 thf(525,plain,((! [A:list_list_node]: ((~ (A = nil_list_node)) => (((tl_list_node @ A) = nil_list_node) => (~ (! [B:list_node]: ~ (A = (cons_list_node @ B @ nil_list_node)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 23.58/11.09 thf(128,axiom,((! [A:node,B:g,C:node]: ((member_node @ A @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ B @ C))) => ((member_node @ A @ (set_node2 @ (alpha_n @ B))) <= (invar @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_old_Opredecessor__is__node)). 23.58/11.09 thf(707,plain,((! [A:node,B:g,C:node]: ((member_node @ A @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ B @ C))) => ((member_node @ A @ (set_node2 @ (alpha_n @ B))) | ~ (invar @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 23.58/11.09 thf(12,axiom,(((append_list_node @ nil_list_node) = (^ [A:list_list_node]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_empty__append__eq__id)). 23.58/11.09 thf(327,plain,(((append_list_node @ nil_list_node) = (^ [A:list_list_node]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 23.58/11.09 thf(239,axiom,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) = (? [C:list_node,D:list_node]: (~ (member_node @ A @ (set_node2 @ C)) & (B = (append_node @ C @ (cons_node @ A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_in__set__conv__decomp__first)). 23.58/11.09 thf(1252,plain,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) = (? [C:list_node,D:list_node]: (~ (member_node @ A @ (set_node2 @ C)) & (B = (append_node @ C @ (cons_node @ A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 23.58/11.09 thf(135,axiom,((! [A:g,B:node,C:node]: ~ (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ nil_node @ C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_old_Opath2__not__Nil2)). 23.58/11.09 thf(739,plain,((! [A:g,B:node,C:node]: ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ nil_node @ C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 23.58/11.09 thf(36,axiom,((! [A:list_list_node]: (((tl_list_node @ A) = nil_list_node) = ((A = nil_list_node) | ? [B:list_node]: (A = (cons_list_node @ B @ nil_list_node)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_tl__Nil)). 23.58/11.09 thf(409,plain,((! [A:list_list_node]: (((tl_list_node @ A) = nil_list_node) = ((A = nil_list_node) | ? [B:list_node]: (A = (cons_list_node @ B @ nil_list_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 23.58/11.09 thf(290,axiom,((! [A:list_node,B:node]: (((A = nil_node) => ((butlast_node @ (cons_node @ B @ A)) = nil_node)) & ((A != nil_node) => ((butlast_node @ (cons_node @ B @ A)) = (cons_node @ B @ (butlast_node @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_butlast_Osimps_I2_J)). 23.58/11.09 thf(1484,plain,((! [A:list_node,B:node]: (((A = nil_node) => ((butlast_node @ (cons_node @ B @ A)) = nil_node)) & ((~ (A = nil_node)) => ((butlast_node @ (cons_node @ B @ A)) = (cons_node @ B @ (butlast_node @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 23.58/11.09 thf(196,axiom,((! [A:g,B:list_node,C:node,D:list_node]: ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (append_node @ B @ (cons_node @ C @ D))) => (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ (append_node @ B @ (cons_node @ C @ nil_node)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_old_Opath__split_I1_J)). 23.58/11.09 thf(1053,plain,((! [A:g,B:list_node,C:node,D:list_node]: ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (append_node @ B @ (cons_node @ C @ D))) => (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (append_node @ B @ (cons_node @ C @ nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 23.58/11.09 thf(14,axiom,((! [A:list_list_node,B:list_list_node]: ((A = (append_list_node @ A @ B)) = (B = nil_list_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_self__append__conv)). 23.58/11.09 thf(331,plain,((! [A:list_list_node,B:list_list_node]: ((A = (append_list_node @ A @ B)) = (B = nil_list_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 23.58/11.09 thf(91,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => ((B = C) => (suffix_node @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_suffix__order_Oord__le__eq__trans)). 23.58/11.09 thf(585,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => ((B = C) => (suffix_node @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 23.58/11.09 thf(154,axiom,((! [A:node,B:list_node,C:node]: ((member_node @ A @ (set_node2 @ B)) => (member_node @ A @ (set_node2 @ (cons_node @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_list_Oset__intros_I2_J)). 23.58/11.09 thf(840,plain,((! [A:node,B:list_node,C:node]: ((member_node @ A @ (set_node2 @ B)) => (member_node @ A @ (set_node2 @ (cons_node @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 23.58/11.09 thf(236,axiom,((! [A:g,B:node,C:list_node,D:node]: ((C != nil_node) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_old_Opath2__not__Nil)). 