%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP195^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:08 AM UTC 2026
% Result : Theorem 20.97s 5.80s
% Output : Refutation 22.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP195^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.27 % Computer : n013.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 20:09:36 UTC 2026
% 0.26/0.28 % CPUTime :
% 0.26/0.28 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.96/0.74 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.22/1.11 % [INFO] Parsing done (364ms).
% 2.22/1.12 % [INFO] Running in sequential loop mode.
% 3.36/1.38 % [INFO] eprover registered as external prover.
% 3.36/1.40 % [INFO] Scanning for conjecture ...
% 4.59/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 345 axioms. Running axiom selection ...
% 4.89/1.80 % [INFO] Axiom selection finished. Selected 258 axioms (removed 87 axioms).
% 6.06/2.12 % [INFO] Problem is higher-order (TPTP THF).
% 6.38/2.15 % [INFO] Type checking passed.
% 6.38/2.16 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 20.34/5.79 % External prover 'e' found a proof!
% 20.34/5.79 % [INFO] Killing All external provers ...
% 20.34/5.79 % Time passed: 5375ms (effective reasoning time: 4671ms)
% 20.34/5.79 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 20.97/5.80 % Axioms used in derivation (258): fact_271_less__linear, fact_284_neq__iff, fact_96_bot__nat__0_Onot__eq__extremum, fact_170_ord__le__eq__subst, fact_118_le0, fact_265_ord__less__eq__trans, fact_111_pinf_I6_J, fact_200_antisym__conv, fact_125_linorder__neqE__nat, fact_134_bot__nat__0_Oextremum__unique, fact_281_dense, fact_16_poly__all__0__iff__0, fact_13_poly__IVT__pos, fact_318_old_Onat_Oinject, fact_317_nat_Oinject, fact_337_le__antisym, fact_285_neq__iff, fact_231_dual__order_Oantisym, fact_269_less__irrefl, fact_28_gr__implies__not__zero, fact_144_order__subst1, fact_321_Suc__less__eq, fact_164_ord__eq__le__subst, fact_133_bot__nat__0_Oextremum__uniqueI, fact_322_Suc__le__mono, fact_323_less__Suc0, fact_98_order__refl, fact_255_less__imp__not__eq2, fact_120_less__imp__le__nat, fact_261_less__imp__not__eq, fact_3_assms, fact_34_zero__reorient, fact_238_not__less__iff__gr__or__eq, fact_188_eq__refl, fact_277_less__asym, fact_55_reflect__poly__at__0__eq__0__iff, fact_121_le__eq__less__or__eq, fact_334_not__less__eq__eq, fact_310_infinite__descent0, fact_235_order_Ostrict__implies__not__eq, fact_221_linorder__wlog, fact_101_minf_I8_J, fact_112_pinf_I6_J, fact_11_not__gr__zero, fact_297_order__less__subst1, fact_288_gt__ex, fact_245_less__imp__not__less, fact_185_linear, fact_266_ord__less__eq__trans, fact_270_less__irrefl, fact_250_linorder__cases, fact_45_rsquarefree__roots, fact_252_less__imp__triv, fact_115_verit__comp__simplify1_I3_J, fact_87_order__0I, fact_41_poly__eq__poly__eq__iff, fact_86_less__eq__real__def, fact_103_minf_I6_J, fact_69_order__root, fact_43_poly__eq__poly__eq__iff, fact_283_order_Oasym, fact_64_poly__shift__0, fact_26_gr__zeroI, fact_42_poly__eq__poly__eq__iff, fact_97_order__refl, fact_7_poly__0, fact_335_Suc__n__not__le__n, fact_19_less__numeral__extra_I3_J, fact_267_ord__eq__less__trans, fact_171_ord__le__eq__subst, fact_306_ord__eq__less__subst, fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062, fact_150_order__subst2, fact_213_order__class_Oorder_Oantisym, fact_37_zero__reorient, fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062, fact_62_next__non__root__interval, fact_46_cross__no__root, fact_88_order__0I, fact_305_ord__eq__less__subst, fact_240_dual__order_Ostrict__trans, fact_224_dual__order_Otrans, fact_192_le__cases, fact_10_poly__0, fact_40_zero__reorient, fact_162_ord__eq__le__subst, fact_141_order__subst1, fact_18_poly__all__0__iff__0, fact_109_pinf_I8_J, fact_44_cross__0, fact_329_transitive__stepwise__le, fact_225_dual__order_Otrans, fact_123_le__neq__implies__less, fact_89_order__0I, fact_73_le__zero__eq, fact_93_not__eq__pos__or__neg__iff__2, fact_289_gt__ex, fact_203_order__class_Oorder_Oeq__iff, fact_301_ord__less__eq__subst, fact_241_linorder__less__wlog, fact_331_Nat_Oex__has__greatest__nat, fact_242_linorder__less__wlog, fact_327_variation__0_I1_J, fact_158_verit__la__disequality, fact_326_variation__0_I2_J, fact_300_ord__less__eq__subst, fact_316_cross__def, fact_47_is__zero__null, fact_314_not__gr0, fact_204_order__class_Oorder_Oeq__iff, fact_140_order__subst1, fact_108_pinf_I8_J, fact_243_exists__least__iff, fact_206_ord__eq__le__trans, fact_135_ex__least__nat__le, fact_179_eq__iff, fact_268_ord__eq__less__trans, fact_303_ord__eq__less__subst, fact_215_order__trans, fact_36_zero__reorient, fact_239_dual__order_Ostrict__trans, fact_234_dual__order_Ostrict__implies__not__eq, fact_197_le__cases3, fact_79_le__numeral__extra_I3_J, fact_29_zero__less__iff__neq__zero, fact_92_not__eq__pos__or__neg__iff__1, fact_324_zero__less__Suc, fact_35_zero__reorient, fact_174_ord__le__eq__subst, fact_263_dual__order_Oasym, fact_294_order__less__subst2, fact_291_order__less__subst2, fact_320_Suc__mono, fact_254_less__imp__not__eq2, fact_218_dual__order_Orefl, fact_191_le__cases, fact_161_ord__eq__le__subst, fact_152_order__subst2, fact_186_linear, fact_68_order__root, fact_325_less__one, fact_280_less__imp__neq, fact_315_gr0I, fact_313_not__less0, fact_27_not__less__zero, fact_244_less__imp__not__less, fact_74_reflect__poly__0, fact_94_neq0__conv, fact_51_poly__cutoff__0, fact_201_antisym__conv, fact_100_minf_I8_J, fact_83_le__numeral__extra_I3_J, fact_124_less__mono__imp__le__mono, fact_274_less__trans, fact_104_minf_I6_J, fact_227_dual__order_Oeq__iff, fact_230_dual__order_Oantisym, fact_129_less__not__refl3, fact_279_less__imp__neq, fact_278_less__asym, fact_276_less__asym_H, fact_237_not__less__iff__gr__or__eq, fact_272_less__linear, fact_302_ord__less__eq__subst, fact_127_nat__less__induct, fact_209_ord__le__eq__trans, fact_119_nat__less__le, fact_328_One__nat__def, fact_262_less__imp__not__eq, fact_153_order__subst2, fact_339_eq__imp__le, fact_122_less__or__eq__imp__le, fact_251_linorder__cases, fact_340_le__trans, fact_336_nat__le__linear, fact_258_less__induct, fact_330_nat__induct__at__least, fact_287_neqE, fact_182_antisym, fact_343_le__SucI, fact_256_antisym__conv3, fact_207_ord__eq__le__trans, fact_282_order_Oasym, fact_20_less__numeral__extra_I3_J, fact_132_nat__neq__iff, fact_236_order_Ostrict__implies__not__eq, fact_259_less__not__sym, fact_286_neqE, fact_260_less__not__sym, fact_131_less__not__refl, fact_189_eq__refl, fact_247_order_Ostrict__trans, fact_198_le__cases3, fact_311_gr__implies__not0, fact_298_order__less__subst1, fact_344_le__SucE, fact_149_order__subst2, fact_78_complete__real, fact_253_less__imp__triv, fact_23_less__numeral__extra_I3_J, fact_246_order_Ostrict__trans, fact_210_ord__le__eq__trans, fact_299_ord__less__eq__subst, fact_0_False, fact_194_order_Otrans, fact_308_verit__comp__simplify1_I1_J, fact_24_less__numeral__extra_I3_J, fact_173_ord__le__eq__subst, fact_39_zero__reorient, fact_30_pderiv__0, fact_212_order__class_Oorder_Oantisym, fact_95_less__nat__zero__code, fact_216_order__trans, fact_233_dual__order_Ostrict__implies__not__eq, fact_195_order_Otrans, fact_248_dual__order_Oirrefl, fact_290_lt__ex, fact_292_order__less__subst2, fact_128_less__irrefl__nat, fact_85_zero__le, fact_126_infinite__descent, fact_136_le__0__eq, fact_137_less__eq__nat_Osimps_I1_J, fact_70_order__root, fact_219_dual__order_Orefl, fact_295_order__less__subst1, fact_63_last__non__root__interval, fact_275_less__asym_H, fact_307_verit__comp__simplify1_I1_J, fact_309_bot__nat__0_Oextremum__strict, fact_159_verit__la__disequality, fact_293_order__less__subst2, fact_222_linorder__wlog, fact_17_poly__all__0__iff__0, fact_117_bot__nat__0_Oextremum, fact_180_eq__iff, fact_338_le__Suc__eq, fact_183_antisym, fact_296_order__less__subst1, fact_12_poly__IVT__neg, fact_319_lessI, fact_304_ord__eq__less__subst, fact_143_order__subst1, fact_228_dual__order_Oeq__iff, fact_273_less__trans, fact_312_less__zeroE, fact_341_Suc__le__D, fact_8_poly__0, fact_333_full__nat__induct, fact_82_le__numeral__extra_I3_J, fact_114_verit__comp__simplify1_I3_J, fact_25_field__lbound__gt__zero, fact_342_le__refl, fact_249_dual__order_Oirrefl, fact_165_ord__eq__le__subst, fact_257_antisym__conv3, fact_130_less__not__refl2, fact_264_dual__order_Oasym
% 20.97/5.80 % No. of inferences in proof: 520
% 20.97/5.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5375 ms resp. 4671 ms w/o parsing
% 22.01/6.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.01/6.07 thf(poly_poly_poly_real_type, type, poly_poly_poly_real: $tType).
