0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39 0.18/0.43 % Computer : n010.cluster.edu 0.18/0.43 % Model : x86_64 x86_64 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.43 % Memory : 8046.5625MB 0.18/0.43 % OS : Linux 6.8.0-71-generic 0.18/0.43 % CPULimit : 1440 0.18/0.43 % WCLimit : 180 0.18/0.43 % DateTime : Mon Jul 27 11:24:04 UTC 2026 0.18/0.43 % CPUTime : 0.18/0.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39 1.12/1.04 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 3.23/1.61 % [INFO] Parsing done (566ms). 3.23/1.64 % [INFO] Running in sequential loop mode. 4.53/2.18 % [INFO] eprover registered as external prover. 4.53/2.19 % [INFO] Scanning for conjecture ... 4.87/2.39 % [INFO] Found a conjecture (or negated_conjecture) and 351 axioms. Running axiom selection ... 5.79/2.68 % [INFO] Axiom selection finished. Selected 239 axioms (removed 112 axioms). 7.43/3.10 % [INFO] Problem is higher-order (TPTP THF). 7.43/3.15 % [INFO] Type checking passed. 7.89/3.16 % [CONFIG] Using configuration: timeout(180) with strategy. Searching for refutation ... 42.45/14.19 % External prover 'e' found a proof! 42.45/14.19 % [INFO] Killing All external provers ... 42.45/14.19 % Time passed: 13599ms (effective reasoning time: 12542ms) 42.45/14.19 % Solved by strategy 42.45/14.19 % Axioms used in derivation (239): fact_162_neq__NilE, fact_241_list__Cons__eq__append__cases, fact_70_old_OEntryPath__suffix, fact_205_list__match__lel__lel, fact_253_neq__Nil__rev__conv, fact_184_min__list_Oinduct, fact_288_split__list__last__prop__iff, fact_67_old_Odominates__unsnoc, fact_282_split__list__last__propE, fact_178_splice_Oinduct, fact_227_list__tail__coinc, fact_289_split__list__first__prop__iff, fact_42_old_Osuccessor__in___092_060alpha_062n, fact_52_old_Opath2__app, fact_101_old_Opath2__split_I2_J, fact_217_mergesort__by__rel__merge_Oinduct, fact_164_list_OdiscI, fact_195_suffix__ConsD2, fact_102_List_Ofinite__set, fact_223_longest__common__prefix_Oinduct, fact_329_suffix__same__cases, fact_87_hd__append2, fact_45_allDefs__finite, fact_44_old_Opath2__split__last__prop, fact_224_strict__sorted_Oinduct, fact_68_non__dominated__predecessor, fact_27_old_OEntry__reaches, fact_341_suffix__bot_Obot_Oextremum__uniqueI, fact_277_in__set__conv__decomp, fact_1_False, fact_332_append_Oleft__neutral, fact_330_finite__list, fact_23_old_Opredecessor__is__node, fact_133_list__ee__eq__leel_I1_J, fact_213_list__nonempty__induct, fact_350_old_OEntry__unreachable, fact_170_list_Oinducts, fact_24_old_Opath2__forget__hd, fact_135_list__ee__eq__leel_I2_J, fact_73_old_OEntry__no__predecessor, fact_18_old_Opath2__in___092_060alpha_062n, fact_6_old_O_092_060alpha_062n__distinct, fact_116_self__append__conv, fact_9_allDefs__disjoint_H, fact_160_list_Odistinct_I1_J, fact_229_distinct__length__2__or__more, fact_304_not__distinct__conv__prefix, fact_323_suffix__order_Oantisym__conv, fact_345_Nil__suffix, fact_31_defAss_H__extend, fact_106_empty__append__eq__id, fact_33_defAss_HI, fact_28_old_Oidom__ex, fact_10_assms_I7_J, fact_283_split__list__first__propE, fact_62_dominates__refl_H, fact_317_suffix__order_Odual__order_Oeq__iff, fact_231_list_Oset__cases, fact_120_append__Nil2, fact_233_set__ConsD, fact_41_defAss__dominating, fact_96_append__same__eq, fact_268_split__list__prop, fact_55_strict__dom__trans_H, fact_300_tl__obtain__elem, fact_32_defAss_H__def, fact_30_FormalSSA__Misc_Odistinct__hd__tl, fact_112_self__append__conv2, fact_334_append__Nil, fact_97_append__assoc, fact_16_old_Opath2__hd__in___092_060alpha_062n, fact_321_suffix__order_Oorder_Oantisym, fact_182_suffix__Cons, fact_99_suffix__order_Odual__order_Orefl, fact_319_suffix__order_Oord__le__eq__trans, fact_63_old_Odominates__path, fact_331_finite__list, fact_64_old_Odominates__mid, fact_259_neq__Nil__revE, fact_34_defAss_HE, fact_118_append__self__conv, fact_158_old_OCons__path2, fact_249_append__eq__Cons__conv, fact_75_old_OEntry__dominates, fact_53_defs__finite, fact_35_defAss__extend, fact_147_list__e__eq__lel_I2_J, fact_114_append__self__conv2, fact_5_old_OEntryPath__distinct, fact_316_suffix__order_Odual__order_Oantisym, fact_157_old_Oempty__path2, fact_83_old_Opath2__snoc, fact_310_list_Oexhaust__sel, fact_69_old_OisIdom__def, fact_293_distinct_Osimps_I2_J, fact_94_list_Oinject, fact_215_map__tailrec__rev_Oinduct, fact_72_old_Odominates__extend, fact_4_rs_H__props_I1_J, fact_336_eq__Nil__appendI, fact_2_old_OEntry__in__graph, fact_59_old_Odominates__antisymm, fact_40_phiDefs__in__allDefs, fact_60_dominates__trans_H, fact_90_same__suffix__nil, fact_149_snoc__suffix__snoc, fact_137_list__se__match_I1_J, fact_327_suffix__order_Oantisym, fact_318_suffix__order_Odual__order_Otrans, fact_348_suffix__appendI, fact_98_append_Oassoc, fact_189_suffix__ConsD, fact_294_distinct__match, fact_125_suffix__Nil, fact_110_Nil__is__append__conv, fact_25_old_OEntry__reachesE, fact_320_suffix__order_Oord__eq__le__trans, fact_11_defNode__eq, fact_324_suffix__order_Oorder__trans, fact_251_Cons__eq__append__conv, fact_19_old_Oinvar, fact_71_old_Odominates__unsnoc_H, fact_273_split__list__propE, fact_139_list__se__match_I2_J, fact_57_old_Odominates__trans, fact_322_suffix__order_Oorder_Oeq__iff, fact_314_append__eq__append__conv2, fact_13_defs__in__allDefs, fact_186_shuffles_Oinduct, fact_204_list__induct__first2, fact_270_xy__in__set__cases, fact_108_append__is__Nil__conv, fact_281_split__list__first__prop, fact_151_suffix__snoc, fact_302_not__distinct__decomp, fact_197_remdups__adj_Ocases, fact_272_split__list__first, fact_315_append__eq__appendI, fact_126_same__suffix__suffix, fact_7_rs_H__props_I3_J, fact_285_in__set__conv__decomp__last, fact_12_rs_H__props_I4_J, fact_61_dominates__antisymm_H, fact_81_in__hd__or__tl__conv, fact_38_defAssI, fact_76_old_OdominatesI, fact_56_old_Ostrict__dom__trans, fact_226_list_Osel_I3_J, fact_8_assms_I10_J, fact_237_list_Oset__intros_I2_J, fact_211_list__all__zip_Oinduct, fact_21_old_Opath2__last__in__ns, fact_228_not__Cons__self2, fact_15_FormalSSA__Misc_Oin__set__tlD, fact_46_old_Opath2__not__Nil, fact_58_old_Odominates__antitrans, fact_326_suffix__order_Oeq__refl, fact_298_tl__Nil, fact_202_remdups__adj_Oinduct, fact_279_in__set__list__format, fact_296_Nil__tl, fact_180_induct__list012, fact_48_mem__Collect__eq, fact_168_list_Oexhaust, fact_50_Collect__mem__eq, fact_129_old_OEntryPath__triv, fact_247_rev__nonempty__induct, fact_145_list__e__eq__lel_I1_J, fact_54_phiDefs__finite, fact_103_List_Ofinite__set, fact_207_successively_Oinduct, fact_104_append_Oright__neutral, fact_306_not__suffix__induct, fact_49_Collect__mem__eq, fact_153_list_Ocollapse, fact_39_defAssD, fact_235_list_Oset__intros_I1_J, fact_225_list_Osel_I1_J, fact_0_old_Opath2__hd, fact_95_same__append__eq, fact_100_suffix__order_Oorder__refl, fact_190_suffix__ConsI, fact_194_list__2pre__induct, fact_183_Cons__eq__appendI, fact_78_old_Oreducible__def, fact_51_old_Opath2__not__Nil2, fact_84_old_Opath2__rev__induct, fact_22_old_Osuccessor__is__node, fact_176_list__induct2_H, fact_131_append1__eq__conv, fact_328_suffix__order_Oeq__iff, fact_93_old_Oelem__set__implies__elem__tl__app__cons, fact_166_revg_Oinduct, fact_91_old_Opath2__induct, fact_291_distinct__singleton, fact_349_suffix__appendD, fact_143_list__se__match_I4_J, fact_43_phiUses__finite, fact_280_split__list__last__prop, fact_77_old_OEntry__iff__unreachable, fact_128_old_OEntry__loop, fact_47_mem__Collect__eq, fact_156_rs__def, fact_325_suffix__order_Oorder_Otrans, fact_261_rev__exhaust, fact_257_rev__induct2_H, fact_245_rev__nonempty__induct2_H, fact_338_distinct_Osimps_I1_J, fact_181_min__list_Ocases, fact_287_in__set__conv__decomp__first, fact_36_assms_I8_J, fact_313_not__distinct__split__distinct, fact_221_mergesort__by__rel__merge__induct, fact_74_old_Odominates__refl, fact_200_append__Cons, fact_346_list_Osel_I2_J, fact_127_old_Opath2__split_I1_J, fact_85_tl__append2, fact_155_hd__Cons__tl, fact_188_transpose_Ocases, fact_239_list__append__eq__Cons__cases, fact_20_old_Opath2__tl__in___092_060alpha_062n, fact_263_rev__induct, fact_265_split__list, fact_275_append__Cons__eq__iff, fact_343_suffix__bot_Obot_Oextremum, fact_172_neq__Nil__conv, fact_123_suffix__bot_Obot_Oextremum__unique, fact_26__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_3_rs_H__props_I2_J, fact_267_split__list__last, fact_82_old_Opath2__cases, fact_65_old_Odominates__def, fact_17_old_Opath2__hd__in__ns, fact_37_defAss__def, fact_308_not__suffix__cases, fact_141_list__se__match_I3_J, fact_199_sorted__wrt_Oinduct, fact_66_old_OdominatesE 42.45/14.19 % No. of inferences in proof: 482 42.45/14.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 13599 ms resp. 12542 ms w/o parsing 43.09/14.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 43.09/14.36 thf(list_l1129649930D_node_type, type, list_l1129649930D_node: $tType). 43.09/14.36 thf(list_P738500740D_node_type, type, list_P738500740D_node: $tType). 43.09/14.36 thf(set_Pr1040144478D_node_type, type, set_Pr1040144478D_node: $tType). 43.09/14.36 thf(produc1453890942D_node_type, type, produc1453890942D_node: $tType). 43.09/14.36 thf(list_P561207620_edgeD_type, type, list_P561207620_edgeD: $tType). 43.09/14.36 thf(option_list_val_type, type, option_list_val: $tType). 43.09/14.36 thf(produc1432036078de_val_type, type, produc1432036078de_val: $tType). 43.09/14.36 thf(list_list_node_type, type, list_list_node: $tType). 43.09/14.36 thf(list_node_type, type, list_node: $tType). 43.09/14.36 thf(list_val_type, type, list_val: $tType). 43.09/14.36 thf(set_node_type, type, set_node: $tType). 43.09/14.36 thf(set_val_type, type, set_val: $tType). 43.09/14.36 thf(node_type, type, node: $tType). 43.09/14.36 thf(val_type, type, val: $tType). 43.09/14.36 thf(g_type, type, g: $tType). 43.09/14.36 thf(finite_finite_node_decl, type, finite_finite_node: (set_node > $o)). 43.09/14.36 thf(finite_finite_val_decl, type, finite_finite_val: (set_val > $o)). 43.09/14.36 thf(graph_1994935542_edgeD_decl, type, graph_1994935542_edgeD: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > ((g > node) > (g > (list_node > $o))))))). 43.09/14.36 thf(graph_1670286392_edgeD_decl, type, graph_1670286392_edgeD: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > ((g > node) > (g > (node > (node > $o)))))))). 43.09/14.36 thf(graph_436675702_edgeD_decl, type, graph_436675702_edgeD: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > ((g > node) > (g > (node > (node > $o)))))))). 43.09/14.36 thf(graph_1947481694_edgeD_decl, type, graph_1947481694_edgeD: ((g > (node > list_P561207620_edgeD)) > (g > (node > list_P738500740D_node)))). 43.09/14.36 thf(graph_1012773594_edgeD_decl, type, graph_1012773594_edgeD: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > (g > (node > (list_node > (node > $o)))))))). 43.09/14.36 thf(graph_272749361_edgeD_decl, type, graph_272749361_edgeD: ((g > (node > list_P561207620_edgeD)) > (g > (node > list_node)))). 43.09/14.36 thf(append_node_decl, type, append_node: (list_node > (list_node > list_node))). 43.09/14.36 thf(distinct_node_decl, type, distinct_node: (list_node > $o)). 43.09/14.36 thf(cons_list_node_decl, type, cons_list_node: (list_node > (list_list_node > list_list_node))). 43.09/14.36 thf(cons_node_decl, type, cons_node: (node > (list_node > list_node))). 43.09/14.36 thf(nil_list_node_decl, type, nil_list_node: list_list_node). 43.09/14.36 thf(nil_Pr1769730692D_node_decl, type, nil_Pr1769730692D_node: list_P738500740D_node). 43.09/14.36 thf(nil_node_decl, type, nil_node: list_node). 43.09/14.36 thf(hd_node_decl, type, hd_node: (list_node > node)). 43.09/14.36 thf(set_node2_decl, type, set_node2: (list_node > set_node)). 43.09/14.36 thf(set_val2_decl, type, set_val2: (list_val > set_val)). 43.09/14.36 thf(tl_node_decl, type, tl_node: (list_node > list_node)). 43.09/14.36 thf(graph_589078910_edgeD_decl, type, graph_589078910_edgeD: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > ((g > node) > (g > $o)))))). 43.09/14.36 thf(sSA_CF139593942de_val_decl, type, sSA_CF139593942de_val: ((g > (node > set_val)) > ((g > (produc1432036078de_val > option_list_val)) > (g > (node > set_val))))). 43.09/14.36 thf(sSA_CF1156973626eD_val_decl, type, sSA_CF1156973626eD_val: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > ((g > node) > ((g > (node > set_val)) > ((g > (produc1432036078de_val > option_list_val)) > (g > (node > (val > $o)))))))))). 43.09/14.36 thf(sSA_CF370335846de_val_decl, type, sSA_CF370335846de_val: ((g > (produc1432036078de_val > option_list_val)) > (g > (node > set_val)))). 43.09/14.36 thf(sSA_CF848637139eD_val_decl, type, sSA_CF848637139eD_val: ((g > list_node) > ((g > (node > list_P561207620_edgeD)) > ((g > (produc1432036078de_val > option_list_val)) > (g > (node > set_val)))))). 43.09/14.36 thf(sSA_CF551432799de_val_decl, type, sSA_CF551432799de_val: ((g > list_node) > ((g > (node > set_val)) > ((g > (produc1432036078de_val > option_list_val)) > (g > (val > node)))))). 43.09/14.36 thf(sSA_CF1252180629de_val_decl, type, sSA_CF1252180629de_val: ((g > list_node) > ((g > (node > set_val)) > ((g > (produc1432036078de_val > option_list_val)) > (g > (val > (val > $o))))))). 43.09/14.36 thf(sSA_CF1558836456eD_val_decl, type, sSA_CF1558836456eD_val: ((g > list_node) > ((g > $o) > ((g > (node > list_P561207620_edgeD)) > ((g > node) > ((g > (node > set_val)) > (g > (node > (val > $o))))))))). 43.09/14.36 thf(collect_node_decl, type, collect_node: ((node > $o) > set_node)). 43.09/14.36 thf(collect_val_decl, type, collect_val: ((val > $o) > set_val)). 43.09/14.36 thf(suffix_node_decl, type, suffix_node: (list_node > (list_node > $o))). 43.09/14.36 thf(member_node_decl, type, member_node: (node > (set_node > $o))). 43.09/14.36 thf(member_val_decl, type, member_val: (val > (set_val > $o))). 43.09/14.36 thf(entry_decl, type, entry: (g > node)). 43.09/14.36 thf(alpha_n_decl, type, alpha_n: (g > list_node)). 43.09/14.36 thf(phi_r_decl, type, phi_r: val). 43.09/14.36 thf(defs_decl, type, defs: (g > (node > set_val))). 43.09/14.36 thf(g2_decl, type, g2: g). 43.09/14.36 thf(inEdges_decl, type, inEdges: (g > (node > list_P561207620_edgeD))). 43.09/14.36 thf(invar_decl, type, invar: (g > $o)). 43.09/14.36 thf(m_decl, type, m: node). 43.09/14.36 thf(ms_decl, type, ms: list_node). 43.09/14.36 thf(n_decl, type, n: node). 43.09/14.36 thf(ns_decl, type, ns: list_node). 43.09/14.36 thf(phis_decl, type, phis: (g > (produc1432036078de_val > option_list_val))). 43.09/14.36 thf(pred_phi_r_decl, type, pred_phi_r: node). 43.09/14.36 thf(r_decl, type, r: val). 43.09/14.36 thf(rs_decl, type, rs: list_node). 43.09/14.36 thf(rs2_decl, type, rs2: list_node). 43.09/14.36 thf(s_decl, type, s: val). 43.09/14.36 thf(111,axiom,((! [A:((node > (node > $o)) > (list_node > (list_node > $o))),B:(node > (node > $o)),C:list_node,D:list_node]: ((! [E:(node > (node > $o))]: (A @ E @ nil_node @ nil_node)) => (((! [E:(node > (node > $o)),F:node,G:list_node]: (A @ E @ (cons_node @ F @ G) @ 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]: ((A @ E @ G @ I) => (A @ E @ (cons_node @ F @ G) @ (cons_node @ H @ I)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_list__all__zip_Oinduct)). 