0.03/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command  : run_Leo-III %s %d THM
0.11/0.32	% Computer : n024.cluster.edu
0.11/0.32	% Model    : x86_64 x86_64
0.11/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory   : 8042.1875MB
0.11/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit : 1440
0.11/0.32	% WCLimit  : 180
0.11/0.32	% DateTime : Thu Jul  4 08:51:24 EDT 2024
0.11/0.33	% CPUTime  : 
0.94/0.85	% [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
1.82/1.10	% [INFO] 	 Parsing done (247ms). 
1.82/1.10	% [INFO] 	 Running in sequential loop mode. 
2.45/1.32	% [INFO] 	 eprover registered as external prover. 
2.66/1.32	% [INFO] 	 Scanning for conjecture ... 
2.77/1.40	% [INFO] 	 Found a conjecture (or negated_conjecture) and 352 axioms. Running axiom selection ... 
3.14/1.50	% [INFO] 	 Axiom selection finished. Selected 352 axioms (removed 0 axioms). 
3.71/1.67	% [INFO] 	 Problem is higher-order (TPTP THF). 
3.92/1.68	% [INFO] 	 Type checking passed. 
3.92/1.69	% [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 ... 
99.43/23.72	% External prover 'e' found a proof!
99.43/23.72	% [INFO] 	 Killing All external provers ... 
99.43/23.72	% Time passed: 23204ms (effective reasoning time: 22610ms)
99.43/23.72	% 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)>
99.43/23.72	% Axioms used in derivation (352): fact_67_le__add__diff__inverse2, fact_34_abs__abs, fact_299_eq__refl, fact_320_left__add__mult__distrib, fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, fact_213_left__diff__distrib_H, fact_41_mult_Oleft__neutral, fact_9_Eq2, fact_196_one__le__numeral, fact_27_numeral__eq__iff, fact_252_order__subst1, fact_301_le__cases, fact_316_nat__le__add__iff1, fact_210_right__diff__distrib_H, fact_93_one__reorient, fact_126_add__mono, fact_65_semiring__norm_I68_J, fact_106_add_Oleft__commute, fact_245_nat__1__add__1, fact_154_diff__eq__eq, fact_193_eq__add__iff1, fact_1_rb1, fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, fact_161_square__diff__one__factored, fact_42_mult_Oleft__neutral, fact_335_diff__le__mono2, fact_62_semiring__norm_I11_J, fact_292_antisym, fact_4_Eq4, fact_223_mult__2__right, fact_109_add__right__imp__eq, fact_311_complete__real, fact_240_order__refl, fact_302_le__cases, fact_287_ord__le__eq__subst, fact_242_semiring__norm_I6_J, fact_347_diff__mult__distrib2, fact_338_mult__le__mono2, fact_231_sin__bound__lemma, fact_189_le__diff__eq, fact_110_add__right__imp__eq, fact_334_le__diff__iff_H, fact_194_numeral__Bit0, fact_100_add_Oassoc, fact_253_order__subst1, fact_308_le__cases3, fact_235_mult__diff__mult, fact_163_mult_Oleft__commute, fact_119_le__iff__add, fact_184_add__le__add__imp__diff__le, fact_201_ordered__ring__class_Ole__add__iff2, fact_350_Nat_Ole__imp__diff__is__add, fact_206_diff__eq__diff__less__eq, fact_198_abs__triangle__ineq, fact_328_Nat_Oadd__diff__assoc, fact_349_diff__commute, fact_243_semiring__norm_I2_J, fact_150_diff__add__eq, fact_183_le__add__diff, fact_22_numeral__le__iff, fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, fact_227_mult__numeral__1__right, fact_38_add__le__cancel__left, fact_122_less__eqE, fact_17_mult__numeral__left__semiring__numeral, fact_218_abs__mult, fact_89_ab__semigroup__add__class_Oadd__ac_I1_J, fact_8_corr__p, fact_113_one__plus__numeral__commute, fact_111_le__num__One__iff, fact_120_add__right__mono, fact_33_abs__idempotent, fact_55_diff__add__cancel, fact_271_ord__eq__le__subst, fact_78_num__double, fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, fact_214_right__diff__distrib, fact_281_ord__le__eq__subst, fact_76_numeral__eq__one__iff, fact_155_group__cancel_Osub1, fact_283_ord__le__eq__subst, fact_112_one__plus__numeral__commute, fact_69_le__add__diff__inverse, fact_244_dbl__simps_I5_J, fact_160_abs__one, fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, fact_291_antisym, fact_32_semiring__norm_I87_J, fact_247_numerals_I1_J, fact_262_order__subst2, fact_229_mult__numeral__1, fact_294_linear, fact_132_add__mono__thms__linordered__semiring_I3_J, fact_323_nat__add__left__cancel__le, fact_307_le__cases3, fact_135_distrib__right, fact_344_le__trans, fact_40_mult_Oright__neutral, fact_59_mem__Collect__eq, fact_268_verit__la__disequality, fact_195_numeral__Bit0, fact_212_left__diff__distrib_H, fact_43_numeral__plus__numeral, fact_174_rho__bound2__def, fact_149_diff__add__eq__diff__diff__swap, fact_16_semiring__norm_I83_J, fact_60_Collect__mem__eq, fact_204_abs__triangle__ineq4, fact_233_rate__2, fact_286_ord__le__eq__subst, fact_277_ord__eq__le__subst, fact_107_add__left__imp__eq, fact_300_le__cases, fact_141_ring__class_Oring__distribs_I1_J, fact_251_order__subst1, fact_5_Eq3, fact_18_mult__numeral__left__semiring__numeral, fact_104_add_Ocommute, fact_191_square__diff__square__factored, fact_288_eq__iff, fact_125_add__mono, fact_73_distrib__left__numeral, fact_158_comm__monoid__mult__class_Omult__1, fact_146_add__implies__diff, fact_332_diff__le__mono, fact_68_le__add__diff__inverse, fact_312_PC__monotone, fact_257_order__subst1, fact_58_abs__1, fact_310_antisym__conv, fact_203_abs__diff__triangle__ineq, fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, fact_254_order__subst1, fact_133_combine__common__factor, fact_232_rate__1, fact_256_order__subst1, fact_219_abs__minus__commute, fact_305_order_Otrans, fact_152_add__diff__eq, fact_57_abs__add__abs, fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062, fact_86_numeral__le__one__iff, fact_147_diff__diff__add, fact_84_one__add__one, fact_282_ord__le__eq__subst, fact_134_combine__common__factor, fact_88_ab__semigroup__add__class_Oadd__ac_I1_J, fact_138_distrib__left, fact_315_nat__eq__add__iff2, fact_64_semiring__norm_I71_J, fact_230_abs__triangle__ineq2__sym, fact_280_ord__le__eq__subst, fact_37_add__le__cancel__left, fact_148_diff__diff__add, fact_317_nat__le__add__iff2, fact_72_distrib__left__numeral, fact_156_mult_Ocomm__neutral, fact_340_mult__le__mono, fact_216_abs__ge__self, fact_313_verit__eq__simplify_I10_J, fact_82_numeral__plus__one, fact_101_add_Oleft__cancel, fact_269_verit__la__disequality, fact_25_abs__triangle__ineq3, fact_75_one__eq__numeral__iff, fact_0_rb2, fact_153_eq__diff__eq, fact_85_one__add__one, fact_49_add__diff__cancel__right, fact_190_diff__le__eq, fact_172_diff__right__commute, fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, fact_348_diff__mult__distrib, fact_205_abs__diff__le__iff, fact_202_ordered__ring__class_Ole__add__iff1, fact_11_left__diff__distrib__numeral, fact_322_nat__mult__eq__1__iff, fact_143_le__numeral__extra_I4_J, fact_258_order__subst2, fact_24_abs__triangle__ineq2, fact_215_left__diff__distrib, fact_327_Nat_Oadd__diff__assoc2, fact_26_numeral__eq__iff, fact_209_diff__mono, fact_274_ord__eq__le__subst, fact_165_mult_Ocommute, fact_289_eq__iff, fact_87_numeral__le__one__iff, fact_246_add__One__commute, fact_115_add__le__imp__le__right, fact_168_mult_Oassoc, fact_309_antisym__conv, fact_234_dbl__simps_I3_J, fact_159_comm__monoid__mult__class_Omult__1, fact_6_corr__q, fact_171_diff__right__commute, fact_61_semiring__norm_I13_J, fact_98_group__cancel_Oadd2, fact_285_ord__le__eq__subst, fact_114_correct__closed, fact_255_order__subst1, fact_295_linear, fact_35_add__le__cancel__right, fact_20_numeral__times__numeral, fact_241_eq__diff__eq_H, fact_318_nat__diff__add__eq1, fact_186_diff__add, fact_63_semiring__norm_I12_J, fact_144_le__numeral__extra_I4_J, fact_326_Nat_Odiff__diff__right, fact_173_diff__eq__diff__eq, fact_331_Nat_Odiff__diff__eq, fact_44_numeral__plus__numeral, fact_30_add__right__cancel, fact_53_add__diff__cancel__left, fact_324_diff__diff__cancel, fact_102_add_Oright__cancel, fact_217_abs__le__D1, fact_129_add__mono__thms__linordered__semiring_I2_J, fact_239_order__refl, fact_336_Nat_Oex__has__greatest__nat, fact_97_group__cancel_Oadd2, fact_71_distrib__right__numeral, fact_50_add__diff__cancel__right, fact_226_mult__numeral__1__right, fact_15_semiring__norm_I85_J, fact_341_le__antisym, fact_279_ord__le__eq__subst, fact_237_okRead1__def, fact_140_comm__semiring__class_Odistrib, fact_80_one__plus__numeral, fact_105_add_Oleft__commute, fact_21_numeral__le__iff, fact_121_add__right__mono, fact_54_add__diff__cancel__left, fact_337_nat__le__linear, fact_108_add__left__imp__eq, fact_66_le__add__diff__inverse2, fact_304_order_Otrans, fact_23_okRead2__def, fact_52_add__diff__cancel__left_H, fact_225_mult__2, fact_275_ord__eq__le__subst, fact_199_numeral__One, fact_192_eq__add__iff2, fact_128_add__mono__thms__linordered__semiring_I1_J, fact_170_ab__semigroup__mult__class_Omult__ac_I1_J, fact_303_order_Otrans, fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_197_one__le__numeral, fact_130_add__mono__thms__linordered__semiring_I2_J, fact_3_Eq1, fact_123_add__left__mono, fact_200_numeral__One, fact_272_ord__eq__le__subst, fact_259_order__subst2, fact_103_add_Ocommute, fact_325_diff__diff__left, fact_345_le__refl, fact_261_order__subst2, fact_263_order__subst2, fact_314_nat__eq__add__iff1, fact_187_add__le__imp__le__diff, fact_330_le__diff__iff, fact_260_order__subst2, fact_164_mult_Oleft__commute, fact_95_group__cancel_Oadd1, fact_139_comm__semiring__class_Odistrib, fact_124_add__left__mono, fact_45_add__numeral__left, fact_248_dbl__def, fact_28_add__left__cancel, fact_7_PC__ie, fact_14_abs__mult__self__eq, fact_116_add__le__imp__le__right, fact_136_distrib__right, fact_151_diff__diff__eq2, fact_346_le__cube, fact_296_linear, fact_298_eq__refl, fact_51_add__diff__cancel__left_H, fact_249_order__subst1, fact_290_eq__iff, fact_238_order__refl, fact_70_distrib__right__numeral, fact_31_add__right__cancel, fact_92_add__mono__thms__linordered__semiring_I4_J, fact_166_mult_Ocommute, fact_264_order__subst2, fact_145_add__implies__diff, fact_81_one__plus__numeral, fact_266_order__subst2, fact_236_verit__eq__simplify_I8_J, fact_12_right__diff__distrib__numeral, fact_118_add__le__imp__le__left, fact_29_add__left__cancel, fact_351_diff__add__inverse2, fact_157_mult_Ocomm__neutral, fact_339_mult__le__mono1, fact_270_ord__eq__le__subst, fact_96_group__cancel_Oadd1, fact_56_add__diff__cancel, fact_39_mult_Oright__neutral, fact_220_left__add__twice, fact_46_add__numeral__left, fact_321_nat__1__eq__mult__iff, fact_83_numeral__plus__one, fact_142_ring__class_Oring__distribs_I2_J, fact_342_le__square, fact_137_distrib__left, fact_273_ord__eq__le__subst, fact_188_add__le__imp__le__diff, fact_319_nat__diff__add__eq2, fact_306_le__cases3, fact_224_mult__2, fact_297_eq__refl, fact_265_order__subst2, fact_13_abs__numeral, fact_222_mult__2__right, fact_221_left__add__twice, fact_167_mult_Oassoc, fact_79_semiring__norm_I69_J, fact_207_diff__right__mono, fact_91_add__mono__thms__linordered__semiring_I4_J, fact_90_is__num__normalize_I1_J, fact_162_rho__bound1__def, fact_2_ie, fact_267_verit__la__disequality, fact_211_right__diff__distrib_H, fact_117_add__le__imp__le__left, fact_36_add__le__cancel__right, fact_48_add__diff__cancel__right_H, fact_99_add_Oassoc, fact_293_antisym, fact_208_diff__left__mono, fact_276_ord__eq__le__subst, fact_343_eq__imp__le, fact_329_eq__diff__iff, fact_333_diff__le__self, fact_185_add__le__add__imp__diff__le, fact_250_order__subst1, fact_19_numeral__times__numeral, fact_127_add__mono__thms__linordered__semiring_I1_J, fact_169_ab__semigroup__mult__class_Omult__ac_I1_J, fact_94_one__reorient, fact_278_ord__eq__le__subst, fact_228_mult__numeral__1, fact_47_add__diff__cancel__right_H, fact_77_numeral__eq__one__iff, fact_74_one__eq__numeral__iff, fact_131_add__mono__thms__linordered__semiring_I3_J, fact_284_ord__le__eq__subst
99.43/23.72	% No. of inferences in proof: 806
99.43/23.72	% SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23204 ms resp. 22610 ms w/o parsing
99.96/23.94	% SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
99.96/23.94	thf(set_real_type, type, set_real: $tType).