% 22.01/6.07 thf(poly_poly_real_type, type, poly_poly_real: $tType).
% 22.01/6.07 thf(poly_poly_nat_type, type, poly_poly_nat: $tType).
% 22.01/6.07 thf(poly_poly_int_type, type, poly_poly_int: $tType).
% 22.01/6.07 thf(poly_real_type, type, poly_real: $tType).
% 22.01/6.07 thf(poly_nat_type, type, poly_nat: $tType).
% 22.01/6.07 thf(poly_int_type, type, poly_int: $tType).
% 22.01/6.07 thf(set_real_type, type, set_real: $tType).
% 22.01/6.07 thf(real_type, type, real: $tType).
% 22.01/6.07 thf(nat_type, type, nat: $tType).
% 22.01/6.07 thf(int_type, type, int: $tType).
% 22.01/6.07 thf(one_one_nat_decl, type, one_one_nat: nat).
% 22.01/6.07 thf(zero_zero_int_decl, type, zero_zero_int: int).
% 22.01/6.07 thf(zero_zero_nat_decl, type, zero_zero_nat: nat).
% 22.01/6.07 thf(zero_zero_poly_int_decl, type, zero_zero_poly_int: poly_int).
% 22.01/6.07 thf(zero_z1423781445y_real_decl, type, zero_z1423781445y_real: poly_poly_real).
% 22.01/6.07 thf(zero_zero_poly_real_decl, type, zero_zero_poly_real: poly_real).
% 22.01/6.07 thf(zero_zero_real_decl, type, zero_zero_real: real).
% 22.01/6.07 thf(suc_decl, type, suc: (nat > nat)).
% 22.01/6.07 thf(ord_less_int_decl, type, ord_less_int: (int > (int > $o))).
% 22.01/6.07 thf(ord_less_nat_decl, type, ord_less_nat: (nat > (nat > $o))).
% 22.01/6.07 thf(ord_less_poly_real_decl, type, ord_less_poly_real: (poly_real > (poly_real > $o))).
% 22.01/6.07 thf(ord_less_real_decl, type, ord_less_real: (real > (real > $o))).
% 22.01/6.07 thf(ord_less_eq_nat_decl, type, ord_less_eq_nat: (nat > (nat > $o))).
% 22.01/6.07 thf(ord_le1180086932y_real_decl, type, ord_le1180086932y_real: (poly_real > (poly_real > $o))).
% 22.01/6.07 thf(ord_less_eq_real_decl, type, ord_less_eq_real: (real > (real > $o))).
% 22.01/6.07 thf(is_zero_real_decl, type, is_zero_real: (poly_real > $o)).
% 22.01/6.07 thf(order_int_decl, type, order_int: (int > (poly_int > nat))).
% 22.01/6.07 thf(order_poly_real_decl, type, order_poly_real: (poly_real > (poly_poly_real > nat))).
% 22.01/6.07 thf(order_real_decl, type, order_real: (real > (poly_real > nat))).
% 22.01/6.07 thf(pderiv_real_decl, type, pderiv_real: (poly_real > poly_real)).
% 22.01/6.07 thf(poly_int2_decl, type, poly_int2: (poly_int > (int > int))).
% 22.01/6.07 thf(poly_poly_real2_decl, type, poly_poly_real2: (poly_poly_real > (poly_real > poly_real))).
% 22.01/6.07 thf(poly_real2_decl, type, poly_real2: (poly_real > (real > real))).
% 22.01/6.07 thf(poly_cutoff_real_decl, type, poly_cutoff_real: (nat > (poly_real > poly_real))).
% 22.01/6.07 thf(poly_shift_real_decl, type, poly_shift_real: (nat > (poly_real > poly_real))).
% 22.01/6.07 thf(reflect_poly_real_decl, type, reflect_poly_real: (poly_real > poly_real)).
% 22.01/6.07 thf(rsquarefree_real_decl, type, rsquarefree_real: (poly_real > $o)).
% 22.01/6.07 thf(sturm_1953858694_cross_decl, type, sturm_1953858694_cross: (poly_real > (real > (real > int)))).
% 22.01/6.07 thf(sturm_469514713_r_pos_decl, type, sturm_469514713_r_pos: (poly_real > (real > $o))).
% 22.01/6.07 thf(sturm_1279781401iation_decl, type, sturm_1279781401iation: (real > (real > int))).
% 22.01/6.07 thf(member_real_decl, type, member_real: (real > (set_real > $o))).
% 22.01/6.07 thf(p_decl, type, p: poly_real).
% 22.01/6.07 thf(x_decl, type, x: real).
% 22.01/6.07 thf(188,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = ((ord_less_real @ B @ A) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_not__less__iff__gr__or__eq)).
% 22.01/6.07 thf(1036,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = ((ord_less_real @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
% 22.01/6.07 thf(149,axiom,((! [A:real,B:real,C:real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_ord__eq__le__trans)).
% 22.01/6.07 thf(846,plain,((! [A:real,B:real,C:real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
% 22.01/6.07 thf(21,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_order__class_Oorder_Oeq__iff)).
% 22.01/6.07 thf(333,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
% 22.01/6.07 thf(160,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_not__less__iff__gr__or__eq)).
% 22.01/6.07 thf(893,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
% 22.01/6.07 thf(260,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_less__not__sym)).
% 22.01/6.07 thf(1315,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])).
% 22.01/6.07 thf(177,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_185_linear)).
% 22.01/6.07 thf(962,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)],[177])).
% 22.01/6.07 thf(59,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((C @ D) => (C @ (suc @ D))))) => (C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_nat__induct__at__least)).
% 22.01/6.07 thf(481,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((C @ D) => (C @ (suc @ D))))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
% 22.01/6.07 thf(129,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_less__irrefl)).
% 22.01/6.07 thf(777,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
% 22.01/6.07 thf(76,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_less__eq__nat_Osimps_I1_J)).
% 22.01/6.07 thf(555,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
% 22.01/6.07 thf(126,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((A = (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_ord__eq__le__subst)).
% 22.01/6.07 thf(762,plain,((! [A:real,B:(real > real),C:real,D:real]: ((A = (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
% 22.01/6.07 thf(258,axiom,((! [A:real,B:real,C:poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ C @ A)) => ((ord_less_real @ (poly_real2 @ C @ B) @ zero_zero_real) => (? [D:real]: ((ord_less_real @ A @ D) & (ord_less_real @ D @ B) & ((poly_real2 @ C @ D) = zero_zero_real)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_poly__IVT__neg)).
