0.07/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.14	% Command  : run_Leo-III %s %d
0.15/0.35	% Computer : n015.cluster.edu
0.15/0.35	% Model    : x86_64 x86_64
0.15/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.15/0.35	% Memory   : 8042.1875MB
0.15/0.35	% OS       : Linux 3.10.0-693.el7.x86_64
0.15/0.35	% CPULimit : 1440
0.15/0.35	% WCLimit  : 180
0.15/0.35	% DateTime : Mon Jul  3 07:14:55 EDT 2023
0.15/0.35	% CPUTime  : 
0.86/0.83	% [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
1.60/1.07	% [INFO] 	 Parsing done (239ms). 
1.60/1.08	% [INFO] 	 Running in sequential loop mode. 
2.29/1.28	% [INFO] 	 eprover registered as external prover. 
2.29/1.28	% [INFO] 	 cvc4 registered as external prover. 
2.29/1.29	% [INFO] 	 Scanning for conjecture ... 
2.64/1.37	% [INFO] 	 Found a conjecture and 359 axioms. Running axiom selection ... 
2.64/1.45	% [INFO] 	 Axiom selection finished. Selected 253 axioms (removed 106 axioms). 
3.28/1.59	% [INFO] 	 Problem is higher-order (TPTP THF). 
3.47/1.60	% [INFO] 	 Type checking passed. 
3.47/1.61	% [CONFIG] 	 Using configuration: timeout(180) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
11.88/3.68	% External prover 'e' found a proof!
11.88/3.68	% [INFO] 	 Killing All external provers ... 
11.88/3.68	% Time passed: 3168ms (effective reasoning time: 2595ms)
11.88/3.68	% Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
11.88/3.68	% Axioms used in derivation (253): fact_351_holomorphic__fun__eq__0__on__connected, fact_286_ball__imageD, fact_108_mult__right__cancel, fact_196_rewriteL__comp__comp, fact_215_image__id, fact_335_order__class_Oorder_Oantisym, fact_31_mult__zero__left, fact_271_le0, fact_185_isomorphism__expand, fact_252_not__one__le__zero, fact_96_mult_Oleft__commute, fact_39_mult__cancel__left, fact_140_funpow__code__def, fact_115_comm__monoid__mult__class_Omult__1, fact_137_set__times__intro, fact_203_nat__mult__eq__cancel__disj, fact_11_eq__id__iff, fact_317_Nat_Oex__has__greatest__nat, fact_321_dual__order_Oeq__iff, fact_276_bot__nat__0_Oextremum__uniqueI, fact_64_mult__cancel__left1, fact_49_mult_Oleft__neutral, fact_126_vector__space__over__itself_Oscale__zero__left, fact_120_funpow__simps__right_I1_J, fact_312_le__refl, fact_198_rewriteL__comp__comp2, fact_314_eq__imp__le, fact_142_funpow__code__def, fact_24__092_060open_062deriv_A_Ig_A_092_060circ_062_Af_J_Aw_A_061_Aderiv_Aid_Aw_092_060close_062, fact_36_mult__eq__0__iff, fact_33_mult__zero__right, fact_80_comp__eq__dest__lhs, fact_7_id__apply, fact_269_image__eqI, fact_22_id__funpow, fact_151_higher__deriv__transform__within__open, fact_118_funpow__simps__right_I1_J, fact_146_mult__cancel1, fact_2_assms_I7_J, fact_58_mult__cancel__right2, fact_157_funpow__mult, fact_145_mult__cancel2, fact_89_mult_Oassoc, fact_272_bot__nat__0_Oextremum, fact_99_divisors__zero, fact_122_vector__space__over__itself_Oscale__one, fact_51_id__comp, fact_214_image__id, fact_212_le__zero__eq, fact_232_mult__nonneg__nonneg, fact_71_comp__def, fact_60_mult__cancel__right1, fact_298_set__eq__subset, fact_302_subset__imageE, fact_85_mult__not__zero, fact_248_mult__mono, fact_295_subset__refl, fact_350_Ln__1, fact_169_vector__space__over__itself_Oscale__right__imp__eq, fact_327_linorder__wlog, fact_177_pointfree__idE, fact_79_funpow__swap1, fact_81_zero__reorient, fact_37_mult__eq__0__iff, fact_197_rewriteR__comp__comp, fact_152_holomorphic__higher__deriv, fact_305_order__refl, fact_182_isomorphism__expand, fact_102_no__zero__divisors, fact_42_mult__cancel__right, fact_262_mult__eq__1, fact_56_assms_I3_J, fact_306_order__refl, fact_310_Sup_OSUP__id__eq, fact_46_mult_Oright__neutral, fact_192_left__right__inverse__eq, fact_300_image__mono, fact_84_mult__not__zero, fact_218_image__comp, fact_83_zero__reorient, fact_282_imageI, fact_303_image__subset__iff, fact_57__092_060open_062deriv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_A_061_Aderiv_A_Ig_A_092_060circ_062_Af_J_Aw_092_060close_062, fact_279_mult__le__mono, fact_69_ab__semigroup__mult__class_Omult__ac_I1_J, fact_289_subsetD, fact_284_bex__imageD, fact_287_rev__image__eqI, fact_114_comm__monoid__mult__class_Omult__1, fact_189_left__right__inverse__eq, fact_258_mult__le__one, fact_240_mult__left__mono, fact_173_fun_Omap__id0, fact_223_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_183_isomorphism__expand, fact_296_Collect__mono, fact_194_left__right__inverse__eq, fact_132_vector__space__over__itself_Oscale__cancel__right, fact_101_no__zero__divisors, fact_333_order__trans, fact_230_mult__nonneg__nonpos, fact_277_mult__le__mono2, fact_171_vector__space__over__itself_Oscale__left__imp__eq, fact_5_id__apply, fact_184_isomorphism__expand, fact_27_zero__neq__one, fact_29_comp__apply, fact_304_subset__image__iff, fact_285_image__cong, fact_200_holomorphic__cong, fact_211_arcosh__1, fact_324_dual__order_Otrans, fact_270_subsetI, fact_178_isomorphism__expand, fact_294_subset__iff, fact_213_image__id, fact_318_dual__order_Oantisym, fact_153_holomorphic__deriv, fact_268_subset__antisym, fact_76_comp__eq__elim, fact_107_mult__right__cancel, fact_68_ab__semigroup__mult__class_Omult__ac_I1_J, fact_124_vector__space__over__itself_Oscale__eq__0__iff, fact_53_funpow__0, fact_121_fun_Omap__id, fact_283_image__iff, fact_55_funpow__0, help_If_1_1_If_001t__Complex__Ocomplex_T, fact_1__092_060open_062_092_060And_062z_O_A_Ideriv_A_094_094_A1_J_Aid_Az_A_061_A_Iif_A1_A_061_A0_Athen_Az_Aelse_Aif_A1_A_061_A1_Athen_A1_058_058_063_Ha_Aelse_A_I0_058_058_063_Ha_J_J_092_060close_062, fact_256_mult__left__le, fact_28__092_060open_062deriv_Af_Aw_A_K_Aderiv_Ag_A_If_Aw_J_A_061_Aderiv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_092_060close_062, fact_25_zero__neq__one, fact_62_mult__cancel__left2, fact_273_less__eq__nat_Osimps_I1_J, fact_330_dual__order_Orefl, fact_73_comp__funpow, fact_217_holomorphic__on__compose__gen, fact_159_funpow__mult, fact_163_vector__space__over__itself_Oscale__scale, fact_147_mult__0__right, fact_165_set__times__elim, fact_149_nat__mult__eq__1__iff, fact_130_vector__space__over__itself_Oscale__cancel__left, fact_186_isomorphism__expand, fact_161_vector__space__over__itself_Oscale__left__commute, fact_143_assms_I4_J, fact_325_dual__order_Otrans, fact_72_comp__assoc, fact_274_le__0__eq, fact_13_eq__id__iff, fact_280_le__square, fact_3_deriv__id, fact_93_mult_Ocommute, fact_154_mult__0, fact_66_assms_I6_J, fact_67_assms_I1_J, fact_105_mult__left__cancel, fact_319_dual__order_Oantisym, fact_267_arsinh__0, fact_299_Collect__mono__iff, fact_87_mem__Collect__eq, fact_219_image__eq__imp__comp, fact_15_higher__deriv__id, fact_207_mult__delta__right, fact_168_fun_Omap__comp, fact_134_mult__if__delta, fact_148_mult__is__0, fact_202_assms_I5_J, fact_222_set__times__mono2__b, fact_112_mult_Ocomm__neutral, fact_309_Sup_OSUP__id__eq, fact_237_mult__right__mono, fact_190_left__right__inverse__eq, fact_75_comp__eq__dest, fact_104_mult__left__cancel, fact_246_mult__mono_H, fact_204_mult__delta__left, fact_12_eq__id__iff, fact_265_artanh__0, fact_234_split__mult__neg__le, fact_195_left__right__inverse__eq, help_If_2_1_If_001t__Complex__Ocomplex_T, fact_220_zero__le, fact_110_comp__eq__id__dest, fact_292_equalityD1, fact_191_left__right__inverse__eq, fact_90_mult_Oassoc, fact_98_divisors__zero, fact_338_ord__le__eq__trans, fact_10_id__def, fact_160_mult__eq__self__implies__10, fact_336_order__class_Oorder_Oantisym, fact_228_mult__nonpos__nonneg, fact_290_equalityE, fact_176_holomorphic__on__linear, fact_329_dual__order_Orefl, fact_45_mult_Oright__neutral, fact_17_one__reorient, help_If_3_1_If_001t__Complex__Ocomplex_T, fact_180_isomorphism__expand, fact_301_image__subsetI, fact_77_funpow__swap1, fact_92_mult_Ocommute, fact_150_nat__1__eq__mult__iff, fact_316_nat__le__linear, fact_255_deriv__left__inverse, fact_332_order__trans, fact_95_mult_Oleft__commute, fact_181_isomorphism__expand, fact_48_mult_Oleft__neutral, fact_226_mult__nonneg__nonpos2, fact_117_funpow__simps__right_I1_J, fact_8_id__def, fact_216_set__times__mono2, fact_311_Sup_OSUP__id__eq, fact_9_id__def, fact_278_mult__le__mono1, fact_43_mult__cancel__right, fact_322_dual__order_Oeq__iff, fact_40_mult__cancel__left, fact_193_left__right__inverse__eq, fact_201_holomorphic__transform, fact_221_holomorphic__on__subset, fact_128_vector__space__over__itself_Oscale__zero__right, fact_23_calculation, fact_297_subset__trans, fact_19_id__funpow, fact_179_isomorphism__expand, fact_315_le__antisym, fact_111_mult_Ocomm__neutral, fact_187_left__right__inverse__eq, fact_175_holomorphic__on__id, fact_155_nat__mult__1__right, fact_288_in__mono, fact_275_bot__nat__0_Oextremum__unique, fact_281_le__cube, fact_6_id__apply, fact_291_subset__eq, fact_174_complex__derivative__transform__within__open, fact_21_id__funpow, fact_34_mult__zero__right, fact_88_Collect__mem__eq, fact_250_zero__le__one, fact_199_rewriteR__comp__comp2, fact_52_comp__id, fact_293_equalityD2, fact_156_nat__mult__1, fact_144_assms_I2_J, fact_254_holomorphic__on__compose, fact_30_mult__zero__left, fact_16_one__reorient, fact_188_left__right__inverse__eq, fact_313_le__trans
11.88/3.68	% No. of inferences in proof: 510
11.88/3.68	% SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3168 ms resp. 2595 ms w/o parsing
12.71/3.83	% SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
12.71/3.83	thf(set_complex_complex_type, type, set_complex_complex: $tType).
12.71/3.83	thf(set_complex_type, type, set_complex: $tType).
12.71/3.83	thf(set_real_type, type, set_real: $tType).
12.71/3.83	thf(set_nat_type, type, set_nat: $tType).
12.71/3.83	thf(complex_type, type, complex: $tType).
12.71/3.83	thf(real_type, type, real: $tType).
12.71/3.83	thf(nat_type, type, nat: $tType).
12.71/3.83	thf(comple372758642hic_on_type, type, comple372758642hic_on: ((complex > complex) > (set_complex > $o))).
12.71/3.83	thf(deriv_complex_type, type, deriv_complex: ((complex > complex) > (complex > complex))).
12.71/3.83	thf(comp_c1610621014omplex_type, type, comp_c1610621014omplex: (((complex > complex) > (complex > complex)) > (((complex > complex) > (complex > complex)) > ((complex > complex) > (complex > complex))))).
12.71/3.83	thf(comp_c881053372omplex_type, type, comp_c881053372omplex: (((complex > complex) > complex) > ((complex > (complex > complex)) > (complex > complex)))).
12.71/3.83	thf(comp_c1884694328l_real_type, type, comp_c1884694328l_real: (((complex > complex) > real) > ((real > (complex > complex)) > (real > real)))).
12.71/3.83	thf(comp_c606622857omplex_type, type, comp_c606622857omplex: ((complex > (complex > complex)) > (((complex > complex) > complex) > ((complex > complex) > (complex > complex))))).
