0.00/0.01 % Leo-III: Strategy 1 (for '60') 24.00/12.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 24.00/12.91 % [INFO] Parsing done (510ms). 24.00/12.91 % [INFO] Running in sequential loop mode. 24.00/12.91 % [CONFIG] Using configuration: timeout(60) with strategy 24.00/12.91 % [INFO] eprover registered as external prover. 24.00/12.91 % [INFO] cvc4 registered as external prover. 24.00/12.91 % [INFO] Parsing finished. Scanning for conjecture ... 24.00/12.91 % [INFO] Found a conjecture and 358 axioms. Running axiom selection ... 24.00/12.91 % [INFO] Axiom selection finished. Selected 195 axioms (removed 163 axioms). 24.00/12.91 % [INFO] Problem is higher-order (TPTP THF). 24.00/12.91 % [INFO] Type checking passed. Searching for refutation ... 24.00/12.91 % External prover 'cvc4' found a proof! 24.00/12.91 % [INFO] Killing All external provers ... 24.00/12.91 % Time passed: 9219ms (effective reasoning time: 8069ms) 24.00/12.91 % Solved by strategy 24.00/12.91 % Axioms used in derivation (195): fact_332_abs__eq__0__iff, fact_100_max_Oabsorb2, fact_60_order__class_Oorder_Oeq__iff, fact_161_one__reorient, fact_316_add__le__same__cancel2, fact_1_corr__m, fact_104_max_OorderI, fact_139_add__diff__cancel__right_H, fact_310_abs__zero, fact_281_nonoverlap, fact_345_add__decreasing2, fact_130_add__right__cancel, fact_230_rts1, fact_320_le__add__same__cancel2, fact_151_add_Oassoc, fact_119_abs__1, fact_122_diff__add__cancel, fact_324_diff__ge__0__iff__ge, fact_86_max_Oabsorb__iff1, fact_78_dual__order_Oantisym, fact_296_add__cancel__left__left, fact_198_abs__ge__self, fact_142_add__right__imp__eq, fact_62_ord__eq__le__trans, fact_298_double__zero, fact_192_diff__add__eq, fact_200_abs__one, fact_50_eq__refl, fact_222_diff__le__eq, fact_141_add__right__imp__eq, fact_227_abs__diff__triangle__ineq, fact_26_order__refl, fact_110_max__def, fact_133_abs__idempotent, fact_46_antisym, fact_8_max_Oidem, fact_5_corr__l__tml, fact_338_add_Ocomm__neutral, fact_313_abs__0, fact_323_zero__le__double__add__iff__zero__le__single__add, fact_72_linorder__wlog, fact_117_le__add__diff__inverse2, fact_3_tml__le__tp, fact_300_add_Oright__neutral, fact_309_diff__self, fact_24_max__absorb1, fact_135_add__le__cancel__right, fact_225_abs__triangle__ineq3, fact_336_add_Ogroup__left__neutral, fact_347_add__increasing2, fact_66_order__class_Oorder_Oantisym, fact_70_dual__order_Orefl, fact_204_max__add__distrib__right, fact_206_max__diff__distrib__left, fact_341_add__decreasing, fact_0_correct__closed, fact_235_sin__bound__lemma, fact_58_antisym__conv, fact_290_add__cancel__right__right, fact_194_add__diff__eq, fact_237_beta__bound2, fact_197_group__cancel_Osub1, fact_40_ord__le__eq__subst, fact_159_ab__semigroup__add__class_Oadd__ac_I1_J, fact_158_add__mono__thms__linordered__semiring_I4_J, fact_224_abs__triangle__ineq2__sym, fact_179_add__mono__thms__linordered__semiring_I2_J, fact_292_add__cancel__right__left, fact_302_add_Oleft__neutral, fact_147_add_Ocommute, fact_196_diff__eq__eq, fact_201_abs__minus__commute, fact_15_max_Oassoc, fact_145_add_Oleft__commute, fact_98_max_OboundedE, fact_175_add__mono, fact_233_rts0d, fact_308_diff__0__right, fact_152_add_Oassoc, fact_167_add__le__imp__le__left, fact_343_add__increasing, fact_19_max_Oleft__commute, fact_52_le__cases, fact_326_abs__of__nonneg, fact_32_order__subst2, fact_48_linear, fact_120_abs__add__abs, fact_195_eq__diff__eq, fact_6_tmi__le__tp, fact_123_add__diff__cancel__left, fact_223_abs__triangle__ineq, fact_297_double__zero__sym, fact_82_max_OcoboundedI1, fact_56_le__cases3, fact_112_max__absorb2, fact_328_abs__le__zero__iff, help_If_2_1_If_001t__Real__Oreal_T, fact_331_zero__reorient, fact_115_le__add__diff__inverse, fact_236_eq__diff__eq_H, fact_108_max_Omono, fact_146_add_Oleft__commute, fact_226_abs__triangle__ineq2, fact_305_diff__zero, fact_193_diff__diff__eq2, fact_84_max_Oabsorb__iff2, fact_219_add__le__imp__le__diff, fact_231_rts1d, fact_143_add__left__imp__eq, fact_125_add__diff__cancel__left_H, fact_17_max_Ocommute, fact_322_double__add__le__zero__iff__single__add__le__zero, fact_28_order__subst1, fact_177_add__mono__thms__linordered__semiring_I1_J, fact_2_corr__p, fact_150_add_Oleft__cancel, fact_184_diff__right__mono, fact_153_group__cancel_Oadd2, fact_154_group__cancel_Oadd2, fact_183_diff__eq__diff__less__eq, fact_202_max__add__distrib__left, fact_36_ord__eq__le__subst, fact_311_abs__eq__0, fact_132_add__left__cancel, fact_285_beta__bound1, fact_340_comm__monoid__add__class_Oadd__0, fact_318_le__add__same__cancel1, fact_284_okRead1__def, fact_149_add_Oright__cancel, fact_129_add__right__cancel, fact_137_add__le__cancel__left, fact_283_readerror, fact_127_add__diff__cancel__right, fact_114_okmaxsync__def, fact_221_le__diff__eq, fact_4_corr__l, fact_94_max_Oorder__iff, fact_102_max_Oabsorb1, fact_21_rte, fact_312_abs__0__eq, fact_164_diff__eq__diff__eq, fact_80_max_OcoboundedI2, fact_157_add__mono__thms__linordered__semiring_I4_J, fact_106_max_OorderE, fact_165_add__le__imp__le__right, fact_76_dual__order_Oeq__iff, fact_131_add__left__cancel, fact_14_IC__bound, fact_22_max_Obounded__iff, fact_349_add__nonneg__nonneg, fact_186_diff__mono, fact_90_max_Ocobounded2, fact_185_diff__left__mono, fact_181_add__mono__thms__linordered__semiring_I3_J, fact_234_okRead2__def, fact_160_ab__semigroup__add__class_Oadd__ac_I1_J, fact_68_order__trans, fact_148_add_Ocommute, fact_54_order_Otrans, fact_170_add__right__mono, fact_88_le__max__iff__disj, fact_156_group__cancel_Oadd1, fact_155_group__cancel_Oadd1, fact_187_add__implies__diff, fact_189_diff__diff__add, help_If_3_1_If_001t__Real__Oreal_T, fact_74_dual__order_Otrans, fact_303_cancel__comm__monoid__add__class_Odiff__cancel, fact_327_abs__le__self__iff, help_If_1_1_If_001t__Real__Oreal_T, fact_96_max_OboundedI, fact_144_add__left__imp__eq, fact_162_diff__right__commute, fact_12_max_Oright__idem, fact_351_add__nonpos__nonpos, fact_173_add__left__mono, fact_228_abs__triangle__ineq4, fact_92_max_Ocobounded1, fact_121_add__diff__cancel, fact_314_add__le__same__cancel1, fact_191_diff__add__eq__diff__diff__swap, fact_229_abs__diff__le__iff, fact_134_abs__abs, fact_7_tli__le__tp, fact_282_rts2a, fact_232_rts0, fact_44_eq__iff, fact_294_add__cancel__left__right, fact_238_rts2b, fact_333_eq__iff__diff__eq__0, fact_10_max_Oleft__idem, fact_335_zero__neq__one, fact_216_add__le__add__imp__diff__le, fact_64_ord__le__eq__trans, fact_199_abs__le__D1 24.00/12.91 % No. of inferences in proof: 394 24.00/12.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9219 ms resp. 8069 ms w/o parsing 24.00/12.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 24.00/12.91 thf(real_type, type, real: $tType). 24.00/12.91 thf(nat_type, type, nat: $tType). 24.00/12.91 thf(genClo1160817912lle_IC_type, type, genClo1160817912lle_IC: (nat > (nat > (real > real)))). 24.00/12.91 thf(genClo721845095Lambda_type, type, genClo721845095Lambda: real). 24.00/12.91 thf(genClo1278781456e_beta_type, type, genClo1278781456e_beta: real). 24.00/12.91 thf(genClo1400225944_theta_type, type, genClo1400225944_theta: (nat > (nat > (nat > real)))). 24.00/12.91 thf(genClo1015804716orrect_type, type, genClo1015804716orrect: (nat > (real > $o))). 24.00/12.91 thf(genClo293725281kRead1_type, type, genClo293725281kRead1: ((nat > real) > (real > ((nat > $o) > $o)))). 24.00/12.91 thf(genClo293725282kRead2_type, type, genClo293725282kRead2: ((nat > real) > ((nat > real) > (real > ((nat > $o) > $o))))). 24.00/12.91 thf(genClo208577157axsync_type, type, genClo208577157axsync: (nat > (real > $o))). 24.00/12.91 thf(genClo1650508560e_rmax_type, type, genClo1650508560e_rmax: real). 24.00/12.91 thf(genClo1651033342e_rmin_type, type, genClo1651033342e_rmin: real). 24.00/12.91 thf(genClo1163638703lle_te_type, type, genClo1163638703lle_te: (nat > (nat > real))). 24.00/12.91 thf(abs_abs_real_type, type, abs_abs_real: (real > real)). 24.00/12.91 thf(minus_minus_real_type, type, minus_minus_real: (real > (real > real))). 24.00/12.91 thf(one_one_nat_type, type, one_one_nat: nat). 