43.09/14.36 thf(809,plain,((! [A:((node > (node > $o)) > (list_node > (list_node > $o))),B:(node > (node > $o)),C:list_node,D:list_node]: ((! [E:(node > (node > $o))]: (A @ (E) @ nil_node @ nil_node)) => ((! [E:(node > (node > $o)),F:node,G:list_node,H:node,I:list_node]: ((A @ (E) @ G @ I) => (A @ (E) @ (cons_node @ F @ G) @ (cons_node @ H @ I)))) => ((! [E:(node > (node > $o)),F:node,G:list_node]: (A @ (E) @ (cons_node @ F @ G) @ nil_node)) => ((! [E:(node > (node > $o)),F:node,G:list_node]: (A @ (E) @ nil_node @ (cons_node @ F @ G))) => (A @ (B) @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 43.09/14.36 thf(202,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/sandbox/benchmark/theBenchmark.p',fact_12_rs_H__props_I4_J)). 43.09/14.36 thf(1168,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)],[202])). 43.09/14.36 thf(222,axiom,((! [A:g,B:node,C:val]: ((sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C) = (! [D:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (entry @ A) @ D @ B) => (? [E:node]: ((member_node @ E @ (set_node2 @ D)) & (member_val @ C @ (sSA_CF139593942de_val @ defs @ phis @ A @ E))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_defAss__def)). 43.09/14.36 thf(1237,plain,((! [A:g,B:node,C:val]: ((sSA_CF1156973626eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ (phis) @ A @ B @ C) = (! [D:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (entry @ A) @ D @ B) => (? [E:node]: ((member_node @ E @ (set_node2 @ D)) & (member_val @ C @ (sSA_CF139593942de_val @ (defs) @ (phis) @ A @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 43.09/14.36 thf(136,axiom,((! [A:g]: (member_node @ (entry @ A) @ (set_node2 @ (alpha_n @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_old_OEntry__in__graph)). 43.09/14.36 thf(909,plain,((! [A:g]: (member_node @ (entry @ A) @ (set_node2 @ (alpha_n @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 43.09/14.36 thf(76,axiom,((! [A:list_node,B:node,C:list_node]: ((((cons_node @ B @ nil_node) = (append_node @ C @ A)) = ((A = (cons_node @ B @ nil_node)) & (C = nil_node))) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_list__se__match_I4_J)). 43.09/14.36 thf(628,plain,((! [A:list_node,B:node,C:list_node]: ((~ (A = nil_node)) => (((cons_node @ B @ nil_node) = (append_node @ C @ A)) = ((A = (cons_node @ B @ nil_node)) & (C = nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 43.09/14.36 thf(212,axiom,((! [A:g,B:node,C:node,D:node,E:list_node]: (((((member_node @ C @ (set_node2 @ E)) <= (invar @ A)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ D)) <= (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D)) <= (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_old_Odominates__mid)). 43.09/14.36 thf(1200,plain,((! [A:g,B:node,C:node,D:node,E:list_node]: ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ C @ D) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ E @ D) => ((invar @ A) => (member_node @ C @ (set_node2 @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 43.09/14.36 thf(86,axiom,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((((! [D:node,E:list_node]: (A @ nil_node @ (append_node @ E @ (cons_node @ D @ nil_node)))) => ((! [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))))) => (A @ B @ C))) <= (! [D:node,E:list_node]: (A @ (append_node @ E @ (cons_node @ D @ nil_node)) @ nil_node))) <= (A @ nil_node @ nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_rev__induct2_H)). 43.09/14.36 thf(683,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)) => ((! [D:node,E:list_node]: (A @ nil_node @ (append_node @ E @ (cons_node @ D @ nil_node)))) => ((! [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))))) => (A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 43.09/14.36 thf(232,axiom,((! [A:g,B:list_node]: ((distinct_node @ B) <= (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_old_OEntryPath__distinct)). 43.09/14.36 thf(1290,plain,((! [A:g,B:list_node]: ((graph_1994935542_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B) => (distinct_node @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 43.09/14.36 thf(178,axiom,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => (C != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_old_Opath2__not__Nil)). 43.09/14.36 thf(1073,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (~ (C = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 43.09/14.36 thf(125,axiom,((! [A:g,B:node]: (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ (cons_node @ B @ nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_old_OEntryPath__triv)). 43.09/14.36 thf(873,plain,((! [A:g,B:node]: (graph_1994935542_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ (cons_node @ B @ nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 43.09/14.36 thf(4,axiom,((! [A:list_node]: ((append_node @ A @ nil_node) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_append_Oright__neutral)). 43.09/14.36 thf(247,plain,((! [A:list_node]: ((append_node @ A @ nil_node) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 43.09/14.36 thf(237,axiom,((! [A:g]: ((graph_589078910_edgeD @ alpha_n @ invar @ inEdges @ entry @ A) = (! [B:node,C:list_node]: ((? [D:node]: (! [E:node]: ((member_node @ E @ (set_node2 @ C)) => (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ E)) & (member_node @ D @ (set_node2 @ C)))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_old_Oreducible__def)). 43.09/14.36 thf(1305,plain,((! [A:g]: ((graph_589078910_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A) = (! [B:node,C:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ B) => (? [D:node]: (! [E:node]: ((member_node @ E @ (set_node2 @ C)) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ D @ E)) & (member_node @ D @ (set_node2 @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 43.09/14.36 thf(70,axiom,((! [A:list_node,B:list_node,C:(list_node > (list_node > $o))]: ((~ (suffix_node @ 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))) <= (D != F))) => ((! [D:node,E:list_node,F:node,G:list_node]: ((D = F) => (((C @ E @ G) => (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node)))) <= (~ (suffix_node @ E @ G))))) => (C @ A @ B))) <= (! [D:node,E:list_node]: (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ nil_node)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_not__suffix__induct)). 43.09/14.36 thf(597,plain,((! [A:list_node,B:list_node,C:(list_node > (list_node > $o))]: ((~ (suffix_node @ A @ B)) => ((! [D:node,E:list_node]: (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ nil_node)) => ((! [D:node,E:list_node,F:node,G:list_node]: ((~ (D = F)) => (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node))))) => ((! [D:node,E:list_node,F:node,G:list_node]: ((D = F) => ((~ (suffix_node @ E @ G)) => ((C @ E @ G) => (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node))))))) => (C @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 43.09/14.36 thf(179,axiom,((! [A:node,B:list_node]: ((distinct_node @ (cons_node @ A @ B)) = (~ (member_node @ A @ (set_node2 @ B)) & (distinct_node @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_distinct_Osimps_I2_J)). 43.09/14.36 thf(1078,plain,((! [A:node,B:list_node]: ((distinct_node @ (cons_node @ A @ B)) = (~ (member_node @ A @ (set_node2 @ B)) & (distinct_node @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 43.09/14.36 thf(194,axiom,((! [A:node,B:node,C:list_node]: (((A = B) | (member_node @ A @ (set_node2 @ C))) <= (member_node @ A @ (set_node2 @ (cons_node @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_set__ConsD)). 43.09/14.36 thf(1137,plain,((! [A:node,B:node,C:list_node]: ((member_node @ A @ (set_node2 @ (cons_node @ B @ C))) => ((A = B) | (member_node @ A @ (set_node2 @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 43.09/14.36 thf(228,axiom,((! [A:g,B:node]: ((((B != (entry @ A)) => (? [C:node]: (! [D:node]: ((D = C) <= (graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D)) & (graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C)))) <= (member_node @ B @ (set_node2 @ (alpha_n @ A)))) <= (invar @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_old_Oidom__ex)). 43.09/14.36 thf(1275,plain,((! [A:g,B:node]: ((invar @ A) => ((member_node @ B @ (set_node2 @ (alpha_n @ A))) => ((~ (B = (entry @ A))) => (? [C:node]: (! [D:node]: ((graph_1670286392_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ D) => (D = C)) & (graph_1670286392_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 43.09/14.36 thf(112,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ (append_node @ A @ B) @ C) => (suffix_node @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_suffix__appendD)). 43.09/14.36 thf(814,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)],[112])). 43.09/14.36 thf(219,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/sandbox/benchmark/theBenchmark.p',fact_4_rs_H__props_I1_J)). 43.09/14.36 thf(1222,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)],[219])). 43.09/14.36 thf(84,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/sandbox/benchmark/theBenchmark.p',fact_251_Cons__eq__append__conv)). 43.09/14.36 thf(670,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)],[84])). 43.09/14.36 thf(157,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/sandbox/benchmark/theBenchmark.p',fact_287_in__set__conv__decomp__first)). 43.09/14.36 thf(1001,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)],[157])). 43.09/14.36 thf(224,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]: ((B @ C) & (member_node @ C @ (set_node2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_split__list__propE)). 43.09/14.36 thf(1243,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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 43.09/14.36 thf(105,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/sandbox/benchmark/theBenchmark.p',fact_182_suffix__Cons)). 43.09/14.36 thf(782,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)],[105])). 43.09/14.36 thf(10,axiom,((! [A:list_node]: ((A != nil_node) => (~ (! [B:list_node,C:node]: (A != (append_node @ B @ (cons_node @ C @ nil_node)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_rev__exhaust)). 43.09/14.36 thf(288,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)],[10])). 43.09/14.36 thf(226,axiom,((! [A:node,B:list_node,C:node]: ((((((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))))))) => (~ ((! [D:list_node,E:list_node,F:list_node]: (B != (append_node @ D @ (cons_node @ C @ (append_node @ E @ (cons_node @ A @ F)))))) <= (A != C)))) <= ((A = C) => (! [D:list_node,E:list_node]: (B != (append_node @ D @ (cons_node @ C @ E)))))) <= (member_node @ C @ (set_node2 @ B))) <= (member_node @ A @ (set_node2 @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_xy__in__set__cases)). 43.09/14.36 thf(1254,plain,((! [A:node,B:list_node,C:node]: ((member_node @ A @ (set_node2 @ B)) => ((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)))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 43.09/14.36 thf(173,axiom,((! [A:node,B:g,C:node]: ((member_node @ A @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ B @ C))) => ((invar @ B) => (member_node @ A @ (set_node2 @ (alpha_n @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_old_Opredecessor__is__node)). 43.09/14.36 thf(1055,plain,((! [A:node,B:g,C:node]: ((member_node @ A @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ B @ C))) => ((invar @ B) => (member_node @ A @ (set_node2 @ (alpha_n @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 43.09/14.36 thf(231,axiom,((! [A:set_node]: ((finite_finite_node @ A) => (? [B:list_node]: ((set_node2 @ B) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_finite__list)). 43.09/14.36 thf(1287,plain,((! [A:set_node]: ((finite_finite_node @ A) => (? [B:list_node]: ((set_node2 @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 43.09/14.36 thf(106,axiom,((! [A:(list_node > $o),B:list_node]: ((A @ nil_node) => (((A @ B) <= (! [C:node,D:node,E:list_node]: ((A @ E) => (A @ (cons_node @ C @ (cons_node @ D @ E)))))) <= (! [C:node]: (A @ (cons_node @ C @ nil_node))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_list__induct__first2)). 43.09/14.36 thf(785,plain,((! [A:(list_node > $o),B:list_node]: ((A @ nil_node) => ((! [C:node]: (A @ (cons_node @ C @ nil_node))) => ((! [C:node,D:node,E:list_node]: ((A @ E) => (A @ (cons_node @ C @ (cons_node @ D @ E))))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 43.09/14.36 thf(52,axiom,((! [A:list_node]: (suffix_node @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_suffix__order_Oorder__refl)). 43.09/14.36 thf(504,plain,((! [A:list_node]: (suffix_node @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 43.09/14.36 thf(90,axiom,((! [A:set_val]: ((collect_val @ (^ [B:val]: (member_val @ B @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Collect__mem__eq)). 43.09/14.36 thf(702,plain,((! [A:set_val]: ((collect_val @ (^ [B:val]: (member_val @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 43.09/14.36 thf(109,axiom,((! [A:list_node,B:list_node]: ((nil_node = (append_node @ A @ B)) = ((B = nil_node) & (A = nil_node))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Nil__is__append__conv)). 43.09/14.36 thf(802,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)],[109])). 43.09/14.36 thf(209,axiom,((! [A:node,B:g,C:val]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ B @ A @ C) = (? [D:node]: ((member_node @ D @ (set_node2 @ (alpha_n @ B))) & (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ D @ A) & (member_val @ C @ (sSA_CF139593942de_val @ defs @ phis @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_defAss__dominating)). 43.09/14.36 thf(1191,plain,((! [A:node,B:g,C:val]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((sSA_CF1156973626eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ (phis) @ B @ A @ C) = (? [D:node]: ((member_node @ D @ (set_node2 @ (alpha_n @ B))) & (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ B @ D @ A) & (member_val @ C @ (sSA_CF139593942de_val @ (defs) @ (phis) @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 43.09/14.36 thf(59,axiom,((! [A:list_node]: ((~ (! [B:node,C:list_node]: (A != (cons_node @ B @ C)))) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_list_Oexhaust)). 43.09/14.36 thf(542,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)],[59])). 43.09/14.36 thf(197,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/sandbox/benchmark/theBenchmark.p',fact_285_in__set__conv__decomp__last)). 43.09/14.36 thf(1147,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)],[197])). 