23.58/11.09 thf(1235,plain,((! [A:g,B:node,C:list_node,D:node]: (~ (C = nil_node) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 23.58/11.09 thf(55,axiom,((! [A:list_node]: (prefix_node @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_prefix__order_Odual__order_Orefl)). 23.58/11.09 thf(463,plain,((! [A:list_node]: (prefix_node @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 23.58/11.09 thf(23,axiom,((! [A:list_list_node,B:list_list_node]: ((((butlast_list_node @ (append_list_node @ B @ A)) = (butlast_list_node @ B)) <= (A = nil_list_node)) & ((A != nil_list_node) => ((butlast_list_node @ (append_list_node @ B @ A)) = (append_list_node @ B @ (butlast_list_node @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_butlast__append)). 23.58/11.09 thf(359,plain,((! [A:list_list_node,B:list_list_node]: ((((butlast_list_node @ (append_list_node @ B @ A)) = (butlast_list_node @ B)) | ~ (A = nil_list_node)) & ((~ (A = nil_list_node)) => ((butlast_list_node @ (append_list_node @ B @ A)) = (append_list_node @ B @ (butlast_list_node @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 23.58/11.09 thf(231,axiom,((! [A:((node > (node > $o)) > (list_node > $o)),B:(node > (node > $o)),C:list_node]: ((! [D:(node > (node > $o))]: (A @ D @ nil_node)) => ((! [D:(node > (node > $o)),E:node,F:list_node]: ((A @ D @ F) => (A @ D @ (cons_node @ E @ F)))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_sorted__wrt_Oinduct)). 23.58/11.09 thf(1220,plain,((! [A:((node > (node > $o)) > (list_node > $o)),B:(node > (node > $o)),C:list_node]: ((! [D:(node > (node > $o))]: (A @ (D) @ nil_node)) => ((! [D:(node > (node > $o)),E:node,F:list_node]: ((A @ (D) @ F) => (A @ (D) @ (cons_node @ E @ F)))) => (A @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 23.58/11.09 thf(272,axiom,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((A @ nil_node @ nil_node) => ((! [D:node,E:list_node]: (A @ (append_node @ E @ (cons_node @ D @ nil_node)) @ nil_node)) => (((A @ B @ C) <= (! [D:node,E:list_node,F:node,G:list_node]: ((A @ E @ G) => (A @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node)))))) <= (! [D:node,E:list_node]: (A @ nil_node @ (append_node @ E @ (cons_node @ D @ nil_node))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_rev__induct2_H)). 23.58/11.09 thf(1404,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((A @ nil_node @ nil_node) => ((! [D:node,E:list_node]: (A @ (append_node @ E @ (cons_node @ D @ nil_node)) @ nil_node)) => ((A @ B @ C) | ~ (! [D:node,E:list_node,F:node,G:list_node]: ((A @ E @ G) => (A @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node))))) | ~ (! [D:node,E:list_node]: (A @ nil_node @ (append_node @ E @ (cons_node @ D @ nil_node))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 23.58/11.09 thf(214,axiom,((! [A:list_node]: ((A != nil_node) = (? [B:list_node,C:node]: (A = (append_node @ B @ (cons_node @ C @ nil_node))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_neq__Nil__rev__conv)). 23.58/11.09 thf(1141,plain,((! [A:list_node]: ((~ (A = nil_node)) = (? [B:list_node,C:node]: (A = (append_node @ B @ (cons_node @ C @ nil_node))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 23.58/11.09 thf(98,axiom,(((= @ list_node) = (^ [A:list_node,B:list_node]: ((suffix_node @ B @ A) & (suffix_node @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_suffix__order_Odual__order_Oeq__iff)). 23.58/11.09 thf(612,plain,(((= @ list_node) = (^ [A:list_node,B:list_node]: ((suffix_node @ B @ A) & (suffix_node @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 23.58/11.09 thf(66,axiom,((! [A:node,B:list_node,C:list_node]: ((member_node @ A @ (set_node2 @ (butlast_node @ (append_node @ B @ C)))) <= ((member_node @ A @ (set_node2 @ (butlast_node @ C))) | (member_node @ A @ (set_node2 @ (butlast_node @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_in__set__butlast__appendI)). 23.58/11.09 thf(497,plain,((! [A:node,B:list_node,C:list_node]: ((member_node @ A @ (set_node2 @ (butlast_node @ (append_node @ B @ C)))) | ~ ((member_node @ A @ (set_node2 @ (butlast_node @ C))) | (member_node @ A @ (set_node2 @ (butlast_node @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 23.58/11.09 thf(162,axiom,((! [A:((node > node) > (list_node > (list_node > $o))),B:(node > node),C:list_node,D:list_node]: ((! [E:(node > node),F:list_node]: (A @ E @ nil_node @ F)) => ((! [E:(node > node),F:node,G:list_node,H:list_node]: ((A @ E @ (cons_node @ F @ G) @ H) <= (A @ E @ G @ (cons_node @ (E @ F) @ H)))) => (A @ B @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_map__tailrec__rev_Oinduct)). 