24.00/12.91 thf(one_one_real_type, type, one_one_real: real). 24.00/12.91 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 24.00/12.91 thf(plus_plus_real_type, type, plus_plus_real: (real > (real > real))). 24.00/12.91 thf(zero_zero_real_type, type, zero_zero_real: real). 24.00/12.91 thf(if_real_type, type, if_real: ($o > (real > (real > real)))). 24.00/12.91 thf(ord_less_eq_real_type, type, ord_less_eq_real: (real > (real > $o))). 24.00/12.91 thf(ord_max_real_type, type, ord_max_real: (real > (real > real))). 24.00/12.91 thf(delta_S_type, type, delta_S: real). 24.00/12.91 thf(i_type, type, i: nat). 24.00/12.91 thf(l_type, type, l: nat). 24.00/12.91 thf(m_type, type, m: nat). 24.00/12.91 thf(p_type, type, p: nat). 24.00/12.91 thf(139,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [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))) <= (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_order__subst1)). 24.00/12.91 thf(629,plain,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [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))) | ~ (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 24.00/12.92 thf(52,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ B) => (~ (ord_less_eq_real @ B @ C))) => (((ord_less_eq_real @ B @ A) => (~ (ord_less_eq_real @ A @ C))) => (((~ (ord_less_eq_real @ C @ B)) <= (ord_less_eq_real @ A @ C)) => (((~ ((ord_less_eq_real @ C @ A) => (~ (ord_less_eq_real @ A @ B)))) <= ((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A)))) <= ((~ (ord_less_eq_real @ B @ A)) <= (ord_less_eq_real @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_le__cases3)). 24.00/12.92 thf(347,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ B) => (~ (ord_less_eq_real @ B @ C))) => (((ord_less_eq_real @ B @ A) => (~ (ord_less_eq_real @ A @ C))) => ((~ (ord_less_eq_real @ C @ B) | ~ (ord_less_eq_real @ A @ C)) => (~ ((ord_less_eq_real @ C @ A) => (~ (ord_less_eq_real @ A @ B))) | ~ ((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))) | ~ (~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 24.00/12.92 thf(19,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_add_Oleft__cancel)). 24.00/12.92 thf(249,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)],[19])). 24.00/12.92 thf(89,axiom,((! [A:real]: ((minus_minus_real @ A @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_diff__self)). 24.00/12.92 thf(468,plain,((! [A:real]: ((minus_minus_real @ A @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 24.00/12.92 thf(14,axiom,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_order__class_Oorder_Oeq__iff)). 24.00/12.92 thf(234,plain,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 24.00/12.92 thf(116,axiom,((! [A:real]: ((minus_minus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_diff__0__right)). 24.00/12.92 thf(555,plain,((! [A:real]: ((minus_minus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 24.00/12.92 thf(183,axiom,((! [A:nat,B:nat]: ((ord_less_eq_real @ (genClo1163638703lle_te @ A @ B) @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat))) <= (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rte)). 24.00/12.92 thf(741,plain,((! [A:nat,B:nat]: ((ord_less_eq_real @ (genClo1163638703lle_te @ A @ B) @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat))) | ~ (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 24.00/12.92 thf(59,axiom,((! [A:real,B:real,C:real,D:real]: (((A = B) = (C = D)) <= ((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_diff__eq__diff__eq)). 24.00/12.92 thf(379,plain,((! [A:real,B:real,C:real,D:real]: (((A = B) = (C = D)) | ~ ((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 24.00/12.92 thf(148,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_ord__le__eq__trans)). 24.00/12.92 thf(655,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 24.00/12.92 thf(26,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_add__nonneg__nonneg)). 24.00/12.92 thf(269,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 24.00/12.92 thf(130,axiom,((! [A:real,B:real]: ((if_real @ $true @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Real__Oreal_T)). 24.00/12.92 thf(597,plain,((! [A:real,B:real]: ((if_real @ $true @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 24.00/12.92 thf(61,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_add__diff__cancel__left_H)). 24.00/12.92 thf(385,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 24.00/12.92 thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_120_abs__add__abs)). 24.00/12.92 thf(533,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)],[108])). 24.00/12.92 thf(99,axiom,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_group__cancel_Oadd1)). 24.00/12.92 thf(500,plain,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 24.00/12.92 thf(165,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => (B = (ord_max_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_max_OorderE)). 24.00/12.92 thf(698,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => (B = (ord_max_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 24.00/12.92 thf(153,axiom,((ord_max_real = (^ [A:real,B:real]: (ord_max_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_max_Ocommute)). 24.00/12.92 thf(670,plain,(((ord_max_real) = (^ [A:real,B:real]: (ord_max_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 24.00/12.92 thf(170,axiom,((! [A:nat,B:real,C:nat]: ((ord_less_eq_real @ genClo1651033342e_rmin @ (minus_minus_real @ B @ (genClo1163638703lle_te @ A @ C))) <= ((ord_less_eq_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat)) @ B) & (genClo1015804716orrect @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_rts1)). 24.00/12.92 thf(709,plain,((! [A:nat,B:real,C:nat]: ((ord_less_eq_real @ genClo1651033342e_rmin @ (minus_minus_real @ B @ (genClo1163638703lle_te @ A @ C))) | ~ ((ord_less_eq_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat)) @ B) & (genClo1015804716orrect @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 24.00/12.92 thf(37,axiom,((! [A:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_double__add__le__zero__iff__single__add__le__zero)). 24.00/12.92 thf(301,plain,((! [A:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 24.00/12.92 thf(44,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_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/sandbox2/benchmark/theBenchmark.p',fact_175_add__mono)). 24.00/12.92 thf(320,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_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)],[44])). 24.00/12.92 thf(78,axiom,(((= @ real) = (^ [A:real,B:real]: ((minus_minus_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_eq__iff__diff__eq__0)). 24.00/12.92 thf(436,plain,(((= @ real) = (^ [A:real,B:real]: ((minus_minus_real @ A @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 24.00/12.92 thf(187,axiom,((genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_corr__m)). 24.00/12.92 thf(751,plain,((genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 24.00/12.92 thf(51,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_add__right__mono)). 24.00/12.92 thf(344,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 24.00/12.92 thf(111,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/sandbox2/benchmark/theBenchmark.p',fact_228_abs__triangle__ineq4)). 24.00/12.92 thf(542,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)],[111])). 24.00/12.92 thf(73,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_diff__right__mono)). 24.00/12.92 thf(421,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 24.00/12.92 thf(133,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/sandbox2/benchmark/theBenchmark.p',fact_193_diff__diff__eq2)). 24.00/12.92 thf(606,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)],[133])). 24.00/12.92 thf(197,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (ord_max_real @ A @ B) @ C) => (~ ((ord_less_eq_real @ A @ C) => (~ (ord_less_eq_real @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_max_OboundedE)). 