99.96/23.94	thf(real_type, type, real: $tType).
99.96/23.94	thf(num_type, type, num: $tType).
99.96/23.94	thf(nat_type, type, nat: $tType).
99.96/23.94	thf(genClo1161277105lle_PC_type, type, genClo1161277105lle_PC: (nat > (real > real))).
99.96/23.94	thf(genClo1144207539le_rho_type, type, genClo1144207539le_rho: real).
99.96/23.94	thf(genClo1015804716orrect_type, type, genClo1015804716orrect: (nat > (real > $o))).
99.96/23.94	thf(genClo293725281kRead1_type, type, genClo293725281kRead1: ((nat > real) > (real > ((nat > $o) > $o)))).
99.96/23.94	thf(genClo293725282kRead2_type, type, genClo293725282kRead2: ((nat > real) > ((nat > real) > (real > ((nat > $o) > $o))))).
99.96/23.94	thf(genClo2108747022bound1_type, type, genClo2108747022bound1: ((nat > (real > real)) > $o)).
99.96/23.94	thf(genClo2108747023bound2_type, type, genClo2108747023bound2: ((nat > (real > real)) > $o)).
99.96/23.94	thf(abs_abs_real_type, type, abs_abs_real: (real > real)).
99.96/23.94	thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))).
99.96/23.94	thf(minus_minus_real_type, type, minus_minus_real: (real > (real > real))).
99.96/23.94	thf(one_one_nat_type, type, one_one_nat: nat).
99.96/23.94	thf(one_one_real_type, type, one_one_real: real).
99.96/23.94	thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))).
99.96/23.94	thf(plus_plus_num_type, type, plus_plus_num: (num > (num > num))).
99.96/23.94	thf(plus_plus_real_type, type, plus_plus_real: (real > (real > real))).
99.96/23.94	thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))).
99.96/23.94	thf(times_times_num_type, type, times_times_num: (num > (num > num))).
99.96/23.94	thf(times_times_real_type, type, times_times_real: (real > (real > real))).
99.96/23.94	thf(neg_numeral_dbl_real_type, type, neg_numeral_dbl_real: (real > real)).
99.96/23.94	thf(bit0_type, type, bit0: (num > num)).
99.96/23.94	thf(one_type, type, one: num).
99.96/23.94	thf(numeral_numeral_nat_type, type, numeral_numeral_nat: (num > nat)).
99.96/23.94	thf(numeral_numeral_real_type, type, numeral_numeral_real: (num > real)).
99.96/23.94	thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))).
99.96/23.94	thf(ord_less_eq_num_type, type, ord_less_eq_num: (num > (num > $o))).
99.96/23.94	thf(ord_less_eq_real_type, type, ord_less_eq_real: (real > (real > $o))).
99.96/23.94	thf(collect_real_type, type, collect_real: ((real > $o) > set_real)).
99.96/23.94	thf(member_real_type, type, member_real: (real > (set_real > $o))).
99.96/23.94	thf(c_type, type, c: (nat > (real > real))).
99.96/23.94	thf(d_type, type, d: (nat > (real > real))).
99.96/23.94	thf(p_type, type, p: nat).
99.96/23.94	thf(q_type, type, q: nat).
99.96/23.94	thf(s_type, type, s: real).
99.96/23.94	thf(t_type, type, t: real).
99.96/23.94	thf(89,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__right__cancel)).
99.96/23.94	thf(645,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
99.96/23.94	thf(6,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_diff__le__self)).
99.96/23.94	thf(365,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
99.96/23.94	thf(325,axiom,((genClo1015804716orrect @ p @ t)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_corr__p)).
99.96/23.94	thf(1454,plain,((genClo1015804716orrect @ p @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])).
99.96/23.94	thf(312,axiom,((ord_less_eq_real @ s @ t)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_ie)).
99.96/23.94	thf(1418,plain,((ord_less_eq_real @ s @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])).
99.96/23.94	thf(1,conjecture,((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
99.96/23.94	thf(2,negated_conjecture,((~ (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(neg_conjecture,[status(cth)],[1])).
99.96/23.94	thf(355,plain,((~ (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
99.96/23.94	thf(1576,plain,(((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))) != (ord_less_eq_real @ s @ t))),inference(paramod_ordered,[status(thm)],[1418,355])).
99.96/23.94	thf(1577,plain,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != s) | ((times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != t)),inference(simp,[status(thm)],[1576])).
99.96/23.94	thf(197,axiom,(((neg_numeral_dbl_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_dbl__simps_I3_J)).
99.96/23.94	thf(1045,plain,(((neg_numeral_dbl_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
99.96/23.94	thf(1046,plain,(((numeral_numeral_real @ (bit0 @ one)) = (neg_numeral_dbl_real @ one_one_real))),inference(lifteq,[status(thm)],[1045])).
99.96/23.94	thf(1633,plain,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != s) | ((times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != t)),inference(rewrite,[status(thm)],[1577,1046])).
99.96/23.94	thf(42,axiom,((! [A:num,B:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_numeral__le__iff)).
99.96/23.94	thf(479,plain,((! [A:num,B:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
99.96/23.94	thf(143,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (! [C:nat]: (B != (plus_plus_nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_less__eqE)).
99.96/23.94	thf(846,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (! [C:nat]: ~ (B = (plus_plus_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
99.96/23.94	thf(235,axiom,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_mult_Oright__neutral)).
99.96/23.94	thf(1167,plain,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])).
99.96/23.94	thf(1168,plain,(! [A:real] : (((times_times_real @ A @ one_one_real) = A))),inference(cnf,[status(esa)],[1167])).
99.96/23.94	thf(1169,plain,(! [A:real] : (((times_times_real @ A @ one_one_real) = A))),inference(lifteq,[status(thm)],[1168])).
99.96/23.94	thf(219,axiom,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_eq__refl)).
99.96/23.94	thf(1118,plain,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
99.96/23.94	thf(1119,plain,(! [B:real,A:real] : ((~ (A = B)) | (ord_less_eq_real @ A @ B))),inference(cnf,[status(esa)],[1118])).
99.96/23.94	thf(1120,plain,(! [B:real,A:real] : ((A != B) | (ord_less_eq_real @ A @ B))),inference(lifteq,[status(thm)],[1119])).
99.96/23.94	thf(1121,plain,(! [A:real] : ((ord_less_eq_real @ A @ A))),inference(simp,[status(thm)],[1120])).
99.96/23.94	thf(1634,plain,((~ (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(rewrite,[status(thm)],[355,1046])).
99.96/23.94	thf(1789,plain,(! [A:real] : (((ord_less_eq_real @ A @ A) != (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))))),inference(paramod_ordered,[status(thm)],[1121,1634])).
99.96/23.94	thf(1791,plain,(! [A:real] : ((A != (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))) | (A != (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(simp,[status(thm)],[1789])).
99.96/23.94	thf(1794,plain,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),inference(simp,[status(thm)],[1791])).
99.96/23.94	thf(1853,plain,(! [A:real] : (((times_times_real @ A @ (minus_minus_real @ t @ s)) != (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))) | ((times_times_real @ A @ one_one_real) != (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho)))),inference(paramod_ordered,[status(thm)],[1169,1794])).
99.96/23.94	thf(1870,plain,(! [A:real] : (((times_times_real @ A @ (minus_minus_real @ t @ s)) != (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))) | (A != (neg_numeral_dbl_real @ one_one_real)) | (one_one_real != genClo1144207539le_rho))),inference(simp,[status(thm)],[1853])).
99.96/23.94	thf(1899,plain,(((times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ (minus_minus_real @ t @ s)) != (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))) | (one_one_real != genClo1144207539le_rho)),inference(simp,[status(thm)],[1870])).
99.96/23.94	thf(155,axiom,((! [A:num,B:(num > num),C:num,D:num]: ((((! [E:num,F:num]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ A @ (B @ D))) <= (ord_less_eq_num @ C @ D)) <= (ord_less_eq_num @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_order__subst1)).
99.96/23.94	thf(893,plain,((! [A:num,B:(num > num),C:num,D:num]: (((! [E:num,F:num]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ A @ (B @ D))) | ~ (ord_less_eq_num @ C @ D) | ~ (ord_less_eq_num @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
99.96/23.94	thf(55,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_ord__eq__le__subst)).
99.96/23.94	thf(518,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
99.96/23.94	thf(237,axiom,((! [A:num]: ((one_one_nat = (numeral_numeral_nat @ A)) = (one = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_one__eq__numeral__iff)).
99.96/23.94	thf(1179,plain,((! [A:num]: ((one_one_nat = (numeral_numeral_nat @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
99.96/23.94	thf(276,axiom,((! [A:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_numeral__plus__one)).
99.96/23.94	thf(1295,plain,((! [A:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])).
99.96/23.94	thf(68,axiom,((! [A:num]: (ord_less_eq_num @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_order__refl)).
99.96/23.94	thf(581,plain,((! [A:num]: (ord_less_eq_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
99.96/23.94	thf(582,plain,(! [A:num] : ((ord_less_eq_num @ A @ A))),inference(cnf,[status(esa)],[581])).
99.96/23.94	thf(308,axiom,((! [A:real,B:real]: ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_abs__mult)).
99.96/23.94	thf(1406,plain,((! [A:real,B:real]: ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])).
99.96/23.94	thf(274,axiom,((! [A:real,B:real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_abs__add__abs)).
99.96/23.94	thf(1290,plain,((! [A:real,B:real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])).
99.96/23.94	thf(206,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_diff__le__eq)).
99.96/23.94	thf(1068,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])).
99.96/23.94	thf(321,axiom,((! [A:nat,B:real,C:real]: (((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C)) => (ord_less_eq_real @ (times_times_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (genClo1161277105lle_PC @ A @ C) @ (genClo1161277105lle_PC @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_rate__2)).
99.96/23.94	thf(1443,plain,((! [A:nat,B:real,C:real]: (((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C)) => (ord_less_eq_real @ (times_times_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (genClo1161277105lle_PC @ A @ C) @ (genClo1161277105lle_PC @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])).
99.96/23.94	thf(74,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mult_Oleft__neutral)).
99.96/23.94	thf(595,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])).
99.96/23.94	thf(596,plain,(! [A:nat] : (((times_times_nat @ one_one_nat @ A) = A))),inference(cnf,[status(esa)],[595])).
99.96/23.94	thf(597,plain,(! [A:nat] : (((times_times_nat @ one_one_nat @ A) = A))),inference(lifteq,[status(thm)],[596])).
99.96/23.94	thf(339,axiom,(((numeral_numeral_nat @ one) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_numerals_I1_J)).
99.96/23.94	thf(1486,plain,(((numeral_numeral_nat @ one) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])).
99.96/23.94	thf(150,axiom,((! [A:num,B:num,C:(num > num),D:num]: ((((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_ord__le__eq__subst)).
99.96/23.94	thf(873,plain,((! [A:num,B:num,C:(num > num),D:num]: ((((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
99.96/23.94	thf(246,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ C @ B)) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_add__le__imp__le__diff)).
99.96/23.94	thf(1205,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ C @ B)) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])).
99.96/23.94	thf(343,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (C = (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_eq__add__iff2)).