% 22.01/6.07 thf(1305,plain,((! [A:real,B:real,C:poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ C @ A)) => ((ord_less_real @ (poly_real2 @ C @ B) @ zero_zero_real) => (? [D:real]: ((ord_less_real @ A @ D) & (ord_less_real @ D @ B) & ((poly_real2 @ C @ D) = zero_zero_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])).
% 22.01/6.07 thf(154,axiom,((! [A:set_real]: ((? [B:real]: (member_real @ B @ A)) => ((? [B:real]: ! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B))) => (? [B:real]: (! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B)) & ! [C:real]: ((! [D:real]: ((member_real @ D @ A) => (ord_less_eq_real @ D @ C))) => (ord_less_eq_real @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_complete__real)).
% 22.01/6.07 thf(861,plain,((! [A:set_real]: ((? [B:real]: (member_real @ B @ A)) => ((? [B:real]: ! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B))) => (? [B:real]: (! [C:real]: ((member_real @ C @ A) => (ord_less_eq_real @ C @ B)) & ! [C:real]: ((! [D:real]: ((member_real @ D @ A) => (ord_less_eq_real @ D @ C))) => (ord_less_eq_real @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
% 22.01/6.07 thf(221,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_dual__order_Ostrict__implies__not__eq)).
% 22.01/6.07 thf(1173,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
% 22.01/6.07 thf(255,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_ord__less__eq__subst)).
% 22.01/6.07 thf(1290,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])).
% 22.01/6.07 thf(7,axiom,((! [A:poly_poly_real]: ((zero_z1423781445y_real = A) = (A = zero_z1423781445y_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zero__reorient)).
% 22.01/6.07 thf(276,plain,((! [A:poly_poly_real]: ((zero_z1423781445y_real = A) = (A = zero_z1423781445y_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 22.01/6.07 thf(157,axiom,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_less__imp__triv)).
% 22.01/6.07 thf(878,plain,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])).
% 22.01/6.07 thf(98,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_not__less0)).
% 22.01/6.07 thf(655,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
% 22.01/6.07 thf(209,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (ord_less_eq_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_pinf_I8_J)).
% 22.01/6.07 thf(1137,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (ord_less_eq_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
% 22.01/6.07 thf(58,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_ord__le__eq__subst)).
% 22.01/6.07 thf(472,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
% 22.01/6.07 thf(237,axiom,((p != zero_zero_poly_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms)).
% 22.01/6.07 thf(1233,plain,((~ (p = zero_zero_poly_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
% 22.01/6.07 thf(138,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_bot__nat__0_Oextremum__strict)).
% 22.01/6.07 thf(814,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
% 22.01/6.07 thf(245,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B) | (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_less__linear)).
% 22.01/6.07 thf(1260,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B) | (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
% 22.01/6.07 thf(171,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__not__refl2)).
% 22.01/6.07 thf(930,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
% 22.01/6.07 thf(102,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_order__less__subst1)).
% 22.01/6.07 thf(670,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])).
% 22.01/6.07 thf(227,axiom,(((pderiv_real @ zero_zero_poly_real) = zero_zero_poly_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_pderiv__0)).
% 22.01/6.07 thf(1196,plain,(((pderiv_real @ zero_zero_poly_real) = zero_zero_poly_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])).
% 22.01/6.07 thf(162,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_less__imp__not__eq)).
% 22.01/6.07 thf(898,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
% 22.01/6.07 thf(183,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_less__asym)).
% 22.01/6.07 thf(1001,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
% 22.01/6.07 thf(131,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_not__gr0)).
% 22.01/6.07 thf(782,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])).
% 22.01/6.07 thf(13,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_old_Onat_Oinject)).
% 22.01/6.07 thf(301,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 22.01/6.07 thf(80,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_Suc__le__mono)).
% 22.01/6.07 thf(565,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
% 22.01/6.07 thf(243,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (? [C:real]: ((ord_less_real @ A @ C) & (ord_less_real @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_dense)).
% 22.01/6.07 thf(1254,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (? [C:real]: ((ord_less_real @ A @ C) & (ord_less_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])).
% 22.01/6.07 thf(200,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_ord__less__eq__subst)).
% 22.01/6.07 thf(1095,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
% 22.01/6.07 thf(42,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_dual__order_Oeq__iff)).
% 22.01/6.07 thf(404,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
% 22.01/6.07 thf(113,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_less__nat__zero__code)).
% 22.01/6.07 thf(719,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
% 22.01/6.07 thf(132,axiom,((! [A:nat]: ((A != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_gr__zeroI)).
% 22.01/6.07 thf(785,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
% 22.01/6.07 thf(112,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)))))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_infinite__descent0)).
% 22.01/6.07 thf(702,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
% 22.01/6.07 thf(26,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_eq__iff)).
% 22.01/6.07 thf(344,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 22.01/6.07 thf(251,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_verit__comp__simplify1_I1_J)).
% 22.01/6.07 thf(1279,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])).
% 22.01/6.07 thf(193,axiom,((! [A:real,B:real]: ((A != B) => ((~ (ord_less_real @ A @ B)) => (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_neqE)).
% 22.01/6.07 thf(1059,plain,((! [A:real,B:real]: ((~ (A = B)) => ((~ (ord_less_real @ A @ B)) => (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
% 22.01/6.07 thf(172,axiom,((! [A:int]: ((zero_zero_int = A) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_zero__reorient)).
% 22.01/6.07 thf(934,plain,((! [A:int]: ((zero_zero_int = A) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
% 22.01/6.07 thf(32,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_le__eq__less__or__eq)).
% 22.01/6.07 thf(357,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
% 22.01/6.07 thf(78,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_bot__nat__0_Oextremum__uniqueI)).
% 22.01/6.07 thf(559,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
% 22.01/6.07 thf(94,axiom,((! [A:nat]: ((poly_cutoff_real @ A @ zero_zero_poly_real) = zero_zero_poly_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_poly__cutoff__0)).
% 22.01/6.07 thf(638,plain,((! [A:nat]: ((poly_cutoff_real @ A @ zero_zero_poly_real) = zero_zero_poly_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
% 22.01/6.07 thf(197,axiom,((! [A:poly_real,B:real]: (((poly_real2 @ A @ B) = zero_zero_real) = ((A = zero_zero_poly_real) | ((order_real @ B @ A) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_order__root)).
% 22.01/6.07 thf(1087,plain,((! [A:poly_real,B:real]: (((poly_real2 @ A @ B) = zero_zero_real) = ((A = zero_zero_poly_real) | ~ ((order_real @ B @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
% 22.01/6.07 thf(240,axiom,((rsquarefree_real = (^ [A:poly_real]: ! [B:real]: ~ (((poly_real2 @ A @ B) = zero_zero_real) & ((poly_real2 @ (pderiv_real @ A) @ B) = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_rsquarefree__roots)).
% 22.01/6.07 thf(1247,plain,(((rsquarefree_real) = (^ [A:poly_real]: ! [B:real]: ~ (((poly_real2 @ A @ B) = zero_zero_real) & ((poly_real2 @ (pderiv_real @ A) @ B) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
% 22.01/6.07 thf(10,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_bot__nat__0_Oextremum__unique)).
% 22.01/6.07 thf(284,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 22.01/6.07 thf(158,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_dual__order_Oirrefl)).
% 22.01/6.07 thf(881,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
% 22.01/6.07 thf(18,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_order__subst1)).
% 22.01/6.07 thf(316,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 22.01/6.07 thf(1,conjecture,(((sturm_469514713_r_pos @ p @ x) != (~ ((((poly_real2 @ p @ x) = zero_zero_real) => (sturm_469514713_r_pos @ (pderiv_real @ p) @ x)) & (((poly_real2 @ p @ x) != zero_zero_real) => (ord_less_real @ zero_zero_real @ (poly_real2 @ p @ x))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 22.01/6.07 thf(2,negated_conjecture,((~ ((sturm_469514713_r_pos @ p @ x) != (~ ((((poly_real2 @ p @ x) = zero_zero_real) => (sturm_469514713_r_pos @ (pderiv_real @ p) @ x)) & (((poly_real2 @ p @ x) != zero_zero_real) => (ord_less_real @ zero_zero_real @ (poly_real2 @ p @ x)))))))),inference(neg_conjecture,[status(cth)],[1])).