12.71/3.83	thf(comp_c130555887omplex_type, type, comp_c130555887omplex: ((complex > complex) > ((complex > complex) > (complex > complex)))).
12.71/3.83	thf(comp_c819638635l_real_type, type, comp_c819638635l_real: ((complex > real) > ((real > complex) > (real > real)))).
12.71/3.83	thf(comp_r2009261319omplex_type, type, comp_r2009261319omplex: ((real > (complex > complex)) > (((complex > complex) > real) > ((complex > complex) > (complex > complex))))).
12.71/3.83	thf(comp_r667767405omplex_type, type, comp_r667767405omplex: ((real > complex) > ((complex > real) > (complex > complex)))).
12.71/3.83	thf(comp_real_real_real_type, type, comp_real_real_real: ((real > real) > ((real > real) > (real > real)))).
12.71/3.83	thf(id_complex_complex_type, type, id_complex_complex: ((complex > complex) > (complex > complex))).
12.71/3.83	thf(id_complex_type, type, id_complex: (complex > complex)).
12.71/3.83	thf(id_real_type, type, id_real: (real > real)).
12.71/3.83	thf(id_set1618538368omplex_type, type, id_set1618538368omplex: (set_complex_complex > set_complex_complex)).
12.71/3.83	thf(id_set_complex_type, type, id_set_complex: (set_complex > set_complex)).
12.71/3.83	thf(id_set_real_type, type, id_set_real: (set_real > set_real)).
12.71/3.83	thf(one_one_complex_type, type, one_one_complex: complex).
12.71/3.83	thf(one_one_nat_type, type, one_one_nat: nat).
12.71/3.83	thf(times_times_complex_type, type, times_times_complex: (complex > (complex > complex))).
12.71/3.83	thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))).
12.71/3.83	thf(times_1316095593omplex_type, type, times_1316095593omplex: (set_complex > (set_complex > set_complex))).
12.71/3.83	thf(zero_zero_complex_type, type, zero_zero_complex: complex).
12.71/3.83	thf(zero_zero_nat_type, type, zero_zero_nat: nat).
12.71/3.83	thf(if_complex_type, type, if_complex: ($o > (complex > (complex > complex)))).
12.71/3.83	thf(compow1098280738omplex_type, type, compow1098280738omplex: (nat > (((complex > complex) > (complex > complex)) > ((complex > complex) > (complex > complex))))).
12.71/3.83	thf(compow1667379464omplex_type, type, compow1667379464omplex: (nat > ((complex > complex) > (complex > complex)))).
12.71/3.83	thf(compow_real_real_type, type, compow_real_real: (nat > ((real > real) > (real > real)))).
12.71/3.83	thf(funpow1854104714omplex_type, type, funpow1854104714omplex: (nat > (((complex > complex) > (complex > complex)) > ((complex > complex) > (complex > complex))))).
12.71/3.83	thf(funpow_complex_type, type, funpow_complex: (nat > ((complex > complex) > (complex > complex)))).
12.71/3.83	thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))).
12.71/3.83	thf(ord_le701908932omplex_type, type, ord_le701908932omplex: (set_complex > (set_complex > $o))).
12.71/3.83	thf(collect_complex_type, type, collect_complex: ((complex > $o) > set_complex)).
12.71/3.83	thf(image_944012797omplex_type, type, image_944012797omplex: (((complex > complex) > (complex > complex)) > (set_complex_complex > set_complex_complex))).
12.71/3.83	thf(image_58037603omplex_type, type, image_58037603omplex: ((complex > complex) > (set_complex > set_complex))).
12.71/3.83	thf(image_real_real_type, type, image_real_real: ((real > real) > (set_real > set_real))).
12.71/3.83	thf(topolo935673511omplex_type, type, topolo935673511omplex: (set_complex > $o)).
12.71/3.83	thf(topolo2127351575omplex_type, type, topolo2127351575omplex: (set_complex > $o)).
12.71/3.83	thf(arcosh_complex_type, type, arcosh_complex: (complex > complex)).
12.71/3.83	thf(arsinh_complex_type, type, arsinh_complex: (complex > complex)).
12.71/3.83	thf(artanh_complex_type, type, artanh_complex: (complex > complex)).
12.71/3.83	thf(ln_ln_complex_type, type, ln_ln_complex: (complex > complex)).
12.71/3.83	thf(member_complex_type, type, member_complex: (complex > (set_complex > $o))).
12.71/3.83	thf(s_type, type, s: set_complex).
12.71/3.83	thf(t_type, type, t: set_complex).
12.71/3.83	thf(f_type, type, f: (complex > complex)).
12.71/3.83	thf(g_type, type, g: (complex > complex)).
12.71/3.83	thf(w_type, type, w: complex).
12.71/3.83	thf(75,axiom,((ord_le701908932omplex = (^ [A:set_complex,B:set_complex]: ! [C:complex]: ((member_complex @ C @ A) => (member_complex @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_subset__eq)).
12.71/3.83	thf(479,plain,(((ord_le701908932omplex) = (^ [A:set_complex,B:set_complex]: ! [C:complex]: ((member_complex @ C @ A) => (member_complex @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])).
12.71/3.83	thf(123,axiom,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = ((B = C) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_mult__cancel__left)).
12.71/3.83	thf(628,plain,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = ((B = C) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
12.71/3.83	thf(86,axiom,((id_real = (^ [A:real]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_id__def)).
12.71/3.83	thf(518,plain,(((id_real) = (^ [A:real]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
12.71/3.83	thf(221,axiom,(((arcosh_complex @ one_one_complex) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_arcosh__1)).
12.71/3.83	thf(941,plain,(((arcosh_complex @ one_one_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
12.71/3.83	thf(136,axiom,((! [A:complex,B:complex]: ((if_complex @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Complex__Ocomplex_T)).
12.71/3.83	thf(666,plain,((! [A:complex,B:complex]: ((if_complex @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])).
12.71/3.83	thf(76,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex),E:(complex > complex),F:(complex > complex)]: ((((comp_c130555887omplex @ D @ E) = F) => ((comp_c130555887omplex @ A @ (comp_c130555887omplex @ B @ E)) = (comp_c130555887omplex @ C @ F))) <= ((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_rewriteL__comp__comp2)).
12.71/3.83	thf(481,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex),E:(complex > complex),F:(complex > complex)]: ((((comp_c130555887omplex @ D @ E) = (F)) => ((comp_c130555887omplex @ A @ (comp_c130555887omplex @ B @ E)) = (comp_c130555887omplex @ C @ F))) | ~ ((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
12.71/3.83	thf(33,axiom,((! [A:nat,B:nat]: ((((ord_less_eq_nat @ zero_zero_nat @ B) & (ord_less_eq_nat @ A @ zero_zero_nat)) | ((ord_less_eq_nat @ zero_zero_nat @ A) & (ord_less_eq_nat @ B @ zero_zero_nat))) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_split__mult__neg__le)).
12.71/3.83	thf(352,plain,((! [A:nat,B:nat]: ((((ord_less_eq_nat @ zero_zero_nat @ B) & (ord_less_eq_nat @ A @ zero_zero_nat)) | ((ord_less_eq_nat @ zero_zero_nat @ A) & (ord_less_eq_nat @ B @ zero_zero_nat))) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
12.71/3.83	thf(50,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mult_Ocommute)).
12.71/3.83	thf(408,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
12.71/3.83	thf(88,axiom,((! [A:((complex > complex) > (complex > complex)),B:((complex > complex) > (complex > complex)),C:((complex > complex) > (complex > complex))]: ((((comp_c1610621014omplex @ B @ C) = id_complex_complex) => (A = C)) <= ((comp_c1610621014omplex @ A @ B) = id_complex_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_left__right__inverse__eq)).
12.71/3.83	thf(523,plain,((! [A:((complex > complex) > (complex > complex)),B:((complex > complex) > (complex > complex)),C:((complex > complex) > (complex > complex))]: ((((comp_c1610621014omplex @ B @ C) = (id_complex_complex)) => ((A) = (C))) | ~ ((comp_c1610621014omplex @ A @ B) = (id_complex_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
12.71/3.83	thf(141,axiom,((times_times_complex = (^ [A:complex,B:complex]: (times_times_complex @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_mult_Ocommute)).
12.71/3.83	thf(683,plain,(((times_times_complex) = (^ [A:complex,B:complex]: (times_times_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
12.71/3.83	thf(156,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => (((times_times_complex @ B @ A) = (times_times_complex @ C @ A)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_mult__right__cancel)).
12.71/3.83	thf(730,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => (((times_times_complex @ B @ A) = (times_times_complex @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
12.71/3.83	thf(64,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_mult__is__0)).
12.71/3.83	thf(449,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
12.71/3.83	thf(117,axiom,((! [A:set_complex,B:set_complex,C:complex]: (((member_complex @ C @ A) => (member_complex @ C @ B)) <= (ord_le701908932omplex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_subsetD)).
12.71/3.83	thf(614,plain,((! [A:set_complex,B:set_complex,C:complex]: (((member_complex @ C @ A) => (member_complex @ C @ B)) | ~ (ord_le701908932omplex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
12.71/3.83	thf(61,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ B)) <= (ord_less_eq_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_mult__left__le)).
12.71/3.83	thf(440,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ B)) | ~ (ord_less_eq_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
12.71/3.83	thf(84,axiom,((! [A:nat]: ((compow_real_real @ A @ id_real) = id_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_id__funpow)).
12.71/3.83	thf(511,plain,((! [A:nat]: ((compow_real_real @ A @ id_real) = (id_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
12.71/3.83	thf(42,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_mult__nonneg__nonpos2)).
12.71/3.83	thf(384,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
12.71/3.83	thf(91,axiom,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ C @ B)) = ((B = zero_zero_complex) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mult__cancel__right)).
12.71/3.83	thf(533,plain,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ C @ B)) = ((B = zero_zero_complex) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])).
12.71/3.83	thf(173,axiom,((! [A:(complex > $o),B:(complex > $o)]: ((! [C:complex]: ((B @ C) <= (A @ C))) => (ord_le701908932omplex @ (collect_complex @ A) @ (collect_complex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Collect__mono)).
12.71/3.83	thf(797,plain,((! [A:(complex > $o),B:(complex > $o)]: ((! [C:complex]: ((B @ C) | ~ (A @ C))) => (ord_le701908932omplex @ (collect_complex @ (A)) @ (collect_complex @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])).
12.71/3.83	thf(72,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_dual__order_Oeq__iff)).
12.71/3.83	thf(472,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
12.71/3.83	thf(217,axiom,((zero_zero_complex != one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_zero__neq__one)).
12.71/3.83	thf(930,plain,((~ (zero_zero_complex = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])).
12.71/3.83	thf(189,axiom,((! [A:set_complex,B:set_complex,C:set_complex,D:set_complex,E:complex]: ((ord_le701908932omplex @ A @ B) => (((member_complex @ E @ (times_1316095593omplex @ A @ C)) => (member_complex @ E @ (times_1316095593omplex @ B @ D))) <= (ord_le701908932omplex @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_set__times__mono2__b)).
12.71/3.83	thf(841,plain,((! [A:set_complex,B:set_complex,C:set_complex,D:set_complex,E:complex]: ((ord_le701908932omplex @ A @ B) => (((member_complex @ E @ (times_1316095593omplex @ A @ C)) => (member_complex @ E @ (times_1316095593omplex @ B @ D))) | ~ (ord_le701908932omplex @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
12.71/3.83	thf(22,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_dual__order_Oantisym)).
12.71/3.83	thf(320,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
12.71/3.83	thf(102,axiom,((! [A:set_complex,B:set_complex]: (((A = B) <= (ord_le701908932omplex @ B @ A)) <= (ord_le701908932omplex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_subset__antisym)).
12.71/3.83	thf(565,plain,((! [A:set_complex,B:set_complex]: ((A = B) | ~ (ord_le701908932omplex @ B @ A) | ~ (ord_le701908932omplex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])).
12.71/3.83	thf(147,axiom,((! [A:complex]: (((g @ (f @ A)) = A) <= (member_complex @ A @ s)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_assms_I6_J)).
12.71/3.83	thf(702,plain,((! [A:complex]: (((g @ (f @ A)) = A) | ~ (member_complex @ A @ s)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
12.71/3.83	thf(224,axiom,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_comm__monoid__mult__class_Omult__1)).
12.71/3.83	thf(949,plain,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
12.71/3.83	thf(68,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_ab__semigroup__mult__class_Omult__ac_I1_J)).
12.71/3.83	thf(460,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
12.71/3.83	thf(175,axiom,((((=) @ set_complex) = (^ [A:set_complex,B:set_complex]: ((ord_le701908932omplex @ A @ B) & (ord_le701908932omplex @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_set__eq__subset)).
12.71/3.83	thf(802,plain,((((=) @ set_complex) = (^ [A:set_complex,B:set_complex]: ((ord_le701908932omplex @ A @ B) & (ord_le701908932omplex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
12.71/3.83	thf(30,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_bot__nat__0_Oextremum)).
12.71/3.83	thf(344,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
12.71/3.83	thf(100,axiom,((! [A:(complex > complex),B:(complex > complex),C:set_complex]: ((image_58037603omplex @ A @ (image_58037603omplex @ B @ C)) = (image_58037603omplex @ (comp_c130555887omplex @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_image__comp)).