99.96/23.94	thf(1497,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (C = (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])).
99.96/23.94	thf(196,axiom,((! [A:num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_one__le__numeral)).
99.96/23.94	thf(1043,plain,((! [A:num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
99.96/23.94	thf(1044,plain,(! [A:num] : ((ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)))),inference(cnf,[status(esa)],[1043])).
99.96/23.94	thf(1745,plain,(! [A:num] : ((ord_less_eq_real @ one_one_real @ (neg_numeral_dbl_real @ one_one_real)) | ((numeral_numeral_real @ (bit0 @ one)) != (numeral_numeral_real @ A)))),inference(paramod_ordered,[status(thm)],[1046,1044])).
99.96/23.94	thf(1746,plain,((ord_less_eq_real @ one_one_real @ (neg_numeral_dbl_real @ one_one_real))),inference(pattern_uni,[status(thm)],[1745:[bind(A, $thf(bit0 @ one))]])).
99.96/23.94	thf(1754,plain,(((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))) != (ord_less_eq_real @ one_one_real @ (neg_numeral_dbl_real @ one_one_real)))),inference(paramod_ordered,[status(thm)],[1746,1634])).
99.96/23.94	thf(1756,plain,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != one_one_real) | ((times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != (neg_numeral_dbl_real @ one_one_real))),inference(simp,[status(thm)],[1754])).
99.96/23.94	thf(63,axiom,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => (((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_ord__le__eq__subst)).
99.96/23.94	thf(550,plain,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
99.96/23.94	thf(233,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_abs__1)).
99.96/23.94	thf(1163,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
99.96/23.94	thf(1164,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(lifteq,[status(thm)],[1163])).
99.96/23.94	thf(269,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_add__diff__eq)).
99.96/23.94	thf(1275,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])).
99.96/23.94	thf(133,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_add__le__cancel__right)).
99.96/23.94	thf(814,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
99.96/23.94	thf(292,axiom,((! [A:real,B:real]: ((plus_plus_real @ A @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_left__add__twice)).
99.96/23.94	thf(1354,plain,((! [A:real,B:real]: ((plus_plus_real @ A @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])).
99.96/23.94	thf(97,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_eq__iff)).
99.96/23.94	thf(670,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
99.96/23.94	thf(243,axiom,((! [A:real,B:real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_abs__minus__commute)).
99.96/23.94	thf(1196,plain,((! [A:real,B:real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])).
99.96/23.94	thf(257,axiom,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_mult__numeral__1)).
99.96/23.94	thf(1243,plain,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])).
99.96/23.94	thf(305,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_diff__diff__eq2)).
99.96/23.94	thf(1391,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])).
99.96/23.94	thf(320,axiom,((genClo2108747023bound2 = (^ [A:(nat > (real > real))]: ! [B:nat,C:real,D:real]: ((ord_less_eq_real @ (times_times_real @ (minus_minus_real @ D @ C) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (A @ B @ D) @ (A @ B @ C))) <= ((genClo1015804716orrect @ B @ D) & (ord_less_eq_real @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_rho__bound2__def)).
99.96/23.94	thf(1441,plain,(((genClo2108747023bound2) = (^ [A:(nat > (real > real))]: ! [B:nat,C:real,D:real]: ((ord_less_eq_real @ (times_times_real @ (minus_minus_real @ D @ C) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (A @ B @ D) @ (A @ B @ C))) | ~ ((genClo1015804716orrect @ B @ D) & (ord_less_eq_real @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])).
99.96/23.94	thf(109,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))) <= ((C @ B) = D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_ord__le__eq__subst)).
99.96/23.94	thf(709,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
99.96/23.94	thf(303,axiom,((times_times_real = (^ [A:real,B:real]: (times_times_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_mult_Ocommute)).
99.96/23.94	thf(1385,plain,(((times_times_real) = (^ [A:real,B:real]: (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])).
99.96/23.94	thf(1386,plain,(((times_times_real) = (^ [A:real,B:real]: (times_times_real @ B @ A)))),inference(lifteq,[status(thm)],[1385])).
99.96/23.94	thf(334,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_linear)).
99.96/23.94	thf(1475,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])).
99.96/23.94	thf(66,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_linear)).
99.96/23.94	thf(565,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
99.96/23.94	thf(91,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/sandbox/benchmark/theBenchmark.p',fact_170_ab__semigroup__mult__class_Omult__ac_I1_J)).
99.96/23.94	thf(651,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)],[91])).
99.96/23.94	thf(138,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_eq__refl)).
99.96/23.94	thf(829,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
99.96/23.94	thf(18,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add__diff__cancel__left_H)).
99.96/23.94	thf(404,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
99.96/23.94	thf(152,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_order__refl)).
99.96/23.94	thf(885,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
99.96/23.94	thf(309,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_mult_Oassoc)).
99.96/23.94	thf(1409,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])).
99.96/23.94	thf(273,axiom,((! [A:real]: ((times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ A)) = (times_times_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_abs__mult__self__eq)).
99.96/23.94	thf(1287,plain,((! [A:real]: ((times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ A)) = (times_times_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])).
99.96/23.94	thf(277,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_diff__eq__diff__eq)).
99.96/23.94	thf(1298,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])).
99.96/23.94	thf(265,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_add__left__mono)).
99.96/23.94	thf(1264,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])).
99.96/23.94	thf(283,axiom,((! [A:num,B:num]: (((numeral_numeral_real @ A) = (numeral_numeral_real @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_numeral__eq__iff)).
99.96/23.94	thf(1323,plain,((! [A:num,B:num]: (((numeral_numeral_real @ A) = (numeral_numeral_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])).
99.96/23.94	thf(326,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => (((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => (ord_less_eq_real @ (minus_minus_real @ C @ B) @ D)) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C))) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_add__le__add__imp__diff__le)).
99.96/23.94	thf(1455,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => (((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => (ord_less_eq_real @ (minus_minus_real @ C @ B) @ D)) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C))) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])).
99.96/23.94	thf(241,axiom,((((=) @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_eq__iff)).
99.96/23.94	thf(1191,plain,((((=) @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
99.96/23.94	thf(328,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_add__diff__cancel)).
99.96/23.94	thf(1462,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])).
99.96/23.94	thf(171,axiom,((ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Eq2)).
99.96/23.94	thf(949,plain,((ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
99.96/23.94	thf(36,axiom,((! [A:num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_one__le__numeral)).
99.96/23.94	thf(460,plain,((! [A:num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
99.96/23.94	thf(107,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__mono__thms__linordered__semiring_I4_J)).
99.96/23.94	thf(702,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
99.96/23.94	thf(117,axiom,((! [A:real,B:real,C:real]: ((A = C) <= ((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_add__right__imp__eq)).
99.96/23.94	thf(751,plain,((! [A:real,B:real,C:real]: ((A = C) | ~ ((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
99.96/23.94	thf(134,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ B @ (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_add_Oleft__commute)).
99.96/23.94	thf(817,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ B @ (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
99.96/23.94	thf(145,axiom,((! [A:set_real]: ((collect_real @ (^ [B:real]: (member_real @ B @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Collect__mem__eq)).
99.96/23.94	thf(853,plain,((! [A:set_real]: ((collect_real @ (^ [B:real]: (member_real @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
99.96/23.94	thf(349,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_abs__one)).
99.96/23.94	thf(1514,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])).
99.96/23.94	thf(229,axiom,((ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Eq3)).
99.96/23.94	thf(1147,plain,((ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])).
99.96/23.94	thf(290,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_order__subst2)).
99.96/23.94	thf(1347,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])).
99.96/23.94	thf(218,axiom,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_one__plus__numeral)).
99.96/23.94	thf(1115,plain,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
99.96/23.94	thf(342,axiom,((! [A:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ one_one_real) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_numeral__le__one__iff)).
99.96/23.94	thf(1494,plain,((! [A:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ one_one_real) = (ord_less_eq_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])).
99.96/23.94	thf(1854,plain,(! [A:real] : ((A != (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))) | ((times_times_real @ A @ one_one_real) != (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(paramod_ordered,[status(thm)],[1169,1794])).
99.96/23.94	thf(1875,plain,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho)) | ((minus_minus_real @ t @ s) != one_one_real)),inference(simp,[status(thm)],[1854])).
99.96/23.94	thf(151,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_Nat_Oadd__diff__assoc2)).
99.96/23.94	thf(881,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
99.96/23.94	thf(22,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_diff__add__inverse2)).
99.96/23.94	thf(416,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
99.96/23.94	thf(311,axiom,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_right__diff__distrib__numeral)).
99.96/23.94	thf(1415,plain,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])).
99.96/23.94	thf(9,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_diff__mult__distrib2)).
99.96/23.94	thf(374,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
99.96/23.94	thf(375,plain,(! [C:nat,B:nat,A:nat] : (((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(cnf,[status(esa)],[374])).
99.96/23.94	thf(376,plain,(! [C:nat,B:nat,A:nat] : (((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(lifteq,[status(thm)],[375])).
99.96/23.94	thf(225,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_le__cases)).
99.96/23.94	thf(1136,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
99.96/23.94	thf(231,axiom,((! [A:real,B:real,C:(real > num),D:num]: ((ord_less_eq_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_ord__le__eq__subst)).
99.96/23.94	thf(1151,plain,((! [A:real,B:real,C:(real > num),D:num]: ((ord_less_eq_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])).
99.96/23.94	thf(192,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_distrib__left)).
99.96/23.94	thf(1020,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
99.96/23.94	thf(46,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_add_Oleft__commute)).
99.96/23.94	thf(492,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
99.96/23.94	thf(329,axiom,((! [A:nat,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ (genClo1161277105lle_PC @ A @ C) @ (genClo1161277105lle_PC @ A @ B)) @ (times_times_real @ (minus_minus_real @ C @ B) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho))) <= ((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_rate__1)).
99.96/23.94	thf(1465,plain,((! [A:nat,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ (genClo1161277105lle_PC @ A @ C) @ (genClo1161277105lle_PC @ A @ B)) @ (times_times_real @ (minus_minus_real @ C @ B) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho))) | ~ ((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])).
99.96/23.94	thf(298,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_abs__triangle__ineq3)).
99.96/23.94	thf(1373,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])).
99.96/23.94	thf(30,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/sandbox/benchmark/theBenchmark.p',fact_164_mult_Oleft__commute)).
99.96/23.94	thf(443,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)],[30])).
99.96/23.94	thf(76,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_distrib__left)).
99.96/23.94	thf(602,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
99.96/23.94	thf(300,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_diff__add__eq)).
99.96/23.94	thf(1377,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])).
99.96/23.94	thf(86,axiom,((! [A:num,B:num]: (((ord_less_eq_num @ B @ A) = (B = A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_antisym__conv)).
99.96/23.94	thf(634,plain,((! [A:num,B:num]: (((ord_less_eq_num @ B @ A) = (B = A)) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
99.96/23.94	thf(174,axiom,((ord_less_eq_real @ one_one_real @ one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_le__numeral__extra_I4_J)).
99.96/23.94	thf(956,plain,((ord_less_eq_real @ one_one_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
99.96/23.94	thf(306,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => (((C @ B) = D) => ((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_ord__le__eq__subst)).
99.96/23.94	thf(1394,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => (((C @ B) = D) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])).
99.96/23.94	thf(291,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = ((plus_plus_real @ A @ C) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_eq__diff__eq)).
99.96/23.94	thf(1351,plain,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = ((plus_plus_real @ A @ C) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])).
99.96/23.94	thf(94,axiom,((! [A:real]: ((one_one_real = A) = (A = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_one__reorient)).
99.96/23.94	thf(660,plain,((! [A:real]: ((one_one_real = A) = (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
99.96/23.94	thf(215,axiom,((! [A:num]: ((bit0 @ A) != one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_semiring__norm_I85_J)).
99.96/23.94	thf(1104,plain,((! [A:num]: ~ ((bit0 @ A) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])).
99.96/23.94	thf(51,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_is__num__normalize_I1_J)).
99.96/23.94	thf(507,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
99.96/23.94	thf(102,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2)).
99.96/23.94	thf(687,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])).
99.96/23.94	thf(208,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_less_eq_real @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_ord__le__eq__subst)).
99.96/23.94	thf(1074,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
99.96/23.94	thf(33,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ C @ D) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_add__mono__thms__linordered__semiring_I1_J)).
99.96/23.94	thf(452,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ C @ D) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
99.96/23.94	thf(11,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_diff__le__mono2)).
99.96/23.94	thf(380,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
99.96/23.94	thf(53,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((B = one_one_nat) & (A = one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_nat__mult__eq__1__iff)).