% 22.01/6.07 thf(261,plain,((~ (~ ((sturm_469514713_r_pos @ p @ x) = (~ ((((poly_real2 @ p @ x) = zero_zero_real) => (sturm_469514713_r_pos @ (pderiv_real @ p) @ x)) & ((~ ((poly_real2 @ p @ x) = zero_zero_real)) => (ord_less_real @ zero_zero_real @ (poly_real2 @ p @ x))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 22.01/6.07 thf(139,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_209_ord__le__eq__trans)).
% 22.01/6.07 thf(817,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)],[139])).
% 22.01/6.07 thf(163,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((A != B) => (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_linorder__cases)).
% 22.01/6.07 thf(902,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (A = B)) => (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
% 22.01/6.07 thf(19,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_ord__le__eq__subst)).
% 22.01/6.07 thf(321,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 22.01/6.07 thf(37,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (~ (ord_less_eq_nat @ B @ C))) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => (((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_le__cases3)).
% 22.01/6.07 thf(376,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (~ (ord_less_eq_nat @ B @ C))) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => (((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
% 22.01/6.07 thf(97,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_ord__less__eq__subst)).
% 22.01/6.07 thf(646,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
% 22.01/6.07 thf(173,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 @ A @ C) => (~ (ord_less_eq_real @ C @ B))) => (((ord_less_eq_real @ C @ B) => (~ (ord_less_eq_real @ B @ A))) => (((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))) => (~ ((ord_less_eq_real @ C @ A) => (~ (ord_less_eq_real @ A @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_le__cases3)).
% 22.01/6.07 thf(937,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 @ A @ C) => (~ (ord_less_eq_real @ C @ B))) => (((ord_less_eq_real @ C @ B) => (~ (ord_less_eq_real @ B @ A))) => (((ord_less_eq_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))) => (~ ((ord_less_eq_real @ C @ A) => (~ (ord_less_eq_real @ A @ B))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])).
% 22.01/6.07 thf(223,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_less__asym_H)).
% 22.01/6.07 thf(1183,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
% 22.01/6.07 thf(164,axiom,((! [A:poly_real]: ((zero_zero_poly_real = A) = (A = zero_zero_poly_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zero__reorient)).
% 22.01/6.07 thf(905,plain,((! [A:poly_real]: ((zero_zero_poly_real = A) = (A = zero_zero_poly_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
% 22.01/6.07 thf(119,axiom,((~ (ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_less__numeral__extra_I3_J)).
% 22.01/6.07 thf(734,plain,((~ (ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
% 22.01/6.07 thf(128,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_less__irrefl__nat)).
% 22.01/6.07 thf(774,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])).
% 22.01/6.07 thf(44,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_nat__le__linear)).
% 22.01/6.07 thf(411,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
% 22.01/6.07 thf(229,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_gt__ex)).
% 22.01/6.07 thf(1201,plain,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])).
% 22.01/6.07 thf(201,axiom,((~ (ord_less_real @ zero_zero_real @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_less__numeral__extra_I3_J)).
% 22.01/6.07 thf(1104,plain,((~ (ord_less_real @ zero_zero_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
% 22.01/6.07 thf(63,axiom,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_verit__la__disequality)).
% 22.01/6.07 thf(507,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
% 22.01/6.07 thf(69,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_le__trans)).
% 22.01/6.07 thf(527,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
% 22.01/6.07 thf(16,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_bot__nat__0_Oextremum)).
% 22.01/6.07 thf(312,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 22.01/6.07 thf(12,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_ord__eq__le__subst)).
% 22.01/6.07 thf(292,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 22.01/6.07 thf(231,axiom,((! [A:poly_real]: ((! [B:real]: ((poly_real2 @ A @ B) = zero_zero_real)) = (A = zero_zero_poly_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_poly__all__0__iff__0)).
% 22.01/6.07 thf(1206,plain,((! [A:poly_real]: ((! [B:real]: ((poly_real2 @ A @ B) = zero_zero_real)) = (A = zero_zero_poly_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])).
% 22.01/6.07 thf(5,axiom,((! [A:int]: ((poly_int2 @ zero_zero_poly_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_poly__0)).
% 22.01/6.07 thf(270,plain,((! [A:int]: ((poly_int2 @ zero_zero_poly_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 22.01/6.07 thf(100,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_less__not__refl3)).
% 22.01/6.07 thf(661,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])).
% 22.01/6.07 thf(137,axiom,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_eq__refl)).
% 22.01/6.07 thf(810,plain,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
% 22.01/6.07 thf(28,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_nat__less__le)).
% 22.01/6.07 thf(349,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 22.01/6.07 thf(92,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_less__zeroE)).
% 22.01/6.07 thf(630,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
% 22.01/6.07 thf(133,axiom,((((=) @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_order__class_Oorder_Oeq__iff)).
% 22.01/6.07 thf(788,plain,((((=) @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
% 22.01/6.07 thf(117,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_order_Otrans)).
% 22.01/6.07 thf(729,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
% 22.01/6.07 thf(190,axiom,((! [A:real,B:real,C:poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ C @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ C @ B)) => (? [D:real]: ((ord_less_real @ A @ D) & (ord_less_real @ D @ B) & ((poly_real2 @ C @ D) = zero_zero_real)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_poly__IVT__pos)).
% 22.01/6.07 thf(1042,plain,((! [A:real,B:real,C:poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ C @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ C @ B)) => (? [D:real]: ((ord_less_real @ A @ D) & (ord_less_real @ D @ B) & ((poly_real2 @ C @ D) = zero_zero_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])).
% 22.01/6.07 thf(174,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_verit__comp__simplify1_I1_J)).
% 22.01/6.07 thf(952,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
% 22.01/6.07 thf(51,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_Suc__less__eq)).
% 22.01/6.07 thf(435,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
% 22.01/6.07 thf(101,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_ord__less__eq__trans)).
% 22.01/6.07 thf(665,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
% 22.01/6.07 thf(142,axiom,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_less__numeral__extra_I3_J)).
% 22.01/6.07 thf(830,plain,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
% 22.01/6.07 thf(105,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_neq0__conv)).
% 22.01/6.07 thf(682,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
% 22.01/6.07 thf(74,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_le__cases)).
% 22.01/6.07 thf(551,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])).
% 22.01/6.07 thf(147,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_zero__less__Suc)).
% 22.01/6.07 thf(842,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
% 22.01/6.07 thf(185,axiom,((((?) @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_exists__least__iff)).
% 22.01/6.07 thf(1012,plain,((((?) @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
% 22.01/6.07 thf(202,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_order__less__subst1)).
% 22.01/6.07 thf(1106,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
% 22.01/6.07 thf(168,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_227_dual__order_Oeq__iff)).
% 22.01/6.07 thf(916,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)],[168])).
% 22.01/6.07 thf(56,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_pinf_I6_J)).
% 22.01/6.07 thf(467,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
% 22.01/6.07 thf(110,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_dual__order_Orefl)).
% 22.01/6.07 thf(697,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
% 22.01/6.07 thf(187,axiom,((! [A:(real > (real > $o)),B:real,C:real]: ((! [D:real,E:real]: ((ord_less_real @ D @ E) => (A @ D @ E))) => ((! [D:real]: (A @ D @ D)) => ((! [D:real,E:real]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_linorder__less__wlog)).
% 22.01/6.07 thf(1017,plain,((! [A:(real > (real > $o)),B:real,C:real]: ((! [D:real,E:real]: ((ord_less_real @ D @ E) => (A @ D @ E))) => ((! [D:real]: (A @ D @ D)) => ((! [D:real,E:real]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])).
% 22.01/6.07 thf(89,axiom,((! [A:(real > (real > $o)),B:real,C:real]: ((! [D:real,E:real]: ((ord_less_eq_real @ D @ E) => (A @ D @ E))) => ((! [D:real,E:real]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_linorder__wlog)).
% 22.01/6.07 thf(615,plain,((! [A:(real > (real > $o)),B:real,C:real]: ((! [D:real,E:real]: ((ord_less_eq_real @ D @ E) => (A @ D @ E))) => ((! [D:real,E:real]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
% 22.01/6.07 thf(206,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_ord__less__eq__subst)).
% 22.01/6.07 thf(1121,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])).
% 22.01/6.07 thf(203,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_less__eq__real__def)).
% 22.01/6.07 thf(1111,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
% 22.01/6.07 thf(115,axiom,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_less__Suc0)).
% 22.01/6.07 thf(725,plain,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
% 22.01/6.07 thf(181,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_182_antisym)).
% 22.01/6.07 thf(989,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)],[181])).
% 22.01/6.07 thf(159,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_less__induct)).