12.71/3.83	thf(559,plain,((! [A:(complex > complex),B:(complex > complex),C:set_complex]: ((image_58037603omplex @ (A) @ (image_58037603omplex @ (B) @ C)) = (image_58037603omplex @ (comp_c130555887omplex @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])).
12.71/3.83	thf(126,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:complex]: (((comp_c130555887omplex @ A @ B) = C) => ((A @ (B @ D)) = (C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_comp__eq__dest__lhs)).
12.71/3.83	thf(638,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:complex]: (((comp_c130555887omplex @ A @ B) = (C)) => ((A @ (B @ D)) = (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
12.71/3.83	thf(230,axiom,(((times_times_complex @ (deriv_complex @ f @ w) @ (deriv_complex @ g @ (f @ w))) = (times_times_complex @ (deriv_complex @ g @ (f @ w)) @ (deriv_complex @ f @ w)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28__092_060open_062deriv_Af_Aw_A_K_Aderiv_Ag_A_If_Aw_J_A_061_Aderiv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_092_060close_062)).
12.71/3.83	thf(969,plain,(((times_times_complex @ (deriv_complex @ (f) @ w) @ (deriv_complex @ (g) @ (f @ w))) = (times_times_complex @ (deriv_complex @ (g) @ (f @ w)) @ (deriv_complex @ (f) @ w)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
12.71/3.83	thf(53,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_nat__mult__eq__cancel__disj)).
12.71/3.83	thf(416,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
12.71/3.83	thf(11,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_nat__le__linear)).
12.71/3.83	thf(289,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
12.71/3.83	thf(4,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E)))) <= (! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_linorder__wlog)).
12.71/3.83	thf(261,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) | ~ (! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
12.71/3.83	thf(9,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_comm__monoid__mult__class_Omult__1)).
12.71/3.83	thf(284,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
12.71/3.83	thf(167,axiom,((! [A:complex,B:set_complex,C:complex,D:(complex > complex)]: ((member_complex @ A @ B) => ((member_complex @ C @ (image_58037603omplex @ D @ B)) <= (C = (D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_rev__image__eqI)).
12.71/3.83	thf(770,plain,((! [A:complex,B:set_complex,C:complex,D:(complex > complex)]: ((member_complex @ A @ B) => ((member_complex @ C @ (image_58037603omplex @ (D) @ B)) | ~ (C = (D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
12.71/3.83	thf(215,axiom,((! [A:(set_complex > complex),B:set_complex]: ((A @ (image_58037603omplex @ id_complex @ B)) = (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_Sup_OSUP__id__eq)).
12.71/3.83	thf(924,plain,((! [A:(set_complex > complex),B:set_complex]: ((A @ (image_58037603omplex @ (id_complex) @ B)) = (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])).
12.71/3.83	thf(112,axiom,((! [A:(real > real)]: ((! [B:real]: ((A @ B) = B)) = (A = id_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_eq__id__iff)).
12.71/3.83	thf(591,plain,((! [A:(real > real)]: ((! [B:real]: ((A @ B) = B)) = ((A) = (id_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
12.71/3.83	thf(62,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_nat__mult__1)).
12.71/3.83	thf(443,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
12.71/3.83	thf(249,axiom,(((comp_c130555887omplex @ id_complex) = id_complex_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_fun_Omap__id0)).
12.71/3.83	thf(1040,plain,(((comp_c130555887omplex @ id_complex) = (id_complex_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])).
12.71/3.83	thf(85,axiom,((! [A:set_complex,B:set_complex]: ((ord_le701908932omplex @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_equalityD1)).
12.71/3.83	thf(514,plain,((! [A:set_complex,B:set_complex]: ((ord_le701908932omplex @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
12.71/3.83	thf(105,axiom,((topolo935673511omplex @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_assms_I3_J)).
12.71/3.83	thf(574,plain,((topolo935673511omplex @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
12.71/3.83	thf(229,axiom,((! [A:(complex > complex),B:(complex > complex)]: ((((comp_c130555887omplex @ B @ A) = id_complex) & ((comp_c130555887omplex @ A @ B) = id_complex)) = (! [C:complex]: ((B @ (A @ C)) = C) & ! [C:complex]: ((A @ (B @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_isomorphism__expand)).
12.71/3.83	thf(966,plain,((! [A:(complex > complex),B:(complex > complex)]: ((((comp_c130555887omplex @ B @ A) = (id_complex)) & ((comp_c130555887omplex @ A @ B) = (id_complex))) = (! [C:complex]: ((B @ (A @ C)) = C) & ! [C:complex]: ((A @ (B @ C)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])).
12.71/3.83	thf(251,axiom,((id_complex = (^ [A:complex]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_id__def)).
12.71/3.83	thf(1051,plain,(((id_complex) = (^ [A:complex]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])).
12.71/3.83	thf(8,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ one_one_nat) => ((ord_less_eq_nat @ B @ one_one_nat) => (((times_times_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) & (B = one_one_nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_mult__eq__1)).
12.71/3.83	thf(280,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ one_one_nat) => ((ord_less_eq_nat @ B @ one_one_nat) => (((times_times_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) & (B = one_one_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
12.71/3.83	thf(200,axiom,((funpow1854104714omplex = compow1098280738omplex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_funpow__code__def)).
12.71/3.83	thf(877,plain,(((funpow1854104714omplex) = (compow1098280738omplex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
12.71/3.83	thf(157,axiom,((! [A:(real > real)]: ((compow_real_real @ zero_zero_nat @ A) = id_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_funpow__simps__right_I1_J)).
12.71/3.83	thf(734,plain,((! [A:(real > real)]: ((compow_real_real @ zero_zero_nat @ A) = (id_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])).
12.71/3.83	thf(227,axiom,((! [A:(complex > complex),B:set_complex,C:complex,D:complex]: ((((topolo2127351575omplex @ B) => (((((A @ D) = zero_zero_complex) <= (member_complex @ D @ B)) <= (member_complex @ C @ B)) <= (! [E:nat]: ((compow1098280738omplex @ E @ deriv_complex @ A @ C) = zero_zero_complex)))) <= (topolo935673511omplex @ B)) <= (comple372758642hic_on @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_holomorphic__fun__eq__0__on__connected)).
12.71/3.83	thf(956,plain,((! [A:(complex > complex),B:set_complex,C:complex,D:complex]: (((topolo2127351575omplex @ B) => (((A @ D) = zero_zero_complex) | ~ (member_complex @ D @ B) | ~ (member_complex @ C @ B) | ~ (! [E:nat]: ((compow1098280738omplex @ E @ (deriv_complex) @ (A) @ C) = zero_zero_complex)))) | ~ (topolo935673511omplex @ B) | ~ (comple372758642hic_on @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])).
12.71/3.83	thf(196,axiom,(((arsinh_complex @ zero_zero_complex) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_arsinh__0)).
12.71/3.83	thf(866,plain,(((arsinh_complex @ zero_zero_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
12.71/3.83	thf(46,axiom,((! [A:nat,B:nat,C:(complex > complex)]: ((compow1667379464omplex @ A @ (compow1667379464omplex @ B @ C)) = (compow1667379464omplex @ (times_times_nat @ B @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_funpow__mult)).
12.71/3.83	thf(396,plain,((! [A:nat,B:nat,C:(complex > complex)]: ((compow1667379464omplex @ A @ (compow1667379464omplex @ B @ C)) = (compow1667379464omplex @ (times_times_nat @ B @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
12.71/3.83	thf(134,axiom,((! [A:complex,B:(complex > complex),C:set_complex]: ((member_complex @ A @ (image_58037603omplex @ B @ C)) = (? [D:complex]: ((member_complex @ D @ C) & (A = (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_image__iff)).
12.71/3.83	thf(660,plain,((! [A:complex,B:(complex > complex),C:set_complex]: ((member_complex @ A @ (image_58037603omplex @ (B) @ C)) = (? [D:complex]: ((member_complex @ D @ C) & (A = (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
12.71/3.83	thf(191,axiom,((! [A:(complex > complex),B:set_complex,C:(complex > complex)]: ((comple372758642hic_on @ A @ B) => ((comple372758642hic_on @ (comp_c130555887omplex @ C @ A) @ B) <= (comple372758642hic_on @ C @ (image_58037603omplex @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_holomorphic__on__compose)).
12.71/3.83	thf(849,plain,((! [A:(complex > complex),B:set_complex,C:(complex > complex)]: ((comple372758642hic_on @ (A) @ B) => ((comple372758642hic_on @ (comp_c130555887omplex @ C @ A) @ B) | ~ (comple372758642hic_on @ (C) @ (image_58037603omplex @ (A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])).
12.71/3.83	thf(89,axiom,((! [A:(complex > $o),B:(complex > $o)]: ((ord_le701908932omplex @ (collect_complex @ A) @ (collect_complex @ B)) = (! [C:complex]: ((B @ C) <= (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_Collect__mono__iff)).
12.71/3.83	thf(527,plain,((! [A:(complex > $o),B:(complex > $o)]: ((ord_le701908932omplex @ (collect_complex @ (A)) @ (collect_complex @ (B))) = (! [C:complex]: ((B @ C) | ~ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
12.71/3.83	thf(114,axiom,((! [A:complex,B:complex]: (((B != zero_zero_complex) & (A != zero_zero_complex)) <= ((times_times_complex @ A @ B) != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_mult__not__zero)).
12.71/3.83	thf(602,plain,((! [A:complex,B:complex]: ((~ (B = zero_zero_complex) & ~ (A = zero_zero_complex)) | ((times_times_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
12.71/3.83	thf(234,axiom,(((deriv_complex @ id_complex) = (^ [A:complex]: (one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_deriv__id)).
12.71/3.83	thf(981,plain,(((deriv_complex @ id_complex) = (^ [A:complex]: (one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])).
12.71/3.83	thf(17,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_le__square)).
12.71/3.83	thf(307,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
12.71/3.83	thf(65,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_dual__order_Orefl)).
12.71/3.83	thf(452,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
12.71/3.83	thf(214,axiom,((! [A:(complex > real),B:(real > complex),C:(complex > real)]: ((((comp_r667767405omplex @ B @ C) = id_complex) => (A = C)) <= ((comp_c819638635l_real @ A @ B) = id_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_left__right__inverse__eq)).
12.71/3.83	thf(920,plain,((! [A:(complex > real),B:(real > complex),C:(complex > real)]: ((((comp_r667767405omplex @ B @ C) = (id_complex)) => ((A) = (C))) | ~ ((comp_c819638635l_real @ A @ B) = (id_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
12.71/3.83	thf(95,axiom,((id_real = (^ [A:real]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_id__apply)).
12.71/3.83	thf(546,plain,(((id_real) = (^ [A:real]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])).
12.71/3.83	thf(164,axiom,((! [A:set_complex,B:set_complex]: ((ord_le701908932omplex @ A @ B) => ((A = B) <= (ord_le701908932omplex @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_order__class_Oorder_Oantisym)).
12.71/3.83	thf(761,plain,((! [A:set_complex,B:set_complex]: ((ord_le701908932omplex @ A @ B) => ((A = B) | ~ (ord_le701908932omplex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
12.71/3.83	thf(178,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex)]: (((comp_c130555887omplex @ A @ (comp_c130555887omplex @ B @ D)) = (comp_c130555887omplex @ C @ D)) <= ((comp_c130555887omplex @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_rewriteL__comp__comp)).
12.71/3.83	thf(810,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex)]: (((comp_c130555887omplex @ A @ (comp_c130555887omplex @ B @ D)) = (comp_c130555887omplex @ C @ D)) | ~ ((comp_c130555887omplex @ A @ B) = (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
12.71/3.83	thf(41,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_mult__nonneg__nonpos)).
12.71/3.83	thf(381,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
12.71/3.83	thf(253,axiom,((! [A:complex,B:complex]: ((A = (times_times_complex @ A @ B)) = ((A = zero_zero_complex) | (B = one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_mult__cancel__left1)).
12.71/3.83	thf(1057,plain,((! [A:complex,B:complex]: ((A = (times_times_complex @ A @ B)) = ((A = zero_zero_complex) | (B = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])).
12.71/3.83	thf(210,axiom,(((image_58037603omplex @ id_complex) = id_set_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_image__id)).
12.71/3.83	thf(910,plain,(((image_58037603omplex @ id_complex) = (id_set_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])).
12.71/3.83	thf(204,axiom,((! [A:((complex > complex) > complex),B:(complex > (complex > complex))]: ((((comp_c881053372omplex @ A @ B) = id_complex) & ((comp_c606622857omplex @ B @ A) = id_complex_complex)) = (! [C:complex]: ((A @ (B @ C)) = C) & ! [C:(complex > complex)]: ((B @ (A @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_isomorphism__expand)).