23.58/11.09 thf(859,plain,((! [A:((node > node) > (list_node > (list_node > $o))),B:(node > node),C:list_node,D:list_node]: ((! [E:(node > node),F:list_node]: (A @ (E) @ nil_node @ F)) => ((! [E:(node > node),F:node,G:list_node,H:list_node]: ((A @ (E) @ (cons_node @ F @ G) @ H) | ~ (A @ (E) @ G @ (cons_node @ (E @ F) @ H)))) => (A @ (B) @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 23.58/11.09 thf(237,axiom,((! [A:g,B:list_node,C:(list_node > $o)]: ((((C @ B) <= (! [D:list_node,E:node]: ((graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ D) => (((member_node @ E @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ (hd_node @ D)))) => (C @ (cons_node @ E @ D))) <= (C @ D))))) <= (! [D:node]: (((C @ (cons_node @ D @ nil_node)) <= (invar @ A)) <= (member_node @ D @ (set_node2 @ (alpha_n @ A)))))) <= (graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_old_Opath_Oinducts)). 23.58/11.09 thf(1240,plain,((! [A:g,B:list_node,C:(list_node > $o)]: ((C @ B) | ~ (! [D:list_node,E:node]: ((graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ D) => (((member_node @ E @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ (hd_node @ D)))) => (C @ (cons_node @ E @ D))) | ~ (C @ D)))) | ~ (! [D:node]: ((C @ (cons_node @ D @ nil_node)) | ~ (invar @ A) | ~ (member_node @ D @ (set_node2 @ (alpha_n @ A))))) | ~ (graph_435229452_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 23.58/11.09 thf(156,axiom,(((sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r) != (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062)). 23.58/11.09 thf(845,plain,((~ ((sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r) = (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ r)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 23.58/11.09 thf(56,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ (append_node @ A @ B) @ C) => (suffix_node @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_suffix__appendD)). 23.58/11.09 thf(465,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ (append_node @ A @ B) @ C) => (suffix_node @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 23.58/11.09 thf(103,axiom,((! [A:list_node,B:list_node,C:list_node]: ((A = B) => ((suffix_node @ B @ C) => (suffix_node @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_suffix__order_Oord__eq__le__trans)). 23.58/11.09 thf(627,plain,((! [A:list_node,B:list_node,C:list_node]: ((A = B) => ((suffix_node @ B @ C) => (suffix_node @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 23.58/11.09 thf(82,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ B @ C) => (suffix_node @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_suffix__order_Oorder_Otrans)). 23.58/11.09 thf(556,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ B @ C) => (suffix_node @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 23.58/11.09 thf(117,axiom,((! [A:list_node]: ((suffix_node @ A @ nil_node) = (A = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_suffix__bot_Obot_Oextremum__unique)). 23.58/11.09 thf(671,plain,((! [A:list_node]: ((suffix_node @ A @ nil_node) = (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 23.58/11.09 thf(246,axiom,((~ (member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_rs_H__loopfree)). 23.58/11.09 thf(1289,plain,((~ (member_node @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ r) @ (set_node2 @ (tl_node @ rs))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 23.58/11.09 thf(51,axiom,((! [A:list_node,B:list_node,C:list_list_node,D:list_node,E:list_node,F:list_list_node]: (((cons_list_node @ A @ (cons_list_node @ B @ nil_list_node)) = (append_list_node @ C @ (cons_list_node @ D @ (cons_list_node @ E @ F)))) = ((C = nil_list_node) & (B = E) & (F = nil_list_node) & (A = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_list__ee__eq__leel_I1_J)). 23.58/11.09 thf(450,plain,((! [A:list_node,B:list_node,C:list_list_node,D:list_node,E:list_node,F:list_list_node]: (((cons_list_node @ A @ (cons_list_node @ B @ nil_list_node)) = (append_list_node @ C @ (cons_list_node @ D @ (cons_list_node @ E @ F)))) = ((C = nil_list_node) & (B = E) & (F = nil_list_node) & (A = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 23.58/11.09 thf(201,axiom,((! [A:node,B:list_node,C:list_node,D:list_node,E:list_node]: ((~ (member_node @ A @ (set_node2 @ B))) => ((((append_node @ B @ (cons_node @ A @ C)) = (append_node @ D @ (cons_node @ A @ E))) = ((C = E) & (B = D))) <= (~ (member_node @ A @ (set_node2 @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_append__Cons__eq__iff)). 23.58/11.09 thf(1084,plain,((! [A:node,B:list_node,C:list_node,D:list_node,E:list_node]: ((~ (member_node @ A @ (set_node2 @ B))) => ((((append_node @ B @ (cons_node @ A @ C)) = (append_node @ D @ (cons_node @ A @ E))) = ((C = E) & (B = D))) | (member_node @ A @ (set_node2 @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 23.58/11.09 thf(181,axiom,((! [A:list_node,B:node,C:node,D:list_node,E:node,F:node]: (((append_node @ A @ (cons_node @ B @ (cons_node @ C @ D))) = (cons_node @ E @ (cons_node @ F @ nil_node))) = ((A = nil_node) & (D = nil_node) & (F = C) & (E = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_list__ee__eq__leel_I2_J)). 