24.00/12.92 thf(770,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (ord_max_real @ A @ B) @ C) => (~ ((ord_less_eq_real @ A @ C) => (~ (ord_less_eq_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 24.00/12.92 thf(12,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/sandbox2/benchmark/theBenchmark.p',fact_191_diff__add__eq__diff__diff__swap)). 24.00/12.92 thf(228,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)],[12])). 24.00/12.92 thf(33,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = B) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_add__cancel__left__left)). 24.00/12.92 thf(289,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = B) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 24.00/12.92 thf(97,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_le__add__same__cancel1)). 24.00/12.92 thf(492,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 24.00/12.92 thf(58,axiom,((! [A:real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_abs__0__eq)). 24.00/12.92 thf(376,plain,((! [A:real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 24.00/12.92 thf(137,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_order__class_Oorder_Oantisym)). 24.00/12.92 thf(623,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 24.00/12.92 thf(92,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/sandbox2/benchmark/theBenchmark.p',fact_135_add__le__cancel__right)). 24.00/12.92 thf(480,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)],[92])). 24.00/12.92 thf(194,axiom,((genClo1015804716orrect @ p @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_corr__p)). 24.00/12.92 thf(766,plain,((genClo1015804716orrect @ p @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 24.00/12.92 thf(65,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_add__diff__cancel__right_H)). 24.00/12.92 thf(397,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 24.00/12.92 thf(180,axiom,((! [A:real,B:real,C:real]: ((ord_max_real @ A @ (ord_max_real @ B @ C)) = (ord_max_real @ B @ (ord_max_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_max_Oleft__commute)). 24.00/12.92 thf(734,plain,((! [A:real,B:real,C:real]: ((ord_max_real @ A @ (ord_max_real @ B @ C)) = (ord_max_real @ B @ (ord_max_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 24.00/12.92 thf(84,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/sandbox2/benchmark/theBenchmark.p',fact_179_add__mono__thms__linordered__semiring_I2_J)). 24.00/12.92 thf(453,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)],[84])). 24.00/12.92 thf(149,axiom,((ord_less_eq_real @ genClo1278781456e_beta @ genClo1651033342e_rmin)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_nonoverlap)). 24.00/12.92 thf(660,plain,((ord_less_eq_real @ genClo1278781456e_beta @ genClo1651033342e_rmin)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 24.00/12.92 thf(17,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_le__add__same__cancel2)). 24.00/12.92 thf(243,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 24.00/12.92 thf(101,axiom,((! [A:real,B:real]: (((B = A) <= (ord_less_eq_real @ B @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_dual__order_Oantisym)). 24.00/12.92 thf(507,plain,((! [A:real,B:real]: ((B = A) | ~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 24.00/12.92 thf(41,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_add_Oright__cancel)). 24.00/12.92 thf(312,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)],[41])). 24.00/12.92 thf(6,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 @ A @ B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_add__mono__thms__linordered__semiring_I3_J)). 24.00/12.92 thf(206,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 @ A @ B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 24.00/12.92 thf(34,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_abs__1)). 24.00/12.92 thf(292,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 24.00/12.92 thf(103,axiom,((! [A:real,B:real,C:real,D:real]: ((((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => ((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => (ord_less_eq_real @ (minus_minus_real @ C @ B) @ D))) <= (ord_less_eq_real @ C @ (plus_plus_real @ D @ B))) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_add__le__add__imp__diff__le)). 24.00/12.92 thf(512,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => ((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => (ord_less_eq_real @ (minus_minus_real @ C @ B) @ D))) | ~ (ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 24.00/12.92 thf(156,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (ord_max_real @ B @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_max_OcoboundedI1)). 24.00/12.92 thf(678,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (ord_max_real @ B @ C)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 24.00/12.92 thf(150,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (ord_max_real @ B @ C)) = ((ord_less_eq_real @ A @ B) | (ord_less_eq_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_le__max__iff__disj)). 24.00/12.92 thf(661,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (ord_max_real @ B @ C)) = ((ord_less_eq_real @ A @ B) | (ord_less_eq_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 24.00/12.92 thf(113,axiom,((! [A:real,B:real]: (((plus_plus_real @ (minus_minus_real @ B @ A) @ A) = B) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_le__add__diff__inverse2)). 24.00/12.92 thf(546,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)],[113])). 24.00/12.92 thf(192,axiom,((! [A:nat,B:nat]: ((ord_less_eq_real @ (minus_minus_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)) @ (genClo1163638703lle_te @ A @ B)) @ genClo1650508560e_rmax) <= (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_rts0d)). 24.00/12.92 thf(761,plain,((! [A:nat,B:nat]: ((ord_less_eq_real @ (minus_minus_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)) @ (genClo1163638703lle_te @ A @ B)) @ genClo1650508560e_rmax) | ~ (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 24.00/12.92 thf(173,axiom,((! [A:nat,B:nat,C:nat]: ((genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat))) => ((genClo1015804716orrect @ C @ (genClo1163638703lle_te @ C @ B)) => (ord_less_eq_real @ (minus_minus_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)) @ (genClo1163638703lle_te @ C @ B)) @ (plus_plus_real @ genClo1650508560e_rmax @ genClo1278781456e_beta)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_beta__bound2)). 24.00/12.92 thf(714,plain,((! [A:nat,B:nat,C:nat]: ((genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat))) => ((genClo1015804716orrect @ C @ (genClo1163638703lle_te @ C @ B)) => (ord_less_eq_real @ (minus_minus_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)) @ (genClo1163638703lle_te @ C @ B)) @ (plus_plus_real @ genClo1650508560e_rmax @ genClo1278781456e_beta)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 24.00/12.92 thf(185,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (ord_max_real @ B @ C)) = (ord_max_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_max__add__distrib__right)). 24.00/12.92 thf(746,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (ord_max_real @ B @ C)) = (ord_max_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 24.00/12.92 thf(23,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_add__increasing2)). 24.00/12.92 thf(260,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 24.00/12.92 thf(118,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/sandbox2/benchmark/theBenchmark.p',fact_159_ab__semigroup__add__class_Oadd__ac_I1_J)). 24.00/12.92 thf(561,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)],[118])). 24.00/12.92 thf(36,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = C) => (A = (minus_minus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_add__implies__diff)). 24.00/12.92 thf(297,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = C) => (A = (minus_minus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 24.00/12.92 thf(74,axiom,((zero_zero_real != one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_zero__neq__one)). 