43.09/14.36 thf(124,axiom,((! [A:g,B:node,C:node]: ~ (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ nil_node @ C))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_old_Opath2__not__Nil2)). 43.09/14.36 thf(870,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)],[124])). 43.09/14.36 thf(151,axiom,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C))) => (~ (! [C:list_node,D:node]: (((B @ D) => (~ (! [E:node]: ((member_node @ E @ (set_node2 @ C)) => (~ (B @ E)))))) <= (? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_split__list__first__propE)). 43.09/14.36 thf(969,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]: (A = (append_node @ C @ (cons_node @ D @ E)))) => ((B @ D) => (~ (! [E:node]: ((member_node @ E @ (set_node2 @ C)) => (~ (B @ E)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 43.09/14.36 thf(8,axiom,((! [A:node,B:list_node,C:node,D:list_node]: ((suffix_node @ B @ D) <= (suffix_node @ (cons_node @ A @ B) @ (cons_node @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_suffix__ConsD2)). 43.09/14.36 thf(284,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)],[8])). 43.09/14.36 thf(189,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/sandbox/benchmark/theBenchmark.p',fact_18_old_Opath2__in___092_060alpha_062n)). 43.09/14.36 thf(1115,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)) => (member_node @ E @ (set_node2 @ (alpha_n @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 43.09/14.36 thf(16,axiom,((! [A:g]: ((graph_272749361_edgeD @ inEdges @ A @ (entry @ A)) = nil_node))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_old_OEntry__no__predecessor)). 43.09/14.36 thf(321,plain,((! [A:g]: ((graph_272749361_edgeD @ (inEdges) @ A @ (entry @ A)) = nil_node))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 43.09/14.36 thf(25,axiom,((! [A:node,B:list_node]: (nil_node != (cons_node @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_list_Odistinct_I1_J)). 43.09/14.36 thf(376,plain,((! [A:node,B:list_node]: ~ (nil_node = (cons_node @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 43.09/14.36 thf(74,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/sandbox/benchmark/theBenchmark.p',fact_151_suffix__snoc)). 43.09/14.36 thf(623,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)],[74])). 43.09/14.36 thf(114,axiom,((! [A:list_node,B:node,C:list_node]: ((A = (cons_node @ B @ C)) => (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_list_OdiscI)). 43.09/14.36 thf(834,plain,((! [A:list_node,B:node,C:list_node]: ((A = (cons_node @ B @ C)) => (~ (A = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 43.09/14.36 thf(149,axiom,((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_assms_I7_J)). 43.09/14.36 thf(966,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)],[149])). 43.09/14.36 thf(236,axiom,((! [A:g,B:node,C:node,D:node]: (((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D) <= (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D)) <= (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_dominates__trans_H)). 43.09/14.36 thf(1302,plain,((! [A:g,B:node,C:node,D:node]: ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ C @ D) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 43.09/14.36 thf(98,axiom,((! [A:list_node,B:list_node,C:list_node]: ((A = B) => ((suffix_node @ A @ C) <= (suffix_node @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_suffix__order_Oord__eq__le__trans)). 43.09/14.36 thf(756,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)],[98])). 43.09/14.36 thf(203,axiom,((! [A:g,B:node,C:node,D:node]: ((invar @ A) => (((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D) => (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D)) <= (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_old_Odominates__trans)). 43.09/14.36 thf(1169,plain,((! [A:g,B:node,C:node,D:node]: ((invar @ A) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ C @ D) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 43.09/14.36 thf(32,axiom,((! [A:node,B:list_node]: ((hd_node @ (cons_node @ A @ B)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_list_Osel_I1_J)). 43.09/14.36 thf(397,plain,((! [A:node,B:list_node]: ((hd_node @ (cons_node @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 43.09/14.36 thf(6,axiom,((! [A:list_val]: (finite_finite_val @ (set_val2 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_List_Ofinite__set)). 43.09/14.36 thf(265,plain,((! [A:list_val]: (finite_finite_val @ (set_val2 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 43.09/14.36 thf(118,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/sandbox/benchmark/theBenchmark.p',fact_200_append__Cons)). 43.09/14.36 thf(849,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)],[118])). 43.09/14.36 thf(11,axiom,((! [A:list_node]: (suffix_node @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_suffix__order_Odual__order_Orefl)). 43.09/14.36 thf(292,plain,((! [A:list_node]: (suffix_node @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 43.09/14.36 thf(26,axiom,((! [A:list_node]: ((A != nil_node) = (? [B:list_node,C:node]: (A = (append_node @ B @ (cons_node @ C @ nil_node))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_neq__Nil__rev__conv)). 43.09/14.36 thf(380,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)],[26])). 43.09/14.36 thf(60,axiom,((! [A:list_node,B:(list_node > $o)]: ((A != nil_node) => (((! [C:node,D:list_node]: (((B @ (cons_node @ C @ D)) <= (B @ D)) <= (D != nil_node))) => (B @ A)) <= (! [C:node]: (B @ (cons_node @ C @ nil_node))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_list__nonempty__induct)). 43.09/14.36 thf(546,plain,((! [A:list_node,B:(list_node > $o)]: ((~ (A = nil_node)) => ((! [C:node]: (B @ (cons_node @ C @ nil_node))) => ((! [C:node,D:list_node]: ((~ (D = nil_node)) => ((B @ D) => (B @ (cons_node @ C @ D))))) => (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 43.09/14.36 thf(99,axiom,((! [A:list_node]: ((~ (distinct_node @ A)) => (? [B:list_node,C:list_node,D:list_node,E:node]: (A = (append_node @ B @ (append_node @ (cons_node @ E @ nil_node) @ (append_node @ C @ (append_node @ (cons_node @ E @ nil_node) @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_not__distinct__decomp)). 43.09/14.36 thf(761,plain,((! [A:list_node]: ((~ (distinct_node @ A)) => (? [B:list_node,C:list_node,D:list_node,E:node]: (A = (append_node @ B @ (append_node @ (cons_node @ E @ nil_node) @ (append_node @ C @ (append_node @ (cons_node @ E @ nil_node) @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 43.09/14.36 thf(170,axiom,((! [A:list_node]: ((distinct_node @ A) => (~ (member_node @ (hd_node @ A) @ (set_node2 @ (tl_node @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_FormalSSA__Misc_Odistinct__hd__tl)). 43.09/14.36 thf(1047,plain,((! [A:list_node]: ((distinct_node @ A) => (~ (member_node @ (hd_node @ A) @ (set_node2 @ (tl_node @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 43.09/14.36 thf(18,axiom,((! [A:node,B:list_node]: ((cons_node @ A @ B) != B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_not__Cons__self2)). 43.09/14.36 thf(334,plain,((! [A:node,B:list_node]: ~ ((cons_node @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 43.09/14.36 thf(182,axiom,((! [A:g,B:node,C:val,D:list_node]: ((sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (entry @ A) @ D @ B) => (~ (! [E:node]: ((~ (member_val @ C @ (defs @ A @ E))) <= (member_node @ E @ (set_node2 @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_defAss_HE)). 43.09/14.36 thf(1091,plain,((! [A:g,B:node,C:val,D:list_node]: ((sSA_CF1558836456eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ A @ B @ C) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (entry @ A) @ D @ B) => (~ (! [E:node]: ((member_node @ E @ (set_node2 @ D)) => (~ (member_val @ C @ (defs @ A @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 43.09/14.36 thf(169,axiom,((! [A:node,B:g,C:node]: (((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C @ A) <= (! [D:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ (entry @ B) @ D @ A) => (member_node @ C @ (set_node2 @ D))))) <= (member_node @ A @ (set_node2 @ (alpha_n @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_old_OdominatesI)). 43.09/14.36 thf(1042,plain,((! [A:node,B:g,C:node]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((! [D:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ B @ (entry @ B) @ D @ A) => (member_node @ C @ (set_node2 @ D)))) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ B @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 43.09/14.36 thf(217,axiom,((! [A:list_node]: (finite_finite_node @ (set_node2 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_List_Ofinite__set)). 43.09/14.36 thf(1217,plain,((! [A:list_node]: (finite_finite_node @ (set_node2 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 43.09/14.36 thf(61,axiom,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((! [D:node,E:list_node,F:node,G:list_node]: ((A @ (cons_node @ D @ E) @ (cons_node @ F @ G)) <= ((A @ E @ G) <= (D = F)))) => ((! [D:list_node]: (A @ nil_node @ D)) => ((! [D:list_node]: (A @ D @ nil_node)) => (A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_longest__common__prefix_Oinduct)). 43.09/14.36 thf(561,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((! [D:node,E:list_node,F:node,G:list_node]: (((D = F) => (A @ E @ G)) => (A @ (cons_node @ D @ E) @ (cons_node @ F @ G)))) => ((! [D:list_node]: (A @ nil_node @ D)) => ((! [D:list_node]: (A @ D @ nil_node)) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 43.09/14.36 thf(35,axiom,((! [A:(list_node > $o),B:list_node]: (((! [C:node,D:list_node]: ((A @ (cons_node @ C @ D)) <= (A @ D))) => (A @ B)) <= (A @ nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_strict__sorted_Oinduct)). 43.09/14.36 thf(407,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)],[35])). 43.09/14.36 thf(39,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))) = ((E = B) & (F = C) & (D = nil_node) & (A = nil_node))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_list__ee__eq__leel_I2_J)). 43.09/14.36 thf(429,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))) = ((E = B) & (F = C) & (D = nil_node) & (A = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 43.09/14.36 thf(148,axiom,((! [A:list_node,B:(node > $o)]: ((? [C:list_node,D:node]: ((B @ D) & ! [E:node]: ((~ (B @ E)) <= (member_node @ E @ (set_node2 @ C))) & ? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E))))) <= (? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_split__list__first__prop)). 43.09/14.36 thf(957,plain,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A)))) => (? [C:list_node,D:node]: ((B @ D) & ! [E:node]: ((member_node @ E @ (set_node2 @ C)) => (~ (B @ E))) & ? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 43.09/14.36 thf(220,axiom,((! [A:g,B:node,C:node,D:node]: ((invar @ A) => ((((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ D) & (C != D)) => ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D) & (B != D))) <= ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C) & (B != C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_old_Ostrict__dom__trans)). 43.09/14.36 thf(1223,plain,((! [A:g,B:node,C:node,D:node]: ((invar @ A) => (((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) & ~ (B = C)) => (((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ C @ D) & ~ (C = D)) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ D) & ~ (B = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 43.09/14.36 thf(131,axiom,((! [A:set_node]: ((collect_node @ (^ [B:node]: (member_node @ B @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Collect__mem__eq)). 43.09/14.36 thf(894,plain,((! [A:set_node]: ((collect_node @ (^ [B:node]: (member_node @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 43.09/14.36 thf(117,axiom,((! [A:node,B:list_node,C:list_node]: ((suffix_node @ (cons_node @ A @ B) @ C) => (suffix_node @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_suffix__ConsD)). 43.09/14.36 thf(847,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)],[117])). 43.09/14.36 thf(127,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))) = ((B = D) & (C = E))) <= (~ (member_node @ A @ (set_node2 @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_append__Cons__eq__iff)). 43.09/14.36 thf(879,plain,((! [A:node,B:list_node,C:list_node,D:list_node,E:list_node]: ((~ (member_node @ A @ (set_node2 @ B))) => ((~ (member_node @ A @ (set_node2 @ C))) => (((append_node @ B @ (cons_node @ A @ C)) = (append_node @ D @ (cons_node @ A @ E))) = ((B = D) & (C = E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 43.09/14.36 thf(82,axiom,((((=) @ list_node) = (^ [A:list_node,B:list_node]: ((suffix_node @ A @ B) & (suffix_node @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_suffix__order_Odual__order_Oeq__iff)). 43.09/14.36 thf(665,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)],[82])). 43.09/14.36 thf(67,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/sandbox/benchmark/theBenchmark.p',fact_166_revg_Oinduct)). 43.09/14.36 thf(583,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((! [D:list_node]: (A @ nil_node @ D)) => ((! [D:node,E:list_node,F:list_node]: ((A @ E @ (cons_node @ D @ F)) => (A @ (cons_node @ D @ E) @ F))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 43.09/14.36 thf(48,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:node,G:list_node]: ((A @ E @ (cons_node @ F @ G)) => ((A @ (cons_node @ D @ E) @ (cons_node @ F @ G)) <= (A @ (cons_node @ D @ E) @ G))))) <= (! [D:list_node]: (A @ D @ nil_node)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_shuffles_Oinduct)). 43.09/14.36 thf(461,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((! [D:list_node]: (A @ nil_node @ D)) => ((! [D:list_node]: (A @ D @ nil_node)) => ((! [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))))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 43.09/14.36 thf(215,axiom,((! [A:node,B:g,C:node,D:val]: (((member_node @ C @ (set_node2 @ (alpha_n @ B))) => (((member_val @ D @ (sSA_CF139593942de_val @ defs @ phis @ B @ C)) => (A = C)) <= (member_val @ D @ (sSA_CF139593942de_val @ defs @ phis @ B @ A)))) <= (member_node @ A @ (set_node2 @ (alpha_n @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_allDefs__disjoint_H)). 43.09/14.36 thf(1210,plain,((! [A:node,B:g,C:node,D:val]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((member_node @ C @ (set_node2 @ (alpha_n @ B))) => ((member_val @ D @ (sSA_CF139593942de_val @ (defs) @ (phis) @ B @ A)) => ((member_val @ D @ (sSA_CF139593942de_val @ (defs) @ (phis) @ B @ C)) => (A = C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 43.09/14.36 thf(166,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/sandbox/benchmark/theBenchmark.p',fact_127_old_Opath2__split_I1_J)). 43.09/14.36 thf(1027,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)],[166])). 