% 22.01/6.07 thf(884,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
% 22.01/6.07 thf(216,axiom,((sturm_1953858694_cross = (^ [A:poly_real,B:real,C:real]: (sturm_1279781401iation @ (poly_real2 @ A @ B) @ (poly_real2 @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_cross__def)).
% 22.01/6.07 thf(1160,plain,(((sturm_1953858694_cross) = (^ [A:poly_real,B:real,C:real]: (sturm_1279781401iation @ (poly_real2 @ A @ B) @ (poly_real2 @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
% 22.01/6.07 thf(24,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_antisym)).
% 22.01/6.07 thf(339,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 22.01/6.07 thf(214,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_dual__order_Oasym)).
% 22.01/6.07 thf(1155,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
% 22.01/6.07 thf(104,axiom,((! [A:poly_int,B:int]: (((poly_int2 @ A @ B) != zero_zero_int) => ((order_int @ B @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_order__0I)).
% 22.01/6.07 thf(679,plain,((! [A:poly_int,B:int]: ((~ ((poly_int2 @ A @ B) = zero_zero_int)) => ((order_int @ B @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
% 22.01/6.07 thf(189,axiom,((! [A:real]: ((sturm_1279781401iation @ A @ zero_zero_real) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_variation__0_I2_J)).
% 22.01/6.07 thf(1039,plain,((! [A:real]: ((sturm_1279781401iation @ A @ zero_zero_real) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
% 22.01/6.07 thf(180,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat]: (A @ D @ D)) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_linorder__less__wlog)).
% 22.01/6.07 thf(970,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat]: (A @ D @ D)) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])).
% 22.01/6.07 thf(39,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_order__subst1)).
% 22.01/6.07 thf(393,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
% 22.01/6.07 thf(246,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_order__less__subst2)).
% 22.01/6.07 thf(1263,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])).
% 22.01/6.07 thf(166,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_less__linear)).
% 22.01/6.07 thf(911,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
% 22.01/6.07 thf(35,axiom,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_Suc__n__not__le__n)).
% 22.01/6.07 thf(371,plain,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 22.01/6.07 thf(90,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_order__subst2)).
% 22.01/6.07 thf(622,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
% 22.01/6.07 thf(145,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_less__asym_H)).
% 22.01/6.07 thf(837,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
% 22.01/6.07 thf(212,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_lt__ex)).
% 22.01/6.07 thf(1150,plain,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])).
% 22.01/6.07 thf(241,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_less__asym)).
% 22.01/6.07 thf(1249,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
% 22.01/6.07 thf(93,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_order__less__subst2)).
% 22.01/6.07 thf(633,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
% 22.01/6.07 thf(170,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_ord__eq__less__subst)).
% 22.01/6.07 thf(921,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
% 22.01/6.07 thf(192,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_ord__less__eq__trans)).
% 22.01/6.07 thf(1054,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
% 22.01/6.07 thf(220,axiom,((! [A:real,B:real,C:poly_real]: ((! [D:real]: (((ord_less_real @ A @ D) & (ord_less_eq_real @ D @ B)) => ((poly_real2 @ C @ D) != zero_zero_real))) = (! [D:real]: (((ord_less_real @ A @ D) & (ord_less_eq_real @ D @ B)) => (ord_less_real @ zero_zero_real @ (poly_real2 @ C @ D))) | ! [D:real]: (((ord_less_real @ A @ D) & (ord_less_eq_real @ D @ B)) => (ord_less_real @ (poly_real2 @ C @ D) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_not__eq__pos__or__neg__iff__1)).
% 22.01/6.07 thf(1170,plain,((! [A:real,B:real,C:poly_real]: ((! [D:real]: (((ord_less_real @ A @ D) & (ord_less_eq_real @ D @ B)) => (~ ((poly_real2 @ C @ D) = zero_zero_real)))) = (! [D:real]: (((ord_less_real @ A @ D) & (ord_less_eq_real @ D @ B)) => (ord_less_real @ zero_zero_real @ (poly_real2 @ C @ D))) | ! [D:real]: (((ord_less_real @ A @ D) & (ord_less_eq_real @ D @ B)) => (ord_less_real @ (poly_real2 @ C @ D) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])).
% 22.01/6.07 thf(40,axiom,((! [A:poly_poly_real,B:poly_poly_real]: (((poly_poly_real2 @ A) = (poly_poly_real2 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_poly__eq__poly__eq__iff)).
% 22.01/6.07 thf(398,plain,((! [A:poly_poly_real,B:poly_poly_real]: (((poly_poly_real2 @ A) = (poly_poly_real2 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
% 22.01/6.07 thf(195,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: ((A = (B @ C)) => ((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_ord__eq__less__subst)).
% 22.01/6.07 thf(1071,plain,((! [A:nat,B:(real > nat),C:real,D:real]: ((A = (B @ C)) => ((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
% 22.01/6.07 thf(219,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_verit__comp__simplify1_I3_J)).
% 22.01/6.07 thf(1167,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
% 22.01/6.07 thf(70,axiom,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_ord__eq__le__trans)).
% 22.01/6.07 thf(530,plain,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
% 22.01/6.07 thf(224,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_order_Ostrict__implies__not__eq)).
% 22.01/6.07 thf(1185,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
% 22.01/6.07 thf(123,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_less__imp__neq)).
% 22.01/6.07 thf(750,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
% 22.01/6.07 thf(242,axiom,((! [A:real,B:real]: ((A != B) = ((ord_less_real @ A @ B) | (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_neq__iff)).
% 22.01/6.07 thf(1251,plain,((! [A:real,B:real]: ((~ (A = B)) = ((ord_less_real @ A @ B) | (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
% 22.01/6.07 thf(249,axiom,((! [A:poly_real,B:real]: (((poly_real2 @ A @ B) != zero_zero_real) => ((order_real @ B @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_order__0I)).
% 22.01/6.07 thf(1273,plain,((! [A:poly_real,B:real]: ((~ ((poly_real2 @ A @ B) = zero_zero_real)) => ((order_real @ B @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])).
% 22.01/6.07 thf(3,axiom,((! [A:poly_int]: ((zero_zero_poly_int = A) = (A = zero_zero_poly_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zero__reorient)).
% 22.01/6.07 thf(264,plain,((! [A:poly_int]: ((zero_zero_poly_int = A) = (A = zero_zero_poly_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 22.01/6.07 thf(152,axiom,(((reflect_poly_real @ zero_zero_poly_real) = zero_zero_poly_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_reflect__poly__0)).
% 22.01/6.07 thf(856,plain,(((reflect_poly_real @ zero_zero_poly_real) = zero_zero_poly_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
% 22.01/6.07 thf(8,axiom,((! [A:poly_int]: ((! [B:int]: ((poly_int2 @ A @ B) = zero_zero_int)) = (A = zero_zero_poly_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_poly__all__0__iff__0)).
% 22.01/6.07 thf(279,plain,((! [A:poly_int]: ((! [B:int]: ((poly_int2 @ A @ B) = zero_zero_int)) = (A = zero_zero_poly_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 22.01/6.07 thf(83,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_linorder__wlog)).
% 22.01/6.07 thf(573,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
% 22.01/6.07 thf(65,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A != B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_le__neq__implies__less)).
% 22.01/6.07 thf(513,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (A = B)) => (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
% 22.01/6.07 thf(50,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_order__subst2)).
% 22.01/6.07 thf(430,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
% 22.01/6.07 thf(79,axiom,((! [A:poly_poly_real,B:poly_real]: (((poly_poly_real2 @ A @ B) = zero_zero_poly_real) = ((A = zero_z1423781445y_real) | ((order_poly_real @ B @ A) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_order__root)).
% 22.01/6.07 thf(562,plain,((! [A:poly_poly_real,B:poly_real]: (((poly_poly_real2 @ A @ B) = zero_zero_poly_real) = ((A = zero_z1423781445y_real) | ~ ((order_poly_real @ B @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
% 22.01/6.07 thf(109,axiom,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_less__one)).
% 22.01/6.07 thf(694,plain,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
% 22.01/6.07 thf(118,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_dual__order_Oasym)).
% 22.01/6.07 thf(732,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
% 22.01/6.07 thf(176,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_order_Ostrict__implies__not__eq)).
% 22.01/6.07 thf(958,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])).
% 22.01/6.07 thf(45,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_le0)).
% 22.01/6.07 thf(413,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
% 22.01/6.07 thf(156,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zero__reorient)).
% 22.01/6.07 thf(875,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
% 22.01/6.07 thf(141,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_dual__order_Ostrict__implies__not__eq)).