99.96/23.94	thf(512,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((B = one_one_nat) & (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
99.96/23.94	thf(319,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add__diff__cancel__right)).
99.96/23.94	thf(1438,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])).
99.96/23.94	thf(244,axiom,((! [A:nat,B:real,C:real]: (((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C)) => (genClo1015804716orrect @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_correct__closed)).
99.96/23.94	thf(1199,plain,((! [A:nat,B:real,C:real]: (((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C)) => (genClo1015804716orrect @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
99.96/23.94	thf(120,axiom,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_ord__le__eq__subst)).
99.96/23.94	thf(761,plain,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
99.96/23.94	thf(288,axiom,((! [A:num]: ~ (ord_less_eq_num @ (bit0 @ A) @ one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_semiring__norm_I69_J)).
99.96/23.94	thf(1336,plain,((! [A:num]: ~ (ord_less_eq_num @ (bit0 @ A) @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])).
99.96/23.94	thf(1337,plain,((~ (? [A:num]: (ord_less_eq_num @ (bit0 @ A) @ one)))),inference(miniscope,[status(thm)],[1336])).
99.96/23.94	thf(1338,plain,(! [A:num] : ((~ (ord_less_eq_num @ (bit0 @ A) @ one)))),inference(cnf,[status(esa)],[1337])).
99.96/23.94	thf(331,axiom,((genClo293725281kRead1 = (^ [A:(nat > real),B:real,C:(nat > $o)]: ! [D:nat,E:nat]: (((C @ E) & (C @ D)) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ D) @ (A @ E))) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_okRead1__def)).
99.96/23.94	thf(1470,plain,(((genClo293725281kRead1) = (^ [A:(nat > real),B:real,C:(nat > $o)]: ! [D:nat,E:nat]: (((C @ E) & (C @ D)) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ D) @ (A @ E))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])).
99.96/23.94	thf(366,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(cnf,[status(esa)],[365])).
99.96/23.94	thf(1560,plain,((~ (ord_less_eq_real @ one_one_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))) | ((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != (abs_abs_real @ one_one_real))),inference(paramod_ordered,[status(thm)],[1164,355])).
99.96/23.94	thf(1561,plain,((~ (ord_less_eq_real @ one_one_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))) | ((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real)),inference(simp,[status(thm)],[1560])).
99.96/23.94	thf(1578,plain,(((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real) | ((ord_less_eq_real @ s @ t) != (ord_less_eq_real @ one_one_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(paramod_ordered,[status(thm)],[1418,1561])).
99.96/23.94	thf(1581,plain,(((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real) | (s != one_one_real) | ((times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != t)),inference(simp,[status(thm)],[1578])).
99.96/23.94	thf(1636,plain,(((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real) | (s != one_one_real) | ((times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != t)),inference(rewrite,[status(thm)],[1581,1046])).
99.96/23.94	thf(198,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_abs__triangle__ineq4)).
99.96/23.94	thf(1047,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
99.96/23.94	thf(202,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_add__diff__cancel__right_H)).
99.96/23.94	thf(1057,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
99.96/23.94	thf(268,axiom,(((plus_plus_num @ one @ one) = (bit0 @ one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_semiring__norm_I2_J)).
99.96/23.94	thf(1273,plain,(((plus_plus_num @ one @ one) = (bit0 @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])).
99.96/23.94	thf(1274,plain,(((plus_plus_num @ one @ one) = (bit0 @ one))),inference(lifteq,[status(thm)],[1273])).
99.96/23.94	thf(304,axiom,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F))))) <= (ord_less_eq_real @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_order__subst1)).
99.96/23.94	thf(1387,plain,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))))) | ~ (ord_less_eq_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])).
99.96/23.94	thf(175,axiom,((! [A:num,B:num,C:real]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ (numeral_numeral_real @ B) @ C)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_add__numeral__left)).
99.96/23.94	thf(957,plain,((! [A:num,B:num,C:real]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ (numeral_numeral_real @ B) @ C)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
99.96/23.94	thf(137,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_order__subst1)).
99.96/23.94	thf(825,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
99.96/23.94	thf(351,axiom,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_ord__eq__le__subst)).
99.96/23.94	thf(1519,plain,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])).
99.96/23.94	thf(261,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_nat__1__add__1)).
99.96/23.94	thf(1255,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])).
99.96/23.94	thf(148,axiom,((! [A:num,B:nat,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ A) @ B) @ (times_times_nat @ (numeral_numeral_nat @ A) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_distrib__left__numeral)).
99.96/23.94	thf(862,plain,((! [A:num,B:nat,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ A) @ B) @ (times_times_nat @ (numeral_numeral_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
99.96/23.94	thf(75,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (A = B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_add__mono__thms__linordered__semiring_I2_J)).
99.96/23.94	thf(598,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (A = B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])).
99.96/23.94	thf(1487,plain,(((numeral_numeral_nat @ one) = one_one_nat)),inference(lifteq,[status(thm)],[1486])).
99.96/23.94	thf(26,axiom,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (ord_less_eq_num @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_eq__iff)).
99.96/23.94	thf(429,plain,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (ord_less_eq_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
99.96/23.94	thf(1747,plain,(! [A:num] : (((ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)) != (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))))),inference(paramod_ordered,[status(thm)],[1044,1634])).
99.96/23.94	thf(1751,plain,(! [A:num] : (((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != one_one_real) | ((numeral_numeral_real @ A) != (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(simp,[status(thm)],[1747])).
99.96/23.94	thf(135,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_linear)).
99.96/23.94	thf(820,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)],[135])).
99.96/23.94	thf(19,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_left__diff__distrib_H)).
99.96/23.94	thf(407,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
99.96/23.94	thf(85,axiom,((! [A:num,B:num,C:(num > nat),D:nat]: ((((! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) <= (ord_less_eq_nat @ (C @ B) @ D)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_order__subst2)).
99.96/23.94	thf(630,plain,((! [A:num,B:num,C:(num > nat),D:nat]: (((! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ (ord_less_eq_nat @ (C @ B) @ D) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
99.96/23.94	thf(126,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_add_Oassoc)).
99.96/23.94	thf(788,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
99.96/23.94	thf(297,axiom,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (bit0 @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_semiring__norm_I13_J)).
99.96/23.94	thf(1370,plain,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (bit0 @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])).
99.96/23.94	thf(4,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_diff__mult__distrib)).
99.96/23.94	thf(359,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
99.96/23.94	thf(360,plain,(! [C:nat,B:nat,A:nat] : (((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(cnf,[status(esa)],[359])).
99.96/23.94	thf(361,plain,(! [C:nat,B:nat,A:nat] : (((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(lifteq,[status(thm)],[360])).
99.96/23.94	thf(83,axiom,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_le__numeral__extra_I4_J)).
99.96/23.94	thf(625,plain,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
99.96/23.94	thf(69,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ (minus_minus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_add__le__imp__le__diff)).
99.96/23.94	thf(583,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ (minus_minus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
99.96/23.94	thf(248,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_eq_real @ A @ (plus_plus_real @ B @ C)) & (ord_less_eq_real @ (minus_minus_real @ B @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_abs__diff__le__iff)).
99.96/23.94	thf(1210,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_eq_real @ A @ (plus_plus_real @ B @ C)) & (ord_less_eq_real @ (minus_minus_real @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])).
99.96/23.94	thf(271,axiom,((! [A:real,B:real,C:num]: ((times_times_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ C)) = (minus_minus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_left__diff__distrib__numeral)).
99.96/23.94	thf(1281,plain,((! [A:real,B:real,C:num]: ((times_times_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ C)) = (minus_minus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])).
99.96/23.94	thf(189,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= ((ord_less_eq_real @ C @ D) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_add__mono__thms__linordered__semiring_I1_J)).
99.96/23.94	thf(1012,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ ((ord_less_eq_real @ C @ D) & (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
99.96/23.94	thf(232,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: ((ord_less_eq_nat @ A @ (B @ C)) => (((! [E:real,F:real]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))) <= (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_order__subst1)).
99.96/23.94	thf(1159,plain,((! [A:nat,B:(real > nat),C:real,D:real]: ((ord_less_eq_nat @ A @ (B @ C)) => (((! [E:real,F:real]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))) | ~ (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
99.96/23.94	thf(461,plain,(! [A:num] : ((ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),inference(cnf,[status(esa)],[460])).
99.96/23.94	thf(307,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ C @ B)) <= ((plus_plus_real @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_add__implies__diff)).
99.96/23.94	thf(1402,plain,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ C @ B)) | ~ ((plus_plus_real @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])).
99.96/23.94	thf(294,axiom,((! [A:real,B:(num > real),C:num,D:num]: ((((ord_less_eq_real @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_less_eq_num @ C @ D)) <= (ord_less_eq_real @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_order__subst1)).
99.96/23.94	thf(1360,plain,((! [A:real,B:(num > real),C:num,D:num]: ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_less_eq_num @ C @ D) | ~ (ord_less_eq_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])).
99.96/23.94	thf(105,axiom,((! [A:real,B:(real > $o)]: ((member_real @ A @ (collect_real @ B)) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mem__Collect__eq)).
99.96/23.94	thf(697,plain,((! [A:real,B:(real > $o)]: ((member_real @ A @ (collect_real @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
99.96/23.94	thf(267,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (ord_less_eq_real @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__le__cancel__left)).
99.96/23.94	thf(1270,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (ord_less_eq_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])).
99.96/23.94	thf(217,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= ((C = D) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_add__mono__thms__linordered__semiring_I3_J)).
99.96/23.94	thf(1111,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ ((C = D) & (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])).
99.96/23.94	thf(212,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_one__add__one)).
99.96/23.94	thf(1096,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])).
99.96/23.94	thf(187,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_right__diff__distrib)).
99.96/23.94	thf(1006,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])).
99.96/23.94	thf(354,axiom,((! [A:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_numeral__plus__one)).
99.96/23.94	thf(1534,plain,((! [A:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])).
99.96/23.94	thf(191,axiom,((! [A:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ one_one_real) = (times_times_real @ (plus_plus_real @ A @ one_one_real) @ (minus_minus_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_square__diff__one__factored)).
99.96/23.94	thf(1017,plain,((! [A:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ one_one_real) = (times_times_real @ (plus_plus_real @ A @ one_one_real) @ (minus_minus_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])).
99.96/23.94	thf(299,axiom,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) = (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Eq1)).
99.96/23.94	thf(1375,plain,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) = (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])).
99.96/23.94	thf(226,axiom,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ (bit0 @ one))) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_mult__2__right)).
99.96/23.94	thf(1138,plain,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ (bit0 @ one))) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
99.96/23.94	thf(3,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_diff__commute)).
99.96/23.94	thf(356,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
99.96/23.94	thf(125,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D))) <= (A = (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_group__cancel_Oadd1)).
99.96/23.94	thf(783,plain,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D))) | ~ (A = (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
99.96/23.94	thf(285,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_le__add__diff__inverse)).
99.96/23.94	thf(1329,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])).
99.96/23.94	thf(209,axiom,((! [A:num,B:num,C:(num > real),D:real]: ((ord_less_eq_num @ A @ B) => (((ord_less_eq_real @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F)))) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_ord__le__eq__subst)).
99.96/23.94	thf(1082,plain,((! [A:num,B:num,C:(num > real),D:real]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
99.96/23.94	thf(44,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_mult_Ocomm__neutral)).
99.96/23.94	thf(486,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
99.96/23.94	thf(487,plain,(! [A:nat] : (((times_times_nat @ A @ one_one_nat) = A))),inference(cnf,[status(esa)],[486])).
99.96/23.94	thf(488,plain,(! [A:nat] : (((times_times_nat @ A @ one_one_nat) = A))),inference(lifteq,[status(thm)],[487])).
99.96/23.94	thf(164,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_combine__common__factor)).
99.96/23.94	thf(933,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
99.96/23.94	thf(238,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D)) <= ((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_diff__eq__diff__less__eq)).
99.96/23.94	thf(1182,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D)) | ~ ((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
99.96/23.94	thf(314,axiom,((! [A:num,B:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_numeral__plus__numeral)).
99.96/23.94	thf(1424,plain,((! [A:num,B:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])).
99.96/23.94	thf(56,axiom,((! [A:nat,B:(num > nat),C:num,D:num]: ((((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))) <= (ord_less_eq_num @ C @ D)) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_order__subst1)).
99.96/23.94	thf(526,plain,((! [A:nat,B:(num > nat),C:num,D:num]: ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_num @ C @ D) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
99.96/23.94	thf(87,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (minus_minus_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_nat__diff__add__eq2)).
99.96/23.94	thf(637,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (minus_minus_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
99.96/23.94	thf(45,axiom,((! [A:num,B:num,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (times_times_nat @ (numeral_numeral_nat @ B) @ C)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_mult__numeral__left__semiring__numeral)).