43.09/14.36 thf(210,axiom,((rs2 = (append_node @ rs @ (cons_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r) @ nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_rs__def)). 43.09/14.36 thf(1195,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)],[210])). 43.09/14.36 thf(17,axiom,((! [A:node,B:list_node,C:node,D:list_node]: (((B = D) & (A = C)) <= ((cons_node @ A @ B) = (cons_node @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_list__tail__coinc)). 43.09/14.36 thf(324,plain,((! [A:node,B:list_node,C:node,D:list_node]: (((cons_node @ A @ B) = (cons_node @ C @ D)) => ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 43.09/14.36 thf(161,axiom,((! [A:val,B:g,C:node]: ((member_val @ A @ (defs @ B @ C)) => (member_val @ A @ (sSA_CF139593942de_val @ defs @ phis @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_defs__in__allDefs)). 43.09/14.36 thf(1012,plain,((! [A:val,B:g,C:node]: ((member_val @ A @ (defs @ B @ C)) => (member_val @ A @ (sSA_CF139593942de_val @ (defs) @ (phis) @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 43.09/14.36 thf(139,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]: ((member_node @ F @ (set_node2 @ E)) => (~ (B @ F))) & (B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_split__list__last__prop__iff)). 43.09/14.36 thf(916,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]: ((member_node @ F @ (set_node2 @ E)) => (~ (B @ F))) & (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 43.09/14.36 thf(49,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/sandbox/benchmark/theBenchmark.p',fact_126_same__suffix__suffix)). 43.09/14.36 thf(467,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)],[49])). 43.09/14.36 thf(119,axiom,((! [A:list_node,B:list_node,C:list_node]: (((append_node @ A @ B) = (append_node @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_same__append__eq)). 43.09/14.36 thf(852,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)],[119])). 43.09/14.36 thf(41,axiom,((! [A:list_node,B:list_node]: ((suffix_node @ (append_node @ A @ B) @ B) = (A = nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_same__suffix__nil)). 43.09/14.36 thf(435,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)],[41])). 43.09/14.36 thf(88,axiom,((! [A:val,B:(val > $o)]: ((member_val @ A @ (collect_val @ B)) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_mem__Collect__eq)). 43.09/14.36 thf(697,plain,((! [A:val,B:(val > $o)]: ((member_val @ A @ (collect_val @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 43.09/14.36 thf(196,axiom,((! [A:g,B:node,C:val]: ((! [D:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (entry @ A) @ D @ B) => (? [E:node]: ((member_val @ C @ (defs @ A @ E)) & (member_node @ E @ (set_node2 @ D)))))) => (sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_defAss_HI)). 43.09/14.36 thf(1143,plain,((! [A:g,B:node,C:val]: ((! [D:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (entry @ A) @ D @ B) => (? [E:node]: ((member_val @ C @ (defs @ A @ E)) & (member_node @ E @ (set_node2 @ D)))))) => (sSA_CF1558836456eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 43.09/14.36 thf(187,axiom,((! [A:g,B:node,C:node]: ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C) => ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B) => (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_dominates__antisymm_H)). 43.09/14.36 thf(1111,plain,((! [A:g,B:node,C:node]: ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ C @ B) => (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 43.09/14.36 thf(183,axiom,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F) => (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ C @ (tl_node @ E)) @ F))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_old_Opath2__app)). 43.09/14.36 thf(1096,plain,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ D @ E @ F) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ (append_node @ C @ (tl_node @ E)) @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 43.09/14.36 thf(159,axiom,(((tl_node @ nil_node) = nil_node)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_list_Osel_I2_J)). 43.09/14.36 thf(1006,plain,(((tl_node @ nil_node) = nil_node)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 43.09/14.36 thf(29,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/sandbox/benchmark/theBenchmark.p',fact_97_append__assoc)). 43.09/14.36 thf(388,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)],[29])). 43.09/14.36 thf(69,axiom,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_suffix__order_Oeq__refl)). 43.09/14.36 thf(593,plain,((! [A:list_node,B:list_node]: ((A = B) => (suffix_node @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 43.09/14.36 thf(190,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))) => ((member_node @ C @ (set_node2 @ (alpha_n @ B))) <= (invar @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_old_Osuccessor__is__node)). 43.09/14.36 thf(1118,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) => (member_node @ C @ (set_node2 @ (alpha_n @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 43.09/14.36 thf(153,axiom,((! [A:g,B:node,C:list_node,D:node,E:(node > $o)]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => ((? [F:node]: ((member_node @ F @ (set_node2 @ C)) & (E @ F))) => (~ (! [F:node,G:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ F @ G @ D) => ((E @ F) => ((! [H:node]: ((~ (E @ H)) <= (member_node @ H @ (set_node2 @ (tl_node @ G))))) => (~ (suffix_node @ G @ C))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_old_Opath2__split__last__prop)). 43.09/14.36 thf(980,plain,((! [A:g,B:node,C:list_node,D:node,E:(node > $o)]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => ((? [F:node]: ((member_node @ F @ (set_node2 @ C)) & (E @ F))) => (~ (! [F:node,G:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ F @ G @ D) => ((E @ F) => ((! [H:node]: ((member_node @ H @ (set_node2 @ (tl_node @ G))) => (~ (E @ H)))) => (~ (suffix_node @ G @ C))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 43.09/14.36 thf(34,axiom,((! [A:list_node,B:list_node,C:node]: ((A != nil_node) => (((append_node @ A @ B) = (cons_node @ C @ nil_node)) = ((B = nil_node) & (A = (cons_node @ C @ nil_node))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_list__se__match_I1_J)). 43.09/14.36 thf(403,plain,((! [A:list_node,B:list_node,C:node]: ((~ (A = nil_node)) => (((append_node @ A @ B) = (cons_node @ C @ nil_node)) = ((B = nil_node) & (A = (cons_node @ C @ nil_node))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 43.09/14.36 thf(97,axiom,((! [A:list_node,B:list_node,C:list_node]: (((suffix_node @ B @ C) => (suffix_node @ A @ C)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_suffix__order_Oorder_Otrans)). 43.09/14.36 thf(753,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)],[97])). 43.09/14.36 thf(56,axiom,((((=) @ list_node) = (^ [A:list_node,B:list_node]: ((suffix_node @ A @ B) & (suffix_node @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_suffix__order_Oorder_Oeq__iff)). 43.09/14.36 thf(526,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)],[56])). 43.09/14.36 thf(216,axiom,((! [A:g,B:node,C:node,D:node,E:list_node]: ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C) => ((~ (member_node @ B @ (set_node2 @ (tl_node @ E)))) => (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_old_Odominates__extend)). 43.09/14.36 thf(1214,plain,((! [A:g,B:node,C:node,D:node,E:list_node]: ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ D @ E @ C) => ((~ (member_node @ B @ (set_node2 @ (tl_node @ E)))) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 43.09/14.36 thf(168,axiom,((! [A:g,B:node,C:list_node,D:node,E:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ E @ (cons_node @ E @ C) @ D) <= (member_node @ E @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_old_OCons__path2)). 43.09/14.36 thf(1039,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 @ (graph_272749361_edgeD @ (inEdges) @ A @ B))) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ E @ (cons_node @ E @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 43.09/14.36 thf(233,axiom,((! [A:node,B:g]: ((finite_finite_val @ (sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A)) <= (member_node @ A @ (set_node2 @ (alpha_n @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_phiUses__finite)). 43.09/14.36 thf(1292,plain,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => (finite_finite_val @ (sSA_CF848637139eD_val @ (alpha_n) @ (inEdges) @ (phis) @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 43.09/14.36 thf(143,axiom,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => (member_node @ B @ (set_node2 @ (alpha_n @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_old_Opath2__hd__in___092_060alpha_062n)). 43.09/14.36 thf(933,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (member_node @ B @ (set_node2 @ (alpha_n @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 43.09/14.36 thf(163,axiom,((! [A:list_node]: ((A != nil_node) => ((cons_node @ (hd_node @ A) @ (tl_node @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_hd__Cons__tl)). 43.09/14.36 thf(1016,plain,((! [A:list_node]: ((~ (A = nil_node)) => ((cons_node @ (hd_node @ A) @ (tl_node @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 43.09/14.36 thf(214,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/sandbox/benchmark/theBenchmark.p',fact_237_list_Oset__intros_I2_J)). 43.09/14.36 thf(1207,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)],[214])). 43.09/14.36 thf(188,axiom,((member_val @ r @ (sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_rs_H__props_I3_J)). 43.09/14.36 thf(1114,plain,((member_val @ r @ (sSA_CF848637139eD_val @ (alpha_n) @ (inEdges) @ (phis) @ g2 @ pred_phi_r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 43.09/14.36 thf(155,axiom,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => (finite_finite_val @ (sSA_CF139593942de_val @ defs @ phis @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_allDefs__finite)). 43.09/14.36 thf(997,plain,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => (finite_finite_val @ (sSA_CF139593942de_val @ (defs) @ (phis) @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 43.09/14.36 thf(184,axiom,((! [A:node,B:list_node]: (member_node @ A @ (set_node2 @ (cons_node @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_list_Oset__intros_I1_J)). 43.09/14.36 thf(1099,plain,((! [A:node,B:list_node]: (member_node @ A @ (set_node2 @ (cons_node @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 43.09/14.36 thf(198,axiom,((! [A:g,B:node,C:node]: ((~ ((member_node @ C @ (set_node2 @ (alpha_n @ A))) => (~ (! [D:list_node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (entry @ A) @ D @ C) => (member_node @ B @ (set_node2 @ D))))))) <= (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_old_OdominatesE)). 43.09/14.36 thf(1150,plain,((! [A:g,B:node,C:node]: ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => (~ ((member_node @ C @ (set_node2 @ (alpha_n @ A))) => (~ (! [D:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (entry @ A) @ D @ C) => (member_node @ B @ (set_node2 @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 43.09/14.36 thf(221,axiom,((! [A:g,B:node,C:node,D:node,E:list_node]: ((invar @ A) => ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C) => (((! [F:node]: ((F != B) <= (member_node @ F @ (set_node2 @ (tl_node @ E))))) => (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_old_Odominates__unsnoc_H)). 43.09/14.36 thf(1231,plain,((! [A:g,B:node,C:node,D:node,E:list_node]: ((invar @ A) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ D @ E @ C) => ((! [F:node]: ((member_node @ F @ (set_node2 @ (tl_node @ E))) => (~ (F = B)))) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 43.09/14.36 thf(175,axiom,((graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_rs_H__props_I2_J)). 43.09/14.36 thf(1060,plain,((graph_1994935542_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ g2 @ rs)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 43.09/14.36 thf(137,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/sandbox/benchmark/theBenchmark.p',fact_83_old_Opath2__snoc)). 43.09/14.36 thf(911,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)],[137])). 43.09/14.37 thf(104,axiom,((! [A:list_node]: ((append_node @ nil_node @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_append_Oleft__neutral)). 43.09/14.37 thf(779,plain,((! [A:list_node]: ((append_node @ nil_node @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 43.09/14.37 thf(3,axiom,((! [A:list_node]: ((suffix_node @ A @ nil_node) = (A = nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_suffix__Nil)). 43.09/14.37 thf(244,plain,((! [A:list_node]: ((suffix_node @ A @ nil_node) = (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 43.09/14.37 thf(145,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/sandbox/benchmark/theBenchmark.p',fact_20_old_Opath2__tl__in___092_060alpha_062n)). 43.09/14.37 thf(938,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (member_node @ D @ (set_node2 @ (alpha_n @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 43.09/14.37 thf(22,axiom,((! [A:node]: (distinct_node @ (cons_node @ A @ nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_distinct__singleton)). 43.09/14.37 thf(360,plain,((! [A:node]: (distinct_node @ (cons_node @ A @ nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 43.09/14.37 thf(110,axiom,((! [A:list_node,B:node,C:list_node]: ((A != nil_node) => (((cons_node @ B @ nil_node) = (append_node @ A @ C)) = ((C = nil_node) & (A = (cons_node @ B @ nil_node))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_list__se__match_I3_J)). 43.09/14.37 thf(805,plain,((! [A:list_node,B:node,C:list_node]: ((~ (A = nil_node)) => (((cons_node @ B @ nil_node) = (append_node @ A @ C)) = ((C = nil_node) & (A = (cons_node @ B @ nil_node))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 43.09/14.37 thf(141,axiom,((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_assms_I8_J)). 43.09/14.37 thf(921,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)],[141])). 43.09/14.37 thf(230,axiom,((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_assms_I10_J)). 43.09/14.37 thf(1286,plain,((sSA_CF1252180629de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ phi_r @ r)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 43.09/14.37 thf(208,axiom,((! [A:g,B:node]: (((member_node @ B @ (set_node2 @ (alpha_n @ A))) => (((graph_272749361_edgeD @ inEdges @ A @ B) = nil_node) = (B = (entry @ A)))) <= (invar @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_old_OEntry__iff__unreachable)). 43.09/14.37 thf(1187,plain,((! [A:g,B:node]: ((invar @ A) => ((member_node @ B @ (set_node2 @ (alpha_n @ A))) => (((graph_272749361_edgeD @ (inEdges) @ A @ B) = nil_node) = (B = (entry @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 43.09/14.37 thf(81,axiom,((! [A:list_node,B:list_node]: (((suffix_node @ B @ A) = (B = A)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_suffix__order_Oantisym__conv)). 