% 22.01/6.07 thf(826,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
% 22.01/6.07 thf(95,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_212_order__class_Oorder_Oantisym)).
% 22.01/6.07 thf(641,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)],[95])).
% 22.01/6.07 thf(248,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_less__imp__not__less)).
% 22.01/6.07 thf(1271,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])).
% 22.01/6.07 thf(259,axiom,((! [A:real,B:real,C:poly_real]: ((! [D:real]: (((ord_less_eq_real @ A @ D) & (ord_less_real @ D @ B)) => ((poly_real2 @ C @ D) != zero_zero_real))) = (! [D:real]: (((ord_less_eq_real @ A @ D) & (ord_less_real @ D @ B)) => (ord_less_real @ zero_zero_real @ (poly_real2 @ C @ D))) | ! [D:real]: (((ord_less_eq_real @ A @ D) & (ord_less_real @ D @ B)) => (ord_less_real @ (poly_real2 @ C @ D) @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_not__eq__pos__or__neg__iff__2)).
% 22.01/6.07 thf(1312,plain,((! [A:real,B:real,C:poly_real]: ((! [D:real]: (((ord_less_eq_real @ A @ D) & (ord_less_real @ D @ B)) => (~ ((poly_real2 @ C @ D) = zero_zero_real)))) = (! [D:real]: (((ord_less_eq_real @ A @ D) & (ord_less_real @ D @ B)) => (ord_less_real @ zero_zero_real @ (poly_real2 @ C @ D))) | ! [D:real]: (((ord_less_eq_real @ A @ D) & (ord_less_real @ D @ B)) => (ord_less_real @ (poly_real2 @ C @ D) @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])).
% 22.01/6.07 thf(61,axiom,((! [A:poly_int,B:poly_int]: (((poly_int2 @ A) = (poly_int2 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_poly__eq__poly__eq__iff)).
% 22.01/6.07 thf(498,plain,((! [A:poly_int,B:poly_int]: (((poly_int2 @ A) = (poly_int2 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
% 22.01/6.07 thf(22,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_minf_I6_J)).
% 22.01/6.07 thf(335,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 22.01/6.07 thf(198,axiom,((! [A:poly_real,B:poly_real]: (((poly_real2 @ A) = (poly_real2 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_poly__eq__poly__eq__iff)).
% 22.01/6.07 thf(1090,plain,((! [A:poly_real,B:poly_real]: (((poly_real2 @ A) = (poly_real2 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
% 22.01/6.07 thf(135,axiom,((! [A:nat]: ((poly_shift_real @ A @ zero_zero_poly_real) = zero_zero_poly_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_poly__shift__0)).
% 22.01/6.07 thf(804,plain,((! [A:nat]: ((poly_shift_real @ A @ zero_zero_poly_real) = zero_zero_poly_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])).
% 22.01/6.07 thf(244,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (~ (ord_less_eq_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_minf_I8_J)).
% 22.01/6.07 thf(1258,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (~ (ord_less_eq_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
% 22.01/6.07 thf(38,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_linear)).
% 22.01/6.07 thf(391,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
% 22.01/6.07 thf(210,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (ord_less_eq_real @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_minf_I6_J)).
% 22.01/6.07 thf(1139,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (ord_less_eq_real @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])).
% 22.01/6.07 thf(232,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_less__imp__neq)).
% 22.01/6.07 thf(1209,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
% 22.01/6.07 thf(43,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_order__subst2)).
% 22.01/6.07 thf(406,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
% 22.01/6.07 thf(252,axiom,((! [A:real]: ((poly_real2 @ zero_zero_poly_real @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_poly__0)).
% 22.01/6.07 thf(1282,plain,((! [A:real]: ((poly_real2 @ zero_zero_poly_real @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])).
% 22.01/6.07 thf(47,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_verit__comp__simplify1_I3_J)).
% 22.01/6.07 thf(419,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
% 22.01/6.07 thf(120,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_neq__iff)).
% 22.01/6.07 thf(736,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
% 22.01/6.07 thf(196,axiom,((! [A:poly_real,B:real]: ((A != zero_zero_poly_real) => (~ (! [C:real]: ((ord_less_real @ C @ B) => (~ (! [D:real]: (((ord_less_eq_real @ C @ D) & (ord_less_real @ D @ B)) => ((poly_real2 @ A @ D) != zero_zero_real)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_last__non__root__interval)).
% 22.01/6.07 thf(1080,plain,((! [A:poly_real,B:real]: ((~ (A = zero_zero_poly_real)) => (~ (! [C:real]: ((ord_less_real @ C @ B) => (~ (! [D:real]: (((ord_less_eq_real @ C @ D) & (ord_less_real @ D @ B)) => (~ ((poly_real2 @ A @ D) = zero_zero_real))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
% 22.01/6.07 thf(153,axiom,((! [A:poly_poly_real,B:poly_real]: (((poly_poly_real2 @ A @ B) != zero_zero_poly_real) => ((order_poly_real @ B @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_order__0I)).
% 22.01/6.07 thf(858,plain,((! [A:poly_poly_real,B:poly_real]: ((~ ((poly_poly_real2 @ A @ B) = zero_zero_poly_real)) => ((order_poly_real @ B @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
% 22.01/6.07 thf(71,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_eq__imp__le)).
% 22.01/6.07 thf(535,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
% 22.01/6.07 thf(217,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ A) => (ord_less_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_dual__order_Ostrict__trans)).
% 22.01/6.07 thf(1162,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ A) => (ord_less_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])).
% 22.01/6.07 thf(178,axiom,((! [A:real,B:real]: ((A = B) | ~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_verit__la__disequality)).
% 22.01/6.07 thf(964,plain,((! [A:real,B:real]: ((A = B) | ~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
% 22.01/6.07 thf(222,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & (ord_less_real @ C @ A) & (ord_less_real @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_field__lbound__gt__zero)).
% 22.01/6.07 thf(1177,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & (ord_less_real @ C @ A) & (ord_less_real @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
% 22.01/6.07 thf(20,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_antisym__conv)).
% 22.01/6.07 thf(330,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 22.01/6.07 thf(54,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_le__SucI)).
% 22.01/6.07 thf(462,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
% 22.01/6.07 thf(228,axiom,((! [A:poly_real]: (((poly_real2 @ (reflect_poly_real @ A) @ zero_zero_real) = zero_zero_real) = (A = zero_zero_poly_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_reflect__poly__at__0__eq__0__iff)).
% 22.01/6.07 thf(1198,plain,((! [A:poly_real]: (((poly_real2 @ (reflect_poly_real @ A) @ zero_zero_real) = zero_zero_real) = (A = zero_zero_poly_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
% 22.01/6.07 thf(233,axiom,((! [A:poly_real,B:real]: ((A != zero_zero_poly_real) => (~ (! [C:real]: ((ord_less_real @ B @ C) => (~ (! [D:real]: (((ord_less_real @ B @ D) & (ord_less_eq_real @ D @ C)) => ((poly_real2 @ A @ D) != zero_zero_real)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_next__non__root__interval)).
% 22.01/6.07 thf(1213,plain,((! [A:poly_real,B:real]: ((~ (A = zero_zero_poly_real)) => (~ (! [C:real]: ((ord_less_real @ B @ C) => (~ (! [D:real]: (((ord_less_real @ B @ D) & (ord_less_eq_real @ D @ C)) => (~ ((poly_real2 @ A @ D) = zero_zero_real))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
% 22.01/6.07 thf(239,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_pinf_I6_J)).
% 22.01/6.07 thf(1245,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
% 22.01/6.07 thf(130,axiom,((is_zero_real = (^ [A:poly_real]: (A = zero_zero_poly_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_is__zero__null)).
% 22.01/6.07 thf(780,plain,(((is_zero_real) = (^ [A:poly_real]: (A = zero_zero_poly_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])).
% 22.01/6.07 thf(87,axiom,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_ord__eq__less__trans)).
% 22.01/6.07 thf(608,plain,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
% 22.01/6.07 thf(204,axiom,((! [A:real,B:real,C:$o]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ A) => (C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_less__imp__triv)).
% 22.01/6.07 thf(1113,plain,((! [A:real,B:real,C:$o]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
% 22.01/6.07 thf(52,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_ord__le__eq__subst)).
% 22.01/6.07 thf(438,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
% 22.01/6.07 thf(99,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_nat__neq__iff)).
% 22.01/6.07 thf(658,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])).