24.00/12.92 thf(424,plain,((~ (zero_zero_real = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 24.00/12.92 thf(68,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_abs__le__D1)). 24.00/12.92 thf(407,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)],[68])). 24.00/12.92 thf(178,axiom,((! [A:real,B:real]: ((ord_max_real @ (ord_max_real @ A @ B) @ B) = (ord_max_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_max_Oright__idem)). 24.00/12.92 thf(729,plain,((! [A:real,B:real]: ((ord_max_real @ (ord_max_real @ A @ B) @ B) = (ord_max_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 24.00/12.92 thf(20,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_add__cancel__left__right)). 24.00/12.92 thf(252,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 24.00/12.92 thf(53,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_add__left__mono)). 24.00/12.92 thf(361,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 24.00/12.92 thf(86,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/sandbox2/benchmark/theBenchmark.p',fact_123_add__diff__cancel__left)). 24.00/12.92 thf(461,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)],[86])). 24.00/12.92 thf(190,axiom,((ord_less_eq_real = (^ [A:real,B:real]: (B = (ord_max_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_max_Oorder__iff)). 24.00/12.92 thf(757,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: (B = (ord_max_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 24.00/12.92 thf(31,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/sandbox2/benchmark/theBenchmark.p',fact_234_okRead2__def)). 24.00/12.92 thf(285,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)],[31])). 24.00/12.92 thf(126,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/sandbox2/benchmark/theBenchmark.p',fact_219_add__le__imp__le__diff)). 24.00/12.92 thf(583,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)],[126])). 24.00/12.92 thf(106,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => (((ord_less_eq_real @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F))))) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_ord__le__eq__subst)). 24.00/12.92 thf(522,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 24.00/12.92 thf(105,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_le__add__diff__inverse)). 24.00/12.92 thf(519,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 24.00/12.92 thf(43,axiom,((! [A:real,B:real,C:real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_diff__eq__eq)). 24.00/12.92 thf(317,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)],[43])). 24.00/12.92 thf(67,axiom,((! [A:real,B:real,C:real]: ((B = C) <= ((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_add__left__imp__eq)). 24.00/12.92 thf(403,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)],[67])). 24.00/12.92 thf(62,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_add_Ocommute)). 24.00/12.92 thf(388,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 24.00/12.92 thf(95,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/sandbox2/benchmark/theBenchmark.p',fact_226_abs__triangle__ineq2)). 24.00/12.92 thf(488,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)],[95])). 24.00/12.92 thf(143,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/sandbox2/benchmark/theBenchmark.p',fact_177_add__mono__thms__linordered__semiring_I1_J)). 24.00/12.92 thf(642,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)],[143])). 24.00/12.92 thf(128,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) | (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_linear)). 24.00/12.92 thf(590,plain,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) | (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 24.00/12.92 thf(46,axiom,((! [A:nat,B:nat,C:nat]: ((A = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_add__right__imp__eq)). 24.00/12.92 thf(328,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)],[46])). 24.00/12.92 thf(90,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ A) => (ord_less_eq_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_dual__order_Otrans)). 24.00/12.92 thf(471,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ A) => (ord_less_eq_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 24.00/12.92 thf(64,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((((ord_less_eq_real @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F)))) <= (ord_less_eq_real @ (C @ B) @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_order__subst2)). 24.00/12.92 thf(393,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) | ~ (ord_less_eq_real @ (C @ B) @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 24.00/12.92 thf(145,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/sandbox2/benchmark/theBenchmark.p',fact_223_abs__triangle__ineq)). 24.00/12.92 thf(647,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)],[145])). 24.00/12.92 thf(166,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_max_real @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_max_Oabsorb__iff1)). 24.00/12.92 thf(701,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_max_real @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 24.00/12.92 thf(85,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) & (A = B)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add__mono__thms__linordered__semiring_I4_J)). 24.00/12.92 thf(457,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((C = D) & (A = B)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 24.00/12.92 thf(121,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_abs__of__nonneg)). 24.00/12.92 thf(569,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 24.00/12.92 thf(25,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/sandbox2/benchmark/theBenchmark.p',fact_152_add_Oassoc)). 24.00/12.92 thf(266,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)],[25])). 24.00/12.92 thf(140,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) => (A = B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_antisym)). 24.00/12.92 thf(633,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) => (A = B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 24.00/12.92 thf(117,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_add_Oleft__neutral)). 24.00/12.92 thf(558,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 24.00/12.92 thf(107,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_comm__monoid__add__class_Oadd__0)). 24.00/12.92 thf(530,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 24.00/12.92 thf(70,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/sandbox2/benchmark/theBenchmark.p',fact_222_diff__le__eq)). 24.00/12.92 thf(412,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)],[70])). 24.00/12.92 thf(76,axiom,(((abs_abs_real @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_abs__zero)). 24.00/12.92 thf(430,plain,(((abs_abs_real @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 24.00/12.92 thf(161,axiom,((! [A:nat,B:nat]: ((genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat))) => (ord_less_eq_real @ genClo1651033342e_rmin @ (minus_minus_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)) @ (genClo1163638703lle_te @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_rts1d)). 24.00/12.92 thf(689,plain,((! [A:nat,B:nat]: ((genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat))) => (ord_less_eq_real @ genClo1651033342e_rmin @ (minus_minus_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)) @ (genClo1163638703lle_te @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 24.00/12.92 thf(81,axiom,((! [A:real]: ((minus_minus_real @ A @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_cancel__comm__monoid__add__class_Odiff__cancel)). 24.00/12.92 thf(444,plain,((! [A:real]: ((minus_minus_real @ A @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 24.00/12.92 thf(163,axiom,((genClo1015804716orrect @ l @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_corr__l)). 