43.09/14.37 thf(662,plain,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 43.09/14.37 thf(129,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/sandbox/benchmark/theBenchmark.p',fact_277_in__set__conv__decomp)). 43.09/14.37 thf(888,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)],[129])). 43.09/14.37 thf(135,axiom,((! [A:g,B:node]: ((invar @ A) => ((member_node @ B @ (set_node2 @ (alpha_n @ A))) => (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_old_Odominates__refl)). 43.09/14.37 thf(906,plain,((! [A:g,B:node]: ((invar @ A) => ((member_node @ B @ (set_node2 @ (alpha_n @ A))) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 43.09/14.37 thf(225,axiom,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A)))) = (? [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/sandbox/benchmark/theBenchmark.p',fact_289_split__list__first__prop__iff)). 43.09/14.37 thf(1251,plain,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((B @ C) & (member_node @ C @ (set_node2 @ A)))) = (? [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)],[225])). 43.09/14.37 thf(55,axiom,((! [A:(list_node > $o),B:list_node]: (((A @ B) <= (A @ nil_node)) <= (! [C:node,D:list_node]: ((! [E:node,F:list_node]: ((A @ D) <= (D = (cons_node @ E @ F)))) => (A @ (cons_node @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_min__list_Oinduct)). 43.09/14.37 thf(513,plain,((! [A:(list_node > $o),B:list_node]: ((! [C:node,D:list_node]: ((! [E:node,F:list_node]: ((D = (cons_node @ E @ F)) => (A @ D))) => (A @ (cons_node @ C @ D)))) => ((A @ nil_node) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 43.09/14.37 thf(218,axiom,((! [A:list_node]: ((A != nil_node) => (A = (cons_node @ (hd_node @ A) @ (tl_node @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_list_Oexhaust__sel)). 43.09/14.37 thf(1219,plain,((! [A:list_node]: ((~ (A = nil_node)) => (A = (cons_node @ (hd_node @ A) @ (tl_node @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 43.09/14.37 thf(64,axiom,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = nil_node) = ((A = nil_node) & (B = nil_node))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_append__is__Nil__conv)). 43.09/14.37 thf(573,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)],[64])). 43.09/14.37 thf(44,axiom,((! [A:set_val]: ((finite_finite_val @ A) => (? [B:list_val]: ((set_val2 @ B) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_finite__list)). 43.09/14.37 thf(444,plain,((! [A:set_val]: ((finite_finite_val @ A) => (? [B:list_val]: ((set_val2 @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 43.09/14.37 thf(93,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ (append_node @ C @ B)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_suffix__appendI)). 43.09/14.37 thf(733,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)],[93])). 43.09/14.37 thf(199,axiom,((! [A:g,B:node,C:val]: ((sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C) = (! [D:list_node]: ((? [E:node]: ((member_node @ E @ (set_node2 @ D)) & (member_val @ C @ (defs @ A @ E)))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (entry @ A) @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_defAss_H__def)). 43.09/14.37 thf(1154,plain,((! [A:g,B:node,C:val]: ((sSA_CF1558836456eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ A @ B @ C) = (! [D:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (entry @ A) @ D @ B) => (? [E:node]: ((member_node @ E @ (set_node2 @ D)) & (member_val @ C @ (defs @ A @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 43.09/14.37 thf(37,axiom,((! [A:node,B:node,C:list_node]: ((distinct_node @ (cons_node @ A @ (cons_node @ B @ C))) = ((A != B) & (distinct_node @ (cons_node @ A @ C)) & (distinct_node @ (cons_node @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_distinct__length__2__or__more)). 43.09/14.37 thf(423,plain,((! [A:node,B:node,C:list_node]: ((distinct_node @ (cons_node @ A @ (cons_node @ B @ C))) = (~ (A = B) & (distinct_node @ (cons_node @ A @ C)) & (distinct_node @ (cons_node @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 43.09/14.37 thf(87,axiom,((! [A:list_node,B:list_node,C:node]: ((suffix_node @ A @ B) => (suffix_node @ A @ (cons_node @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_suffix__ConsI)). 43.09/14.37 thf(694,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)],[87])). 43.09/14.37 thf(192,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/sandbox/benchmark/theBenchmark.p',fact_280_split__list__last__prop)). 43.09/14.37 thf(1125,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]: ((member_node @ F @ (set_node2 @ E)) => (~ (B @ F))) & (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 43.09/14.37 thf(9,axiom,((! [A:list_node]: (suffix_node @ nil_node @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_suffix__bot_Obot_Oextremum)). 43.09/14.37 thf(286,plain,((! [A:list_node]: (suffix_node @ nil_node @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 43.09/14.37 thf(96,axiom,((! [A:list_node,B:list_node,C:node,D:list_node]: (((append_node @ A @ B) = (cons_node @ C @ D)) => (((A = nil_node) => (B != (cons_node @ C @ D))) => (~ (! [E:list_node]: ((A = (cons_node @ C @ E)) => ((append_node @ E @ B) != D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_list__append__eq__Cons__cases)). 43.09/14.37 thf(743,plain,((! [A:list_node,B:list_node,C:node,D:list_node]: (((append_node @ A @ B) = (cons_node @ C @ D)) => (((A = nil_node) => (~ (B = (cons_node @ C @ D)))) => (~ (! [E:list_node]: ((A = (cons_node @ C @ E)) => (~ ((append_node @ E @ B) = D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 43.09/14.37 thf(126,axiom,((! [A:g,B:list_node,C:list_node]: ((((graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C) <= (C != nil_node)) <= (suffix_node @ C @ B)) <= (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_old_OEntryPath__suffix)). 43.09/14.37 thf(875,plain,((! [A:g,B:list_node,C:list_node]: ((graph_1994935542_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B) => ((suffix_node @ C @ B) => ((~ (C = nil_node)) => (graph_1994935542_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 43.09/14.37 thf(30,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/sandbox/benchmark/theBenchmark.p',fact_98_append_Oassoc)). 43.09/14.37 thf(391,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)],[30])). 43.09/14.37 thf(144,axiom,((! [A:g,B:node,C:list_node,D:node,E:list_node,F:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ (cons_node @ D @ E) @ F) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ (append_node @ C @ (cons_node @ D @ E)) @ F)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_old_Opath2__split_I2_J)). 43.09/14.37 thf(936,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)],[144])). 43.09/14.37 thf(174,axiom,((! [A:val,B:g,C:node]: ((member_val @ A @ (sSA_CF370335846de_val @ phis @ B @ C)) => (member_val @ A @ (sSA_CF139593942de_val @ defs @ phis @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_phiDefs__in__allDefs)). 43.09/14.37 thf(1058,plain,((! [A:val,B:g,C:node]: ((member_val @ A @ (sSA_CF370335846de_val @ (phis) @ B @ C)) => (member_val @ A @ (sSA_CF139593942de_val @ (defs) @ (phis) @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 43.09/14.37 thf(140,axiom,((! [A:g]: ((invar @ A) => (distinct_node @ (alpha_n @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_old_O_092_060alpha_062n__distinct)). 43.09/14.37 thf(919,plain,((! [A:g]: ((invar @ A) => (distinct_node @ (alpha_n @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 43.09/14.37 thf(100,axiom,((! [A:list_node,B:list_node]: ((A = (append_node @ A @ B)) = (B = nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_self__append__conv)). 43.09/14.37 thf(764,plain,((! [A:list_node,B:list_node]: ((A = (append_node @ A @ B)) = (B = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 43.09/14.37 thf(229,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/sandbox/benchmark/theBenchmark.p',fact_81_in__hd__or__tl__conv)). 43.09/14.37 thf(1282,plain,((! [A:list_node,B:node]: ((~ (A = nil_node)) => (((B = (hd_node @ A)) | (member_node @ B @ (set_node2 @ (tl_node @ A)))) = (member_node @ B @ (set_node2 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 43.09/14.37 thf(94,axiom,((! [A:list_node]: ((~ (! [B:node,C:list_node]: (A != (cons_node @ B @ C)))) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_neq__NilE)). 43.09/14.37 thf(736,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)],[94])). 43.09/14.37 thf(154,axiom,((! [A:node,B:list_node]: (((! [C:list_node]: (B != (cons_node @ A @ C))) => (~ (! [C:node,D:list_node]: ((B = (cons_node @ C @ D)) => (~ (member_node @ A @ (set_node2 @ D))))))) <= (member_node @ A @ (set_node2 @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_list_Oset__cases)). 43.09/14.37 thf(990,plain,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ B)) => ((! [C:list_node]: ~ (B = (cons_node @ A @ C))) => (~ (! [C:node,D:list_node]: ((B = (cons_node @ C @ D)) => (~ (member_node @ A @ (set_node2 @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 43.09/14.37 thf(54,axiom,((! [A:list_node]: ((A != nil_node) => ((~ (! [B:node,C:node,D:list_node]: (A != (cons_node @ B @ (cons_node @ C @ D))))) <= (! [B:node]: (A != (cons_node @ B @ nil_node))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_remdups__adj_Ocases)). 43.09/14.37 thf(509,plain,((! [A:list_node]: ((~ (A = nil_node)) => ((! [B:node]: ~ (A = (cons_node @ B @ nil_node))) => (~ (! [B:node,C:node,D:list_node]: ~ (A = (cons_node @ B @ (cons_node @ C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 43.09/14.37 thf(23,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/sandbox/benchmark/theBenchmark.p',fact_170_list_Oinducts)). 43.09/14.37 thf(362,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)],[23])). 43.09/14.37 thf(62,axiom,((! [A:list_node,B:list_node]: (((hd_node @ (append_node @ A @ B)) = (hd_node @ A)) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_hd__append2)). 43.09/14.37 thf(567,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)],[62])). 43.09/14.37 thf(21,axiom,((! [A:(list_node > $o),B:list_node]: ((((! [C:node,D:node,E:list_node]: ((A @ E) => ((A @ (cons_node @ D @ E)) => (A @ (cons_node @ C @ (cons_node @ D @ E)))))) => (A @ B)) <= (! [C:node]: (A @ (cons_node @ C @ nil_node)))) <= (A @ nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_induct__list012)). 43.09/14.37 thf(345,plain,((! [A:(list_node > $o),B:list_node]: ((A @ nil_node) => ((! [C:node]: (A @ (cons_node @ C @ nil_node))) => ((! [C:node,D:node,E:list_node]: ((A @ E) => ((A @ (cons_node @ D @ E)) => (A @ (cons_node @ C @ (cons_node @ D @ E)))))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 43.09/14.37 thf(113,axiom,((! [A:list_node,B:node,C:list_node,D:list_node,E:node,F:list_node]: (((append_node @ A @ (cons_node @ B @ C)) = (append_node @ D @ (cons_node @ E @ F))) => ((! [G:list_node]: ((A = (append_node @ D @ (cons_node @ E @ G))) => (F != (append_node @ G @ (cons_node @ B @ C))))) => ((~ (! [G:list_node]: ((D = (append_node @ A @ (cons_node @ B @ G))) => (C != (append_node @ G @ (cons_node @ E @ F)))))) <= (((E = B) => (F != C)) <= (D = A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_list__match__lel__lel)). 43.09/14.37 thf(816,plain,((! [A:list_node,B:node,C:list_node,D:list_node,E:node,F:list_node]: (((append_node @ A @ (cons_node @ B @ C)) = (append_node @ D @ (cons_node @ E @ F))) => ((! [G:list_node]: ((A = (append_node @ D @ (cons_node @ E @ G))) => (~ (F = (append_node @ G @ (cons_node @ B @ C)))))) => (((D = A) => ((E = B) => (~ (F = C)))) => (~ (! [G:list_node]: ((D = (append_node @ A @ (cons_node @ B @ G))) => (~ (C = (append_node @ G @ (cons_node @ E @ F)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 43.09/14.37 thf(108,axiom,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = B) = (A = nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_append__self__conv2)). 43.09/14.37 thf(799,plain,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = B) = (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 43.09/14.37 thf(89,axiom,((! [A:list_node]: (suffix_node @ nil_node @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_Nil__suffix)). 43.09/14.37 thf(700,plain,((! [A:list_node]: (suffix_node @ nil_node @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 43.09/14.37 thf(75,axiom,((((=) @ list_node) = (^ [A:list_node,B:list_node]: ((suffix_node @ A @ B) & (suffix_node @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_suffix__order_Oeq__iff)). 43.09/14.37 thf(626,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)],[75])). 43.09/14.37 thf(205,axiom,((! [A:g,B:node,C:node]: ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C) => ((invar @ A) => (~ (! [D:list_node]: ~ (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ D @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_old_Odominates__path)). 43.09/14.37 thf(1177,plain,((! [A:g,B:node,C:node]: ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((invar @ A) => (~ (! [D:list_node]: ~ (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 43.09/14.37 thf(176,axiom,((! [A:g,B:node,C:node]: ((invar @ A) => ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C) => ((B = C) <= (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_old_Odominates__antisymm)). 43.09/14.37 thf(1061,plain,((! [A:g,B:node,C:node]: ((invar @ A) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ C @ B) => (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 43.09/14.37 thf(78,axiom,((! [A:g]: ((invar @ A) => ((graph_1947481694_edgeD @ inEdges @ A @ (entry @ A)) = nil_Pr1769730692D_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_old_OEntry__unreachable)). 43.09/14.37 thf(636,plain,((! [A:g]: ((invar @ A) => ((graph_1947481694_edgeD @ (inEdges) @ A @ (entry @ A)) = nil_Pr1769730692D_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 43.09/14.37 thf(123,axiom,((! [A:g,B:node]: (finite_finite_val @ (defs @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_defs__finite)). 43.09/14.37 thf(868,plain,((! [A:g,B:node]: (finite_finite_val @ (defs @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 43.09/14.37 thf(7,axiom,((! [A:(list_node > $o),B:list_node]: (((! [C:node]: (A @ (cons_node @ C @ nil_node))) => ((A @ B) <= (! [C:node,D:node,E:list_node]: ((((A @ (cons_node @ D @ E)) <= (C != D)) => (A @ (cons_node @ C @ (cons_node @ D @ E)))) <= ((A @ (cons_node @ C @ E)) <= (C = D)))))) <= (A @ nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_remdups__adj_Oinduct)). 