% 22.01/6.07 thf(106,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_224_dual__order_Otrans)).
% 22.01/6.07 thf(685,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)],[106])).
% 22.01/6.07 thf(67,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_not__less__eq__eq)).
% 22.01/6.07 thf(521,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
% 22.01/6.07 thf(4,axiom,((! [A:poly_real]: ((poly_poly_real2 @ zero_z1423781445y_real @ A) = zero_zero_poly_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_poly__0)).
% 22.01/6.07 thf(267,plain,((! [A:poly_real]: ((poly_poly_real2 @ zero_z1423781445y_real @ A) = zero_zero_poly_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 22.01/6.07 thf(150,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_not__gr__zero)).
% 22.01/6.07 thf(851,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
% 22.01/6.07 thf(114,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_antisym__conv3)).
% 22.01/6.07 thf(722,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
% 22.01/6.07 thf(103,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_gr__implies__not0)).
% 22.01/6.07 thf(675,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
% 22.01/6.07 thf(73,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_dual__order_Otrans)).
% 22.01/6.07 thf(548,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
% 22.01/6.07 thf(36,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_pinf_I8_J)).
% 22.01/6.07 thf(374,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
% 22.01/6.07 thf(66,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_order__subst2)).
% 22.01/6.07 thf(516,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
% 22.01/6.07 thf(25,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_le__refl)).
% 22.01/6.07 thf(342,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 22.01/6.07 thf(31,axiom,((one_one_nat = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_One__nat__def)).
% 22.01/6.07 thf(355,plain,((one_one_nat = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 22.01/6.07 thf(124,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_order__subst1)).
% 22.01/6.07 thf(754,plain,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])).
% 22.01/6.07 thf(75,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_less__imp__le__nat)).
% 22.01/6.07 thf(553,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])).
% 22.01/6.07 thf(191,axiom,((! [A:real,B:real,C:real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_ord__eq__less__trans)).
% 22.01/6.07 thf(1049,plain,((! [A:real,B:real,C:real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])).
% 22.01/6.07 thf(230,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_less__trans)).
% 22.01/6.07 thf(1203,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
% 22.01/6.07 thf(85,axiom,((! [A:poly_int,B:int]: (((poly_int2 @ A @ B) = zero_zero_int) = ((A = zero_zero_poly_int) | ((order_int @ B @ A) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_order__root)).
% 22.01/6.07 thf(589,plain,((! [A:poly_int,B:int]: (((poly_int2 @ A @ B) = zero_zero_int) = ((A = zero_zero_poly_int) | ~ ((order_int @ B @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
% 22.01/6.07 thf(84,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: ((A = (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_ord__eq__le__subst)).
% 22.01/6.07 thf(580,plain,((! [A:nat,B:(real > nat),C:real,D:real]: ((A = (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
% 22.01/6.07 thf(9,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_dual__order_Orefl)).
% 22.01/6.07 thf(282,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 22.01/6.07 thf(235,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_order__less__subst2)).
% 22.01/6.07 thf(1225,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])).
% 22.01/6.07 thf(121,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_ord__le__eq__subst)).
% 22.01/6.07 thf(739,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_eq_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
% 22.01/6.07 thf(236,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__irrefl)).
% 22.01/6.07 thf(1230,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
% 22.01/6.07 thf(77,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_minf_I8_J)).
% 22.01/6.07 thf(557,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
% 22.01/6.07 thf(184,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_nat__less__induct)).
% 22.01/6.07 thf(1003,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
% 22.01/6.07 thf(257,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_order__less__subst1)).
% 22.01/6.07 thf(1300,plain,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])).
% 22.01/6.07 thf(33,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_full__nat__induct)).
% 22.01/6.07 thf(359,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 22.01/6.07 thf(207,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_order_Ostrict__trans)).
% 22.01/6.07 thf(1130,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
% 22.01/6.07 thf(253,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_dual__order_Oirrefl)).
% 22.01/6.07 thf(1285,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])).
% 22.01/6.07 thf(234,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_order__less__subst1)).
% 22.01/6.07 thf(1220,plain,((! [A:nat,B:(real > nat),C:real,D:real]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])).
% 22.01/6.07 thf(211,axiom,((! [A:real,B:real,C:poly_real]: ((ord_less_real @ A @ B) => ((! [D:real]: (((ord_less_real @ A @ D) & (ord_less_real @ D @ B)) => ((poly_real2 @ C @ D) != zero_zero_real))) => ((sturm_1953858694_cross @ C @ A @ B) = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_cross__no__root)).
% 22.01/6.07 thf(1141,plain,((! [A:real,B:real,C:poly_real]: ((ord_less_real @ A @ B) => ((! [D:real]: (((ord_less_real @ A @ D) & (ord_less_real @ D @ B)) => (~ ((poly_real2 @ C @ D) = zero_zero_real)))) => ((sturm_1953858694_cross @ C @ A @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])).
% 22.01/6.07 thf(88,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_order_Oasym)).
% 22.01/6.07 thf(613,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
% 22.01/6.07 thf(17,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zero__le)).
% 22.01/6.07 thf(314,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 22.01/6.07 thf(82,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_Suc__mono)).
% 22.01/6.07 thf(571,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
% 22.01/6.07 thf(91,axiom,((! [A:real,B:real]: ((sturm_1953858694_cross @ zero_zero_poly_real @ A @ B) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_cross__0)).
% 22.01/6.07 thf(627,plain,((! [A:real,B:real]: ((sturm_1953858694_cross @ zero_zero_poly_real @ A @ B) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])).
% 22.01/6.07 thf(72,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_ord__eq__le__subst)).
% 22.01/6.07 thf(539,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_eq_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
% 22.01/6.07 thf(215,axiom,((! [A:real]: ((sturm_1279781401iation @ zero_zero_real @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_variation__0_I1_J)).
% 22.01/6.07 thf(1157,plain,((! [A:real]: ((sturm_1279781401iation @ zero_zero_real @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])).
% 22.01/6.07 thf(107,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_order__trans)).
% 22.01/6.07 thf(688,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
% 22.01/6.07 thf(68,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_order__trans)).
% 22.01/6.07 thf(524,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
% 22.01/6.07 thf(125,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_dual__order_Oantisym)).
% 22.01/6.07 thf(759,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
% 22.01/6.07 thf(225,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_less__imp__not__eq)).
% 22.01/6.07 thf(1189,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
% 22.01/6.07 thf(127,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_less__not__refl)).
% 22.01/6.07 thf(771,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
% 22.01/6.07 thf(34,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_le__zero__eq)).
% 22.01/6.07 thf(368,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
% 22.01/6.07 thf(148,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_191_le__cases)).
% 22.01/6.07 thf(844,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)],[148])).
% 22.01/6.07 thf(250,axiom,((! [A:real]: ((zero_zero_real = A) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_zero__reorient)).
% 22.01/6.07 thf(1276,plain,((! [A:real]: ((zero_zero_real = A) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])).
% 22.01/6.07 thf(111,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_order_Ostrict__trans)).
% 22.01/6.07 thf(699,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
% 22.01/6.07 thf(14,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_ord__le__eq__trans)).
% 22.01/6.07 thf(304,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 22.01/6.07 thf(194,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((A = (B @ C)) => ((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_ord__eq__less__subst)).
% 22.01/6.07 thf(1062,plain,((! [A:real,B:(real > real),C:real,D:real]: ((A = (B @ C)) => ((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
% 22.01/6.07 thf(29,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_order_Otrans)).
% 22.01/6.07 thf(351,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 22.01/6.07 thf(41,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_nat_Oinject)).
% 22.01/6.07 thf(401,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
% 22.01/6.07 thf(161,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_order__refl)).
% 22.01/6.07 thf(896,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
% 22.01/6.07 thf(122,axiom,((((=) @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_eq__iff)).
% 22.01/6.08 thf(748,plain,((((=) @ real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
% 22.01/6.08 thf(81,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_le__0__eq)).
% 22.01/6.08 thf(568,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
% 22.01/6.08 thf(167,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_less__imp__not__less)).
% 22.01/6.08 thf(914,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
% 22.01/6.08 thf(64,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_Suc__le__D)).
% 22.01/6.08 thf(510,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
% 22.01/6.08 thf(226,axiom,(((poly_real2 @ p @ x) != zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False)).
% 22.01/6.08 thf(1193,plain,((~ ((poly_real2 @ p @ x) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
% 22.01/6.08 thf(143,axiom,((! [A:nat,B:nat]: ((A != B) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_linorder__neqE__nat)).