24.00/12.92 thf(694,plain,((genClo1015804716orrect @ l @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 24.00/12.92 thf(179,axiom,((! [A:real,B:real]: (ord_less_eq_real @ A @ (ord_max_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_max_Ocobounded2)). 24.00/12.92 thf(732,plain,((! [A:real,B:real]: (ord_less_eq_real @ A @ (ord_max_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 24.00/12.92 thf(184,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (ord_max_real @ C @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_max_OcoboundedI2)). 24.00/12.92 thf(743,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (ord_max_real @ C @ B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 24.00/12.92 thf(30,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_add__left__imp__eq)). 24.00/12.92 thf(281,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)],[30])). 24.00/12.92 thf(124,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_abs__le__zero__iff)). 24.00/12.92 thf(577,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 24.00/12.92 thf(171,axiom,((ord_max_real = (^ [A:real,B:real]: (if_real @ (ord_less_eq_real @ A @ B) @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_max__def)). 24.00/12.92 thf(711,plain,(((ord_max_real) = (^ [A:real,B:real]: (if_real @ (ord_less_eq_real @ A @ B) @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 24.00/12.92 thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_221_le__diff__eq)). 24.00/12.92 thf(382,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)],[60])). 24.00/12.92 thf(122,axiom,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_add_Oright__neutral)). 24.00/12.92 thf(572,plain,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 24.00/12.92 thf(172,axiom,((ord_less_eq_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_tli__le__tp)). 24.00/12.92 thf(713,plain,((ord_less_eq_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 24.00/12.92 thf(88,axiom,((genClo293725281kRead1 = (^ [A:(nat > real),B:real,C:(nat > $o)]: ! [D:nat,E:nat]: (((C @ D) & (C @ E)) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ D) @ (A @ E))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_okRead1__def)). 24.00/12.92 thf(466,plain,(((genClo293725281kRead1) = (^ [A:(nat > real),B:real,C:(nat > $o)]: ! [D:nat,E:nat]: (((C @ D) & (C @ E)) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (A @ D) @ (A @ E))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 24.00/12.92 thf(48,axiom,((! [A:real,B:real]: ((if_real @ $false @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Real__Oreal_T)). 24.00/12.92 thf(335,plain,((! [A:real,B:real]: ((if_real @ $false @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 24.00/12.92 thf(15,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D)) <= ((C = D) & (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_add__mono__thms__linordered__semiring_I4_J)). 24.00/12.92 thf(236,plain,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D)) | ~ ((C = D) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 24.00/12.92 thf(154,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (ord_max_real @ A @ B) @ C) = ((ord_less_eq_real @ B @ C) & (ord_less_eq_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_max_Obounded__iff)). 24.00/12.92 thf(672,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (ord_max_real @ A @ B) @ C) = ((ord_less_eq_real @ B @ C) & (ord_less_eq_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 24.00/12.92 thf(157,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)) @ (genClo1163638703lle_te @ C @ B))) <= (genClo1015804716orrect @ C @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)))) <= (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_beta__bound1)). 24.00/12.92 thf(681,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)) @ (genClo1163638703lle_te @ C @ B))) | ~ (genClo1015804716orrect @ C @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat))) | ~ (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ B @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 24.00/12.92 thf(28,axiom,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_eq__refl)). 24.00/12.92 thf(274,plain,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 24.00/12.92 thf(120,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/sandbox2/benchmark/theBenchmark.p',fact_224_abs__triangle__ineq2__sym)). 24.00/12.92 thf(567,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)],[120])). 24.00/12.92 thf(181,axiom,((! [A:nat,B:nat,C:nat]: (((genClo1015804716orrect @ B @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat))) & (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat)))) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (genClo1400225944_theta @ A @ (plus_plus_nat @ C @ one_one_nat) @ B) @ (genClo1160817912lle_IC @ B @ C @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat))))) @ genClo721845095Lambda)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_readerror)). 24.00/12.92 thf(737,plain,((! [A:nat,B:nat,C:nat]: (((genClo1015804716orrect @ B @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat))) & (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat)))) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (genClo1400225944_theta @ A @ (plus_plus_nat @ C @ one_one_nat) @ B) @ (genClo1160817912lle_IC @ B @ C @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat))))) @ genClo721845095Lambda)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 24.00/12.92 thf(146,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_add__decreasing)). 24.00/12.92 thf(649,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 24.00/12.92 thf(134,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((((! [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))) <= (ord_less_eq_real @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_ord__eq__le__subst)). 24.00/12.92 thf(609,plain,((! [A:real,B:(real > real),C:real,D:real]: (((! [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))) | ~ (ord_less_eq_real @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 24.00/12.92 thf(45,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_ord__eq__le__trans)). 24.00/12.92 thf(323,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 24.00/12.92 thf(93,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/sandbox2/benchmark/theBenchmark.p',fact_137_add__le__cancel__left)). 24.00/12.92 thf(483,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)],[93])). 24.00/12.92 thf(16,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_abs__le__self__iff)). 24.00/12.92 thf(240,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 24.00/12.92 thf(138,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ A @ C) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_order_Otrans)). 24.00/12.92 thf(626,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ A @ C) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 24.00/12.92 thf(1,conjecture,((genClo1015804716orrect @ m @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 24.00/12.92 thf(2,negated_conjecture,((~ (genClo1015804716orrect @ m @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i))))),inference(neg_conjecture,[status(cth)],[1])). 24.00/12.92 thf(198,plain,((~ (genClo1015804716orrect @ m @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 24.00/12.92 thf(55,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/sandbox2/benchmark/theBenchmark.p',fact_229_abs__diff__le__iff)). 24.00/12.92 thf(367,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)],[55])). 24.00/12.92 thf(115,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/sandbox2/benchmark/theBenchmark.p',fact_160_ab__semigroup__add__class_Oadd__ac_I1_J)). 24.00/12.92 thf(552,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)],[115])). 24.00/12.92 thf(8,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/sandbox2/benchmark/theBenchmark.p',fact_154_group__cancel_Oadd2)). 