12.71/3.83	thf(894,plain,((! [A:((complex > complex) > complex),B:(complex > (complex > complex))]: ((((comp_c881053372omplex @ (A) @ B) = (id_complex)) & ((comp_c606622857omplex @ B @ A) = (id_complex_complex))) = (! [C:complex]: ((A @ (B @ C)) = C) & ! [C:(complex > complex)]: ((B @ (A @ C)) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
12.71/3.83	thf(245,axiom,((! [A:complex]: (((one_one_nat = zero_zero_nat) => ((compow1098280738omplex @ one_one_nat @ deriv_complex @ id_complex @ A) = A)) & ((one_one_nat != zero_zero_nat) => ((compow1098280738omplex @ one_one_nat @ deriv_complex @ id_complex @ A) = one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062z_O_A_Ideriv_A_094_094_A1_J_Aid_Az_A_061_A_Iif_A1_A_061_A0_Athen_Az_Aelse_Aif_A1_A_061_A1_Athen_A1_058_058_063_Ha_Aelse_A_I0_058_058_063_Ha_J_J_092_060close_062)).
12.71/3.83	thf(1021,plain,((! [A:complex]: (((one_one_nat = zero_zero_nat) => ((compow1098280738omplex @ one_one_nat @ (deriv_complex) @ (id_complex) @ A) = A)) & ((~ (one_one_nat = zero_zero_nat)) => ((compow1098280738omplex @ one_one_nat @ (deriv_complex) @ (id_complex) @ A) = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
12.71/3.83	thf(32,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_le__0__eq)).
12.71/3.83	thf(349,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
12.71/3.83	thf(182,axiom,((! [A:(real > (complex > complex)),B:((complex > complex) > real),C:(real > (complex > complex))]: (((comp_r2009261319omplex @ A @ B) = id_complex_complex) => ((A = C) <= ((comp_c1884694328l_real @ B @ C) = id_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_left__right__inverse__eq)).
12.71/3.83	thf(820,plain,((! [A:(real > (complex > complex)),B:((complex > complex) > real),C:(real > (complex > complex))]: (((comp_r2009261319omplex @ A @ B) = (id_complex_complex)) => (((A) = (C)) | ~ ((comp_c1884694328l_real @ (B) @ C) = (id_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
12.71/3.83	thf(14,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_mult_Ocomm__neutral)).
12.71/3.83	thf(297,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
12.71/3.83	thf(58,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_ordered__comm__semiring__class_Ocomm__mult__left__mono)).
12.71/3.83	thf(429,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
12.71/3.83	thf(6,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_le__cube)).
12.71/3.83	thf(275,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
12.71/3.83	thf(179,axiom,((! [A:set_complex,B:set_complex,C:set_complex]: (((ord_le701908932omplex @ A @ C) <= (ord_le701908932omplex @ B @ C)) <= (ord_le701908932omplex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_order__trans)).
12.71/3.83	thf(815,plain,((! [A:set_complex,B:set_complex,C:set_complex]: ((ord_le701908932omplex @ A @ C) | ~ (ord_le701908932omplex @ B @ C) | ~ (ord_le701908932omplex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
12.71/3.83	thf(250,axiom,((! [A:$o,B:complex]: (((~ (A)) => ((times_times_complex @ (if_complex @ A @ one_one_complex @ zero_zero_complex) @ B) = zero_zero_complex)) & ((A) => ((times_times_complex @ (if_complex @ A @ one_one_complex @ zero_zero_complex) @ B) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_mult__if__delta)).
12.71/3.83	thf(1042,plain,((! [A:$o,B:complex]: (((~ (A)) => ((times_times_complex @ (if_complex @ A @ one_one_complex @ zero_zero_complex) @ B) = zero_zero_complex)) & ((A) => ((times_times_complex @ (if_complex @ A @ one_one_complex @ zero_zero_complex) @ B) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])).
12.71/3.83	thf(225,axiom,((member_complex @ w @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I7_J)).
12.71/3.83	thf(952,plain,((member_complex @ w @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
12.71/3.83	thf(36,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_mult__0)).
12.71/3.83	thf(361,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
12.71/3.83	thf(121,axiom,((comple372758642hic_on @ f @ s)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_assms_I1_J)).
12.71/3.83	thf(625,plain,((comple372758642hic_on @ (f) @ s)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
12.71/3.83	thf(201,axiom,((! [A:set_complex,B:(complex > complex),C:set_complex]: ((ord_le701908932omplex @ A @ (image_58037603omplex @ B @ C)) => (~ (! [D:set_complex]: ((A != (image_58037603omplex @ B @ D)) <= (ord_le701908932omplex @ D @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_subset__imageE)).
12.71/3.83	thf(879,plain,((! [A:set_complex,B:(complex > complex),C:set_complex]: ((ord_le701908932omplex @ A @ (image_58037603omplex @ (B) @ C)) => (~ (! [D:set_complex]: (~ (A = (image_58037603omplex @ (B) @ D)) | ~ (ord_le701908932omplex @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
12.71/3.83	thf(192,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_zero__neq__one)).
12.71/3.83	thf(852,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
12.71/3.83	thf(97,axiom,((! [A:set_complex,B:set_complex,C:set_complex]: (((ord_le701908932omplex @ A @ C) <= (ord_le701908932omplex @ B @ C)) <= (ord_le701908932omplex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_subset__trans)).
12.71/3.83	thf(551,plain,((! [A:set_complex,B:set_complex,C:set_complex]: ((ord_le701908932omplex @ A @ C) | ~ (ord_le701908932omplex @ B @ C) | ~ (ord_le701908932omplex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
12.71/3.83	thf(149,axiom,((! [A:(real > (complex > complex)),B:((complex > complex) > real)]: ((((comp_c1884694328l_real @ B @ A) = id_real) & ((comp_r2009261319omplex @ A @ B) = id_complex_complex)) = (! [C:real]: ((B @ (A @ C)) = C) & ! [C:(complex > complex)]: ((A @ (B @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_isomorphism__expand)).
12.71/3.83	thf(710,plain,((! [A:(real > (complex > complex)),B:((complex > complex) > real)]: ((((comp_c1884694328l_real @ (B) @ A) = (id_real)) & ((comp_r2009261319omplex @ A @ B) = (id_complex_complex))) = (! [C:real]: ((B @ (A @ C)) = C) & ! [C:(complex > complex)]: ((A @ (B @ C)) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
12.71/3.83	thf(242,axiom,((! [A:(complex > complex)]: ((! [B:complex]: ((A @ B) = B)) = (A = id_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_eq__id__iff)).
12.71/3.83	thf(1012,plain,((! [A:(complex > complex)]: ((! [B:complex]: ((A @ B) = B)) = ((A) = (id_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
12.71/3.83	thf(109,axiom,((ord_le701908932omplex = (^ [A:set_complex,B:set_complex]: ! [C:complex]: ((member_complex @ C @ B) <= (member_complex @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_subset__iff)).
12.71/3.83	thf(583,plain,(((ord_le701908932omplex) = (^ [A:set_complex,B:set_complex]: ! [C:complex]: ((member_complex @ C @ B) | ~ (member_complex @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
12.71/3.83	thf(185,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mult_Oassoc)).
12.71/3.83	thf(830,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
12.71/3.83	thf(199,axiom,((! [A:set_complex]: ((collect_complex @ (^ [B:complex]: (member_complex @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Collect__mem__eq)).
12.71/3.83	thf(874,plain,((! [A:set_complex]: ((collect_complex @ (^ [B:complex]: (member_complex @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])).
12.71/3.83	thf(21,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((A = C) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_mult__cancel2)).
12.71/3.83	thf(317,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((A = C) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
12.71/3.83	thf(130,axiom,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = ((B = C) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_vector__space__over__itself_Oscale__cancel__left)).
12.71/3.83	thf(650,plain,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = ((B = C) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])).
12.71/3.83	thf(240,axiom,((! [A:set_complex]: (comple372758642hic_on @ id_complex @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_holomorphic__on__id)).
12.71/3.83	thf(1006,plain,((! [A:set_complex]: (comple372758642hic_on @ (id_complex) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
12.71/3.83	thf(237,axiom,((! [A:nat,B:complex]: ((((compow1098280738omplex @ A @ deriv_complex @ id_complex @ B) = B) <= (A = zero_zero_nat)) & ((A != zero_zero_nat) => (((A != one_one_nat) => ((compow1098280738omplex @ A @ deriv_complex @ id_complex @ B) = zero_zero_complex)) & (((compow1098280738omplex @ A @ deriv_complex @ id_complex @ B) = one_one_complex) <= (A = one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_higher__deriv__id)).
12.71/3.83	thf(989,plain,((! [A:nat,B:complex]: ((((compow1098280738omplex @ A @ (deriv_complex) @ (id_complex) @ B) = B) | ~ (A = zero_zero_nat)) & ((~ (A = zero_zero_nat)) => (((~ (A = one_one_nat)) => ((compow1098280738omplex @ A @ (deriv_complex) @ (id_complex) @ B) = zero_zero_complex)) & (((compow1098280738omplex @ A @ (deriv_complex) @ (id_complex) @ B) = one_one_complex) | ~ (A = one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
12.71/3.83	thf(170,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex),E:complex]: (((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ C @ D)) => ((A @ (B @ E)) = (C @ (D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_comp__eq__dest)).
12.71/3.83	thf(783,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex),E:complex]: (((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ C @ D)) => ((A @ (B @ E)) = (C @ (D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
12.71/3.83	thf(55,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) & (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_nat__mult__eq__1__iff)).
12.71/3.83	thf(420,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) & (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
12.71/3.83	thf(246,axiom,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:complex]: ((comple372758642hic_on @ A @ B) => ((comple372758642hic_on @ C @ B) => ((topolo935673511omplex @ B) => ((member_complex @ D @ B) => ((! [E:complex]: ((member_complex @ E @ B) => ((A @ E) = (C @ E)))) => ((deriv_complex @ A @ D) = (deriv_complex @ C @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_complex__derivative__transform__within__open)).
12.71/3.83	thf(1028,plain,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:complex]: ((comple372758642hic_on @ (A) @ B) => ((comple372758642hic_on @ (C) @ B) => ((topolo935673511omplex @ B) => ((member_complex @ D @ B) => ((! [E:complex]: ((member_complex @ E @ B) => ((A @ E) = (C @ E)))) => ((deriv_complex @ (A) @ D) = (deriv_complex @ (C) @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])).
12.71/3.83	thf(78,axiom,((! [A:complex]: ((zero_zero_complex = A) = (A = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_zero__reorient)).
12.71/3.83	thf(488,plain,((! [A:complex]: ((zero_zero_complex = A) = (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
12.71/3.83	thf(218,axiom,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mult_Oright__neutral)).
12.71/3.83	thf(933,plain,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
12.71/3.83	thf(98,axiom,((funpow_complex = compow1667379464omplex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_funpow__code__def)).
12.71/3.83	thf(554,plain,(((funpow_complex) = (compow1667379464omplex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
12.71/3.83	thf(137,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_ab__semigroup__mult__class_Omult__ac_I1_J)).
12.71/3.83	thf(669,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
12.71/3.83	thf(207,axiom,((! [A:complex,B:complex]: ((A = (times_times_complex @ B @ A)) = ((B = one_one_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_mult__cancel__right1)).
12.71/3.83	thf(901,plain,((! [A:complex,B:complex]: ((A = (times_times_complex @ B @ A)) = ((B = one_one_complex) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
12.71/3.83	thf(140,axiom,((! [A:set_complex,B:set_complex]: ((A = B) => (ord_le701908932omplex @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_equalityD2)).
12.71/3.83	thf(679,plain,((! [A:set_complex,B:set_complex]: ((A = B) => (ord_le701908932omplex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
12.71/3.83	thf(25,axiom,((! [A:nat,B:nat]: (((B != zero_zero_nat) => ((times_times_nat @ A @ B) != zero_zero_nat)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_no__zero__divisors)).
12.71/3.83	thf(328,plain,((! [A:nat,B:nat]: (((~ (B = zero_zero_nat)) => (~ ((times_times_nat @ A @ B) = zero_zero_nat))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
12.71/3.83	thf(1,conjecture,(((deriv_complex @ id_complex @ w) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
12.71/3.83	thf(2,negated_conjecture,((~ ((deriv_complex @ id_complex @ w) = one_one_complex))),inference(neg_conjecture,[status(cth)],[1])).
12.71/3.83	thf(256,plain,((~ ((deriv_complex @ (id_complex) @ w) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
12.71/3.83	thf(120,axiom,((! [A:complex,B:(complex > $o)]: ((member_complex @ A @ (collect_complex @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_mem__Collect__eq)).
12.71/3.83	thf(622,plain,((! [A:complex,B:(complex > $o)]: ((member_complex @ A @ (collect_complex @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
12.71/3.83	thf(45,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_bot__nat__0_Oextremum__uniqueI)).
12.71/3.83	thf(393,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
12.71/3.83	thf(129,axiom,((! [A:nat]: ((compow1098280738omplex @ A @ id_complex_complex) = id_complex_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_id__funpow)).
12.71/3.83	thf(647,plain,((! [A:nat]: ((compow1098280738omplex @ A @ id_complex_complex) = (id_complex_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
12.71/3.83	thf(159,axiom,((! [A:complex,B:set_complex,C:set_complex]: ((~ (! [D:complex,E:complex]: (((~ (member_complex @ E @ C)) <= (member_complex @ D @ B)) <= (A = (times_times_complex @ D @ E))))) <= (member_complex @ A @ (times_1316095593omplex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_set__times__elim)).