% 22.01/6.08 thf(832,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
% 22.01/6.08 thf(27,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_le__antisym)).
% 22.01/6.08 thf(346,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
% 22.01/6.08 thf(11,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_less__mono__imp__le__mono)).
% 22.01/6.08 thf(287,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 22.01/6.08 thf(205,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_nat @ A @ B) => ((ord_less_real @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_order__less__subst2)).
% 22.01/6.08 thf(1116,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_nat @ A @ B) => ((ord_less_real @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
% 22.01/6.08 thf(208,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_less__imp__not__eq2)).
% 22.01/6.08 thf(1133,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
% 22.01/6.08 thf(53,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq_nat @ A @ B) => ((! [D:nat]: (C @ D @ D)) => ((! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_transitive__stepwise__le)).
% 22.01/6.08 thf(447,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq_nat @ A @ B) => ((! [D:nat]: (C @ D @ D)) => ((! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
% 22.01/6.08 thf(179,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_less__trans)).
% 22.01/6.08 thf(967,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
% 22.01/6.08 thf(144,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_gt__ex)).
% 22.01/6.08 thf(835,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
% 22.01/6.08 thf(151,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_less__not__sym)).
% 22.01/6.08 thf(854,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
% 22.01/6.08 thf(6,axiom,((! [A:poly_poly_real]: ((! [B:poly_real]: ((poly_poly_real2 @ A @ B) = zero_zero_poly_real)) = (A = zero_z1423781445y_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_poly__all__0__iff__0)).
% 22.01/6.08 thf(273,plain,((! [A:poly_poly_real]: ((! [B:poly_real]: ((poly_poly_real2 @ A @ B) = zero_zero_poly_real)) = (A = zero_z1423781445y_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 22.01/6.08 thf(48,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_order__subst1)).
% 22.01/6.08 thf(422,plain,((! [A:nat,B:(real > nat),C:real,D:real]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
% 22.01/6.08 thf(134,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ zero_zero_nat)) => (? [C:nat]: ((ord_less_eq_nat @ C @ B) & ! [D:nat]: ((ord_less_nat @ D @ C) => (~ (A @ D))) & (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_ex__least__nat__le)).
% 22.01/6.08 thf(790,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ zero_zero_nat)) => (? [C:nat]: ((ord_less_eq_nat @ C @ B) & ! [D:nat]: ((ord_less_nat @ D @ C) => (~ (A @ D))) & (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
% 22.01/6.08 thf(169,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_bot__nat__0_Onot__eq__extremum)).
% 22.01/6.08 thf(918,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
% 22.01/6.08 thf(136,axiom,((! [A:nat]: ((A != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_gr0I)).
% 22.01/6.08 thf(807,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])).
% 22.01/6.08 thf(254,axiom,(((ord_less_real @ zero_zero_real @ (poly_real2 @ p @ x)) => (sturm_469514713_r_pos @ p @ x))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062)).
% 22.01/6.08 thf(1288,plain,(((ord_less_real @ zero_zero_real @ (poly_real2 @ p @ x)) => (sturm_469514713_r_pos @ p @ x))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])).
% 22.01/6.08 thf(218,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_order_Oasym)).
% 22.01/6.08 thf(1165,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
% 22.01/6.08 thf(175,axiom,((! [A:nat,B:nat]: ((A != B) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_neqE)).
% 22.01/6.08 thf(955,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
% 22.01/6.08 thf(46,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_eq__refl)).
% 22.01/6.08 thf(415,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
% 22.01/6.08 thf(116,axiom,((ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_le__numeral__extra_I3_J)).
% 22.01/6.08 thf(728,plain,((ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
% 22.01/6.08 thf(238,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_ord__eq__less__subst)).
% 22.01/6.08 thf(1236,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
% 22.01/6.08 thf(55,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_order__class_Oorder_Oantisym)).
% 22.01/6.08 thf(464,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
% 22.01/6.08 thf(247,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((A != B) => (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_linorder__cases)).
% 22.01/6.08 thf(1268,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((~ (A = B)) => (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
% 22.01/6.08 thf(96,axiom,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_less__numeral__extra_I3_J)).
% 22.01/6.08 thf(644,plain,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
% 22.01/6.08 thf(140,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_gr__implies__not__zero)).
% 22.01/6.08 thf(822,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
% 22.01/6.08 thf(256,axiom,((ord_less_eq_real @ zero_zero_real @ zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_le__numeral__extra_I3_J)).
% 22.01/6.08 thf(1299,plain,((ord_less_eq_real @ zero_zero_real @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])).
% 22.01/6.08 thf(108,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_antisym__conv)).
% 22.01/6.08 thf(691,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
% 22.01/6.08 thf(155,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_less__imp__not__eq2)).
% 22.01/6.08 thf(871,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
% 22.01/6.08 thf(62,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) | (A = B)) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_less__or__eq__imp__le)).
% 22.01/6.08 thf(501,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) | (A = B)) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
% 22.01/6.08 thf(199,axiom,(((sturm_469514713_r_pos @ p @ x) => (ord_less_real @ zero_zero_real @ (poly_real2 @ p @ x)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062)).
% 22.01/6.08 thf(1093,plain,(((sturm_469514713_r_pos @ p @ x) => (ord_less_real @ zero_zero_real @ (poly_real2 @ p @ x)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])).
% 22.01/6.08 thf(146,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_not__less__zero)).
% 22.01/6.08 thf(839,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
% 22.01/6.08 thf(213,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((~ (ord_less_real @ B @ A)) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_antisym__conv3)).
% 22.01/6.08 thf(1152,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((~ (ord_less_real @ B @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
% 22.01/6.08 thf(49,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_le__SucE)).
% 22.01/6.08 thf(427,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
% 22.01/6.08 thf(165,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_dual__order_Ostrict__trans)).
% 22.01/6.08 thf(908,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
% 22.01/6.08 thf(182,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_infinite__descent)).
% 22.01/6.08 thf(992,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
% 22.01/6.08 thf(23,axiom,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_lessI)).
% 22.01/6.08 thf(337,plain,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 22.01/6.08 thf(57,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((ord_less_eq_nat @ A @ B) | (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_le__Suc__eq)).
% 22.01/6.08 thf(469,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((ord_less_eq_nat @ A @ B) | (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
% 22.01/6.08 thf(30,axiom,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_le__numeral__extra_I3_J)).
% 22.01/6.08 thf(354,plain,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 22.01/6.08 thf(15,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_dual__order_Oantisym)).
% 22.01/6.08 thf(309,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 22.01/6.08 thf(86,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_Nat_Oex__has__greatest__nat)).
% 22.01/6.08 thf(592,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
% 22.01/6.08 thf(60,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_order__refl)).
% 22.01/6.08 thf(496,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
% 22.01/6.08 thf(186,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zero__less__iff__neq__zero)).
% 22.01/6.08 thf(1014,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])).
% 22.01/6.08 thf(1337,plain,(($false)),inference(e,[status(thm)],[1036,846,333,893,1315,962,481,777,555,762,1305,861,1173,1290,276,878,655,1137,472,1233,814,1260,930,670,1196,898,1001,782,301,565,1254,1095,404,719,785,702,344,1279,1059,934,357,559,638,1087,1247,284,881,316,261,817,902,321,376,646,937,1183,905,734,774,411,1201,1104,507,527,312,292,1206,270,661,810,349,630,788,729,1042,952,435,665,830,682,551,842,1012,1106,916,467,697,1017,615,1121,1111,725,989,884,1160,339,1155,679,1039,970,393,1263,911,371,622,837,1150,1249,633,921,1054,1170,398,1071,1167,530,1185,750,1251,1273,264,856,279,573,513,430,562,694,732,958,413,875,826,641,1271,1312,498,335,1090,804,1258,391,1139,1209,406,1282,419,736,1080,858,535,1162,964,1177,330,462,1198,1213,1245,780,608,1113,438,658,685,521,267,851,722,675,548,374,516,342,355,754,553,1049,1203,589,580,282,1225,739,1230,557,1003,1300,359,1130,1285,1220,1141,613,314,571,627,539,1157,688,524,759,1189,771,368,844,1276,699,304,1062,351,401,896,748,568,914,510,1193,832,346,287,1116,1133,447,967,835,854,273,422,790,918,807,1288,1165,955,415,728,1236,464,1268,644,822,1299,691,871,501,1093,839,1152,427,908,992,337,469,354,309,592,496,1014])).
% 22.01/6.08 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.01/6.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------