24.00/12.92 thf(213,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)],[8])). 24.00/12.92 thf(177,axiom,((! [A:real,B:real]: ((A = (ord_max_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_max_OorderI)). 24.00/12.92 thf(726,plain,((! [A:real,B:real]: ((A = (ord_max_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 24.00/12.92 thf(159,axiom,((! [A:real]: ((ord_max_real @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_max_Oidem)). 24.00/12.92 thf(685,plain,((! [A:real]: ((ord_max_real @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 24.00/12.92 thf(196,axiom,((! [A:nat,B:real,C:nat]: (((ord_less_eq_real @ B @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat))) & (genClo1015804716orrect @ A @ B)) => (ord_less_eq_real @ (minus_minus_real @ B @ (genClo1163638703lle_te @ A @ C)) @ genClo1650508560e_rmax)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_rts0)). 24.00/12.92 thf(768,plain,((! [A:nat,B:real,C:nat]: (((ord_less_eq_real @ B @ (genClo1163638703lle_te @ A @ (plus_plus_nat @ C @ one_one_nat))) & (genClo1015804716orrect @ A @ B)) => (ord_less_eq_real @ (minus_minus_real @ B @ (genClo1163638703lle_te @ A @ C)) @ genClo1650508560e_rmax)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 24.00/12.92 thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_192_diff__add__eq)). 24.00/12.92 thf(278,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)],[29])). 24.00/12.92 thf(10,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_add__le__same__cancel2)). 24.00/12.92 thf(223,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 24.00/12.92 thf(39,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) = (B = A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_antisym__conv)). 24.00/12.92 thf(306,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) = (B = A)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 24.00/12.92 thf(11,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/sandbox2/benchmark/theBenchmark.p',fact_167_add__le__imp__le__left)). 24.00/12.92 thf(226,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)],[11])). 24.00/12.92 thf(141,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = (B = (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_eq__diff__eq_H)). 24.00/12.92 thf(636,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)],[141])). 24.00/12.92 thf(164,axiom,((! [A:real,B:real]: (((ord_max_real @ B @ A) = B) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_max_Oabsorb1)). 24.00/12.92 thf(695,plain,((! [A:real,B:real]: (((ord_max_real @ B @ A) = B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 24.00/12.92 thf(100,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_abs__one)). 24.00/12.92 thf(505,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 24.00/12.92 thf(79,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ C) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_add__decreasing2)). 24.00/12.92 thf(438,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ C) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 24.00/12.92 thf(21,axiom,((! [A:real,B:real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_abs__minus__commute)). 24.00/12.92 thf(255,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)],[21])). 24.00/12.92 thf(186,axiom,((! [A:nat,B:nat,C:real,D:nat]: (((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ (plus_plus_real @ (genClo1163638703lle_te @ B @ D) @ genClo1278781456e_beta) @ C) & (genClo1015804716orrect @ B @ C)) => (ord_less_eq_real @ (genClo1163638703lle_te @ A @ D) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_rts2a)). 24.00/12.92 thf(749,plain,((! [A:nat,B:nat,C:real,D:nat]: (((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ (plus_plus_real @ (genClo1163638703lle_te @ B @ D) @ genClo1278781456e_beta) @ C) & (genClo1015804716orrect @ B @ C)) => (ord_less_eq_real @ (genClo1163638703lle_te @ A @ D) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 24.00/12.92 thf(96,axiom,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_dual__order_Oeq__iff)). 24.00/12.92 thf(490,plain,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 24.00/12.92 thf(155,axiom,((! [A:real,B:real]: (((ord_max_real @ A @ B) = B) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_max_Oabsorb2)). 24.00/12.92 thf(675,plain,((! [A:real,B:real]: (((ord_max_real @ A @ B) = B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 24.00/12.92 thf(135,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_add__diff__cancel)). 24.00/12.92 thf(617,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 24.00/12.92 thf(104,axiom,((! [A:real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_double__zero)). 24.00/12.92 thf(516,plain,((! [A:real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 24.00/12.92 thf(125,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/sandbox2/benchmark/theBenchmark.p',fact_194_add__diff__eq)). 24.00/12.92 thf(580,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)],[125])). 24.00/12.92 thf(168,axiom,((! [A:real,B:real,C:real]: ((ord_max_real @ (ord_max_real @ A @ B) @ C) = (ord_max_real @ A @ (ord_max_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_max_Oassoc)). 24.00/12.92 thf(705,plain,((! [A:real,B:real,C:real]: ((ord_max_real @ (ord_max_real @ A @ B) @ C) = (ord_max_real @ A @ (ord_max_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 24.00/12.92 thf(182,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_max_real @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_max_Oabsorb__iff2)). 24.00/12.92 thf(739,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_max_real @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 24.00/12.92 thf(69,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_add_Ogroup__left__neutral)). 24.00/12.92 thf(409,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 24.00/12.92 thf(24,axiom,((! [A:real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_abs__eq__0__iff)). 24.00/12.92 thf(263,plain,((! [A:real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 24.00/12.92 thf(3,axiom,((! [A:$o]: ((A = $true) | (A = $false)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Real__Oreal_T)). 24.00/12.92 thf(199,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 24.00/12.92 thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_146_add_Oleft__commute)). 24.00/12.92 thf(441,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)],[80])). 24.00/12.92 thf(174,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ (ord_max_real @ A @ C) @ (ord_max_real @ B @ D)) <= (ord_less_eq_real @ C @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_max_Omono)). 24.00/12.92 thf(717,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (ord_max_real @ A @ C) @ (ord_max_real @ B @ D)) | ~ (ord_less_eq_real @ C @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 24.00/12.92 thf(49,axiom,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_abs__abs)). 24.00/12.92 thf(338,plain,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 24.00/12.92 thf(112,axiom,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_abs__ge__self)). 24.00/12.92 thf(544,plain,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 24.00/12.92 thf(127,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/sandbox2/benchmark/theBenchmark.p',fact_153_group__cancel_Oadd2)). 24.00/12.92 thf(585,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)],[127])). 24.00/12.92 thf(56,axiom,((! [A:real]: ((zero_zero_real = A) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_zero__reorient)). 24.00/12.92 thf(370,plain,((! [A:real]: ((zero_zero_real = A) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 24.00/12.92 thf(167,axiom,((genClo208577157axsync = (^ [A:nat,B:real]: ! [C:nat,D:nat]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (genClo1160817912lle_IC @ C @ A @ (ord_max_real @ (genClo1163638703lle_te @ C @ A) @ (genClo1163638703lle_te @ D @ A))) @ (genClo1160817912lle_IC @ D @ A @ (ord_max_real @ (genClo1163638703lle_te @ C @ A) @ (genClo1163638703lle_te @ D @ A))))) @ B) <= ((genClo1015804716orrect @ D @ (ord_max_real @ (genClo1163638703lle_te @ C @ A) @ (genClo1163638703lle_te @ D @ A))) & (genClo1015804716orrect @ C @ (ord_max_real @ (genClo1163638703lle_te @ C @ A) @ (genClo1163638703lle_te @ D @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_okmaxsync__def)). 