23.58/11.09 thf(976,plain,((! [A:list_node,B:node,C:node,D:list_node,E:node,F:node]: (((append_node @ A @ (cons_node @ B @ (cons_node @ C @ D))) = (cons_node @ E @ (cons_node @ F @ nil_node))) = ((A = nil_node) & (D = nil_node) & (F = C) & (E = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 23.58/11.09 thf(123,axiom,((! [A:list_node,B:list_list_node,C:list_node,D:list_list_node]: (((cons_list_node @ A @ nil_list_node) = (append_list_node @ B @ (cons_list_node @ C @ D))) = ((B = nil_list_node) & (C = A) & (D = nil_list_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_list__e__eq__lel_I1_J)). 23.58/11.09 thf(688,plain,((! [A:list_node,B:list_list_node,C:list_node,D:list_list_node]: (((cons_list_node @ A @ nil_list_node) = (append_list_node @ B @ (cons_list_node @ C @ D))) = ((B = nil_list_node) & (C = A) & (D = nil_list_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 23.58/11.09 thf(168,axiom,((! [A:node,B:g]: (((invar @ B) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ A @ (cons_node @ A @ nil_node) @ A)) <= (member_node @ A @ (set_node2 @ (alpha_n @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_old_Oempty__path2)). 23.58/11.09 thf(903,plain,((! [A:node,B:g]: (((invar @ B) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ B @ A @ (cons_node @ A @ nil_node) @ A)) | ~ (member_node @ A @ (set_node2 @ (alpha_n @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 23.58/11.09 thf(257,axiom,(((i != (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r)) => (((m != i) <= (i != (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r))) => (~ ((i != (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r)) => (m = i)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 23.58/11.09 thf(1341,plain,(((~ (i = (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r))) => ((~ (m = i) | (i = (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r))) => (~ ((~ (i = (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r))) => (m = i)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 23.58/11.09 thf(289,axiom,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: (((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ C @ (tl_node @ E)) @ F) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_old_Opath2__app)). 23.58/11.09 thf(1481,plain,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ (append_node @ C @ (tl_node @ E)) @ F) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ D @ E @ F) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 23.58/11.09 thf(111,axiom,((! [A:list_node]: (prefix_node @ nil_node @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_prefix__code_I1_J)). 23.58/11.09 thf(652,plain,((! [A:list_node]: (prefix_node @ nil_node @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 23.58/11.09 thf(104,axiom,((! [A:set_node]: ((collect_node @ (^ [B:node]: (member_node @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Collect__mem__eq)). 23.58/11.09 thf(632,plain,((! [A:set_node]: ((collect_node @ (^ [B:node]: (member_node @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 23.58/11.09 thf(149,axiom,((! [A:(list_node > $o),B:list_node]: (((! [C:node,D:list_node]: ((A @ D) => (A @ (cons_node @ C @ D)))) => (A @ B)) <= (A @ nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_list_Oinducts)). 23.58/11.09 thf(813,plain,((! [A:(list_node > $o),B:list_node]: (((! [C:node,D:list_node]: ((A @ D) => (A @ (cons_node @ C @ D)))) => (A @ B)) | ~ (A @ nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 23.58/11.09 thf(269,axiom,((! [A:list_node]: ((~ (! [B:list_node,C:node]: (A != (append_node @ B @ (cons_node @ C @ nil_node))))) <= (A != nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_neq__Nil__revE)). 23.58/11.09 thf(1385,plain,((! [A:list_node]: (~ (! [B:list_node,C:node]: ~ (A = (append_node @ B @ (cons_node @ C @ nil_node)))) | (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 23.58/11.09 thf(86,axiom,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ (butlast_node @ B))) => (member_node @ A @ (set_node2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_in__set__butlastD)). 23.58/11.09 thf(568,plain,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ (butlast_node @ B))) => (member_node @ A @ (set_node2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 23.58/11.09 thf(172,axiom,((! [A:g,B:node,C:list_node,D:node]: ((member_node @ D @ (set_node2 @ C)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_old_Opath2__last__in__ns)). 23.58/11.09 thf(914,plain,((! [A:g,B:node,C:list_node,D:node]: ((member_node @ D @ (set_node2 @ C)) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 23.58/11.09 thf(45,axiom,((! [A:list_node,B:list_list_node,C:list_node,D:list_list_node]: (((cons_list_node @ A @ B) = (cons_list_node @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_list_Oinject)). 23.58/11.09 thf(433,plain,((! [A:list_node,B:list_list_node,C:list_node,D:list_list_node]: (((cons_list_node @ A @ B) = (cons_list_node @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 23.58/11.09 thf(281,axiom,((ri = (append_node @ tmp @ (cons_node @ i @ nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__092_060open_062ri_A_061_Atmp_A_064_A_091i_093_092_060close_062)). 