43.09/14.37 thf(267,plain,((! [A:(list_node > $o),B:list_node]: ((A @ nil_node) => ((! [C:node]: (A @ (cons_node @ C @ nil_node))) => ((! [C:node,D:node,E:list_node]: (((C = D) => (A @ (cons_node @ C @ E))) => (((~ (C = D)) => (A @ (cons_node @ D @ E))) => (A @ (cons_node @ C @ (cons_node @ D @ E)))))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 43.09/14.37 thf(42,axiom,((! [A:list_node,B:list_node]: (((B = A) <= (suffix_node @ B @ A)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_suffix__order_Odual__order_Oantisym)). 43.09/14.37 thf(438,plain,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 43.09/14.37 thf(142,axiom,((! [A:g,B:node,C:list_node,D:node,E:(node > (list_node > (node > $o)))]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => (((E @ B @ C @ D) <= (! [F:list_node,G:node,H:node]: (((E @ H @ F @ D) => ((E @ G @ (cons_node @ G @ F) @ D) <= (member_node @ G @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ H))))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ H @ F @ D)))) <= ((invar @ A) => (E @ D @ (cons_node @ D @ nil_node) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_old_Opath2__induct)). 43.09/14.37 thf(922,plain,((! [A:g,B:node,C:list_node,D:node,E:(node > (list_node > (node > $o)))]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (((invar @ A) => (E @ D @ (cons_node @ D @ nil_node) @ D)) => ((! [F:list_node,G:node,H:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ H @ F @ D) => ((E @ H @ F @ D) => ((member_node @ G @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ H))) => (E @ G @ (cons_node @ G @ F) @ D))))) => (E @ B @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 43.09/14.37 thf(80,axiom,((! [A:list_node,B:list_node,C:node]: ((((append_node @ B @ A) = (cons_node @ C @ nil_node)) = ((B = nil_node) & (A = (cons_node @ C @ nil_node)))) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_list__se__match_I2_J)). 43.09/14.37 thf(658,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)],[80])). 43.09/14.37 thf(47,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]: (((E @ F @ H) => (A @ E @ G @ (cons_node @ H @ I))) => ((A @ E @ (cons_node @ F @ G) @ (cons_node @ H @ I)) <= ((A @ E @ (cons_node @ F @ G) @ I) <= (~ (E @ F @ H)))))) => (((A @ B @ C @ D) <= (! [E:(node > (node > $o)),F:node,G:list_node]: (A @ E @ nil_node @ (cons_node @ F @ G)))) <= (! [E:(node > (node > $o)),F:list_node]: (A @ E @ F @ nil_node)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_mergesort__by__rel__merge_Oinduct)). 43.09/14.37 thf(455,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]: (((E @ F @ H) => (A @ (E) @ G @ (cons_node @ H @ I))) => (((~ (E @ F @ H)) => (A @ (E) @ (cons_node @ F @ G) @ I)) => (A @ (E) @ (cons_node @ F @ G) @ (cons_node @ H @ I))))) => ((! [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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 43.09/14.37 thf(128,axiom,((! [A:g,B:node,C:val,D:node,E:list_node]: ((sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C) => (((sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ D @ C) <= (! [F:node]: ((~ (member_val @ C @ (sSA_CF139593942de_val @ defs @ phis @ A @ F))) <= (member_node @ F @ (set_node2 @ (tl_node @ E)))))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_defAss__extend)). 43.09/14.37 thf(883,plain,((! [A:g,B:node,C:val,D:node,E:list_node]: ((sSA_CF1156973626eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ (phis) @ A @ B @ C) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ D @ E @ B) => ((! [F:node]: ((member_node @ F @ (set_node2 @ (tl_node @ E))) => (~ (member_val @ C @ (sSA_CF139593942de_val @ (defs) @ (phis) @ A @ F))))) => (sSA_CF1156973626eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ (phis) @ A @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 43.09/14.37 thf(31,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/sandbox/benchmark/theBenchmark.p',fact_318_suffix__order_Odual__order_Otrans)). 43.09/14.37 thf(394,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ C @ A) => (suffix_node @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 43.09/14.37 thf(13,axiom,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = A) = (B = nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_append__self__conv)). 43.09/14.37 thf(306,plain,((! [A:list_node,B:list_node]: (((append_node @ A @ B) = A) = (B = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 43.09/14.37 thf(38,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) & (D = nil_node) & (C = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_list__e__eq__lel_I1_J)). 43.09/14.37 thf(426,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) & (D = nil_node) & (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 43.09/14.37 thf(213,axiom,((! [A:list_node,B:list_node]: (((tl_node @ (append_node @ A @ B)) = (append_node @ (tl_node @ A) @ B)) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_tl__append2)). 43.09/14.37 thf(1203,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)],[213])). 43.09/14.37 thf(58,axiom,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: (((! [D:node,E:list_node]: (A @ (cons_node @ D @ E) @ nil_node)) => ((! [D:node,E:list_node]: (A @ nil_node @ (cons_node @ D @ E))) => ((! [D:node,E:list_node,F:node,G:list_node]: ((A @ E @ G) => (A @ (cons_node @ D @ E) @ (cons_node @ F @ G)))) => (A @ B @ C)))) <= (A @ nil_node @ nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_list__induct2_H)). 43.09/14.37 thf(531,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((A @ nil_node @ nil_node) => ((! [D:node,E:list_node]: (A @ (cons_node @ D @ E) @ nil_node)) => ((! [D:node,E:list_node]: (A @ nil_node @ (cons_node @ D @ E))) => ((! [D:node,E:list_node,F:node,G:list_node]: ((A @ E @ G) => (A @ (cons_node @ D @ E) @ (cons_node @ F @ G)))) => (A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 43.09/14.37 thf(193,axiom,((! [A:list_node]: (((cons_node @ (hd_node @ A) @ (tl_node @ A)) = A) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_list_Ocollapse)). 43.09/14.37 thf(1134,plain,((! [A:list_node]: ((~ (A = nil_node)) => ((cons_node @ (hd_node @ A) @ (tl_node @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 43.09/14.37 thf(180,axiom,((! [A:g,B:node,C:node,D:node]: ((invar @ A) => ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C) => ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C) => ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B) <= (~ (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_old_Odominates__antitrans)). 43.09/14.37 thf(1081,plain,((! [A:g,B:node,C:node,D:node]: ((invar @ A) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ D @ C) => ((~ (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ D)) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ D @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 43.09/14.37 thf(72,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/sandbox/benchmark/theBenchmark.p',fact_131_append1__eq__conv)). 43.09/14.37 thf(617,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)],[72])). 43.09/14.37 thf(171,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/sandbox/benchmark/theBenchmark.p',fact_265_split__list)). 43.09/14.37 thf(1049,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)],[171])). 43.09/14.37 thf(103,axiom,((! [A:list_node,B:list_node]: ((A = (append_node @ B @ A)) = (B = nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_self__append__conv2)). 43.09/14.37 thf(776,plain,((! [A:list_node,B:list_node]: ((A = (append_node @ B @ A)) = (B = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 43.09/14.37 thf(91,axiom,((! [A:list_node,B:list_node,C:(list_node > (list_node > $o))]: (((B != nil_node) => ((! [D:node,E:node]: (C @ (cons_node @ D @ nil_node) @ (cons_node @ E @ nil_node))) => ((! [D:node,E:list_node,F:node]: ((E != nil_node) => (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (cons_node @ F @ nil_node)))) => (((C @ A @ B) <= (! [D:node,E:list_node,F:node,G:list_node]: ((((G != nil_node) => (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (append_node @ G @ (cons_node @ F @ nil_node)))) <= (E != nil_node)) <= (C @ E @ G)))) <= (! [D:node,E:node,F:list_node]: ((C @ (cons_node @ D @ nil_node) @ (append_node @ F @ (cons_node @ E @ nil_node))) <= (F != nil_node))))))) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_rev__nonempty__induct2_H)). 43.09/14.37 thf(705,plain,((! [A:list_node,B:list_node,C:(list_node > (list_node > $o))]: ((~ (A = nil_node)) => ((~ (B = nil_node)) => ((! [D:node,E:node]: (C @ (cons_node @ D @ nil_node) @ (cons_node @ E @ nil_node))) => ((! [D:node,E:list_node,F:node]: ((~ (E = nil_node)) => (C @ (append_node @ E @ (cons_node @ D @ nil_node)) @ (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,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))))))) => (C @ A @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 43.09/14.37 thf(15,axiom,((! [A:(list_node > $o),B:list_node]: (((A @ B) <= (! [C:node,D:list_node]: ((A @ (append_node @ D @ (cons_node @ C @ nil_node))) <= (A @ D)))) <= (A @ nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_rev__induct)). 43.09/14.37 thf(310,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)],[15])). 43.09/14.37 thf(66,axiom,((! [A:list_node,B:list_node,C:list_node]: (((append_node @ A @ B) = (append_node @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_append__same__eq)). 43.09/14.37 thf(580,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)],[66])). 43.09/14.37 thf(120,axiom,((! [A:((node > node) > (list_node > (list_node > $o))),B:(node > node),C:list_node,D:list_node]: (((! [E:(node > node),F:node,G:list_node,H:list_node]: ((A @ E @ G @ (cons_node @ (E @ F) @ H)) => (A @ E @ (cons_node @ F @ G) @ H))) => (A @ B @ C @ D)) <= (! [E:(node > node),F:list_node]: (A @ E @ nil_node @ F))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_map__tailrec__rev_Oinduct)). 43.09/14.37 thf(855,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) @ G @ (cons_node @ (E @ F) @ H)) => (A @ (E) @ (cons_node @ F @ G) @ H))) => (A @ (B) @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 43.09/14.37 thf(85,axiom,((! [A:node,B:list_node,C:list_node,D:list_node]: (((cons_node @ A @ B) = (append_node @ C @ D)) => (((C = nil_node) => (D != (cons_node @ A @ B))) => (~ (! [E:list_node]: (((append_node @ E @ D) != B) <= (C = (cons_node @ A @ E))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_list__Cons__eq__append__cases)). 43.09/14.37 thf(673,plain,((! [A:node,B:list_node,C:list_node,D:list_node]: (((cons_node @ A @ B) = (append_node @ C @ D)) => (((C = nil_node) => (~ (D = (cons_node @ A @ B)))) => (~ (! [E:list_node]: ((C = (cons_node @ A @ E)) => (~ ((append_node @ E @ D) = B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 43.09/14.37 thf(43,axiom,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_suffix__order_Oantisym)). 43.09/14.37 thf(441,plain,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 43.09/14.37 thf(240,axiom,((! [A:list_node]: ((((tl_node @ A) = nil_node) => (~ (! [B:node]: (A != (cons_node @ B @ nil_node))))) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_tl__obtain__elem)). 43.09/14.37 thf(1317,plain,((! [A:list_node]: ((~ (A = nil_node)) => (((tl_node @ A) = nil_node) => (~ (! [B:node]: ~ (A = (cons_node @ B @ nil_node)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 43.09/14.37 thf(19,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/sandbox/benchmark/theBenchmark.p',fact_324_suffix__order_Oorder__trans)). 43.09/14.37 thf(338,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)],[19])). 43.09/14.37 thf(147,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/sandbox/benchmark/theBenchmark.p',fact_272_split__list__first)). 43.09/14.37 thf(951,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)],[147])). 43.09/14.37 thf(50,axiom,((! [A:list_node,B:list_node]: ((((A != nil_node) => (B != nil_node)) => ((! [C:node,D:list_node]: ((! [E:node,F:list_node]: ((B = (append_node @ F @ (cons_node @ E @ nil_node))) => ((E = C) => (suffix_node @ D @ F)))) <= (A = (append_node @ D @ (cons_node @ C @ nil_node))))) => (~ (! [C:node]: ((! [D:node]: ((D = C) <= (? [E:list_node]: (B = (append_node @ E @ (cons_node @ D @ nil_node)))))) <= (? [D:list_node]: (A = (append_node @ D @ (cons_node @ C @ nil_node))))))))) <= (~ (suffix_node @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_not__suffix__cases)). 43.09/14.37 thf(470,plain,((! [A:list_node,B:list_node]: ((~ (suffix_node @ A @ B)) => (((~ (A = nil_node)) => (~ (B = 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]: ((? [E:list_node]: (B = (append_node @ E @ (cons_node @ D @ nil_node)))) => (D = C))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 43.09/14.37 thf(65,axiom,((! [A:list_node]: ((~ (! [B:list_node,C:node]: (A != (append_node @ B @ (cons_node @ C @ nil_node))))) <= (A != nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_neq__Nil__revE)). 43.09/14.37 thf(576,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)],[65])). 43.09/14.37 thf(165,axiom,((! [A:g,B:list_node]: ((invar @ A) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (entry @ A) @ B @ (entry @ A)) => (B = (cons_node @ (entry @ A) @ nil_node)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_old_OEntry__loop)). 43.09/14.37 thf(1023,plain,((! [A:g,B:list_node]: ((invar @ A) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (entry @ A) @ B @ (entry @ A)) => (B = (cons_node @ (entry @ A) @ nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 43.09/14.37 thf(71,axiom,((! [A:list_node,B:list_node]: ((A = (append_node @ nil_node @ B)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_eq__Nil__appendI)). 43.09/14.37 thf(613,plain,((! [A:list_node,B:list_node]: ((A = B) => (A = (append_node @ nil_node @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 43.09/14.37 thf(172,axiom,((! [A:g,B:node,C:node]: ((graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C) = ((C != B) & (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ C @ B) & ! [D:node]: ((member_node @ D @ (set_node2 @ (alpha_n @ A))) => (((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ B) & (D != B)) => (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ D @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_old_OisIdom__def)). 43.09/14.37 thf(1052,plain,((! [A:g,B:node,C:node]: ((graph_1670286392_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) = (~ (C = B) & (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ C @ B) & ! [D:node]: ((member_node @ D @ (set_node2 @ (alpha_n @ A))) => (((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ D @ B) & ~ (D = B)) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 43.09/14.37 thf(122,axiom,((! [A:g,B:node,C:list_node,D:node]: ((B = (hd_node @ C)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_old_Opath2__hd)). 43.09/14.37 thf(864,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)],[122])). 43.09/14.37 thf(160,axiom,((! [A:node,B:g,C:val]: ((((sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ C) = A) <= (member_val @ C @ (sSA_CF139593942de_val @ defs @ phis @ B @ A))) <= (member_node @ A @ (set_node2 @ (alpha_n @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_defNode__eq)). 