24.00/12.92 thf(703,plain,(((genClo208577157axsync) = (^ [A:nat,B:real]: ! [C:nat,D:nat]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (genClo1160817912lle_IC @ C @ A @ (ord_max_real @ (genClo1163638703lle_te @ C @ A) @ (genClo1163638703lle_te @ D @ A))) @ (genClo1160817912lle_IC @ D @ A @ (ord_max_real @ (genClo1163638703lle_te @ C @ A) @ (genClo1163638703lle_te @ D @ A))))) @ B) | ~ ((genClo1015804716orrect @ D @ (ord_max_real @ (genClo1163638703lle_te @ C @ A) @ (genClo1163638703lle_te @ D @ A))) & (genClo1015804716orrect @ C @ (ord_max_real @ (genClo1163638703lle_te @ C @ A) @ (genClo1163638703lle_te @ D @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 24.00/12.92 thf(131,axiom,((! [A:real]: ((minus_minus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_diff__zero)). 24.00/12.92 thf(600,plain,((! [A:real]: ((minus_minus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 24.00/12.92 thf(13,axiom,((! [A:real,B:real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_add__cancel__right__left)). 24.00/12.92 thf(231,plain,((! [A:real,B:real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 24.00/12.92 thf(83,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real) <= (ord_less_eq_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_add__nonpos__nonpos)). 24.00/12.92 thf(450,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real) | ~ (ord_less_eq_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 24.00/12.92 thf(110,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_add__right__cancel)). 24.00/12.92 thf(539,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)],[110])). 24.00/12.92 thf(5,axiom,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_diff__add__cancel)). 24.00/12.92 thf(203,plain,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 24.00/12.92 thf(160,axiom,((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (genClo1160817912lle_IC @ l @ i @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i))) @ (genClo1160817912lle_IC @ m @ i @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i))))) @ delta_S)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_IC__bound)). 24.00/12.92 thf(688,plain,((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (genClo1160817912lle_IC @ l @ i @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i))) @ (genClo1160817912lle_IC @ m @ i @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i))))) @ delta_S)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 24.00/12.92 thf(98,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/sandbox2/benchmark/theBenchmark.p',fact_235_sin__bound__lemma)). 24.00/12.92 thf(495,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)],[98])). 24.00/12.92 thf(191,axiom,((! [A:nat,B:nat,C:nat]: (((genClo1015804716orrect @ B @ (genClo1163638703lle_te @ B @ C)) & (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ C))) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (genClo1163638703lle_te @ A @ C) @ (genClo1163638703lle_te @ B @ C))) @ genClo1278781456e_beta)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_rts2b)). 24.00/12.92 thf(759,plain,((! [A:nat,B:nat,C:nat]: (((genClo1015804716orrect @ B @ (genClo1163638703lle_te @ B @ C)) & (genClo1015804716orrect @ A @ (genClo1163638703lle_te @ A @ C))) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (genClo1163638703lle_te @ A @ C) @ (genClo1163638703lle_te @ B @ C))) @ genClo1278781456e_beta)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 24.00/12.92 thf(9,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/sandbox2/benchmark/theBenchmark.p',fact_155_group__cancel_Oadd1)). 24.00/12.92 thf(218,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)],[9])). 24.00/12.92 thf(38,axiom,(((abs_abs_real @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_abs__0)). 24.00/12.92 thf(304,plain,(((abs_abs_real @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 24.00/12.92 thf(22,axiom,((plus_plus_real = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_add_Ocommute)). 24.00/12.92 thf(258,plain,(((plus_plus_real) = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 24.00/12.92 thf(147,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ (plus_plus_real @ A @ C)) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_add__increasing)). 24.00/12.92 thf(652,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ (plus_plus_real @ A @ C)) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 24.00/12.92 thf(63,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/sandbox2/benchmark/theBenchmark.p',fact_186_diff__mono)). 24.00/12.92 thf(390,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)],[63])). 24.00/12.92 thf(72,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_diff__ge__0__iff__ge)). 24.00/12.92 thf(418,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 24.00/12.92 thf(18,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/sandbox2/benchmark/theBenchmark.p',fact_127_add__diff__cancel__right)). 24.00/12.92 thf(246,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)],[18])). 24.00/12.92 thf(102,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_dual__order_Orefl)). 24.00/12.92 thf(510,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 24.00/12.92 thf(152,axiom,((! [A:real,B:real]: ((ord_max_real @ A @ (ord_max_real @ A @ B)) = (ord_max_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_max_Oleft__idem)). 24.00/12.92 thf(667,plain,((! [A:real,B:real]: ((ord_max_real @ A @ (ord_max_real @ A @ B)) = (ord_max_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 24.00/12.92 thf(158,axiom,((genClo1015804716orrect @ l @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_corr__l__tml)). 24.00/12.92 thf(684,plain,((genClo1015804716orrect @ l @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 24.00/12.92 thf(114,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = ((plus_plus_real @ A @ C) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_eq__diff__eq)). 24.00/12.92 thf(549,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)],[114])). 24.00/12.92 thf(109,axiom,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_add_Ocomm__neutral)). 24.00/12.92 thf(536,plain,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 24.00/12.92 thf(32,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/sandbox2/benchmark/theBenchmark.p',fact_225_abs__triangle__ineq3)). 24.00/12.92 thf(287,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)],[32])). 24.00/12.92 thf(193,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (ord_max_real @ A @ B) @ C) = (ord_max_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_max__add__distrib__left)). 24.00/12.92 thf(763,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (ord_max_real @ A @ B) @ C) = (ord_max_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 24.00/12.92 thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_165_add__le__imp__le__right)). 24.00/12.92 thf(272,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)],[27])). 24.00/12.92 thf(136,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_add__left__cancel)). 24.00/12.92 thf(620,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)],[136])). 24.00/12.92 thf(188,axiom,((! [A:nat,B:real,C:real]: (((genClo1015804716orrect @ A @ C) & (ord_less_eq_real @ B @ C)) => (genClo1015804716orrect @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_correct__closed)). 24.00/12.92 thf(752,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)],[188])). 24.00/12.92 thf(82,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_zero__le__double__add__iff__zero__le__single__add)). 24.00/12.92 thf(447,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 24.00/12.92 thf(42,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/sandbox2/benchmark/theBenchmark.p',fact_227_abs__diff__triangle__ineq)). 