23.58/11.09 thf(1440,plain,((ri = (append_node @ tmp @ (cons_node @ i @ nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 23.58/11.09 thf(253,axiom,((! [A:list_node,B:(node > $o)]: ((~ (! [C:list_node,D:node,E:list_node]: (((B @ D) => (~ (! [F:node]: ((~ (B @ F)) <= (member_node @ F @ (set_node2 @ E)))))) <= (A = (append_node @ C @ (cons_node @ D @ E)))))) <= (? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_split__list__last__propE)). 23.58/11.09 thf(1308,plain,((! [A:list_node,B:(node > $o)]: (~ (! [C:list_node,D:node,E:list_node]: (((B @ D) => (~ (! [F:node]: (~ (B @ F) | ~ (member_node @ F @ (set_node2 @ E)))))) | ~ (A = (append_node @ C @ (cons_node @ D @ E))))) | ~ (? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 23.58/11.09 thf(61,axiom,((! [A:list_node]: ((suffix_node @ A @ nil_node) = (A = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_suffix__Nil)). 23.58/11.09 thf(478,plain,((! [A:list_node]: ((suffix_node @ A @ nil_node) = (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 23.58/11.09 thf(228,axiom,((! [A:node,B:list_node,C:list_node,D:list_node]: (((cons_node @ A @ B) = (append_node @ C @ D)) = (? [E:list_node]: (((cons_node @ A @ E) = C) & (B = (append_node @ E @ D))) | ((C = nil_node) & ((cons_node @ A @ B) = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_Cons__eq__append__conv)). 23.58/11.09 thf(1212,plain,((! [A:node,B:list_node,C:list_node,D:list_node]: (((cons_node @ A @ B) = (append_node @ C @ D)) = (? [E:list_node]: (((cons_node @ A @ E) = C) & (B = (append_node @ E @ D))) | ((C = nil_node) & ((cons_node @ A @ B) = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 23.58/11.09 thf(29,axiom,((! [A:list_node,B:list_node]: (((A = nil_node) => ((hd_node @ (append_node @ A @ B)) = (hd_node @ B))) & ((A != nil_node) => ((hd_node @ (append_node @ A @ B)) = (hd_node @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_hd__append)). 23.58/11.09 thf(383,plain,((! [A:list_node,B:list_node]: (((A = nil_node) => ((hd_node @ (append_node @ A @ B)) = (hd_node @ B))) & ((~ (A = nil_node)) => ((hd_node @ (append_node @ A @ B)) = (hd_node @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 23.58/11.09 thf(122,axiom,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => (~ (! [C:list_node]: (B != (append_node @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_suffixE)). 23.58/11.09 thf(684,plain,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => (~ (! [C:list_node]: ~ (B = (append_node @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 23.58/11.09 thf(19,axiom,((! [A:list_list_node]: ((append_list_node @ A @ nil_list_node) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_append__Nil2)). 23.58/11.09 thf(346,plain,((! [A:list_list_node]: ((append_list_node @ A @ nil_list_node) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 23.58/11.09 thf(282,axiom,((! [A:g,B:node,C:list_node,D:node,E:(node > $o)]: (((? [F:node]: ((E @ F) & (member_node @ F @ (set_node2 @ C)))) => (~ (! [F:node,G:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ G @ F) => (((~ (prefix_node @ G @ C)) <= (! [H:node]: ((member_node @ H @ (set_node2 @ (butlast_node @ G))) => (~ (E @ H))))) <= (E @ F)))))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_old_Opath2__split__first__prop)). 23.58/11.09 thf(1442,plain,((! [A:g,B:node,C:list_node,D:node,E:(node > $o)]: (((? [F:node]: ((E @ F) & (member_node @ F @ (set_node2 @ C)))) => (~ (! [F:node,G:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ G @ F) => (~ (prefix_node @ G @ C) | ~ (! [H:node]: ((member_node @ H @ (set_node2 @ (butlast_node @ G))) => (~ (E @ H)))) | ~ (E @ F)))))) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 23.58/11.09 thf(77,axiom,(((butlast_list_node @ nil_list_node) = nil_list_node)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_butlast_Osimps_I1_J)). 23.58/11.09 thf(536,plain,(((butlast_list_node @ nil_list_node) = nil_list_node)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 23.58/11.09 thf(131,axiom,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((((A @ B @ C) <= (! [D:node,E:list_node,F:node,G:list_node]: ((A @ E @ (cons_node @ F @ G)) => ((A @ (cons_node @ D @ E) @ G) => (A @ (cons_node @ D @ E) @ (cons_node @ F @ G)))))) <= (! [D:list_node]: (A @ D @ nil_node))) <= (! [D:list_node]: (A @ nil_node @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_shuffles_Oinduct)). 23.58/11.09 thf(716,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((A @ B @ C) | ~ (! [D:node,E:list_node,F:node,G:list_node]: ((A @ E @ (cons_node @ F @ G)) => ((A @ (cons_node @ D @ E) @ G) => (A @ (cons_node @ D @ E) @ (cons_node @ F @ G))))) | ~ (! [D:list_node]: (A @ D @ nil_node)) | ~ (! [D:list_node]: (A @ nil_node @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 23.58/11.09 thf(138,axiom,((! [A:node,B:list_node,C:node,D:list_node]: (((cons_node @ A @ nil_node) = (append_node @ B @ (cons_node @ C @ D))) = ((B = nil_node) & (C = A) & (D = nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_list__e__eq__lel_I1_J)). 