12.71/3.83	thf(738,plain,((! [A:complex,B:set_complex,C:set_complex]: (~ (! [D:complex,E:complex]: (~ (member_complex @ E @ C) | ~ (member_complex @ D @ B) | ~ (A = (times_times_complex @ D @ E)))) | ~ (member_complex @ A @ (times_1316095593omplex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
12.71/3.83	thf(153,axiom,((id_complex_complex = (^ [A:(complex > complex)]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_id__apply)).
12.71/3.83	thf(721,plain,(((id_complex_complex) = (^ [A:(complex > complex)]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
12.71/3.83	thf(39,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mult_Oright__neutral)).
12.71/3.83	thf(371,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
12.71/3.83	thf(254,axiom,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:set_complex,E:complex]: (((((((! [F:complex]: ((member_complex @ F @ B) => ((C @ (A @ F)) = F))) => ((member_complex @ E @ B) => ((times_times_complex @ (deriv_complex @ A @ E) @ (deriv_complex @ C @ (A @ E))) = one_one_complex))) <= (ord_le701908932omplex @ (image_58037603omplex @ A @ B) @ D)) <= (topolo935673511omplex @ D)) <= (topolo935673511omplex @ B)) <= (comple372758642hic_on @ C @ D)) <= (comple372758642hic_on @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_deriv__left__inverse)).
12.71/3.83	thf(1060,plain,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:set_complex,E:complex]: (((! [F:complex]: ((member_complex @ F @ B) => ((C @ (A @ F)) = F))) => ((member_complex @ E @ B) => ((times_times_complex @ (deriv_complex @ (A) @ E) @ (deriv_complex @ (C) @ (A @ E))) = one_one_complex))) | ~ (ord_le701908932omplex @ (image_58037603omplex @ (A) @ B) @ D) | ~ (topolo935673511omplex @ D) | ~ (topolo935673511omplex @ B) | ~ (comple372758642hic_on @ (C) @ D) | ~ (comple372758642hic_on @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])).
12.71/3.83	thf(67,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_le__antisym)).
12.71/3.83	thf(457,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
12.71/3.83	thf(83,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex)]: ((comp_c130555887omplex @ A @ (comp_c130555887omplex @ B @ C)) = (comp_c130555887omplex @ (comp_c130555887omplex @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_fun_Omap__comp)).
12.71/3.83	thf(508,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex)]: ((comp_c130555887omplex @ A @ (comp_c130555887omplex @ B @ C)) = (comp_c130555887omplex @ (comp_c130555887omplex @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
12.71/3.83	thf(19,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_mult__nonneg__nonneg)).
12.71/3.83	thf(311,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
12.71/3.83	thf(90,axiom,((! [A:complex,B:complex]: ((if_complex @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Complex__Ocomplex_T)).
12.71/3.83	thf(530,plain,((! [A:complex,B:complex]: ((if_complex @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
12.71/3.83	thf(226,axiom,((! [A:(complex > complex)]: ((comp_c130555887omplex @ A @ id_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_comp__id)).
12.71/3.83	thf(953,plain,((! [A:(complex > complex)]: ((comp_c130555887omplex @ A @ id_complex) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
12.71/3.83	thf(152,axiom,((! [A:(set_complex_complex > (complex > complex)),B:set_complex_complex]: ((A @ (image_944012797omplex @ id_complex_complex @ B)) = (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_Sup_OSUP__id__eq)).
12.71/3.83	thf(718,plain,((! [A:(set_complex_complex > (complex > complex)),B:set_complex_complex]: ((A @ (image_944012797omplex @ (id_complex_complex) @ B)) = (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
12.71/3.83	thf(183,axiom,((! [A:(set_real > real),B:set_real]: ((A @ (image_real_real @ id_real @ B)) = (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_Sup_OSUP__id__eq)).
12.71/3.83	thf(824,plain,((! [A:(set_real > real),B:set_real]: ((A @ (image_real_real @ (id_real) @ B)) = (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
12.71/3.83	thf(161,axiom,((! [A:((complex > complex) > (complex > complex)),B:((complex > complex) > (complex > complex))]: ((((comp_c1610621014omplex @ B @ A) = id_complex_complex) & ((comp_c1610621014omplex @ A @ B) = id_complex_complex)) = (! [C:(complex > complex)]: ((A @ (B @ C)) = C) & ! [C:(complex > complex)]: ((B @ (A @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_isomorphism__expand)).
12.71/3.83	thf(745,plain,((! [A:((complex > complex) > (complex > complex)),B:((complex > complex) > (complex > complex))]: ((((comp_c1610621014omplex @ B @ A) = (id_complex_complex)) & ((comp_c1610621014omplex @ A @ B) = (id_complex_complex))) = (! [C:(complex > complex)]: ((A @ (B @ C)) = (C)) & ! [C:(complex > complex)]: ((B @ (A @ C)) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
12.71/3.83	thf(181,axiom,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_zero__le__one)).
12.71/3.83	thf(819,plain,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])).
12.71/3.83	thf(56,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_mult__right__mono)).
12.71/3.83	thf(423,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
12.71/3.83	thf(48,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_bot__nat__0_Oextremum__unique)).
12.71/3.83	thf(402,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
12.71/3.83	thf(160,axiom,(((image_944012797omplex @ id_complex_complex) = id_set1618538368omplex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_image__id)).
12.71/3.83	thf(743,plain,(((image_944012797omplex @ (id_complex_complex)) = (id_set1618538368omplex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
12.71/3.83	thf(107,axiom,((! [A:(complex > complex),B:set_complex,C:(complex > $o)]: ((? [D:complex]: ((member_complex @ D @ B) & (C @ (A @ D)))) <= (? [D:complex]: ((C @ D) & (member_complex @ D @ (image_58037603omplex @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_bex__imageD)).
12.71/3.83	thf(577,plain,((! [A:(complex > complex),B:set_complex,C:(complex > $o)]: (? [D:complex]: ((member_complex @ D @ B) & (C @ (A @ D))) | ~ (? [D:complex]: ((C @ D) & (member_complex @ D @ (image_58037603omplex @ (A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
12.71/3.83	thf(12,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_mult_Oleft__neutral)).
12.71/3.83	thf(291,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
12.71/3.83	thf(52,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_order__class_Oorder_Oantisym)).
12.71/3.83	thf(413,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
12.71/3.83	thf(101,axiom,((! [A:set_complex,B:set_complex]: (((B = A) <= (ord_le701908932omplex @ B @ A)) <= (ord_le701908932omplex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_dual__order_Oantisym)).
12.71/3.83	thf(562,plain,((! [A:set_complex,B:set_complex]: ((B = A) | ~ (ord_le701908932omplex @ B @ A) | ~ (ord_le701908932omplex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
12.71/3.83	thf(208,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = A) = ((B = one_one_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__cancel__left2)).
12.71/3.83	thf(904,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = A) = ((B = one_one_complex) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
12.71/3.83	thf(232,axiom,((! [A:(complex > real),B:(real > complex)]: ((((comp_c819638635l_real @ A @ B) = id_real) & ((comp_r667767405omplex @ B @ A) = id_complex)) = (! [C:complex]: ((B @ (A @ C)) = C) & ! [C:real]: ((A @ (B @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_isomorphism__expand)).
12.71/3.83	thf(975,plain,((! [A:(complex > real),B:(real > complex)]: ((((comp_c819638635l_real @ A @ B) = (id_real)) & ((comp_r667767405omplex @ B @ A) = (id_complex))) = (! [C:complex]: ((B @ (A @ C)) = C) & ! [C:real]: ((A @ (B @ C)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
12.71/3.83	thf(219,axiom,((! [A:(complex > complex)]: ((comp_c130555887omplex @ id_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_fun_Omap__id)).
12.71/3.83	thf(936,plain,((! [A:(complex > complex)]: ((comp_c130555887omplex @ id_complex @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
12.71/3.83	thf(171,axiom,((! [A:((complex > complex) > (complex > complex))]: ((compow1098280738omplex @ zero_zero_nat @ A) = id_complex_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_funpow__simps__right_I1_J)).
12.71/3.83	thf(787,plain,((! [A:((complex > complex) > (complex > complex))]: ((compow1098280738omplex @ zero_zero_nat @ A) = (id_complex_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
12.71/3.83	thf(150,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = ((B = zero_zero_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_mult__eq__0__iff)).
12.71/3.83	thf(713,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = ((B = zero_zero_complex) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
12.71/3.83	thf(70,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_mult__cancel__left)).
12.71/3.83	thf(466,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
12.71/3.83	thf(176,axiom,((! [A:(real > real),B:(real > real)]: ((((comp_real_real_real @ B @ A) = id_real) & ((comp_real_real_real @ A @ B) = id_real)) = (! [C:real]: ((B @ (A @ C)) = C) & ! [C:real]: ((A @ (B @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_isomorphism__expand)).
12.71/3.83	thf(804,plain,((! [A:(real > real),B:(real > real)]: ((((comp_real_real_real @ B @ A) = (id_real)) & ((comp_real_real_real @ A @ B) = (id_real))) = (! [C:real]: ((B @ (A @ C)) = C) & ! [C:real]: ((A @ (B @ C)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])).
12.71/3.83	thf(93,axiom,((! [A:complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_vector__space__over__itself_Oscale__zero__right)).
12.71/3.83	thf(540,plain,((! [A:complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
12.71/3.83	thf(138,axiom,((! [A:set_complex,B:set_complex,C:set_complex,D:set_complex]: ((ord_le701908932omplex @ A @ B) => ((ord_le701908932omplex @ C @ D) => (ord_le701908932omplex @ (times_1316095593omplex @ A @ C) @ (times_1316095593omplex @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_set__times__mono2)).
12.71/3.83	thf(672,plain,((! [A:set_complex,B:set_complex,C:set_complex,D:set_complex]: ((ord_le701908932omplex @ A @ B) => ((ord_le701908932omplex @ C @ D) => (ord_le701908932omplex @ (times_1316095593omplex @ A @ C) @ (times_1316095593omplex @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
12.71/3.83	thf(165,axiom,((! [A:(complex > complex),B:set_complex,C:(complex > $o)]: ((! [D:complex]: ((C @ D) <= (member_complex @ D @ (image_58037603omplex @ A @ B)))) => (! [D:complex]: ((member_complex @ D @ B) => (C @ (A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_ball__imageD)).
12.71/3.83	thf(764,plain,((! [A:(complex > complex),B:set_complex,C:(complex > $o)]: ((! [D:complex]: ((C @ D) | ~ (member_complex @ D @ (image_58037603omplex @ (A) @ B)))) => (! [D:complex]: ((member_complex @ D @ B) => (C @ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
12.71/3.83	thf(54,axiom,((! [A:$o]: ((A = ($true)) | (A = ($false))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Complex__Ocomplex_T)).
12.71/3.83	thf(419,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
12.71/3.83	thf(158,axiom,((ord_le701908932omplex @ (image_58037603omplex @ f @ s) @ t)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_assms_I5_J)).
12.71/3.83	thf(737,plain,((ord_le701908932omplex @ (image_58037603omplex @ (f) @ s) @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
12.71/3.83	thf(16,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_mult__left__cancel)).
12.71/3.83	thf(303,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
12.71/3.83	thf(195,axiom,((! [A:complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_vector__space__over__itself_Oscale__zero__left)).
12.71/3.83	thf(863,plain,((! [A:complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
12.71/3.83	thf(74,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_zero__le)).
12.71/3.83	thf(477,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])).
12.71/3.83	thf(43,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_le__zero__eq)).
12.71/3.83	thf(387,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
12.71/3.83	thf(80,axiom,((comp_c130555887omplex = (^ [A:(complex > complex),B:(complex > complex),C:complex]: (A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_comp__apply)).
12.71/3.83	thf(494,plain,(((comp_c130555887omplex) = (^ [A:(complex > complex),B:(complex > complex),C:complex]: (A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
12.71/3.83	thf(124,axiom,((! [A:(real > real),B:(real > real),C:(real > real)]: ((((comp_real_real_real @ B @ C) = id_real) => (A = C)) <= ((comp_real_real_real @ A @ B) = id_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_left__right__inverse__eq)).
12.71/3.83	thf(631,plain,((! [A:(real > real),B:(real > real),C:(real > real)]: ((((comp_real_real_real @ B @ C) = (id_real)) => ((A) = (C))) | ~ ((comp_real_real_real @ A @ B) = (id_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])).
12.71/3.83	thf(194,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex),E:(complex > complex),F:(complex > complex)]: ((((comp_c130555887omplex @ (comp_c130555887omplex @ E @ A) @ B) = (comp_c130555887omplex @ F @ D)) <= ((comp_c130555887omplex @ E @ C) = F)) <= ((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_rewriteR__comp__comp2)).
12.71/3.83	thf(858,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex),E:(complex > complex),F:(complex > complex)]: (((comp_c130555887omplex @ (comp_c130555887omplex @ E @ A) @ B) = (comp_c130555887omplex @ F @ D)) | ~ ((comp_c130555887omplex @ E @ C) = (F)) | ~ ((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
12.71/3.83	thf(115,axiom,((! [A:((complex > complex) > (complex > complex)),B:(complex > complex)]: ((compow1098280738omplex @ zero_zero_nat @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_funpow__0)).