24.00/12.92 thf(315,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)],[42])). 24.00/12.92 thf(77,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) => (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_add__right__imp__eq)). 24.00/12.92 thf(432,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)],[77])). 24.00/12.92 thf(57,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_one__reorient)). 24.00/12.92 thf(373,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 24.00/12.92 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/sandbox2/benchmark/theBenchmark.p',fact_151_add_Oassoc)). 24.00/12.92 thf(603,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])). 24.00/12.92 thf(119,axiom,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_abs__idempotent)). 24.00/12.92 thf(564,plain,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 24.00/12.92 thf(7,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_diff__eq__diff__less__eq)). 24.00/12.92 thf(210,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 24.00/12.92 thf(35,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/sandbox2/benchmark/theBenchmark.p',fact_185_diff__left__mono)). 24.00/12.92 thf(294,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)],[35])). 24.00/12.92 thf(50,axiom,((! [A:real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_double__zero__sym)). 24.00/12.92 thf(341,plain,((! [A:real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 24.00/12.92 thf(151,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ (ord_max_real @ A @ C) @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_max_OboundedI)). 24.00/12.92 thf(664,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ (ord_max_real @ A @ C) @ B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 24.00/12.92 thf(66,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/sandbox2/benchmark/theBenchmark.p',fact_68_order__trans)). 24.00/12.92 thf(400,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)],[66])). 24.00/12.92 thf(175,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (ord_max_real @ A @ B) @ C) = (ord_max_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_max__diff__distrib__left)). 24.00/12.92 thf(720,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (ord_max_real @ A @ B) @ C) = (ord_max_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 24.00/12.92 thf(71,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ A) = (ord_less_eq_real @ B @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_add__le__same__cancel1)). 24.00/12.92 thf(415,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ A) = (ord_less_eq_real @ B @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 24.00/12.92 thf(91,axiom,((! [A:(real > (real > $o)),B:real,C:real]: (((A @ B @ C) <= (! [D:real,E:real]: ((A @ E @ D) => (A @ D @ E)))) <= (! [D:real,E:real]: ((A @ D @ E) <= (ord_less_eq_real @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_linorder__wlog)). 24.00/12.92 thf(474,plain,((! [A:(real > (real > $o)),B:real,C:real]: ((A @ B @ C) | ~ (! [D:real,E:real]: ((A @ E @ D) => (A @ D @ E))) | ~ (! [D:real,E:real]: ((A @ D @ E) | ~ (ord_less_eq_real @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 24.00/12.92 thf(195,axiom,((ord_less_eq_real @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)) @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_tml__le__tp)). 24.00/12.92 thf(767,plain,((ord_less_eq_real @ (ord_max_real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)) @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 24.00/12.92 thf(87,axiom,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_eq__iff)). 24.00/12.92 thf(464,plain,(((= @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 24.00/12.92 thf(47,axiom,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_add__cancel__right__right)). 24.00/12.92 thf(332,plain,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 24.00/12.92 thf(123,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_order__refl)). 24.00/12.92 thf(575,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 24.00/12.92 thf(75,axiom,((! [A:real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_abs__eq__0)). 24.00/12.92 thf(427,plain,((! [A:real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 24.00/12.92 thf(144,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_add__right__cancel)). 24.00/12.92 thf(644,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)],[144])). 24.00/12.92 thf(176,axiom,((! [A:real,B:real]: (((ord_max_real @ B @ A) = B) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_max__absorb1)). 24.00/12.92 thf(723,plain,((! [A:real,B:real]: (((ord_max_real @ B @ A) = B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 24.00/12.92 thf(4,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/sandbox2/benchmark/theBenchmark.p',fact_145_add_Oleft__commute)). 24.00/12.92 thf(200,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)],[4])). 24.00/12.92 thf(162,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_max_real @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_max__absorb2)). 24.00/12.92 thf(691,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_max_real @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 24.00/12.92 thf(94,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_le__cases)). 24.00/12.92 thf(486,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)],[94])). 24.00/12.92 thf(40,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_add__left__cancel)). 24.00/12.92 thf(309,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)],[40])). 24.00/12.92 thf(142,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/sandbox2/benchmark/theBenchmark.p',fact_162_diff__right__commute)). 24.00/12.92 thf(639,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)],[142])). 24.00/12.92 thf(189,axiom,((! [A:real,B:real]: (ord_less_eq_real @ A @ (ord_max_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_max_Ocobounded1)). 24.00/12.92 thf(755,plain,((! [A:real,B:real]: (ord_less_eq_real @ A @ (ord_max_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 24.00/12.92 thf(129,axiom,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_group__cancel_Osub1)). 24.00/12.92 thf(592,plain,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 24.00/12.92 thf(54,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/sandbox2/benchmark/theBenchmark.p',fact_189_diff__diff__add)). 24.00/12.92 thf(364,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)],[54])). 24.00/12.92 thf(169,axiom,((ord_less_eq_real @ (genClo1163638703lle_te @ m @ i) @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_tmi__le__tp)). 24.00/12.92 thf(708,plain,((ord_less_eq_real @ (genClo1163638703lle_te @ m @ i) @ (genClo1163638703lle_te @ p @ (plus_plus_nat @ i @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 24.00/12.92 thf(836,plain,($false),inference(cvc4,[status(thm)],[629,347,249,468,234,555,741,379,655,269,597,385,533,500,698,670,709,301,320,436,751,344,542,421,606,770,228,289,492,376,623,480,766,397,734,453,660,243,507,312,206,292,512,678,661,546,761,714,746,260,561,297,424,407,729,252,361,461,757,285,583,522,519,317,403,388,488,642,590,328,471,393,647,701,457,569,266,633,558,530,412,430,689,444,694,732,743,281,577,711,382,572,713,466,335,236,672,681,274,567,737,649,609,323,483,240,626,198,367,552,213,726,685,768,278,223,306,226,636,695,505,438,255,749,490,675,617,516,580,705,739,409,263,199,441,717,338,544,585,370,703,600,231,450,539,203,688,495,759,218,304,258,652,390,418,246,510,667,684,549,536,287,763,272,620,752,447,315,432,373,603,564,210,294,341,664,400,720,415,474,767,464,332,575,427,644,723,200,691,486,309,639,755,592,364,708])). 24.00/12.92 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 24.00/12.92 % [INFO] Killing All external provers ... 24.00/12.92 FINAL WATCH: 21.7 CPU 9.7 WC 24.00/12.92 Killed 1 orphans 24.00/12.92 Killed 1 orphans 24.00/12.92 Killed 1 orphans 24.00/12.92 EOF