23.58/11.09 thf(752,plain,((! [A:node,B:list_node,C:node,D:list_node]: (((cons_node @ A @ nil_node) = (append_node @ B @ (cons_node @ C @ D))) = ((B = nil_node) & (C = A) & (D = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 23.58/11.09 thf(50,axiom,((! [A:list_node,B:list_node,C:list_node]: (((suffix_node @ C @ A) => (suffix_node @ C @ B)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_suffix__order_Odual__order_Otrans)). 23.58/11.09 thf(447,plain,((! [A:list_node,B:list_node,C:list_node]: (((suffix_node @ C @ A) => (suffix_node @ C @ B)) | ~ (suffix_node @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 23.58/11.09 thf(8,axiom,((! [A:list_list_node]: ((append_list_node @ A @ nil_list_node) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_append_Oright__neutral)). 23.58/11.09 thf(315,plain,((! [A:list_list_node]: ((append_list_node @ A @ nil_list_node) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 23.58/11.09 thf(153,axiom,((~ (! [A:list_node]: (ri != (append_node @ A @ (cons_node @ i @ nil_node)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062tmp_O_Ari_A_061_Atmp_A_064_A_091i_093_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 23.58/11.09 thf(835,plain,((~ (! [A:list_node]: ~ (ri = (append_node @ A @ (cons_node @ i @ nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 23.58/11.09 thf(268,axiom,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) => (? [C:list_node,D:list_node]: ((B = (append_node @ C @ (cons_node @ A @ D))) & ~ (member_node @ A @ (set_node2 @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_split__list__first)). 23.58/11.09 thf(1380,plain,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) => (? [C:list_node,D:list_node]: ((B = (append_node @ C @ (cons_node @ A @ D))) & ~ (member_node @ A @ (set_node2 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 23.58/11.09 thf(41,axiom,((! [A:list_node]: ((append_node @ nil_node @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_append__Nil)). 23.58/11.09 thf(422,plain,((! [A:list_node]: ((append_node @ nil_node @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 23.58/11.09 thf(184,axiom,((! [A:node,B:list_node,C:node,D:list_node]: ((suffix_node @ (cons_node @ A @ B) @ (cons_node @ C @ D)) => (suffix_node @ B @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_suffix__ConsD2)). 23.58/11.09 thf(999,plain,((! [A:node,B:list_node,C:node,D:list_node]: ((suffix_node @ (cons_node @ A @ B) @ (cons_node @ C @ D)) => (suffix_node @ B @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 23.58/11.09 thf(101,axiom,((! [A:list_node,B:list_node,C:list_node,D:list_node,E:list_node]: (((append_node @ A @ B) = C) => (((append_node @ A @ D) = (append_node @ C @ E)) <= (D = (append_node @ B @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_append__eq__appendI)). 23.58/11.09 thf(620,plain,((! [A:list_node,B:list_node,C:list_node,D:list_node,E:list_node]: (((append_node @ A @ B) = C) => (((append_node @ A @ D) = (append_node @ C @ E)) | ~ (D = (append_node @ B @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 23.58/11.09 thf(59,axiom,((prefix_node @ ms2 @ ms)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_ms_H__props_I2_J)). 23.58/11.09 thf(474,plain,((prefix_node @ ms2 @ ms)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 23.58/11.09 thf(197,axiom,((! [A:node,B:list_node,C:node]: (((member_node @ C @ (set_node2 @ B)) => (((A = C) => (! [D:list_node,E:list_node]: (B != (append_node @ D @ (cons_node @ C @ E))))) => (((A != C) => (! [D:list_node,E:list_node,F:list_node]: (B != (append_node @ D @ (cons_node @ A @ (append_node @ E @ (cons_node @ C @ F))))))) => (~ ((A != C) => (! [D:list_node,E:list_node,F:list_node]: (B != (append_node @ D @ (cons_node @ C @ (append_node @ E @ (cons_node @ A @ F))))))))))) <= (member_node @ A @ (set_node2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_xy__in__set__cases)). 23.58/11.09 thf(1056,plain,((! [A:node,B:list_node,C:node]: (((member_node @ C @ (set_node2 @ B)) => (((A = C) => (! [D:list_node,E:list_node]: ~ (B = (append_node @ D @ (cons_node @ C @ E))))) => (((~ (A = C)) => (! [D:list_node,E:list_node,F:list_node]: ~ (B = (append_node @ D @ (cons_node @ A @ (append_node @ E @ (cons_node @ C @ F))))))) => (~ ((~ (A = C)) => (! [D:list_node,E:list_node,F:list_node]: ~ (B = (append_node @ D @ (cons_node @ C @ (append_node @ E @ (cons_node @ A @ F))))))))))) | ~ (member_node @ A @ (set_node2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 23.58/11.09 thf(33,axiom,((! [A:list_node,B:list_node]: ((A = (append_node @ A @ B)) = (B = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_self__append__conv)). 23.58/11.09 thf(400,plain,((! [A:list_node,B:list_node]: ((A = (append_node @ A @ B)) = (B = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 23.58/11.09 thf(105,axiom,((! [A:set_val]: ((collect_val @ (^ [B:val]: (member_val @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Collect__mem__eq)). 