43.09/14.37 thf(1008,plain,((! [A:node,B:g,C:val]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((member_val @ C @ (sSA_CF139593942de_val @ (defs) @ (phis) @ B @ A)) => ((sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ B @ C) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 43.09/14.37 thf(63,axiom,((! [A:g]: (invar @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_old_Oinvar)). 43.09/14.37 thf(571,plain,((! [A:g]: (invar @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 43.09/14.37 thf(227,axiom,((! [A:node,B:list_node,C:list_node,D:node]: ((member_node @ A @ (set_node2 @ (tl_node @ (append_node @ C @ (cons_node @ D @ B))))) <= (member_node @ A @ (set_node2 @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_old_Oelem__set__implies__elem__tl__app__cons)). 43.09/14.37 thf(1272,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)],[227])). 43.09/14.37 thf(223,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/sandbox/benchmark/theBenchmark.p',fact_42_old_Osuccessor__in___092_060alpha_062n)). 43.09/14.37 thf(1240,plain,((! [A:g,B:node]: ((~ ((graph_272749361_edgeD @ (inEdges) @ A @ B) = nil_node)) => ((invar @ A) => (member_node @ B @ (set_node2 @ (alpha_n @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 43.09/14.37 thf(28,axiom,(((append_node @ nil_node) = (^ [A:list_node]: (A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_empty__append__eq__id)). 43.09/14.37 thf(386,plain,(((append_node @ nil_node) = (^ [A:list_node]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 43.09/14.37 thf(152,axiom,((! [A:node,B:g]: (((? [C:list_node]: (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ (entry @ B) @ C @ A)) <= (invar @ B)) <= (member_node @ A @ (set_node2 @ (alpha_n @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_old_OEntry__reaches)). 43.09/14.37 thf(978,plain,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((invar @ B) => (? [C:list_node]: (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ B @ (entry @ B) @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 43.09/14.37 thf(195,axiom,((! [A:list_node]: (((tl_node @ A) = nil_node) = ((A = nil_node) | ? [B:node]: (A = (cons_node @ B @ nil_node)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_tl__Nil)). 43.09/14.37 thf(1140,plain,((! [A:list_node]: (((tl_node @ A) = nil_node) = ((A = nil_node) | ? [B:node]: (A = (cons_node @ B @ nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 43.09/14.37 thf(5,axiom,((! [A:list_node,B:(list_node > $o)]: ((A != nil_node) => ((! [C:node]: (B @ (cons_node @ C @ nil_node))) => ((B @ A) <= (! [C:node,D:list_node]: ((D != nil_node) => ((B @ (append_node @ D @ (cons_node @ C @ nil_node))) <= (B @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_rev__nonempty__induct)). 43.09/14.37 thf(250,plain,((! [A:list_node,B:(list_node > $o)]: ((~ (A = nil_node)) => ((! [C:node]: (B @ (cons_node @ C @ nil_node))) => ((! [C:node,D:list_node]: ((~ (D = nil_node)) => ((B @ D) => (B @ (append_node @ D @ (cons_node @ C @ nil_node)))))) => (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 43.09/14.37 thf(206,axiom,((! [A:g,B:node,C:node,D:node]: (((((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ D) <= (B != C)) <= (member_node @ D @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ C)))) <= (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C)) <= (invar @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_old_Odominates__unsnoc)). 43.09/14.37 thf(1180,plain,((! [A:g,B:node,C:node,D:node]: ((invar @ A) => ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) => ((member_node @ D @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ C))) => ((~ (B = C)) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 43.09/14.37 thf(134,axiom,((! [A:node,B:list_node]: ((tl_node @ (cons_node @ A @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_list_Osel_I3_J)). 43.09/14.37 thf(903,plain,((! [A:node,B:list_node]: ((tl_node @ (cons_node @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 43.09/14.37 thf(130,axiom,((! [A:list_node]: ((nil_node = (tl_node @ A)) = ((A = nil_node) | ? [B:node]: (A = (cons_node @ B @ nil_node)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_Nil__tl)). 43.09/14.37 thf(891,plain,((! [A:list_node]: ((nil_node = (tl_node @ A)) = ((A = nil_node) | ? [B:node]: (A = (cons_node @ B @ nil_node)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 43.09/14.37 thf(116,axiom,((! [A:list_node]: ((suffix_node @ A @ nil_node) = (A = nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_suffix__bot_Obot_Oextremum__unique)). 43.09/14.37 thf(844,plain,((! [A:list_node]: ((suffix_node @ A @ nil_node) = (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 43.09/14.37 thf(102,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/sandbox/benchmark/theBenchmark.p',fact_178_splice_Oinduct)). 43.09/14.37 thf(771,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((! [D:list_node]: (A @ nil_node @ D)) => ((! [D:node,E:list_node,F:list_node]: ((A @ F @ E) => (A @ (cons_node @ D @ E) @ F))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 43.09/14.37 thf(186,axiom,((! [A:list_node]: ((~ (distinct_node @ A)) = (? [B:list_node,C:node,D:list_node]: ((A = (append_node @ B @ (cons_node @ C @ D))) & (distinct_node @ B) & (member_node @ C @ (set_node2 @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_not__distinct__conv__prefix)). 43.09/14.37 thf(1108,plain,((! [A:list_node]: ((~ (distinct_node @ A)) = (? [B:list_node,C:node,D:list_node]: ((A = (append_node @ B @ (cons_node @ C @ D))) & (distinct_node @ B) & (member_node @ C @ (set_node2 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 43.09/14.37 thf(46,axiom,((! [A:list_node,B:list_node,C:list_node]: (((B = C) => (suffix_node @ A @ C)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_suffix__order_Oord__le__eq__trans)). 43.09/14.37 thf(450,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)],[46])). 43.09/14.37 thf(181,axiom,((! [A:list_node]: ((~ (! [B:node,C:list_node]: ((distinct_node @ C) => ((! [D:list_node]: (A != (append_node @ C @ (append_node @ (cons_node @ B @ nil_node) @ D)))) <= (member_node @ B @ (set_node2 @ C)))))) <= (~ (distinct_node @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_not__distinct__split__distinct)). 43.09/14.37 thf(1084,plain,((! [A:list_node]: ((~ (distinct_node @ A)) => (~ (! [B:node,C:list_node]: ((distinct_node @ C) => ((member_node @ B @ (set_node2 @ C)) => (! [D:list_node]: ~ (A = (append_node @ C @ (append_node @ (cons_node @ B @ nil_node) @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 43.09/14.37 thf(200,axiom,((! [A:node,B:node,C:g,D:node]: ((((A != D) & (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ D)) <= ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ B @ D) & (B != D))) <= ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ C @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_strict__dom__trans_H)). 43.09/14.37 thf(1157,plain,((! [A:node,B:node,C:g,D:node]: (((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ C @ A @ B) & ~ (A = B)) => (((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ C @ B @ D) & ~ (B = D)) => (~ (A = D) & (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ C @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 43.09/14.37 thf(241,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/sandbox/benchmark/theBenchmark.p',fact_82_old_Opath2__cases)). 43.09/14.37 thf(1321,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (((C = (cons_node @ B @ nil_node)) => (~ (D = B))) => (~ ((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)],[241])). 43.09/14.37 thf(68,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/sandbox/benchmark/theBenchmark.p',fact_315_append__eq__appendI)). 43.09/14.37 thf(588,plain,((! [A:list_node,B:list_node,C:list_node,D:list_node,E:list_node]: (((append_node @ A @ B) = C) => ((D = (append_node @ B @ E)) => ((append_node @ A @ D) = (append_node @ C @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 43.09/14.37 thf(185,axiom,((~ (! [A:list_node,B:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ A @ B) => (((member_val @ r @ (sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ B)) => (~ (member_node @ B @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r)))))) <= (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 43.09/14.37 thf(1101,plain,((~ (! [A:list_node,B:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ g2 @ (sSA_CF551432799de_val @ (alpha_n) @ (defs) @ (phis) @ g2 @ r) @ A @ B) => ((graph_1994935542_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ g2 @ A) => ((member_val @ r @ (sSA_CF848637139eD_val @ (alpha_n) @ (inEdges) @ (phis) @ g2 @ B)) => (~ (member_node @ B @ (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)],[185])). 43.09/14.37 thf(77,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/sandbox/benchmark/theBenchmark.p',fact_188_transpose_Ocases)). 43.09/14.37 thf(632,plain,((! [A:list_list_node]: ((~ (A = nil_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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 43.09/14.37 thf(36,axiom,((! [A:((node > (node > $o)) > (list_node > $o)),B:(node > (node > $o)),C:list_node]: (((! [D:(node > (node > $o)),E:node,F:list_node]: ((A @ D @ (cons_node @ E @ F)) <= (A @ D @ F))) => (A @ B @ C)) <= (! [D:(node > (node > $o))]: (A @ D @ nil_node))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_sorted__wrt_Oinduct)). 43.09/14.37 thf(418,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)],[36])). 43.09/14.37 thf(167,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/sandbox/benchmark/theBenchmark.p',fact_282_split__list__last__propE)). 43.09/14.37 thf(1030,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) => (~ (! [F:node]: ((member_node @ F @ (set_node2 @ E)) => (~ (B @ F)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 43.09/14.37 thf(138,axiom,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ (tl_node @ B))) => (member_node @ A @ (set_node2 @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_FormalSSA__Misc_Oin__set__tlD)). 43.09/14.37 thf(914,plain,((! [A:node,B:list_node]: ((member_node @ A @ (set_node2 @ (tl_node @ B))) => (member_node @ A @ (set_node2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 43.09/14.37 thf(238,axiom,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((~ (! [C:node]: ((member_node @ C @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ B @ A))) => (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ C)))) <= (A != (entry @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_non__dominated__predecessor)). 43.09/14.37 thf(1308,plain,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((~ (A = (entry @ B))) => (~ (! [C:node]: ((member_node @ C @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ B @ A))) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ B @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 43.09/14.37 thf(27,axiom,((! [A:list_node]: ((append_node @ nil_node @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_append__Nil)). 43.09/14.37 thf(383,plain,((! [A:list_node]: ((append_node @ nil_node @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 43.09/14.37 thf(133,axiom,((! [A:node,B:g]: (((invar @ B) => (~ (! [C:list_node]: ((~ (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ C)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ (entry @ B) @ C @ A))))) <= (member_node @ A @ (set_node2 @ (alpha_n @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_old_OEntry__reachesE)). 43.09/14.37 thf(899,plain,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((invar @ B) => (~ (! [C:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ B @ (entry @ B) @ C @ A) => (~ (graph_1994935542_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 43.09/14.37 thf(83,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/sandbox/benchmark/theBenchmark.p',fact_149_snoc__suffix__snoc)). 43.09/14.37 thf(667,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)],[83])). 43.09/14.37 thf(234,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/sandbox/benchmark/theBenchmark.p',fact_267_split__list__last)). 43.09/14.37 thf(1294,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)],[234])). 43.09/14.37 thf(45,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)))) = ((A = D) & (F = nil_node) & (B = E) & (C = nil_node))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_list__ee__eq__leel_I1_J)). 43.09/14.37 thf(447,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)))) = ((A = D) & (F = nil_node) & (B = E) & (C = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 43.09/14.37 thf(40,axiom,((! [A:list_node]: ((suffix_node @ A @ nil_node) => (A = nil_node)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_suffix__bot_Obot_Oextremum__uniqueI)). 43.09/14.37 thf(432,plain,((! [A:list_node]: ((suffix_node @ A @ nil_node) => (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 43.09/14.37 thf(150,axiom,((! [A:g,B:node]: (finite_finite_val @ (sSA_CF370335846de_val @ phis @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_phiDefs__finite)). 43.09/14.37 thf(967,plain,((! [A:g,B:node]: (finite_finite_val @ (sSA_CF370335846de_val @ (phis) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 43.09/14.37 thf(24,axiom,((! [A:list_node]: ((A != nil_node) = (? [B:node,C:list_node]: (A = (cons_node @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_neq__Nil__conv)). 43.09/14.37 thf(373,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)],[24])). 43.09/14.37 thf(156,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/sandbox/benchmark/theBenchmark.p',fact_24_old_Opath2__forget__hd)). 43.09/14.37 thf(999,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (hd_node @ C) @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 43.09/14.37 thf(73,axiom,((! [A:node,B:list_node,C:node,D:list_node]: (((cons_node @ A @ B) = (cons_node @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_list_Oinject)). 43.09/14.37 thf(620,plain,((! [A:node,B:list_node,C:node,D:list_node]: (((cons_node @ A @ B) = (cons_node @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 43.09/14.37 thf(1,conjecture,((~ (member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)). 43.09/14.37 thf(2,negated_conjecture,((~ (~ (member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs)))))),inference(neg_conjecture,[status(cth)],[1])). 43.09/14.37 thf(242,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)],[2])). 43.09/14.37 thf(12,axiom,((! [A:(list_node > (list_node > $o)),B:(node > (node > $o)),C:list_node,D:list_node]: ((! [E:list_node]: (A @ E @ nil_node)) => ((((A @ C @ D) <= (! [E:node,F:list_node,G:node,H:list_node]: (((A @ (cons_node @ E @ F) @ (cons_node @ G @ H)) <= (A @ (cons_node @ E @ F) @ H)) <= (~ (B @ E @ G))))) <= (! [E:node,F:list_node,G:node,H:list_node]: ((B @ E @ G) => ((A @ (cons_node @ E @ F) @ (cons_node @ G @ H)) <= (A @ F @ (cons_node @ G @ H)))))) <= (! [E:list_node]: (A @ nil_node @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_mergesort__by__rel__merge__induct)). 