99.96/23.94	thf(489,plain,((! [A:num,B:num,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (times_times_nat @ (numeral_numeral_nat @ B) @ C)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
99.96/23.94	thf(62,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_le__add__diff)).
99.96/23.94	thf(547,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
99.96/23.94	thf(108,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_order_Otrans)).
99.96/23.94	thf(706,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
99.96/23.94	thf(313,axiom,((! [A:real,B:real,C:real,D:real]: ((A = B) => ((ord_less_eq_real @ (abs_abs_real @ C) @ D) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ C) @ B)) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_sin__bound__lemma)).
99.96/23.94	thf(1419,plain,((! [A:real,B:real,C:real,D:real]: ((A = B) => ((ord_less_eq_real @ (abs_abs_real @ C) @ D) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ C) @ B)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])).
99.96/23.94	thf(101,axiom,((plus_plus_real = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_add_Ocommute)).
99.96/23.94	thf(685,plain,(((plus_plus_real) = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
99.96/23.94	thf(686,plain,(((plus_plus_real) = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),inference(lifteq,[status(thm)],[685])).
99.96/23.94	thf(41,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add__right__mono)).
99.96/23.94	thf(476,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
99.96/23.94	thf(247,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_right__diff__distrib_H)).
99.96/23.94	thf(1207,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
99.96/23.94	thf(72,axiom,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) => (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_le__cases)).
99.96/23.94	thf(590,plain,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) => (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
99.96/23.94	thf(264,axiom,((! [A:num]: ((times_times_num @ A @ one) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_semiring__norm_I11_J)).
99.96/23.94	thf(1261,plain,((! [A:num]: ((times_times_num @ A @ one) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])).
99.96/23.94	thf(1262,plain,(! [A:num] : (((times_times_num @ A @ one) = A))),inference(cnf,[status(esa)],[1261])).
99.96/23.94	thf(1263,plain,(! [A:num] : (((times_times_num @ A @ one) = A))),inference(lifteq,[status(thm)],[1262])).
99.96/23.94	thf(106,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_mult_Ocommute)).
99.96/23.94	thf(700,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
99.96/23.94	thf(701,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(lifteq,[status(thm)],[700])).
99.96/23.94	thf(324,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = (B = (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_eq__diff__eq_H)).
99.96/23.94	thf(1451,plain,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = (B = (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])).
99.96/23.94	thf(254,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D))) <= (A = (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_group__cancel_Osub1)).
99.96/23.94	thf(1231,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D))) | ~ (A = (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])).
99.96/23.94	thf(1192,plain,(((^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))) = ((=) @ real))),inference(lifteq,[status(thm)],[1191])).
99.96/23.94	thf(186,axiom,((! [A:num,B:(real > num),C:real,D:real]: ((ord_less_eq_num @ A @ (B @ C)) => (((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))) <= (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_order__subst1)).
99.96/23.94	thf(1002,plain,((! [A:num,B:(real > num),C:real,D:real]: ((ord_less_eq_num @ A @ (B @ C)) => (((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))) | ~ (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])).
99.96/23.94	thf(316,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_left__add__twice)).
99.96/23.94	thf(1429,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])).
99.96/23.94	thf(258,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ B @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_mult_Oleft__commute)).
99.96/23.94	thf(1246,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ B @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])).
99.96/23.94	thf(77,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_nat__add__left__cancel__le)).
99.96/23.94	thf(605,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
99.96/23.94	thf(54,axiom,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((A = one_one_nat) & (B = one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_nat__1__eq__mult__iff)).
99.96/23.94	thf(515,plain,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((A = one_one_nat) & (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
99.96/23.94	thf(259,axiom,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_abs__abs)).
99.96/23.94	thf(1249,plain,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])).
99.96/23.94	thf(353,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D)) <= (ord_less_eq_real @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_order__subst2)).
99.96/23.94	thf(1530,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D)) | ~ (ord_less_eq_real @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])).
99.96/23.94	thf(302,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= (ord_less_eq_real @ C @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_add__mono)).
99.96/23.94	thf(1382,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ (ord_less_eq_real @ C @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])).
99.96/23.94	thf(223,axiom,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ C)) @ (abs_abs_real @ (minus_minus_real @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_abs__diff__triangle__ineq)).
99.96/23.94	thf(1131,plain,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ C)) @ (abs_abs_real @ (minus_minus_real @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
99.96/23.94	thf(92,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))) <= (ord_less_eq_nat @ (C @ B) @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_order__subst2)).
99.96/23.94	thf(654,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_less_eq_nat @ (C @ B) @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
99.96/23.94	thf(203,axiom,(((minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Eq4)).
99.96/23.94	thf(1060,plain,(((minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
99.96/23.94	thf(35,axiom,((! [A:num,B:num]: (((A = B) <= (ord_less_eq_num @ B @ A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_antisym)).
99.96/23.94	thf(457,plain,((! [A:num,B:num]: ((A = B) | ~ (ord_less_eq_num @ B @ A) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
99.96/23.94	thf(287,axiom,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_verit__eq__simplify_I8_J)).
99.96/23.94	thf(1333,plain,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])).
99.96/23.94	thf(317,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_comm__monoid__mult__class_Omult__1)).
99.96/23.94	thf(1432,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])).
99.96/23.94	thf(1433,plain,(! [A:real] : (((times_times_real @ one_one_real @ A) = A))),inference(cnf,[status(esa)],[1432])).
99.96/23.94	thf(1434,plain,(! [A:real] : (((times_times_real @ one_one_real @ A) = A))),inference(lifteq,[status(thm)],[1433])).
99.96/23.94	thf(245,axiom,((! [A:num]: ((neg_numeral_dbl_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_dbl__simps_I5_J)).
99.96/23.94	thf(1202,plain,((! [A:num]: ((neg_numeral_dbl_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
99.96/23.94	thf(166,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_abs__triangle__ineq)).
99.96/23.94	thf(938,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
99.96/23.94	thf(201,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_comm__semiring__class_Odistrib)).
99.96/23.94	thf(1054,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
99.96/23.94	thf(236,axiom,((! [A:set_real]: ((? [B:real]: (member_real @ B @ A)) => ((? [B:real]: ! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B))) => (? [B:real]: (! [C:real]: ((! [D:real]: ((ord_less_eq_real @ D @ C) <= (member_real @ D @ A))) => (ord_less_eq_real @ B @ C)) & ! [C:real]: ((ord_less_eq_real @ C @ B) <= (member_real @ C @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_complete__real)).
99.96/23.94	thf(1170,plain,((! [A:set_real]: ((? [B:real]: (member_real @ B @ A)) => ((? [B:real]: ! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B))) => (? [B:real]: (! [C:real]: ((! [D:real]: ((ord_less_eq_real @ D @ C) | ~ (member_real @ D @ A))) => (ord_less_eq_real @ B @ C)) & ! [C:real]: ((ord_less_eq_real @ C @ B) | ~ (member_real @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
99.96/23.94	thf(16,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__diff__cancel__left)).
99.96/23.94	thf(398,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
99.96/23.94	thf(57,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_nat__le__linear)).
99.96/23.94	thf(530,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
99.96/23.94	thf(162,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_add__mono)).
99.96/23.94	thf(926,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
99.96/23.94	thf(64,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_nat__diff__add__eq1)).
99.96/23.94	thf(558,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
99.96/23.94	thf(207,axiom,((! [A:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_numeral__le__one__iff)).
99.96/23.94	thf(1071,plain,((! [A:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (ord_less_eq_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
99.96/23.94	thf(194,axiom,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_mult__2)).
99.96/23.94	thf(1026,plain,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
99.96/23.94	thf(173,axiom,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_diff__add__cancel)).
99.96/23.94	thf(953,plain,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])).
99.96/23.94	thf(239,axiom,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_semiring__norm_I87_J)).
99.96/23.94	thf(1185,plain,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
99.96/23.94	thf(122,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_diff__add)).
99.96/23.94	thf(773,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
99.96/23.94	thf(128,axiom,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((plus_plus_real @ D @ A) = (plus_plus_real @ B @ (plus_plus_real @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_group__cancel_Oadd2)).
99.96/23.94	thf(794,plain,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((plus_plus_real @ D @ A) = (plus_plus_real @ B @ (plus_plus_real @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])).
99.96/23.94	thf(270,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (minus_minus_real @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__diff__cancel__left)).
99.96/23.94	thf(1278,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (minus_minus_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])).
99.96/23.94	thf(81,axiom,((! [A:num,B:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_numeral__plus__numeral)).
99.96/23.94	thf(618,plain,((! [A:num,B:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
99.96/23.94	thf(430,plain,(((^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (ord_less_eq_num @ B @ A))) = ((=) @ num))),inference(lifteq,[status(thm)],[429])).
99.96/23.94	thf(146,axiom,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ A @ C) <= (ord_less_eq_num @ B @ C)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_order_Otrans)).
99.96/23.94	thf(856,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ C) | ~ (ord_less_eq_num @ B @ C) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
99.96/23.94	thf(278,axiom,((! [A:num,B:(real > num),C:real,D:real]: ((A = (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_num @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_ord__eq__le__subst)).
99.96/23.94	thf(1301,plain,((! [A:num,B:(real > num),C:real,D:real]: ((A = (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_num @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])).
99.96/23.94	thf(65,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_comm__semiring__class_Odistrib)).
99.96/23.94	thf(562,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
99.96/23.94	thf(24,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_diff__diff__left)).
99.96/23.94	thf(423,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
99.96/23.94	thf(104,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ab__semigroup__add__class_Oadd__ac_I1_J)).
99.96/23.94	thf(694,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
99.96/23.94	thf(114,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__add__diff__inverse)).
99.96/23.94	thf(732,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
99.96/23.94	thf(142,axiom,((! [A:num,B:num,C:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ (numeral_numeral_nat @ B) @ C)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_add__numeral__left)).
99.96/23.94	thf(843,plain,((! [A:num,B:num,C:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ (numeral_numeral_nat @ B) @ C)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
99.96/23.94	thf(21,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_diff__diff__add)).
99.96/23.94	thf(413,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
99.96/23.94	thf(252,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_numeral__Bit0)).
99.96/23.94	thf(1226,plain,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])).
99.96/23.94	thf(340,axiom,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_distrib__left__numeral)).
99.96/23.94	thf(1488,plain,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])).
99.96/23.94	thf(88,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc)).
99.96/23.94	thf(641,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
99.96/23.94	thf(345,axiom,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_abs__idempotent)).
99.96/23.94	thf(1503,plain,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])).
99.96/23.94	thf(165,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_abs__triangle__ineq2__sym)).
99.96/23.94	thf(936,plain,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
99.96/23.94	thf(381,plain,((! [A:nat,B:nat]: (! [C:nat]: (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(miniscope,[status(thm)],[380])).
99.96/23.94	thf(382,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) | (~ (ord_less_eq_nat @ A @ B)))),inference(cnf,[status(esa)],[381])).
99.96/23.94	thf(280,axiom,((! [A:num,B:num,C:(num > real),D:real]: ((((ord_less_eq_real @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F))))) <= (ord_less_eq_real @ (C @ B) @ D)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_order__subst2)).
99.96/23.94	thf(1312,plain,((! [A:num,B:num,C:(num > real),D:real]: ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) | ~ (ord_less_eq_real @ (C @ B) @ D) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])).
99.96/23.94	thf(48,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_distrib__right)).
99.96/23.94	thf(498,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
99.96/23.94	thf(1558,plain,(((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))) != (ord_less_eq_real @ one_one_real @ one_one_real))),inference(paramod_ordered,[status(thm)],[956,355])).
99.96/23.94	thf(1559,plain,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != one_one_real) | ((times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != one_one_real)),inference(simp,[status(thm)],[1558])).
99.96/23.94	thf(1635,plain,(((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != one_one_real) | ((times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != one_one_real)),inference(rewrite,[status(thm)],[1559,1046])).
99.96/23.94	thf(1105,plain,((~ (? [A:num]: ((bit0 @ A) = one)))),inference(miniscope,[status(thm)],[1104])).
99.96/23.94	thf(1106,plain,(! [A:num] : ((~ ((bit0 @ A) = one)))),inference(cnf,[status(esa)],[1105])).
99.96/23.94	thf(1107,plain,(! [A:num] : (((bit0 @ A) != one))),inference(lifteq,[status(thm)],[1106])).
99.96/23.94	thf(286,axiom,((genClo1015804716orrect @ q @ t)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_corr__q)).
99.96/23.94	thf(1332,plain,((genClo1015804716orrect @ q @ t)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])).