23.58/11.09 thf(635,plain,((! [A:set_val]: ((collect_val @ (^ [B:val]: (member_val @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 23.58/11.09 thf(126,axiom,((! [A:(list_node > $o),B:list_node]: ((A @ nil_node) => ((! [C:node,D:list_node]: ((A @ D) => (A @ (append_node @ D @ (cons_node @ C @ nil_node))))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_rev__induct)). 23.58/11.09 thf(696,plain,((! [A:(list_node > $o),B:list_node]: ((A @ nil_node) => ((! [C:node,D:list_node]: ((A @ D) => (A @ (append_node @ D @ (cons_node @ C @ nil_node))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 23.58/11.09 thf(38,axiom,(((butlast_node @ nil_node) = nil_node)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_butlast_Osimps_I1_J)). 23.58/11.09 thf(415,plain,(((butlast_node @ nil_node) = nil_node)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 23.58/11.09 thf(259,axiom,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((! [D:list_node]: (A @ nil_node @ D)) => ((A @ B @ C) <= (! [D:node,E:list_node,F:list_node]: ((A @ (cons_node @ D @ E) @ F) <= (A @ E @ (cons_node @ D @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_revg_Oinduct)). 23.58/11.09 thf(1352,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((! [D:list_node]: (A @ nil_node @ D)) => ((A @ B @ C) | ~ (! [D:node,E:list_node,F:list_node]: ((A @ (cons_node @ D @ E) @ F) | ~ (A @ E @ (cons_node @ D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 23.58/11.09 thf(89,axiom,((! [A:list_list_node,B:list_node]: (((A = nil_list_node) => ((butlast_list_node @ (cons_list_node @ B @ A)) = nil_list_node)) & (((butlast_list_node @ (cons_list_node @ B @ A)) = (cons_list_node @ B @ (butlast_list_node @ A))) <= (A != nil_list_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_butlast_Osimps_I2_J)). 23.58/11.09 thf(575,plain,((! [A:list_list_node,B:list_node]: (((A = nil_list_node) => ((butlast_list_node @ (cons_list_node @ B @ A)) = nil_list_node)) & (((butlast_list_node @ (cons_list_node @ B @ A)) = (cons_list_node @ B @ (butlast_list_node @ A))) | (A = nil_list_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 23.58/11.09 thf(108,axiom,((! [A:list_node,B:list_node]: ((A = (append_node @ B @ A)) = (B = nil_node)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_self__append__conv2)). 23.58/11.09 thf(644,plain,((! [A:list_node,B:list_node]: ((A = (append_node @ B @ A)) = (B = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 23.58/11.09 thf(170,axiom,((! [A:list_node,B:list_node,C:node]: ((suffix_node @ A @ (append_node @ B @ (cons_node @ C @ nil_node))) = (? [D:list_node]: ((A = (append_node @ D @ (cons_node @ C @ nil_node))) & (suffix_node @ D @ B)) | (A = nil_node))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_suffix__snoc)). 23.58/11.09 thf(908,plain,((! [A:list_node,B:list_node,C:node]: ((suffix_node @ A @ (append_node @ B @ (cons_node @ C @ nil_node))) = (? [D:list_node]: ((A = (append_node @ D @ (cons_node @ C @ nil_node))) & (suffix_node @ D @ B)) | (A = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 23.58/11.09 thf(158,axiom,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (hd_node @ C) @ C @ D) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_old_Opath2__forget__hd)). 23.58/11.09 thf(850,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (hd_node @ C) @ C @ D) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 23.58/11.09 thf(186,axiom,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) => (? [C:list_node,D:list_node]: (B = (append_node @ C @ (cons_node @ A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_split__list)). 23.58/11.09 thf(1004,plain,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) => (? [C:list_node,D:list_node]: (B = (append_node @ C @ (cons_node @ A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 23.58/11.09 thf(250,axiom,((! [A:node,B:list_node,C:node,D:list_node]: ((prefix_node @ (cons_node @ A @ B) @ (cons_node @ C @ D)) = ((prefix_node @ B @ D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_Cons__prefix__Cons)). 23.58/11.09 thf(1299,plain,((! [A:node,B:list_node,C:node,D:list_node]: ((prefix_node @ (cons_node @ A @ B) @ (cons_node @ C @ D)) = ((prefix_node @ B @ D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 23.58/11.09 thf(124,axiom,((prefix_node @ ri @ rs2)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_ri__props_I4_J)). 23.58/11.09 thf(691,plain,((prefix_node @ ri @ rs2)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 23.58/11.09 thf(48,axiom,((! [A:list_node]: (prefix_node @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_prefix__order_Oorder__refl)). 23.58/11.09 thf(442,plain,((! [A:list_node]: (prefix_node @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 23.58/11.09 thf(210,axiom,((! [A:g,B:node,C:list_node,D:node]: ((member_node @ D @ (set_node2 @ (alpha_n @ A))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_old_Opath2__tl__in___092_060alpha_062n)). 