43.09/14.37 thf(294,plain,((! [A:(list_node > (list_node > $o)),B:(node > (node > $o)),C:list_node,D:list_node]: ((! [E:list_node]: (A @ E @ nil_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) @ H) => (A @ (cons_node @ E @ F) @ (cons_node @ G @ H))))) => (A @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 43.09/14.37 thf(239,axiom,((! [A:g,B:node]: (((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ (entry @ A) @ B) <= (member_node @ B @ (set_node2 @ (alpha_n @ A)))) <= (invar @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_old_OEntry__dominates)). 43.09/14.37 thf(1314,plain,((! [A:g,B:node]: ((invar @ A) => ((member_node @ B @ (set_node2 @ (alpha_n @ A))) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ (entry @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 43.09/14.37 thf(20,axiom,((! [A:list_node]: ((A = nil_node) <= (! [B:node,C:list_node]: (A != (cons_node @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_min__list_Ocases)). 43.09/14.37 thf(341,plain,((! [A:list_node]: ((! [B:node,C:list_node]: ~ (A = (cons_node @ B @ C))) => (A = nil_node)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 43.09/14.37 thf(53,axiom,((! [A:list_node,B:list_node]: (((suffix_node @ B @ A) => (A = B)) <= (suffix_node @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_suffix__order_Oorder_Oantisym)). 43.09/14.37 thf(506,plain,((! [A:list_node,B:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 43.09/14.37 thf(177,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/sandbox/benchmark/theBenchmark.p',fact_268_split__list__prop)). 43.09/14.37 thf(1065,plain,((! [A:list_node,B:(node > $o)]: ((? [C:node]: ((member_node @ C @ (set_node2 @ A)) & (B @ C))) => (? [C:list_node,D:node]: ((B @ D) & ? [E:list_node]: (A = (append_node @ C @ (cons_node @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 43.09/14.37 thf(201,axiom,((! [A:g,B:node,C:node]: ((graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ A @ B @ C) = (! [D:list_node]: ((member_node @ B @ (set_node2 @ D)) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (entry @ A) @ D @ C)) & (member_node @ C @ (set_node2 @ (alpha_n @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_old_Odominates__def)). 43.09/14.37 thf(1165,plain,((! [A:g,B:node,C:node]: ((graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ A @ B @ C) = (! [D:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (entry @ A) @ D @ C) => (member_node @ B @ (set_node2 @ D))) & (member_node @ C @ (set_node2 @ (alpha_n @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 43.09/14.37 thf(107,axiom,((! [A:list_node,B:list_node,C:node,D:list_node]: (((append_node @ A @ B) = (cons_node @ C @ D)) = (((B = (cons_node @ C @ D)) & (A = nil_node)) | ? [E:list_node]: (((append_node @ E @ B) = D) & (A = (cons_node @ C @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_append__eq__Cons__conv)). 43.09/14.37 thf(796,plain,((! [A:list_node,B:list_node,C:node,D:list_node]: (((append_node @ A @ B) = (cons_node @ C @ D)) = (((B = (cons_node @ C @ D)) & (A = nil_node)) | ? [E:list_node]: (((append_node @ E @ B) = D) & (A = (cons_node @ C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 43.09/14.37 thf(204,axiom,((! [A:g,B:node,C:val,D:list_node]: (((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (entry @ A) @ D @ B) => (? [E:node]: ((member_val @ C @ (sSA_CF139593942de_val @ defs @ phis @ A @ E)) & (member_node @ E @ (set_node2 @ D))))) <= (sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_defAssD)). 43.09/14.37 thf(1172,plain,((! [A:g,B:node,C:val,D:list_node]: ((sSA_CF1156973626eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ (phis) @ A @ B @ C) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (entry @ A) @ D @ B) => (? [E:node]: ((member_val @ C @ (sSA_CF139593942de_val @ (defs) @ (phis) @ A @ E)) & (member_node @ E @ (set_node2 @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 43.09/14.37 thf(132,axiom,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => (graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ B @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_dominates__refl_H)). 43.09/14.37 thf(897,plain,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => (graph_436675702_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ B @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 43.09/14.37 thf(101,axiom,((! [A:list_node,B:node,C:list_node,D:list_node,E:list_node]: ((distinct_node @ (append_node @ A @ (cons_node @ B @ C))) => (((append_node @ A @ (cons_node @ B @ C)) = (append_node @ D @ (cons_node @ B @ E))) = ((A = D) & (C = E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_distinct__match)). 43.09/14.37 thf(767,plain,((! [A:list_node,B:node,C:list_node,D:list_node,E:list_node]: ((distinct_node @ (append_node @ A @ (cons_node @ B @ C))) => (((append_node @ A @ (cons_node @ B @ C)) = (append_node @ D @ (cons_node @ B @ E))) = ((A = D) & (C = E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 43.09/14.37 thf(33,axiom,((! [A:list_node]: ((append_node @ A @ nil_node) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_append__Nil2)). 43.09/14.37 thf(400,plain,((! [A:list_node]: ((append_node @ A @ nil_node) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 43.09/14.37 thf(211,axiom,((! [A:node,B:(node > $o)]: ((member_node @ A @ (collect_node @ B)) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_mem__Collect__eq)). 43.09/14.37 thf(1197,plain,((! [A:node,B:(node > $o)]: ((member_node @ A @ (collect_node @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 43.09/14.37 thf(115,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]: (A @ D @ (cons_node @ E @ nil_node))) => ((A @ B @ C) <= (! [D:(node > (node > $o)),E:node,F:node,G:list_node]: ((A @ D @ (cons_node @ F @ G)) => (A @ D @ (cons_node @ E @ (cons_node @ F @ G)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_successively_Oinduct)). 43.09/14.37 thf(839,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]: (A @ (D) @ (cons_node @ E @ nil_node))) => ((! [D:(node > (node > $o)),E:node,F:node,G:list_node]: ((A @ (D) @ (cons_node @ F @ G)) => (A @ (D) @ (cons_node @ E @ (cons_node @ F @ G))))) => (A @ (B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 43.09/14.37 thf(121,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/sandbox/benchmark/theBenchmark.p',fact_279_in__set__list__format)). 43.09/14.37 thf(860,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)],[121])). 43.09/14.37 thf(164,axiom,((! [A:g,B:node,C:val]: ((! [D:list_node]: ((? [E:node]: ((member_val @ C @ (sSA_CF139593942de_val @ defs @ phis @ A @ E)) & (member_node @ E @ (set_node2 @ D)))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ (entry @ A) @ D @ B))) => (sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_defAssI)). 43.09/14.37 thf(1019,plain,((! [A:g,B:node,C:val]: ((! [D:list_node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ (entry @ A) @ D @ B) => (? [E:node]: ((member_val @ C @ (sSA_CF139593942de_val @ (defs) @ (phis) @ A @ E)) & (member_node @ E @ (set_node2 @ D)))))) => (sSA_CF1156973626eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ (phis) @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 43.09/14.37 thf(57,axiom,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ C @ B) => ((suffix_node @ C @ A) | (suffix_node @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_suffix__same__cases)). 43.09/14.37 thf(528,plain,((! [A:list_node,B:list_node,C:list_node]: ((suffix_node @ A @ B) => ((suffix_node @ C @ B) => ((suffix_node @ C @ A) | (suffix_node @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 43.09/14.37 thf(158,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/sandbox/benchmark/theBenchmark.p',fact_21_old_Opath2__last__in__ns)). 43.09/14.37 thf(1004,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (member_node @ D @ (set_node2 @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 43.09/14.37 thf(235,axiom,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D) => (member_node @ B @ (set_node2 @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_old_Opath2__hd__in__ns)). 43.09/14.37 thf(1299,plain,((! [A:g,B:node,C:list_node,D:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (member_node @ B @ (set_node2 @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 43.09/14.37 thf(191,axiom,((! [A:g,B:node,C:val,D:node,E:list_node]: ((sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ B @ C) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ B) => ((sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ A @ D @ C) <= (! [F:node]: ((~ (member_val @ C @ (defs @ A @ F))) <= (member_node @ F @ (set_node2 @ (tl_node @ E)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_defAss_H__extend)). 43.09/14.37 thf(1120,plain,((! [A:g,B:node,C:val,D:node,E:list_node]: ((sSA_CF1558836456eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ A @ B @ C) => ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ D @ E @ B) => ((! [F:node]: ((member_node @ F @ (set_node2 @ (tl_node @ E))) => (~ (member_val @ C @ (defs @ A @ F))))) => (sSA_CF1558836456eD_val @ (alpha_n) @ (invar) @ (inEdges) @ (entry) @ (defs) @ A @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 43.09/14.37 thf(51,axiom,((! [A:list_node,B:node,C:list_node,D:node]: (((append_node @ A @ (cons_node @ B @ C)) = (cons_node @ D @ nil_node)) = ((B = D) & (C = nil_node) & (A = nil_node))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_list__e__eq__lel_I2_J)). 43.09/14.37 thf(501,plain,((! [A:list_node,B:node,C:list_node,D:node]: (((append_node @ A @ (cons_node @ B @ C)) = (cons_node @ D @ nil_node)) = ((B = D) & (C = nil_node) & (A = nil_node))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 43.09/14.37 thf(92,axiom,((! [A:node,B:list_node,C:list_node,D:list_node,E:list_node]: (((cons_node @ A @ B) = C) => (((cons_node @ A @ D) = (append_node @ C @ E)) <= (D = (append_node @ B @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_Cons__eq__appendI)). 43.09/14.37 thf(728,plain,((! [A:node,B:list_node,C:list_node,D:list_node,E:list_node]: (((cons_node @ A @ B) = C) => ((D = (append_node @ B @ E)) => ((cons_node @ A @ D) = (append_node @ C @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 43.09/14.37 thf(95,axiom,((! [A:list_node,B:list_node,C:list_node,D:list_node]: (((append_node @ A @ B) = (append_node @ C @ D)) = (? [E:list_node]: ((((append_node @ A @ E) = C) & (B = (append_node @ E @ D))) | (((append_node @ E @ B) = D) & (A = (append_node @ C @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_append__eq__append__conv2)). 43.09/14.37 thf(740,plain,((! [A:list_node,B:list_node,C:list_node,D:list_node]: (((append_node @ A @ B) = (append_node @ C @ D)) = (? [E:list_node]: ((((append_node @ A @ E) = C) & (B = (append_node @ E @ D))) | (((append_node @ E @ B) = D) & (A = (append_node @ C @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 43.09/14.37 thf(146,axiom,((! [A:g,B:node,C:list_node,D:node,E:(node > (list_node > (node > $o)))]: ((((member_node @ B @ (set_node2 @ (alpha_n @ A))) => (E @ B @ (cons_node @ B @ nil_node) @ B)) => ((E @ B @ C @ D) <= (! [F:list_node,G:node,H:node]: ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ G) => (((member_node @ G @ (set_node2 @ (graph_272749361_edgeD @ inEdges @ A @ H))) => (E @ B @ (append_node @ F @ (cons_node @ H @ nil_node)) @ H)) <= (E @ B @ F @ G)))))) <= (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_old_Opath2__rev__induct)). 43.09/14.37 thf(940,plain,((! [A:g,B:node,C:list_node,D:node,E:(node > (list_node > (node > $o)))]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ C @ D) => (((member_node @ B @ (set_node2 @ (alpha_n @ A))) => (E @ B @ (cons_node @ B @ nil_node) @ B)) => ((! [F:list_node,G:node,H:node]: ((graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ A @ B @ F @ G) => ((E @ B @ F @ G) => ((member_node @ G @ (set_node2 @ (graph_272749361_edgeD @ (inEdges) @ A @ H))) => (E @ B @ (append_node @ F @ (cons_node @ H @ nil_node)) @ H))))) => (E @ B @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 43.09/14.37 thf(207,axiom,((r != phi_r)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_False)). 43.09/14.37 thf(1184,plain,((~ (r = phi_r))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 43.09/14.37 thf(14,axiom,((distinct_node @ nil_node)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_distinct_Osimps_I1_J)). 43.09/14.37 thf(309,plain,((distinct_node @ nil_node)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 43.09/14.37 thf(79,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/sandbox/benchmark/theBenchmark.p',fact_194_list__2pre__induct)). 43.09/14.37 thf(639,plain,((! [A:(list_node > (list_node > $o)),B:list_node,C:list_node]: ((A @ nil_node @ nil_node) => ((! [D:node,E:list_node,F:list_node]: ((A @ E @ F) => (A @ (cons_node @ D @ E) @ F))) => ((! [D:node,E:list_node,F:list_node]: ((A @ E @ F) => (A @ E @ (cons_node @ D @ F)))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 43.09/14.37 thf(162,axiom,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ B @ A @ (cons_node @ A @ nil_node) @ A) <= (invar @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_old_Oempty__path2)). 43.09/14.37 thf(1014,plain,((! [A:node,B:g]: ((member_node @ A @ (set_node2 @ (alpha_n @ B))) => ((invar @ B) => (graph_1012773594_edgeD @ (alpha_n) @ (invar) @ (inEdges) @ B @ A @ (cons_node @ A @ nil_node) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 43.09/14.37 thf(1411,plain,(($false)),inference(e,[status(thm)],[809,1168,1237,909,628,1200,683,1290,1073,873,247,1305,597,1078,1137,1275,814,1222,670,1001,1243,782,288,1254,1055,1287,785,504,702,802,1191,542,1147,870,969,284,1115,321,376,623,834,966,1302,756,1169,397,265,849,292,380,546,761,1047,334,1091,1042,1217,561,407,429,957,1223,894,847,879,665,583,461,1210,1027,1195,324,1012,916,467,852,435,697,1143,1111,1096,1006,388,593,1118,980,403,753,526,1214,1039,1292,933,1016,1207,1114,997,1099,1150,1231,1060,911,779,244,938,360,805,921,1286,1187,662,888,906,1251,513,1219,573,444,733,1154,423,694,1125,286,743,875,391,936,1058,919,764,1282,736,990,509,362,567,345,816,799,700,626,1177,1061,636,868,267,438,922,658,455,883,394,306,426,1203,531,1134,1081,617,1049,776,705,310,580,855,673,441,1317,338,951,470,576,1023,613,1052,864,1008,571,1272,1240,386,978,1140,250,1180,903,891,844,771,1108,450,1084,1157,1321,588,1101,632,418,1030,914,1308,383,899,667,1294,447,432,967,373,999,620,242,294,1314,341,506,1065,1165,796,1172,897,767,400,1197,839,860,1019,528,1004,1299,1120,501,728,740,940,1184,309,639,1014])). 43.09/14.37 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 43.09/14.37 % [INFO] Killing All external provers ... 0.21/14.47 EOF