12.71/3.83	thf(609,plain,((! [A:((complex > complex) > (complex > complex)),B:(complex > complex)]: ((compow1098280738omplex @ zero_zero_nat @ (A) @ B) = (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
12.71/3.83	thf(23,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_mult__cancel__right)).
12.71/3.83	thf(323,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
12.71/3.83	thf(113,axiom,((! [A:set_complex,B:set_complex,C:(complex > complex),D:(complex > complex)]: ((((image_58037603omplex @ C @ A) = (image_58037603omplex @ D @ B)) <= (! [E:complex]: (((C @ E) = (D @ E)) <= (member_complex @ E @ B)))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_image__cong)).
12.71/3.83	thf(594,plain,((! [A:set_complex,B:set_complex,C:(complex > complex),D:(complex > complex)]: (((image_58037603omplex @ (C) @ A) = (image_58037603omplex @ (D) @ B)) | ~ (! [E:complex]: (((C @ E) = (D @ E)) | ~ (member_complex @ E @ B))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
12.71/3.83	thf(155,axiom,((! [A:complex,B:complex,C:complex]: ((((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = (B = C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_mult__left__cancel)).
12.71/3.83	thf(726,plain,((! [A:complex,B:complex,C:complex]: ((((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = (B = C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
12.71/3.83	thf(87,axiom,((! [A:(complex > complex),B:set_complex,C:set_complex]: ((ord_le701908932omplex @ (image_58037603omplex @ A @ B) @ C) = (! [D:complex]: ((member_complex @ D @ B) => (member_complex @ (A @ D) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_image__subset__iff)).
12.71/3.83	thf(520,plain,((! [A:(complex > complex),B:set_complex,C:set_complex]: ((ord_le701908932omplex @ (image_58037603omplex @ (A) @ B) @ C) = (! [D:complex]: ((member_complex @ D @ B) => (member_complex @ (A @ D) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
12.71/3.83	thf(122,axiom,((! [A:set_complex]: (ord_le701908932omplex @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_subset__refl)).
12.71/3.83	thf(626,plain,((! [A:set_complex]: (ord_le701908932omplex @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
12.71/3.83	thf(222,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = B) = ((A = one_one_complex) | (B = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_mult__cancel__right2)).
12.71/3.83	thf(943,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = B) = ((A = one_one_complex) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
12.71/3.83	thf(235,axiom,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_mult_Oleft__neutral)).
12.71/3.83	thf(983,plain,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])).
12.71/3.83	thf(47,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ A)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_mult__mono_H)).
12.71/3.83	thf(399,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ A) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
12.71/3.83	thf(184,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (times_times_complex @ B @ C)) = (times_times_complex @ B @ (times_times_complex @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_vector__space__over__itself_Oscale__left__commute)).
12.71/3.83	thf(827,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (times_times_complex @ B @ C)) = (times_times_complex @ B @ (times_times_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
12.71/3.83	thf(145,axiom,((! [A:complex,B:complex]: (((B != zero_zero_complex) => ((times_times_complex @ A @ B) != zero_zero_complex)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_no__zero__divisors)).
12.71/3.83	thf(695,plain,((! [A:complex,B:complex]: (((~ (B = zero_zero_complex)) => (~ ((times_times_complex @ A @ B) = zero_zero_complex))) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
12.71/3.83	thf(169,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_zero__reorient)).
12.71/3.83	thf(780,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
12.71/3.83	thf(202,axiom,((! [A:set_complex,B:set_complex,C:(complex > complex),D:(complex > complex)]: ((((comple372758642hic_on @ C @ A) = (comple372758642hic_on @ D @ B)) <= (! [E:complex]: (((C @ E) = (D @ E)) <= (member_complex @ E @ A)))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_holomorphic__cong)).
12.71/3.83	thf(883,plain,((! [A:set_complex,B:set_complex,C:(complex > complex),D:(complex > complex)]: (((comple372758642hic_on @ (C) @ A) = (comple372758642hic_on @ (D) @ B)) | ~ (! [E:complex]: (((C @ E) = (D @ E)) | ~ (member_complex @ E @ A))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
12.71/3.83	thf(243,axiom,((! [A:(real > complex),B:(complex > real)]: ((((comp_r667767405omplex @ A @ B) = id_complex) & ((comp_c819638635l_real @ B @ A) = id_real)) = (! [C:complex]: ((A @ (B @ C)) = C) & ! [C:real]: ((B @ (A @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_isomorphism__expand)).
12.71/3.83	thf(1015,plain,((! [A:(real > complex),B:(complex > real)]: ((((comp_r667767405omplex @ A @ B) = (id_complex)) & ((comp_c819638635l_real @ B @ A) = (id_real))) = (! [C:complex]: ((A @ (B @ C)) = C) & ! [C:real]: ((B @ (A @ C)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])).
12.71/3.83	thf(236,axiom,((! [A:(complex > complex),B:set_complex,C:nat]: (((comple372758642hic_on @ (compow1098280738omplex @ C @ deriv_complex @ A) @ B) <= (topolo935673511omplex @ B)) <= (comple372758642hic_on @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_holomorphic__higher__deriv)).
12.71/3.83	thf(986,plain,((! [A:(complex > complex),B:set_complex,C:nat]: ((comple372758642hic_on @ (compow1098280738omplex @ C @ (deriv_complex) @ A) @ B) | ~ (topolo935673511omplex @ B) | ~ (comple372758642hic_on @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
12.71/3.83	thf(238,axiom,((! [A:(real > complex),B:(complex > real),C:(real > complex)]: (((comp_r667767405omplex @ A @ B) = id_complex) => (((comp_c819638635l_real @ B @ C) = id_real) => (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_left__right__inverse__eq)).
12.71/3.83	thf(1000,plain,((! [A:(real > complex),B:(complex > real),C:(real > complex)]: (((comp_r667767405omplex @ A @ B) = (id_complex)) => (((comp_c819638635l_real @ B @ C) = (id_real)) => ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
12.71/3.83	thf(5,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((? [D:nat]: (! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E)) & (A @ D))) <= (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_Nat_Oex__has__greatest__nat)).
12.71/3.83	thf(267,plain,((! [A:(nat > $o),B:nat,C:nat]: (? [D:nat]: (! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E)) & (A @ D)) | ~ (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
12.71/3.83	thf(82,axiom,((! [A:(complex > complex),B:complex]: ((compow1667379464omplex @ zero_zero_nat @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_funpow__0)).
12.71/3.83	thf(505,plain,((! [A:(complex > complex),B:complex]: ((compow1667379464omplex @ zero_zero_nat @ (A) @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
12.71/3.83	thf(131,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex)]: (((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ C @ D)) => (! [E:complex]: ((A @ (B @ E)) = (C @ (D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_comp__eq__elim)).
12.71/3.83	thf(653,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex)]: (((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ C @ D)) => (! [E:complex]: ((A @ (B @ E)) = (C @ (D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])).
12.71/3.83	thf(133,axiom,((id_complex_complex = (^ [A:(complex > complex)]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_id__def)).
12.71/3.83	thf(658,plain,(((id_complex_complex) = (^ [A:(complex > complex)]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
12.71/3.83	thf(211,axiom,(((times_times_complex @ (deriv_complex @ f @ w) @ (deriv_complex @ g @ (f @ w))) = (deriv_complex @ id_complex @ w))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_calculation)).
12.71/3.83	thf(912,plain,(((times_times_complex @ (deriv_complex @ (f) @ w) @ (deriv_complex @ (g) @ (f @ w))) = (deriv_complex @ (id_complex) @ w))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])).
12.71/3.83	thf(142,axiom,((! [A:complex,B:set_complex,C:complex,D:set_complex]: (((member_complex @ C @ D) => (member_complex @ (times_times_complex @ A @ C) @ (times_1316095593omplex @ B @ D))) <= (member_complex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_set__times__intro)).
12.71/3.83	thf(685,plain,((! [A:complex,B:set_complex,C:complex,D:set_complex]: (((member_complex @ C @ D) => (member_complex @ (times_times_complex @ A @ C) @ (times_1316095593omplex @ B @ D))) | ~ (member_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
12.71/3.83	thf(255,axiom,((! [A:((complex > complex) > complex),B:(complex > (complex > complex)),C:((complex > complex) > complex)]: (((comp_c881053372omplex @ A @ B) = id_complex) => (((comp_c606622857omplex @ B @ C) = id_complex_complex) => (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_left__right__inverse__eq)).
12.71/3.83	thf(1066,plain,((! [A:((complex > complex) > complex),B:(complex > (complex > complex)),C:((complex > complex) > complex)]: (((comp_c881053372omplex @ (A) @ B) = (id_complex)) => (((comp_c606622857omplex @ B @ C) = (id_complex_complex)) => ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])).
12.71/3.83	thf(197,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (times_times_complex @ B @ C)) = (times_times_complex @ (times_times_complex @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_vector__space__over__itself_Oscale__scale)).
12.71/3.83	thf(868,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (times_times_complex @ B @ C)) = (times_times_complex @ (times_times_complex @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
12.71/3.83	thf(247,axiom,((! [A:nat]: ((compow1667379464omplex @ A @ id_complex) = id_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_id__funpow)).
12.71/3.83	thf(1034,plain,((! [A:nat]: ((compow1667379464omplex @ A @ id_complex) = (id_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
12.71/3.83	thf(139,axiom,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:set_complex,E:(complex > complex)]: (((image_58037603omplex @ (comp_c130555887omplex @ E @ A) @ B) = (image_58037603omplex @ (comp_c130555887omplex @ E @ C) @ D)) <= ((image_58037603omplex @ A @ B) = (image_58037603omplex @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_image__eq__imp__comp)).
12.71/3.83	thf(675,plain,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:set_complex,E:(complex > complex)]: (((image_58037603omplex @ (comp_c130555887omplex @ E @ A) @ B) = (image_58037603omplex @ (comp_c130555887omplex @ E @ C) @ D)) | ~ ((image_58037603omplex @ (A) @ B) = (image_58037603omplex @ (C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
12.71/3.83	thf(57,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_mult__zero__left)).
12.71/3.83	thf(426,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
12.71/3.83	thf(118,axiom,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ C @ B)) = ((A = C) | (B = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_vector__space__over__itself_Oscale__cancel__right)).
12.71/3.83	thf(617,plain,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ C @ B)) = ((A = C) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
12.71/3.83	thf(220,axiom,(((ln_ln_complex @ one_one_complex) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_Ln__1)).
12.71/3.83	thf(939,plain,(((ln_ln_complex @ one_one_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])).
12.71/3.83	thf(244,axiom,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_vector__space__over__itself_Oscale__one)).
12.71/3.83	thf(1018,plain,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
12.71/3.83	thf(34,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_mult_Oleft__commute)).
12.71/3.83	thf(355,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
12.71/3.83	thf(187,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (times_times_complex @ B @ C)) = (times_times_complex @ B @ (times_times_complex @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_mult_Oleft__commute)).
12.71/3.83	thf(836,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (times_times_complex @ B @ C)) = (times_times_complex @ B @ (times_times_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])).
12.71/3.83	thf(135,axiom,((! [A:set_complex,B:(complex > complex),C:set_complex]: ((ord_le701908932omplex @ (image_58037603omplex @ B @ A) @ C) <= (! [D:complex]: ((member_complex @ D @ A) => (member_complex @ (B @ D) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_image__subsetI)).
12.71/3.83	thf(663,plain,((! [A:set_complex,B:(complex > complex),C:set_complex]: ((ord_le701908932omplex @ (image_58037603omplex @ (B) @ A) @ C) | ~ (! [D:complex]: ((member_complex @ D @ A) => (member_complex @ (B @ D) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])).
12.71/3.83	thf(96,axiom,((! [A:complex,B:set_complex,C:(complex > complex)]: ((member_complex @ A @ B) => (member_complex @ (C @ A) @ (image_58037603omplex @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_imageI)).
12.71/3.83	thf(548,plain,((! [A:complex,B:set_complex,C:(complex > complex)]: ((member_complex @ A @ B) => (member_complex @ (C @ A) @ (image_58037603omplex @ (C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
12.71/3.83	thf(216,axiom,((! [A:(complex > complex)]: ((compow1667379464omplex @ zero_zero_nat @ A) = id_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_funpow__simps__right_I1_J)).
12.71/3.83	thf(927,plain,((! [A:(complex > complex)]: ((compow1667379464omplex @ zero_zero_nat @ A) = (id_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
12.71/3.83	thf(40,axiom,((! [A:nat,B:nat]: (((A != zero_zero_nat) & (B != zero_zero_nat)) <= ((times_times_nat @ A @ B) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_mult__not__zero)).
12.71/3.83	thf(374,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat) & ~ (B = zero_zero_nat)) | ((times_times_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
12.71/3.83	thf(148,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex)]: (((comp_c130555887omplex @ A @ B) = C) => ((comp_c130555887omplex @ (comp_c130555887omplex @ D @ A) @ B) = (comp_c130555887omplex @ D @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_rewriteR__comp__comp)).