23.58/11.09 thf(1120,plain,((! [A:g,B:node,C:list_node,D:node]: ((member_node @ D @ (set_node2 @ (alpha_n @ A))) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 23.58/11.09 thf(16,axiom,((! [A:list_list_node,B:list_node,C:list_list_node]: (((butlast_list_node @ A) = (cons_list_node @ B @ C)) = (? [D:list_node]: (A = (cons_list_node @ B @ (append_list_node @ C @ (cons_list_node @ D @ nil_list_node)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_butlast__eq__cons__conv)). 23.58/11.09 thf(337,plain,((! [A:list_list_node,B:list_node,C:list_list_node]: (((butlast_list_node @ A) = (cons_list_node @ B @ C)) = (? [D:list_node]: (A = (cons_list_node @ B @ (append_list_node @ C @ (cons_list_node @ D @ nil_list_node)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 23.58/11.09 thf(263,axiom,((! [A:g,B:node,C:list_node,D:node,E:node]: (((member_node @ E @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ B))) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ (cons_node @ E @ C) @ D)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_old_OCons__path2)). 23.58/11.09 thf(1367,plain,((! [A:g,B:node,C:list_node,D:node,E:node]: (((member_node @ E @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ B))) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ E @ (cons_node @ E @ C) @ D)) | ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 23.58/11.09 thf(139,axiom,((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_rs_H__props_I1_J)). 23.58/11.09 thf(755,plain,((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ r) @ rs @ pred_phi_r)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 23.58/11.09 thf(202,axiom,((! [A:g,B:node,C:list_node,D:node,E:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => ((member_node @ D @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ E))) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ C @ (cons_node @ E @ nil_node)) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_old_Opath2__snoc)). 23.58/11.09 thf(1088,plain,((! [A:g,B:node,C:list_node,D:node,E:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => ((member_node @ D @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ E))) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ (append_node @ C @ (cons_node @ E @ nil_node)) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 23.58/11.09 thf(6,axiom,((! [A:list_list_node]: ((A != nil_list_node) => ((cons_list_node @ (hd_list_node @ A) @ (tl_list_node @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_list_Ocollapse)). 23.58/11.09 thf(309,plain,((! [A:list_list_node]: ((~ (A = nil_list_node)) => ((cons_list_node @ (hd_list_node @ A) @ (tl_list_node @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 23.58/11.09 thf(114,axiom,((! [A:list_node,B:list_node]: ? [C:list_node,D:list_node,E:list_node]: (((D = nil_node) | ((hd_node @ D) != (hd_node @ E)) | (E = nil_node)) & (B = (append_node @ C @ E)) & (A = (append_node @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_longest__common__prefix)). 23.58/11.09 thf(659,plain,((! [A:list_node,B:list_node]: ? [C:list_node,D:list_node,E:list_node]: (((D = nil_node) | ~ ((hd_node @ D) = (hd_node @ E)) | (E = nil_node)) & (B = (append_node @ C @ E)) & (A = (append_node @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 23.58/11.09 thf(1542,plain,($false),inference(cvc4,[status(thm)],[1190,760,962,1110,481,1024,1469,1315,518,666,1295,1422,1073,1269,597,1437,1173,878,440,614,677,533,550,500,1260,340,538,1078,1426,1001,782,417,565,436,1228,724,570,1430,1323,949,460,1462,1132,559,1147,1319,606,881,1232,638,853,475,1465,1373,1418,485,1151,1020,806,905,1302,756,1109,321,353,966,1377,1215,692,866,453,1394,1351,1433,312,293,956,428,1201,292,380,512,529,1306,810,334,952,349,1217,1370,746,1091,1255,302,625,852,329,1296,757,1281,456,324,916,467,583,830,682,1195,1291,710,742,874,650,1375,403,356,593,420,471,1361,1461,669,1414,590,1039,547,706,647,1451,1266,654,1192,1050,911,721,1429,371,503,515,1249,343,792,508,765,674,1026,398,1035,425,856,573,444,733,601,1135,412,562,1007,1389,843,1226,641,391,713,1107,919,1224,1356,979,1209,406,1117,377,1492,1144,318,1122,863,494,367,609,848,1177,521,983,1198,959,827,1113,1364,1102,431,658,394,306,1166,680,374,1277,487,812,1081,617,1472,1018,553,1049,1181,823,525,707,327,1252,739,409,1484,1053,331,585,840,1235,463,359,1220,1404,1141,612,497,859,1240,845,465,627,556,671,1289,450,1084,976,688,903,1341,1481,652,632,813,1385,568,914,433,1440,1308,478,1212,383,684,346,1442,536,716,752,447,315,835,1380,422,999,620,474,1056,400,635,696,415,1352,575,644,908,850,1004,1299,691,442,1120,337,1367,755,1088,309,659])). 23.58/11.09 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 23.58/11.09 % [INFO] Killing All external provers ... 23.58/11.09 FINAL WATCH: 23.2 CPU 8.9 WC 23.58/11.09 Killed 1 orphans 23.58/11.09 Killed 1 orphans 23.58/11.09 EOF