99.96/23.94	thf(38,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_left__add__mult__distrib)).
99.96/23.94	thf(466,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
99.96/23.94	thf(210,axiom,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (plus_plus_real @ (times_times_real @ C @ B) @ D)) = (plus_plus_real @ (times_times_real @ (plus_plus_real @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_combine__common__factor)).
99.96/23.94	thf(1090,plain,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (plus_plus_real @ (times_times_real @ C @ B) @ D)) = (plus_plus_real @ (times_times_real @ (plus_plus_real @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])).
99.96/23.94	thf(130,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_mult_Oright__neutral)).
99.96/23.94	thf(804,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])).
99.96/23.94	thf(263,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_diff__add__eq__diff__diff__swap)).
99.96/23.94	thf(1258,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])).
99.96/23.94	thf(170,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ C) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_add__le__imp__le__right)).
99.96/23.94	thf(947,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ C) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
99.96/23.94	thf(98,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_Nat_Ole__imp__diff__is__add)).
99.96/23.94	thf(672,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
99.96/23.94	thf(1638,plain,((~ (ord_less_eq_real @ one_one_real @ (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))) | ((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real)),inference(rewrite,[status(thm)],[1561,1046])).
99.96/23.94	thf(251,axiom,((genClo2108747022bound1 = (^ [A:(nat > (real > real))]: ! [B:nat,C:real,D:real]: (((ord_less_eq_real @ C @ D) & (genClo1015804716orrect @ B @ D)) => (ord_less_eq_real @ (minus_minus_real @ (A @ B @ D) @ (A @ B @ C)) @ (times_times_real @ (minus_minus_real @ D @ C) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_rho__bound1__def)).
99.96/23.94	thf(1224,plain,(((genClo2108747022bound1) = (^ [A:(nat > (real > real))]: ! [B:nat,C:real,D:real]: (((ord_less_eq_real @ C @ D) & (genClo1015804716orrect @ B @ D)) => (ord_less_eq_real @ (minus_minus_real @ (A @ B @ D) @ (A @ B @ C)) @ (times_times_real @ (minus_minus_real @ D @ C) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])).
99.96/23.94	thf(180,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_diff__diff__add)).
99.96/23.94	thf(979,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])).
99.96/23.94	thf(157,axiom,((! [A:nat,B:nat,C:num]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ C)) = (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ C)) @ (times_times_nat @ B @ (numeral_numeral_nat @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_distrib__right__numeral)).
99.96/23.94	thf(900,plain,((! [A:nat,B:nat,C:num]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ C)) = (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ C)) @ (times_times_nat @ B @ (numeral_numeral_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])).
99.96/23.94	thf(23,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_le__diff__iff)).
99.96/23.94	thf(419,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
99.96/23.94	thf(10,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_diff__right__commute)).
99.96/23.94	thf(377,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
99.96/23.94	thf(182,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_mult__numeral__1)).
99.96/23.94	thf(990,plain,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
99.96/23.94	thf(184,axiom,((! [A:num,B:num,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_mult__numeral__left__semiring__numeral)).
99.96/23.94	thf(996,plain,((! [A:num,B:num,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
99.96/23.94	thf(5,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_add__diff__cancel__right_H)).
99.96/23.94	thf(362,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
99.96/23.94	thf(67,axiom,((! [A:num,B:num,C:num]: (((~ (ord_less_eq_num @ B @ C)) <= (ord_less_eq_num @ A @ B)) => (((~ (ord_less_eq_num @ A @ C)) <= (ord_less_eq_num @ B @ A)) => (((ord_less_eq_num @ A @ C) => (~ (ord_less_eq_num @ C @ B))) => ((((~ (ord_less_eq_num @ C @ A)) <= (ord_less_eq_num @ B @ C)) => (~ ((~ (ord_less_eq_num @ A @ B)) <= (ord_less_eq_num @ C @ A)))) <= ((ord_less_eq_num @ C @ B) => (~ (ord_less_eq_num @ B @ A))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_le__cases3)).
99.96/23.94	thf(567,plain,((! [A:num,B:num,C:num]: ((~ (ord_less_eq_num @ B @ C) | ~ (ord_less_eq_num @ A @ B)) => ((~ (ord_less_eq_num @ A @ C) | ~ (ord_less_eq_num @ B @ A)) => (((ord_less_eq_num @ A @ C) => (~ (ord_less_eq_num @ C @ B))) => (((~ (ord_less_eq_num @ C @ A) | ~ (ord_less_eq_num @ B @ C)) => (~ (~ (ord_less_eq_num @ A @ B) | ~ (ord_less_eq_num @ C @ A)))) | ~ ((ord_less_eq_num @ C @ B) => (~ (ord_less_eq_num @ B @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
99.96/23.94	thf(80,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_add__le__imp__le__left)).
99.96/23.94	thf(616,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
99.96/23.94	thf(220,axiom,((! [A:num]: (one != (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_semiring__norm_I83_J)).
99.96/23.94	thf(1122,plain,((! [A:num]: ~ (one = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])).
99.96/23.94	thf(154,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_comm__monoid__mult__class_Omult__1)).
99.96/23.94	thf(890,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
99.96/23.94	thf(1471,plain,(((genClo293725281kRead1) = (^ [A:(nat > real),B:real,C:(nat > $o)]: ! [D:nat,E:nat]: (((C @ E) & (C @ D)) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ D) @ (A @ E))) @ B))))),inference(lifteq,[status(thm)],[1470])).
99.96/23.94	thf(7,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__diff__cancel__right)).
99.96/23.94	thf(367,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
99.96/23.94	thf(129,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add)).
99.96/23.94	thf(799,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
99.96/23.94	thf(82,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc)).
99.96/23.94	thf(621,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
99.96/23.94	thf(195,axiom,((! [A:real,B:real,C:real]: (((((ord_less_eq_real @ A @ C) => (~ (ord_less_eq_real @ C @ B))) => ((((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))) => (~ ((~ (ord_less_eq_real @ A @ B)) <= (ord_less_eq_real @ C @ A)))) <= ((ord_less_eq_real @ C @ B) => (~ (ord_less_eq_real @ B @ A))))) <= ((ord_less_eq_real @ B @ A) => (~ (ord_less_eq_real @ A @ C)))) <= ((~ (ord_less_eq_real @ B @ C)) <= (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_le__cases3)).
99.96/23.94	thf(1029,plain,((! [A:real,B:real,C:real]: ((((ord_less_eq_real @ A @ C) => (~ (ord_less_eq_real @ C @ B))) => ((((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))) => (~ (~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ C @ A)))) | ~ ((ord_less_eq_real @ C @ B) => (~ (ord_less_eq_real @ B @ A))))) | ~ ((ord_less_eq_real @ B @ A) => (~ (ord_less_eq_real @ A @ C))) | ~ (~ (ord_less_eq_real @ B @ C) | ~ (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
99.96/23.94	thf(177,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_ord__le__eq__subst)).
99.96/23.94	thf(964,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])).
99.96/23.94	thf(121,axiom,((! [A:num,B:(nat > num),C:nat,D:nat]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_order__subst1)).
99.96/23.94	thf(769,plain,((! [A:num,B:(nat > num),C:nat,D:nat]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
99.96/23.94	thf(168,axiom,((genClo2108747022bound1 @ c)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_rb1)).
99.96/23.94	thf(943,plain,((genClo2108747022bound1 @ (c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])).
99.96/23.94	thf(275,axiom,((! [A:num]: (ord_less_eq_num @ one @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_semiring__norm_I68_J)).
99.96/23.94	thf(1293,plain,((! [A:num]: (ord_less_eq_num @ one @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])).
99.96/23.94	thf(37,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) & (C = D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_add__mono__thms__linordered__semiring_I3_J)).
99.96/23.94	thf(462,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) & (C = D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
99.96/23.94	thf(132,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_ab__semigroup__add__class_Oadd__ac_I1_J)).
99.96/23.94	thf(811,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
99.96/23.94	thf(13,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_right__diff__distrib_H)).
99.96/23.94	thf(387,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
99.96/23.94	thf(119,axiom,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_verit__la__disequality)).
99.96/23.94	thf(758,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
99.96/23.94	thf(289,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: ((((! [E:real,F:real]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))) <= (ord_less_eq_real @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_ord__eq__le__subst)).
99.96/23.94	thf(1339,plain,((! [A:nat,B:(real > nat),C:real,D:real]: (((! [E:real,F:real]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))) | ~ (ord_less_eq_real @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])).
99.96/23.94	thf(84,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_eq__imp__le)).
99.96/23.94	thf(626,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
99.96/23.94	thf(160,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add_Oleft__cancel)).
99.96/23.94	thf(915,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
99.96/23.94	thf(333,axiom,((ord_less_eq_real @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)) @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_PC__ie)).
99.96/23.94	thf(1474,plain,((ord_less_eq_real @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)) @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])).
99.96/23.94	thf(249,axiom,((! [A:real,B:(num > real),C:num,D:num]: ((A = (B @ C)) => (((ord_less_eq_real @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_less_eq_num @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_ord__eq__le__subst)).
99.96/23.94	thf(1213,plain,((! [A:real,B:(num > real),C:num,D:num]: ((A = (B @ C)) => ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_less_eq_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])).
99.96/23.94	thf(322,axiom,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_numeral__Bit0)).
99.96/23.94	thf(1445,plain,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])).
99.96/23.94	thf(124,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/sandbox/benchmark/theBenchmark.p',fact_168_mult_Oassoc)).
99.96/23.94	thf(780,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)],[124])).
99.96/23.94	thf(78,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_Nat_Odiff__diff__right)).
99.96/23.94	thf(608,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
99.96/23.94	thf(15,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_le__diff__iff_H)).
99.96/23.94	thf(394,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
99.96/23.94	thf(318,axiom,((! [A:num]: (((numeral_numeral_nat @ A) = one_one_nat) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_numeral__eq__one__iff)).
99.96/23.94	thf(1435,plain,((! [A:num]: (((numeral_numeral_nat @ A) = one_one_nat) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])).
99.96/23.94	thf(335,axiom,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_mult__numeral__1__right)).
99.96/23.94	thf(1477,plain,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])).
99.96/23.94	thf(295,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_diff__right__commute)).
99.96/23.94	thf(1364,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])).
99.96/23.94	thf(50,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_add_Ocommute)).
99.96/23.94	thf(505,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
99.96/23.94	thf(27,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_le__iff__add)).
99.96/23.94	thf(431,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
99.96/23.94	thf(93,axiom,((neg_numeral_dbl_real = (^ [A:real]: (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_dbl__def)).
99.96/23.94	thf(658,plain,(((neg_numeral_dbl_real) = (^ [A:real]: (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
99.96/23.94	thf(40,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_antisym__conv)).
99.96/23.94	thf(473,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)],[40])).
99.96/23.94	thf(169,axiom,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_mult__2__right)).
99.96/23.94	thf(944,plain,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
99.96/23.94	thf(330,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_semiring__norm_I71_J)).
99.96/23.94	thf(1467,plain,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])).
99.96/23.94	thf(100,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_group__cancel_Oadd2)).
99.96/23.94	thf(680,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])).
99.96/23.94	thf(95,axiom,((! [A:real,B:real,C:real,D:real]: (((C = D) & (A = B)) => ((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__mono__thms__linordered__semiring_I4_J)).
99.96/23.94	thf(663,plain,((! [A:real,B:real,C:real,D:real]: (((C = D) & (A = B)) => ((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])).
99.96/23.94	thf(90,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_mult__le__mono2)).
99.96/23.94	thf(648,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
99.96/23.94	thf(347,axiom,((! [A:num]: ((abs_abs_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_abs__numeral)).
99.96/23.94	thf(1509,plain,((! [A:num]: ((abs_abs_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])).
99.96/23.94	thf(116,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_le__square)).
99.96/23.94	thf(749,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
99.96/23.94	thf(332,axiom,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_abs__ge__self)).
99.96/23.94	thf(1472,plain,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])).
99.96/23.94	thf(228,axiom,(((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_one__add__one)).
99.96/23.94	thf(1145,plain,(((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
99.96/23.94	thf(140,axiom,((! [A:num,B:num,C:(num > num),D:num]: (((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_order__subst2)).
99.96/23.94	thf(836,plain,((! [A:num,B:num,C:(num > num),D:num]: (((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
99.96/23.94	thf(199,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__diff__cancel__left_H)).
99.96/23.94	thf(1049,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])).
99.96/23.94	thf(25,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_le__antisym)).
99.96/23.94	thf(426,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
99.96/23.94	thf(1755,plain,(((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real) | ((ord_less_eq_real @ one_one_real @ (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))) != (ord_less_eq_real @ one_one_real @ (neg_numeral_dbl_real @ one_one_real)))),inference(paramod_ordered,[status(thm)],[1746,1638])).