12.71/3.83	thf(705,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:(complex > complex)]: (((comp_c130555887omplex @ A @ B) = (C)) => ((comp_c130555887omplex @ (comp_c130555887omplex @ D @ A) @ B) = (comp_c130555887omplex @ D @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
12.71/3.83	thf(231,axiom,((! [A:(complex > (complex > complex)),B:((complex > complex) > complex),C:(complex > (complex > complex))]: (((comp_c606622857omplex @ A @ B) = id_complex_complex) => ((A = C) <= ((comp_c881053372omplex @ B @ C) = id_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_left__right__inverse__eq)).
12.71/3.83	thf(971,plain,((! [A:(complex > (complex > complex)),B:((complex > complex) > complex),C:(complex > (complex > complex))]: (((comp_c606622857omplex @ A @ B) = (id_complex_complex)) => (((A) = (C)) | ~ ((comp_c881053372omplex @ (B) @ C) = (id_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])).
12.71/3.83	thf(108,axiom,((! [A:set_complex,B:(complex > complex),C:set_complex]: ((ord_le701908932omplex @ A @ (image_58037603omplex @ B @ C)) = (? [D:set_complex]: ((A = (image_58037603omplex @ B @ D)) & (ord_le701908932omplex @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_subset__image__iff)).
12.71/3.83	thf(580,plain,((! [A:set_complex,B:(complex > complex),C:set_complex]: ((ord_le701908932omplex @ A @ (image_58037603omplex @ (B) @ C)) = (? [D:set_complex]: ((A = (image_58037603omplex @ (B) @ D)) & (ord_le701908932omplex @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
12.71/3.83	thf(193,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_one__reorient)).
12.71/3.83	thf(855,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
12.71/3.83	thf(252,axiom,((! [A:(complex > complex),B:(complex > complex),C:complex]: (((comp_c130555887omplex @ A @ B) = id_complex) => ((A @ (B @ C)) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_pointfree__idE)).
12.71/3.83	thf(1053,plain,((! [A:(complex > complex),B:(complex > complex),C:complex]: (((comp_c130555887omplex @ A @ B) = (id_complex)) => ((A @ (B @ C)) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])).
12.71/3.83	thf(110,axiom,((! [A:nat,B:nat]: (((A = zero_zero_nat) | (B = one_one_nat)) <= (A = (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_mult__eq__self__implies__10)).
12.71/3.83	thf(585,plain,((! [A:nat,B:nat]: ((A = zero_zero_nat) | (B = one_one_nat) | ~ (A = (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
12.71/3.83	thf(69,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_mult__le__mono)).
12.71/3.83	thf(463,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
12.71/3.83	thf(28,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_divisors__zero)).
12.71/3.83	thf(338,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((B = zero_zero_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
12.71/3.83	thf(127,axiom,((topolo935673511omplex @ t)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_assms_I4_J)).
12.71/3.83	thf(643,plain,((topolo935673511omplex @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
12.71/3.83	thf(209,axiom,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_mult_Ocomm__neutral)).
12.71/3.83	thf(907,plain,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
12.71/3.83	thf(27,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_le0)).
12.71/3.83	thf(336,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
12.71/3.83	thf(132,axiom,((! [A:set_complex]: (ord_le701908932omplex @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_dual__order_Orefl)).
12.71/3.83	thf(656,plain,((! [A:set_complex]: (ord_le701908932omplex @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
12.71/3.83	thf(233,axiom,((! [A:complex]: ((one_one_complex = A) = (A = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_one__reorient)).
12.71/3.83	thf(978,plain,((! [A:complex]: ((one_one_complex = A) = (A = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
12.71/3.83	thf(241,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:complex]: (((A @ (B @ D)) = (C @ D)) <= ((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ id_complex @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_comp__eq__id__dest)).
12.71/3.83	thf(1008,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex),D:complex]: (((A @ (B @ D)) = (C @ D)) | ~ ((comp_c130555887omplex @ A @ B) = (comp_c130555887omplex @ id_complex @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
12.71/3.83	thf(20,axiom,((! [A:nat,B:nat,C:((complex > complex) > (complex > complex))]: ((compow1098280738omplex @ A @ (compow1098280738omplex @ B @ C)) = (compow1098280738omplex @ (times_times_nat @ B @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_funpow__mult)).
12.71/3.83	thf(314,plain,((! [A:nat,B:nat,C:((complex > complex) > (complex > complex))]: ((compow1098280738omplex @ A @ (compow1098280738omplex @ B @ C)) = (compow1098280738omplex @ (times_times_nat @ B @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
12.71/3.83	thf(116,axiom,((comp_c130555887omplex = (^ [A:(complex > complex),B:(complex > complex),C:complex]: (A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_comp__def)).
12.71/3.83	thf(612,plain,(((comp_c130555887omplex) = (^ [A:(complex > complex),B:(complex > complex),C:complex]: (A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
12.71/3.83	thf(63,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ B @ one_one_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat))) <= (ord_less_eq_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_mult__le__one)).
12.71/3.83	thf(446,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ B @ one_one_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat))) | ~ (ord_less_eq_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
12.71/3.83	thf(104,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex)]: ((comp_c130555887omplex @ (comp_c130555887omplex @ A @ B) @ C) = (comp_c130555887omplex @ A @ (comp_c130555887omplex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_comp__assoc)).
12.71/3.83	thf(571,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex)]: ((comp_c130555887omplex @ (comp_c130555887omplex @ A @ B) @ C) = (comp_c130555887omplex @ A @ (comp_c130555887omplex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
12.71/3.83	thf(99,axiom,((! [A:((complex > complex) > (complex > complex))]: ((! [B:(complex > complex)]: ((A @ B) = B)) = (A = id_complex_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_eq__id__iff)).
12.71/3.83	thf(556,plain,((! [A:((complex > complex) > (complex > complex))]: ((! [B:(complex > complex)]: ((A @ B) = (B))) = ((A) = (id_complex_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])).
12.71/3.83	thf(143,axiom,((! [A:set_complex,B:set_complex,C:set_complex]: ((ord_le701908932omplex @ A @ B) => ((ord_le701908932omplex @ C @ B) <= (ord_le701908932omplex @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_dual__order_Otrans)).
12.71/3.83	thf(688,plain,((! [A:set_complex,B:set_complex,C:set_complex]: ((ord_le701908932omplex @ A @ B) => ((ord_le701908932omplex @ C @ B) | ~ (ord_le701908932omplex @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
12.71/3.83	thf(203,axiom,((! [A:complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_mult__zero__right)).
12.71/3.83	thf(891,plain,((! [A:complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
12.71/3.83	thf(38,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_mult__nonpos__nonneg)).
12.71/3.83	thf(368,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
12.71/3.83	thf(190,axiom,((! [A:(complex > complex),B:set_complex,C:(complex > complex)]: ((comple372758642hic_on @ A @ B) => ((comple372758642hic_on @ C @ B) <= (! [D:complex]: (((A @ D) = (C @ D)) <= (member_complex @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_holomorphic__transform)).
12.71/3.83	thf(844,plain,((! [A:(complex > complex),B:set_complex,C:(complex > complex)]: ((comple372758642hic_on @ (A) @ B) => ((comple372758642hic_on @ (C) @ B) | ~ (! [D:complex]: (((A @ D) = (C @ D)) | ~ (member_complex @ D @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])).
12.71/3.83	thf(162,axiom,((! [A:complex,B:complex,C:complex]: ((((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) => (B = C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_vector__space__over__itself_Oscale__left__imp__eq)).
12.71/3.83	thf(748,plain,((! [A:complex,B:complex,C:complex]: ((((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) => (B = C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
12.71/3.83	thf(44,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_mult__left__mono)).
12.71/3.83	thf(390,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
12.71/3.83	thf(111,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = ((A = zero_zero_complex) | (B = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_vector__space__over__itself_Oscale__eq__0__iff)).
12.71/3.83	thf(588,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = ((A = zero_zero_complex) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
12.71/3.83	thf(146,axiom,((! [A:set_complex,B:set_complex,C:complex]: ((ord_le701908932omplex @ A @ B) => ((member_complex @ C @ B) <= (member_complex @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_in__mono)).
12.71/3.83	thf(699,plain,((! [A:set_complex,B:set_complex,C:complex]: ((ord_le701908932omplex @ A @ B) => ((member_complex @ C @ B) | ~ (member_complex @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
12.71/3.83	thf(223,axiom,((! [A:(complex > (complex > complex)),B:((complex > complex) > complex)]: ((((comp_c881053372omplex @ B @ A) = id_complex) & ((comp_c606622857omplex @ A @ B) = id_complex_complex)) = (! [C:complex]: ((B @ (A @ C)) = C) & ! [C:(complex > complex)]: ((A @ (B @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_isomorphism__expand)).
12.71/3.83	thf(946,plain,((! [A:(complex > (complex > complex)),B:((complex > complex) > complex)]: ((((comp_c881053372omplex @ (B) @ A) = (id_complex)) & ((comp_c606622857omplex @ A @ B) = (id_complex_complex))) = (! [C:complex]: ((B @ (A @ C)) = C) & ! [C:(complex > complex)]: ((A @ (B @ C)) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
12.71/3.83	thf(3,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_mult__le__mono2)).
12.71/3.83	thf(258,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
12.71/3.83	thf(103,axiom,((! [A:complex,B:complex]: (((B = zero_zero_complex) | (A = zero_zero_complex)) <= ((times_times_complex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_divisors__zero)).
12.71/3.83	thf(568,plain,((! [A:complex,B:complex]: ((B = zero_zero_complex) | (A = zero_zero_complex) | ~ ((times_times_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
12.71/3.83	thf(212,axiom,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex)]: (((A = C) <= ((comp_c130555887omplex @ B @ C) = id_complex)) <= ((comp_c130555887omplex @ A @ B) = id_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_left__right__inverse__eq)).
12.71/3.83	thf(914,plain,((! [A:(complex > complex),B:(complex > complex),C:(complex > complex)]: (((A) = (C)) | ~ ((comp_c130555887omplex @ B @ C) = (id_complex)) | ~ ((comp_c130555887omplex @ A @ B) = (id_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])).
12.71/3.83	thf(206,axiom,(((times_times_complex @ (deriv_complex @ g @ (f @ w)) @ (deriv_complex @ f @ w)) = (deriv_complex @ (comp_c130555887omplex @ g @ f) @ w))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57__092_060open_062deriv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_A_061_Aderiv_A_Ig_A_092_060circ_062_Af_J_Aw_092_060close_062)).
12.71/3.83	thf(899,plain,(((times_times_complex @ (deriv_complex @ (g) @ (f @ w)) @ (deriv_complex @ (f) @ w)) = (deriv_complex @ (comp_c130555887omplex @ g @ f) @ w))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])).
12.71/3.83	thf(31,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_order__trans)).
12.71/3.83	thf(346,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
12.71/3.83	thf(92,axiom,((! [A:((complex > complex) > real),B:(real > (complex > complex)),C:((complex > complex) > real)]: (((comp_c1884694328l_real @ A @ B) = id_real) => (((comp_r2009261319omplex @ B @ C) = id_complex_complex) => (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_left__right__inverse__eq)).
12.71/3.83	thf(536,plain,((! [A:((complex > complex) > real),B:(real > (complex > complex)),C:((complex > complex) > real)]: (((comp_c1884694328l_real @ (A) @ B) = (id_real)) => (((comp_r2009261319omplex @ B @ C) = (id_complex_complex)) => ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
12.71/3.83	thf(151,axiom,((! [A:complex,B:set_complex]: (comple372758642hic_on @ (times_times_complex @ A) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_holomorphic__on__linear)).
12.71/3.83	thf(716,plain,((! [A:complex,B:set_complex]: (comple372758642hic_on @ (times_times_complex @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
12.71/3.83	thf(174,axiom,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_not__one__le__zero)).
12.71/3.83	thf(800,plain,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
12.71/3.83	thf(10,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_order__refl)).
12.71/3.83	thf(287,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
12.71/3.83	thf(15,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_mult__cancel1)).
12.71/3.83	thf(300,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
12.71/3.83	thf(119,axiom,(((image_real_real @ id_real) = id_set_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_image__id)).
12.71/3.83	thf(620,plain,(((image_real_real @ id_real) = (id_set_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
12.71/3.83	thf(163,axiom,((! [A:$o,B:complex,C:complex]: (((A) => ((times_times_complex @ B @ (if_complex @ A @ C @ zero_zero_complex)) = (times_times_complex @ B @ C))) & ((~ (A)) => ((times_times_complex @ B @ (if_complex @ A @ C @ zero_zero_complex)) = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_mult__delta__right)).
12.71/3.83	thf(752,plain,((! [A:$o,B:complex,C:complex]: (((A) => ((times_times_complex @ B @ (if_complex @ A @ C @ zero_zero_complex)) = (times_times_complex @ B @ C))) & ((~ (A)) => ((times_times_complex @ B @ (if_complex @ A @ C @ zero_zero_complex)) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
12.71/3.83	thf(59,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (B = C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_ord__le__eq__trans)).
12.71/3.83	thf(432,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (B = C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
12.71/3.83	thf(180,axiom,((comple372758642hic_on @ g @ t)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_assms_I2_J)).
12.71/3.83	thf(818,plain,((comple372758642hic_on @ (g) @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])).