99.96/23.94	thf(1757,plain,(((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real) | (one_one_real != one_one_real) | ((times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != (neg_numeral_dbl_real @ one_one_real))),inference(simp,[status(thm)],[1755])).
99.96/23.94	thf(1758,plain,(((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real) | ((times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != (neg_numeral_dbl_real @ one_one_real))),inference(simp,[status(thm)],[1757])).
99.96/23.94	thf(123,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_eq__refl)).
99.96/23.94	thf(776,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
99.96/23.94	thf(854,plain,(! [A:set_real] : (((collect_real @ (^ [B:real]: (member_real @ B @ A))) = A))),inference(cnf,[status(esa)],[853])).
99.96/23.94	thf(855,plain,(! [A:set_real] : (((collect_real @ (^ [B:real]: (member_real @ B @ A))) = A))),inference(lifteq,[status(thm)],[854])).
99.96/23.94	thf(350,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mult_Oleft__neutral)).
99.96/23.94	thf(1516,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])).
99.96/23.94	thf(153,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__left__cancel)).
99.96/23.94	thf(887,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
99.96/23.94	thf(1097,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(lifteq,[status(thm)],[1096])).
99.96/23.94	thf(363,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(cnf,[status(esa)],[362])).
99.96/23.94	thf(364,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(lifteq,[status(thm)],[363])).
99.96/23.94	thf(1646,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) = A) | ((plus_plus_nat @ one_one_nat @ one_one_nat) != (plus_plus_nat @ A @ B)))),inference(paramod_ordered,[status(thm)],[1097,364])).
99.96/23.94	thf(1647,plain,(((minus_minus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ one_one_nat) = one_one_nat)),inference(pattern_uni,[status(thm)],[1646:[bind(A, $thf(one_one_nat)),bind(B, $thf(one_one_nat))]])).
99.96/23.94	thf(260,axiom,((! [A:num]: ((ord_less_eq_num @ A @ one) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_le__num__One__iff)).
99.96/23.94	thf(1252,plain,((! [A:num]: ((ord_less_eq_num @ A @ one) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])).
99.96/23.94	thf(213,axiom,((! [A:real,B:real,C:num]: ((times_times_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ C)) = (plus_plus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_distrib__right__numeral)).
99.96/23.94	thf(1098,plain,((! [A:real,B:real,C:num]: ((times_times_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ C)) = (plus_plus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
99.96/23.94	thf(183,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = ((plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) = E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_eq__add__iff1)).
99.96/23.94	thf(993,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = ((plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
99.96/23.94	thf(1748,plain,(! [A:num] : (((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real) | ((ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)) != (ord_less_eq_real @ one_one_real @ (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))))),inference(paramod_ordered,[status(thm)],[1044,1638])).
99.96/23.94	thf(1752,plain,(! [A:num] : (((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real) | (one_one_real != one_one_real) | ((numeral_numeral_real @ A) != (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(simp,[status(thm)],[1748])).
99.96/23.94	thf(1753,plain,(! [A:num] : (((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real) | ((numeral_numeral_real @ A) != (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(simp,[status(thm)],[1752])).
99.96/23.94	thf(266,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_left__diff__distrib_H)).
99.96/23.94	thf(1267,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])).
99.96/23.94	thf(253,axiom,(((numeral_numeral_real @ one) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_numeral__One)).
99.96/23.94	thf(1229,plain,(((numeral_numeral_real @ one) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])).
99.96/23.94	thf(1230,plain,(((numeral_numeral_real @ one) = one_one_real)),inference(lifteq,[status(thm)],[1229])).
99.96/23.94	thf(338,axiom,((genClo293725282kRead2 = (^ [A:(nat > real),B:(nat > real),C:real,D:(nat > $o)]: ! [E:nat]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ E) @ (B @ E))) @ C) <= (D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_okRead2__def)).
99.96/23.94	thf(1484,plain,(((genClo293725282kRead2) = (^ [A:(nat > real),B:(nat > real),C:real,D:(nat > $o)]: ! [E:nat]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ E) @ (B @ E))) @ C) | ~ (D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])).
99.96/23.94	thf(1564,plain,(((times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != one_one_real) | ((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != (abs_abs_real @ one_one_real))),inference(paramod_ordered,[status(thm)],[1164,1559])).
99.96/23.94	thf(1566,plain,(((times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != one_one_real) | ((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real)),inference(simp,[status(thm)],[1564])).
99.96/23.94	thf(1637,plain,(((times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) != one_one_real) | ((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) != one_one_real)),inference(rewrite,[status(thm)],[1566,1046])).
99.96/23.94	thf(127,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 @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_mult__le__mono1)).
99.96/23.94	thf(791,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 @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
99.96/23.94	thf(240,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((A = B) <= (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_antisym)).
99.96/23.94	thf(1188,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((A = B) | ~ (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
99.96/23.94	thf(29,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_le__refl)).
99.96/23.94	thf(441,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
99.96/23.94	thf(110,axiom,((! [A:num,B:num]: (((numeral_numeral_nat @ A) = (numeral_numeral_nat @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_numeral__eq__iff)).
99.96/23.94	thf(717,plain,((! [A:num,B:num]: (((numeral_numeral_nat @ A) = (numeral_numeral_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
99.96/23.94	thf(141,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_add__le__cancel__left)).
99.96/23.94	thf(840,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
99.96/23.94	thf(1971,plain,(! [A:real] : ((A != (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))) | ((times_times_real @ one_one_real @ A) != (times_times_real @ (times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),inference(paramod_ordered,[status(thm)],[1434,1794])).
99.96/23.94	thf(1980,plain,(((times_times_real @ (neg_numeral_dbl_real @ one_one_real) @ genClo1144207539le_rho) != one_one_real) | ((abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) != (minus_minus_real @ t @ s))),inference(simp,[status(thm)],[1971])).
99.96/23.94	thf(159,axiom,((! [A:num,B:(nat > num),C:nat,D:nat]: ((A = (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_ord__eq__le__subst)).
99.96/23.94	thf(907,plain,((! [A:num,B:(nat > num),C:nat,D:nat]: ((A = (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
99.96/23.94	thf(70,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_le__add__diff__inverse2)).
99.96/23.94	thf(585,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
99.96/23.94	thf(8,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_add__implies__diff)).
99.96/23.94	thf(370,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
99.96/23.94	thf(262,axiom,((ord_less_eq_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062)).
99.96/23.94	thf(1257,plain,((ord_less_eq_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])).
99.96/23.94	thf(227,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((((ord_less_eq_real @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_real @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_order__subst1)).
99.96/23.94	thf(1141,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])).
99.96/23.94	thf(193,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_ring__class_Oring__distribs_I2_J)).
99.96/23.94	thf(1023,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
99.96/23.94	thf(315,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_add__le__imp__le__left)).
99.96/23.94	thf(1427,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])).
99.96/23.94	thf(113,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_group__cancel_Oadd1)).
99.96/23.94	thf(727,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
99.96/23.94	thf(31,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_add__left__imp__eq)).
99.96/23.94	thf(446,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
99.96/23.94	thf(79,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2)).
99.96/23.94	thf(612,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
99.96/23.94	thf(147,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 @ C @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_mult__le__mono)).
99.96/23.94	thf(859,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 @ C @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
99.96/23.94	thf(256,axiom,((! [A:num,B:num]: ((times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_numeral__times__numeral)).
99.96/23.94	thf(1240,plain,((! [A:num,B:num]: ((times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])).
99.96/23.94	thf(250,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_mult__2)).
99.96/23.94	thf(1221,plain,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])).
99.96/23.94	thf(272,axiom,((! [A:num]: ((plus_plus_num @ one @ A) = (plus_plus_num @ A @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__One__commute)).
99.96/23.94	thf(1284,plain,((! [A:num]: ((plus_plus_num @ one @ A) = (plus_plus_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])).
99.96/23.94	thf(1485,plain,(((genClo293725282kRead2) = (^ [A:(nat > real),B:(nat > real),C:real,D:(nat > $o)]: ! [E:nat]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ E) @ (B @ E))) @ C) | ~ (D @ E))))),inference(lifteq,[status(thm)],[1484])).
99.96/23.94	thf(200,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_abs__le__D1)).
99.96/23.94	thf(1052,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
99.96/23.94	thf(346,axiom,((! [A:num]: (((numeral_numeral_real @ A) = one_one_real) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_numeral__eq__one__iff)).
99.96/23.94	thf(1506,plain,((! [A:num]: (((numeral_numeral_real @ A) = one_one_real) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])).
99.96/23.94	thf(327,axiom,((! [A:num,B:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_numeral__le__iff)).
99.96/23.94	thf(1459,plain,((! [A:num,B:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])).
99.96/23.94	thf(60,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right)).
99.96/23.94	thf(539,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
99.96/23.94	thf(43,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_Nat_Oadd__diff__assoc)).
99.96/23.94	thf(482,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
99.96/23.94	thf(671,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = ((=) @ nat))),inference(lifteq,[status(thm)],[670])).
99.96/23.94	thf(221,axiom,((! [A:real,B:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = (times_times_real @ (plus_plus_real @ A @ B) @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_square__diff__square__factored)).
99.96/23.94	thf(1126,plain,((! [A:real,B:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = (times_times_real @ (plus_plus_real @ A @ B) @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
99.96/23.94	thf(323,axiom,((! [A:real,B:real]: (((plus_plus_real @ (minus_minus_real @ B @ A) @ A) = B) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_le__add__diff__inverse2)).
99.96/23.94	thf(1448,plain,((! [A:real,B:real]: (((plus_plus_real @ (minus_minus_real @ B @ A) @ A) = B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])).
99.96/23.94	thf(216,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_add__right__mono)).
99.96/23.94	thf(1108,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
99.96/23.94	thf(281,axiom,((! [A:num]: (one != (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_verit__eq__simplify_I10_J)).
99.96/23.94	thf(1316,plain,((! [A:num]: ~ (one = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])).
99.96/23.94	thf(32,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_le__cube)).
99.96/23.94	thf(450,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)],[32])).
99.96/23.94	thf(179,axiom,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_one__plus__numeral)).
99.96/23.94	thf(976,plain,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
99.96/23.94	thf(158,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_nat__le__add__iff1)).
99.96/23.94	thf(903,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
99.96/23.94	thf(47,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__left__cancel)).
99.96/23.94	thf(495,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
99.96/23.94	thf(1146,plain,(((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),inference(lifteq,[status(thm)],[1145])).
99.96/23.94	thf(1654,plain,(((plus_plus_real @ one_one_real @ one_one_real) = (neg_numeral_dbl_real @ one_one_real))),inference(rewrite,[status(thm)],[1146,1046])).
99.96/23.94	thf(310,axiom,((! [A:real,B:real]: ((A = B) | ~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_verit__la__disequality)).
99.96/23.94	thf(1412,plain,((! [A:real,B:real]: ((A = B) | ~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])).
99.96/23.94	thf(284,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)) <= (ord_less_eq_real @ C @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_diff__mono)).
99.96/23.94	thf(1326,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)) | ~ (ord_less_eq_real @ C @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])).
99.96/23.94	thf(71,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add__le__imp__le__right)).
99.96/23.94	thf(588,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
99.96/23.94	thf(204,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_add__le__cancel__right)).
99.96/23.94	thf(1062,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
99.96/23.94	thf(337,axiom,((! [A:real,B:real,C:real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_diff__eq__eq)).
99.96/23.94	thf(1481,plain,((! [A:real,B:real,C:real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])).
99.96/23.94	thf(214,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ C @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_ordered__ring__class_Ole__add__iff2)).
99.96/23.94	thf(1101,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ C @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
99.96/23.94	thf(14,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_Nat_Odiff__diff__eq)).
99.96/23.94	thf(390,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
99.96/23.94	thf(17,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_diff__le__mono)).
99.96/23.94	thf(401,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
99.96/23.94	thf(341,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_left__diff__distrib)).
99.96/23.94	thf(1491,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])).
99.96/23.94	thf(163,axiom,((! [A:nat,B:nat,C:nat]: ((A = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_add__right__imp__eq)).
99.96/23.94	thf(929,plain,((! [A:nat,B:nat,C:nat]: ((A = C) | ~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
99.96/23.94	thf(242,axiom,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_mult__numeral__1__right)).
99.96/23.94	thf(1193,plain,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
99.96/23.94	thf(12,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_eq__diff__iff)).
99.96/23.94	thf(383,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
99.96/23.94	thf(279,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_diff__left__mono)).
99.96/23.94	thf(1309,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])).