12.71/3.83	thf(49,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_nat__mult__1__right)).
12.71/3.83	thf(405,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
12.71/3.83	thf(172,axiom,((! [A:set_complex,B:set_complex]: ((A = B) => (~ ((ord_le701908932omplex @ A @ B) => (~ (ord_le701908932omplex @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_equalityE)).
12.71/3.83	thf(790,plain,((! [A:set_complex,B:set_complex]: ((A = B) => (~ ((ord_le701908932omplex @ A @ B) => (~ (ord_le701908932omplex @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
12.71/3.83	thf(186,axiom,((! [A:(complex > complex),B:nat,C:complex]: ((A @ (compow1667379464omplex @ B @ A @ C)) = (compow1667379464omplex @ B @ A @ (A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_funpow__swap1)).
12.71/3.83	thf(833,plain,((! [A:(complex > complex),B:nat,C:complex]: ((A @ (compow1667379464omplex @ B @ (A) @ C)) = (compow1667379464omplex @ B @ (A) @ (A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])).
12.71/3.83	thf(51,axiom,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((B = one_one_nat) & (A = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_nat__1__eq__mult__iff)).
12.71/3.83	thf(410,plain,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((B = one_one_nat) & (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
12.71/3.83	thf(24,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_less__eq__nat_Osimps_I1_J)).
12.71/3.83	thf(326,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
12.71/3.83	thf(29,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_mult__0__right)).
12.71/3.83	thf(341,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
12.71/3.83	thf(60,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_mult__eq__0__iff)).
12.71/3.83	thf(437,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
12.71/3.83	thf(13,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult_Oassoc)).
12.71/3.83	thf(294,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
12.71/3.83	thf(213,axiom,((id_complex = (^ [A:complex]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_id__apply)).
12.71/3.83	thf(918,plain,(((id_complex) = (^ [A:complex]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
12.71/3.83	thf(35,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_mult__mono)).
12.71/3.83	thf(358,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
12.71/3.83	thf(177,axiom,((! [A:set_complex,B:set_complex,C:(complex > complex)]: ((ord_le701908932omplex @ A @ B) => (ord_le701908932omplex @ (image_58037603omplex @ C @ A) @ (image_58037603omplex @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_image__mono)).
12.71/3.83	thf(807,plain,((! [A:set_complex,B:set_complex,C:(complex > complex)]: ((ord_le701908932omplex @ A @ B) => (ord_le701908932omplex @ (image_58037603omplex @ (C) @ A) @ (image_58037603omplex @ (C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])).
12.71/3.83	thf(205,axiom,(((deriv_complex @ (comp_c130555887omplex @ g @ f) @ w) = (deriv_complex @ id_complex @ w))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24__092_060open_062deriv_A_Ig_A_092_060circ_062_Af_J_Aw_A_061_Aderiv_Aid_Aw_092_060close_062)).
12.71/3.83	thf(897,plain,(((deriv_complex @ (comp_c130555887omplex @ g @ f) @ w) = (deriv_complex @ (id_complex) @ w))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
12.71/3.83	thf(73,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_mult__le__mono1)).
12.71/3.83	thf(474,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
12.71/3.83	thf(166,axiom,((! [A:complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_mult__zero__left)).
12.71/3.83	thf(767,plain,((! [A:complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
12.71/3.83	thf(228,axiom,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:complex,E:nat]: (((comple372758642hic_on @ C @ B) => ((((! [F:complex]: ((member_complex @ F @ B) => ((A @ F) = (C @ F)))) => ((compow1098280738omplex @ E @ deriv_complex @ A @ D) = (compow1098280738omplex @ E @ deriv_complex @ C @ D))) <= (member_complex @ D @ B)) <= (topolo935673511omplex @ B))) <= (comple372758642hic_on @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_higher__deriv__transform__within__open)).
12.71/3.83	thf(960,plain,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:complex,E:nat]: (((comple372758642hic_on @ (C) @ B) => (((! [F:complex]: ((member_complex @ F @ B) => ((A @ F) = (C @ F)))) => ((compow1098280738omplex @ E @ (deriv_complex) @ (A) @ D) = (compow1098280738omplex @ E @ (deriv_complex) @ (C) @ D))) | ~ (member_complex @ D @ B) | ~ (topolo935673511omplex @ B))) | ~ (comple372758642hic_on @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
12.71/3.83	thf(125,axiom,((! [A:(complex > complex),B:set_complex,C:set_complex]: ((comple372758642hic_on @ A @ B) => ((ord_le701908932omplex @ C @ B) => (comple372758642hic_on @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_holomorphic__on__subset)).
12.71/3.83	thf(635,plain,((! [A:(complex > complex),B:set_complex,C:set_complex]: ((comple372758642hic_on @ (A) @ B) => ((ord_le701908932omplex @ C @ B) => (comple372758642hic_on @ (A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
12.71/3.83	thf(188,axiom,((((=) @ set_complex) = (^ [A:set_complex,B:set_complex]: ((ord_le701908932omplex @ B @ A) & (ord_le701908932omplex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_dual__order_Oeq__iff)).
12.71/3.83	thf(839,plain,((((=) @ set_complex) = (^ [A:set_complex,B:set_complex]: ((ord_le701908932omplex @ B @ A) & (ord_le701908932omplex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
12.71/3.83	thf(26,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_eq__imp__le)).
12.71/3.83	thf(332,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
12.71/3.83	thf(106,axiom,((! [A:set_complex]: (ord_le701908932omplex @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_order__refl)).
12.71/3.83	thf(575,plain,((! [A:set_complex]: (ord_le701908932omplex @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
12.71/3.83	thf(128,axiom,((! [A:nat,B:(complex > complex)]: ((compow1098280738omplex @ A @ (comp_c130555887omplex @ B)) = (comp_c130555887omplex @ (compow1667379464omplex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_comp__funpow)).
12.71/3.83	thf(644,plain,((! [A:nat,B:(complex > complex)]: ((compow1098280738omplex @ A @ (comp_c130555887omplex @ B)) = (comp_c130555887omplex @ (compow1667379464omplex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])).
12.71/3.83	thf(154,axiom,((! [A:((complex > complex) > real),B:(real > (complex > complex))]: ((((comp_c1884694328l_real @ A @ B) = id_real) & ((comp_r2009261319omplex @ B @ A) = id_complex_complex)) = (! [C:real]: ((A @ (B @ C)) = C) & ! [C:(complex > complex)]: ((B @ (A @ C)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_isomorphism__expand)).
12.71/3.83	thf(723,plain,((! [A:((complex > complex) > real),B:(real > (complex > complex))]: ((((comp_c1884694328l_real @ (A) @ B) = (id_real)) & ((comp_r2009261319omplex @ B @ A) = (id_complex_complex))) = (! [C:real]: ((A @ (B @ C)) = C) & ! [C:(complex > complex)]: ((B @ (A @ C)) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
12.71/3.83	thf(239,axiom,((! [A:(complex > complex),B:set_complex]: ((comple372758642hic_on @ A @ B) => ((comple372758642hic_on @ (deriv_complex @ A) @ B) <= (topolo935673511omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_holomorphic__deriv)).
12.71/3.83	thf(1004,plain,((! [A:(complex > complex),B:set_complex]: ((comple372758642hic_on @ (A) @ B) => ((comple372758642hic_on @ (deriv_complex @ A) @ B) | ~ (topolo935673511omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
12.71/3.83	thf(198,axiom,((! [A:set_complex,B:set_complex]: ((! [C:complex]: ((member_complex @ C @ A) => (member_complex @ C @ B))) => (ord_le701908932omplex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_subsetI)).
12.71/3.83	thf(871,plain,((! [A:set_complex,B:set_complex]: ((! [C:complex]: ((member_complex @ C @ A) => (member_complex @ C @ B))) => (ord_le701908932omplex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
12.71/3.83	thf(7,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_mult__zero__right)).
12.71/3.83	thf(277,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
12.71/3.83	thf(144,axiom,((! [A:complex,B:complex,C:complex]: (((B = C) <= ((times_times_complex @ B @ A) = (times_times_complex @ C @ A))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_vector__space__over__itself_Oscale__right__imp__eq)).
12.71/3.83	thf(691,plain,((! [A:complex,B:complex,C:complex]: ((B = C) | ~ ((times_times_complex @ B @ A) = (times_times_complex @ C @ A)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
12.71/3.83	thf(77,axiom,(((artanh_complex @ zero_zero_complex) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_artanh__0)).
12.71/3.83	thf(486,plain,(((artanh_complex @ zero_zero_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
12.71/3.83	thf(71,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_le__trans)).
12.71/3.83	thf(469,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
12.71/3.83	thf(18,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_le__refl)).
12.71/3.83	thf(309,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
12.71/3.83	thf(94,axiom,((! [A:((complex > complex) > (complex > complex)),B:nat,C:(complex > complex)]: ((A @ (compow1098280738omplex @ B @ A @ C)) = (compow1098280738omplex @ B @ A @ (A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_funpow__swap1)).
12.71/3.83	thf(543,plain,((! [A:((complex > complex) > (complex > complex)),B:nat,C:(complex > complex)]: ((A @ (compow1098280738omplex @ B @ (A) @ C)) = (compow1098280738omplex @ B @ (A) @ (A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
12.71/3.83	thf(79,axiom,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:set_complex]: ((comple372758642hic_on @ A @ B) => ((comple372758642hic_on @ C @ D) => ((comple372758642hic_on @ (comp_c130555887omplex @ C @ A) @ B) <= (ord_le701908932omplex @ (image_58037603omplex @ A @ B) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_holomorphic__on__compose__gen)).
12.71/3.83	thf(491,plain,((! [A:(complex > complex),B:set_complex,C:(complex > complex),D:set_complex]: ((comple372758642hic_on @ (A) @ B) => ((comple372758642hic_on @ (C) @ D) => ((comple372758642hic_on @ (comp_c130555887omplex @ C @ A) @ B) | ~ (ord_le701908932omplex @ (image_58037603omplex @ (A) @ B) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
12.71/3.83	thf(37,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_mult__right__cancel)).
12.71/3.83	thf(364,plain,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
12.71/3.83	thf(248,axiom,((! [A:(complex > complex)]: ((comp_c130555887omplex @ id_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_id__comp)).
12.71/3.83	thf(1037,plain,((! [A:(complex > complex)]: ((comp_c130555887omplex @ id_complex @ A) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])).
12.71/3.83	thf(168,axiom,((! [A:complex,B:(complex > complex),C:complex,D:set_complex]: (((member_complex @ C @ D) => (member_complex @ A @ (image_58037603omplex @ B @ D))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_image__eqI)).
12.71/3.83	thf(775,plain,((! [A:complex,B:(complex > complex),C:complex,D:set_complex]: (((member_complex @ C @ D) => (member_complex @ A @ (image_58037603omplex @ (B) @ D))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])).
12.71/3.83	thf(81,axiom,((! [A:$o,B:complex,C:complex]: (((A) => ((times_times_complex @ (if_complex @ A @ B @ zero_zero_complex) @ C) = (times_times_complex @ B @ C))) & (((times_times_complex @ (if_complex @ A @ B @ zero_zero_complex) @ C) = zero_zero_complex) <= (~ (A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_mult__delta__left)).
12.71/3.83	thf(496,plain,((! [A:$o,B:complex,C:complex]: (((A) => ((times_times_complex @ (if_complex @ A @ B @ zero_zero_complex) @ C) = (times_times_complex @ B @ C))) & (((times_times_complex @ (if_complex @ A @ B @ zero_zero_complex) @ C) = zero_zero_complex) | (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
12.71/3.83	thf(66,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_dual__order_Otrans)).
12.71/3.83	thf(454,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
12.71/3.83	thf(1073,plain,(($false)),inference(e,[status(thm)],[479,628,518,941,666,481,352,408,523,683,730,449,614,440,511,384,533,797,472,930,841,320,565,702,949,460,802,344,559,638,969,416,289,261,284,770,924,591,443,1040,514,574,966,1051,280,877,734,956,866,396,660,849,527,602,981,307,452,920,546,761,810,381,1057,910,894,1021,349,820,297,429,275,815,1042,952,361,625,879,852,551,710,1012,583,830,874,317,650,1006,989,783,420,1028,488,933,554,669,901,679,328,256,622,393,647,738,721,371,1060,457,508,311,530,953,718,824,745,819,423,402,743,577,291,413,562,904,975,936,787,713,466,804,540,672,764,419,737,303,863,477,387,494,631,858,609,323,594,726,520,626,943,983,399,827,695,780,883,1015,986,1000,267,505,653,658,912,685,1066,868,1034,675,426,617,939,1018,355,836,663,548,927,374,705,971,580,855,1053,585,463,338,643,907,336,656,978,1008,314,612,446,571,556,688,891,368,844,748,390,588,699,946,258,568,914,899,346,536,716,800,287,300,620,752,432,818,405,790,833,410,326,341,437,294,918,358,807,897,474,767,960,635,839,332,575,644,723,1004,871,277,691,486,469,309,543,491,364,1037,775,496,454])).
12.71/3.83	% SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
12.71/3.83	% [INFO] 	 Killing All external provers ... 
12.71/3.85	EOF