99.96/23.94	thf(59,axiom,((! [A:num,B:num]: (~ (ord_less_eq_num @ A @ B) | ~ (ord_less_eq_num @ B @ A) | (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_verit__la__disequality)).
99.96/23.94	thf(536,plain,((! [A:num,B:num]: (~ (ord_less_eq_num @ A @ B) | ~ (ord_less_eq_num @ B @ A) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
99.96/23.94	thf(28,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D))))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_Nat_Oex__has__greatest__nat)).
99.96/23.94	thf(433,plain,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D))))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
99.96/23.94	thf(52,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_le__cases)).
99.96/23.94	thf(510,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
99.96/23.94	thf(96,axiom,((! [A:num,B:num]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_numeral__times__numeral)).
99.96/23.94	thf(667,plain,((! [A:num,B:num]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
99.96/23.94	thf(1294,plain,(! [A:num] : ((ord_less_eq_num @ one @ A))),inference(cnf,[status(esa)],[1293])).
99.96/23.94	thf(224,axiom,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_semiring__norm_I6_J)).
99.96/23.94	thf(1133,plain,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
99.96/23.94	thf(185,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ B @ C)) = (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_le__diff__eq)).
99.96/23.94	thf(999,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ B @ C)) = (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
99.96/23.94	thf(348,axiom,(((numeral_numeral_nat @ one) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_numeral__One)).
99.96/23.94	thf(1512,plain,(((numeral_numeral_nat @ one) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])).
99.96/23.94	thf(432,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(lifteq,[status(thm)],[431])).
99.96/23.94	thf(301,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_abs__triangle__ineq2)).
99.96/23.94	thf(1380,plain,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])).
99.96/23.94	thf(115,axiom,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => (((~ (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)) => (~ ((~ (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ C @ A)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_le__cases3)).
99.96/23.94	thf(735,plain,((! [A:nat,B:nat,C:nat]: ((~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => ((~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ C)) => (~ (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
99.96/23.94	thf(139,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse)).
99.96/23.94	thf(833,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
99.96/23.94	thf(20,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_diff__diff__cancel)).
99.96/23.94	thf(410,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
99.96/23.94	thf(172,axiom,((! [A:num]: ((times_times_num @ (bit0 @ one) @ A) = (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_num__double)).
99.96/23.94	thf(950,plain,((! [A:num]: ((times_times_num @ (bit0 @ one) @ A) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
99.96/23.94	thf(352,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_diff__right__mono)).
99.96/23.94	thf(1527,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])).
99.96/23.94	thf(230,axiom,((! [A:num]: ((one_one_real = (numeral_numeral_real @ A)) = (one = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_one__eq__numeral__iff)).
99.96/23.94	thf(1148,plain,((! [A:num]: ((one_one_real = (numeral_numeral_real @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
99.96/23.94	thf(149,axiom,((! [A:num,B:(num > num),C:num,D:num]: ((((ord_less_eq_num @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_less_eq_num @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_ord__eq__le__subst)).
99.96/23.94	thf(865,plain,((! [A:num,B:(num > num),C:num,D:num]: ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_less_eq_num @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
99.96/23.94	thf(336,axiom,((genClo2108747023bound2 @ d)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_rb2)).
99.96/23.94	thf(1480,plain,((genClo2108747023bound2 @ (d))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])).
99.96/23.94	thf(161,axiom,((! [A:nat,B:(num > nat),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_ord__eq__le__subst)).
99.96/23.94	thf(918,plain,((! [A:nat,B:(num > nat),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
99.96/23.94	thf(506,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(lifteq,[status(thm)],[505])).
99.96/23.94	thf(156,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__right__cancel)).
99.96/23.94	thf(897,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
99.96/23.94	thf(357,plain,(! [C:nat,B:nat,A:nat] : (((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(cnf,[status(esa)],[356])).
99.96/23.94	thf(358,plain,(! [C:nat,B:nat,A:nat] : (((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(lifteq,[status(thm)],[357])).
99.96/23.94	thf(131,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((plus_plus_nat @ (times_times_nat @ B @ C) @ D) = (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = ((plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) = E)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_nat__eq__add__iff1)).
99.96/23.94	thf(807,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((plus_plus_nat @ (times_times_nat @ B @ C) @ D) = (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = ((plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) = E)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])).
99.96/23.94	thf(176,axiom,((! [A:real,B:real,C:(real > num),D:num]: ((((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))) => (ord_less_eq_num @ (C @ A) @ D)) <= (ord_less_eq_num @ (C @ B) @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_order__subst2)).
99.96/23.94	thf(960,plain,((! [A:real,B:real,C:(real > num),D:num]: (((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ (ord_less_eq_num @ (C @ B) @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])).
99.96/23.94	thf(1473,plain,(! [A:real] : ((ord_less_eq_real @ A @ (abs_abs_real @ A)))),inference(cnf,[status(esa)],[1472])).
99.96/23.94	thf(58,axiom,((! [A:real,B:real,C:real]: ((B = C) <= ((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_add__left__imp__eq)).
99.96/23.94	thf(532,plain,((! [A:real,B:real,C:real]: ((B = C) | ~ ((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
99.96/23.94	thf(205,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_ring__class_Oring__distribs_I1_J)).
99.96/23.94	thf(1065,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
99.96/23.94	thf(111,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_add_Oright__cancel)).
99.96/23.94	thf(720,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
99.96/23.94	thf(234,axiom,((! [A:nat,B:real,C:real]: ((ord_less_eq_real @ (genClo1161277105lle_PC @ A @ B) @ (genClo1161277105lle_PC @ A @ C)) <= ((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_PC__monotone)).
99.96/23.94	thf(1165,plain,((! [A:nat,B:real,C:real]: ((ord_less_eq_real @ (genClo1161277105lle_PC @ A @ B) @ (genClo1161277105lle_PC @ A @ C)) | ~ ((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])).
99.96/23.94	thf(211,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ C) <= (ord_less_eq_real @ B @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_order_Otrans)).
99.96/23.94	thf(1093,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ C) | ~ (ord_less_eq_real @ B @ C) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])).
99.96/23.94	thf(255,axiom,((! [A:real,B:real,C:real,D:real]: (((A = B) & (ord_less_eq_real @ C @ D)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_add__mono__thms__linordered__semiring_I2_J)).
99.96/23.94	thf(1236,plain,((! [A:real,B:real,C:real,D:real]: (((A = B) & (ord_less_eq_real @ C @ D)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])).
99.96/23.94	thf(222,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_order__refl)).
99.96/23.94	thf(1129,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
99.96/23.94	thf(293,axiom,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_mult_Ocomm__neutral)).
99.96/23.94	thf(1357,plain,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])).
99.96/23.94	thf(136,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_one__reorient)).
99.96/23.94	thf(822,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])).
99.96/23.94	thf(144,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_add__left__mono)).
99.96/23.94	thf(850,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
99.96/23.94	thf(181,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_ord__eq__le__subst)).
99.96/23.94	thf(982,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])).
99.96/23.94	thf(103,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_add_Oassoc)).
99.96/23.94	thf(691,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
99.96/23.94	thf(442,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ A))),inference(cnf,[status(esa)],[441])).
99.96/23.94	thf(49,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_add__le__add__imp__diff__le)).
99.96/23.94	thf(501,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
99.96/23.94	thf(368,plain,(! [C:nat,B:nat,A:nat] : (((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),inference(cnf,[status(esa)],[367])).
99.96/23.94	thf(369,plain,(! [C:nat,B:nat,A:nat] : (((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),inference(lifteq,[status(thm)],[368])).
99.96/23.94	thf(344,axiom,((! [A:num]: ((times_times_num @ one @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_semiring__norm_I12_J)).
99.96/23.94	thf(1500,plain,((! [A:num]: ((times_times_num @ one @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])).
99.96/23.94	thf(112,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2)).
99.96/23.94	thf(723,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
99.96/23.94	thf(282,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_ab__semigroup__mult__class_Omult__ac_I1_J)).
99.96/23.94	thf(1320,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])).
99.96/23.94	thf(188,axiom,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ (minus_minus_real @ B @ D)) @ (times_times_real @ (minus_minus_real @ A @ C) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_mult__diff__mult)).
99.96/23.94	thf(1009,plain,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ (minus_minus_real @ B @ D)) @ (times_times_real @ (minus_minus_real @ A @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
99.96/23.94	thf(659,plain,(((^ [A:real]: (plus_plus_real @ A @ A)) = (neg_numeral_dbl_real))),inference(lifteq,[status(thm)],[658])).
99.96/23.94	thf(61,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_eq_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_nat__le__add__iff2)).
99.96/23.94	thf(543,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_eq_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
99.96/23.94	thf(73,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_le__trans)).
99.96/23.94	thf(592,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
99.96/23.94	thf(34,axiom,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_one__plus__numeral__commute)).
99.96/23.94	thf(454,plain,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
99.96/23.94	thf(39,axiom,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) <= (ord_less_eq_num @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_order__subst2)).
99.96/23.94	thf(469,plain,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ (ord_less_eq_num @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
99.96/23.94	thf(296,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_ordered__ring__class_Ole__add__iff1)).
99.96/23.94	thf(1367,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])).
99.96/23.94	thf(167,axiom,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_one__plus__numeral__commute)).
99.96/23.94	thf(940,plain,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
99.96/23.94	thf(118,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_antisym)).
99.96/23.94	thf(755,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
99.96/23.94	thf(99,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((plus_plus_nat @ (times_times_nat @ A @ C) @ D) = (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (D = (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_nat__eq__add__iff2)).
99.96/23.94	thf(676,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((plus_plus_nat @ (times_times_nat @ A @ C) @ D) = (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (D = (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])).
99.96/23.94	thf(190,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_distrib__right)).
99.96/23.94	thf(1014,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])).
99.96/23.94	thf(178,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_real @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F))))) <= (ord_less_eq_real @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_order__subst2)).
99.96/23.94	thf(972,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) | ~ (ord_less_eq_real @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
99.96/23.94	thf(34360,plain,(($false)),inference(e,[status(thm)],[645,365,1454,1633,479,846,1899,893,518,1179,1295,582,1406,1290,1068,1443,597,1486,873,1205,1497,1756,550,1164,1275,814,1354,670,1196,1746,1243,1391,1441,709,1386,1475,565,651,829,404,885,1046,1409,1287,1298,1264,1323,1455,1191,1462,949,460,702,751,817,853,1514,1147,1347,1115,1494,1875,881,416,1415,376,1418,1136,1151,1020,492,1465,1373,443,602,1377,634,956,1394,1351,660,1104,507,1169,687,1074,452,380,512,1438,1199,761,1338,1470,366,1636,1047,1057,1163,1274,1387,957,825,1519,1255,862,598,1487,429,1751,820,407,630,788,1370,361,625,583,1210,1281,1634,1012,1159,461,1402,1360,697,1270,1111,1096,1006,1534,1794,1017,1375,1121,1138,356,783,1118,1329,1082,488,933,1182,1424,526,637,489,547,706,1419,686,476,1207,590,1263,701,1451,1231,1192,1002,1429,1246,605,515,1249,1530,1382,1131,654,1060,457,1333,1434,1202,938,1054,1170,398,530,926,558,1071,1026,1167,953,1185,773,794,1278,618,430,1273,856,1301,562,423,694,732,843,413,1226,1488,641,1503,936,382,1312,498,1635,1107,1332,466,1090,804,1258,947,672,1638,1224,979,900,419,1043,377,990,996,362,567,616,1122,890,1471,367,799,621,700,1029,964,769,943,1293,462,811,387,758,1339,626,915,685,1474,1213,1044,1445,780,608,394,1435,1477,1364,505,431,658,473,944,1467,680,663,374,648,1509,749,1472,1145,355,836,1049,426,1758,776,855,1516,887,1647,1252,1098,993,1753,1267,1230,1484,1432,1637,791,1188,441,717,840,1980,359,1336,907,585,370,1257,1141,1023,1427,727,446,595,612,859,1240,1221,1284,1485,1052,1506,1459,539,482,671,581,1126,1448,1108,1316,450,976,903,495,1654,1412,1326,588,1385,1062,1481,1101,390,401,1491,929,1193,383,1309,536,1045,433,510,667,1294,1133,999,1512,432,1229,1380,735,833,410,950,1097,1527,1148,865,1480,918,506,897,358,807,960,1473,532,1065,720,1165,1093,1236,1129,1261,1357,822,850,982,691,442,501,369,1500,723,486,1320,1009,659,543,592,454,364,469,1367,940,755,676,1014,972])).
99.96/23.94	% SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
99.96/23.94	% [INFO] 	 Killing All external provers ... 
100.14/23.98	EOF