0.00/0.00 % Leo-III: Strategy 1 (for '60') 8.12/6.53 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 8.12/6.53 % [INFO] Parsing done (241ms). 8.12/6.53 % [INFO] Running in sequential loop mode. 8.12/6.53 % [CONFIG] Using configuration: timeout(60) with strategy 8.12/6.53 % [INFO] eprover registered as external prover. 8.12/6.53 % [INFO] cvc4 registered as external prover. 8.12/6.53 % [INFO] Parsing finished. Scanning for conjecture ... 8.12/6.53 % [INFO] Found a conjecture and 345 axioms. Running axiom selection ... 8.12/6.53 % [INFO] Axiom selection finished. Selected 135 axioms (removed 210 axioms). 8.12/6.53 % [INFO] Problem is higher-order (TPTP THF). 8.12/6.53 % [INFO] Type checking passed. Searching for refutation ... 8.12/6.53 % External prover 'e' found a proof! 8.12/6.53 % [INFO] Killing All external provers ... 8.12/6.53 % Time passed: 2119ms (effective reasoning time: 1534ms) 8.12/6.53 % Solved by strategy 8.12/6.53 % Axioms used in derivation (135): fact_82_le__cases3, fact_112_zero__le__dist, fact_120_dual__order_Ostrict__iff__order, fact_261_lt__ex, fact_240_less__irrefl, fact_293_UNIV__eq__I, fact_225_less__imp__not__eq2, fact_284_prod__cases, fact_297_closure__UNIV, fact_136_order_Ostrict__trans2, fact_84_antisym__conv, fact_116_order_Onot__eq__order__implies__strict, fact_236_ord__less__eq__trans, fact_194_top_Oextremum__unique, fact_18_top__prod__def, fact_140_not__le__imp__less, fact_290_UNIV__witness, fact_262_order__less__subst2, fact_144_le__imp__less__or__eq, fact_2_xy, fact_170_order__less__le__subst1, fact_105_Collect__mem__eq, fact_115_top__set__def, fact_102_mem__Collect__eq, fact_78_le__cases, fact_37_metric__eq__thm, fact_210_dual__order_Ostrict__trans, fact_38_order__refl, fact_212_linorder__less__wlog, fact_70_eq__iff, fact_15_top__prod__def, fact_295_closure__UNIV, fact_248_less__asym, fact_270_ord__less__eq__subst, fact_76_eq__refl, fact_154_less__imp__le, fact_252_dense, fact_53_order__subst2, fact_253_order_Oasym, fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062, fact_86_order__class_Oorder_Oeq__iff, fact_108_dual__order_Oeq__iff, fact_286_surj__pair, fact_24_top_Oextremum__strict, fact_202_dist__not__less__zero, fact_215_less__imp__not__less, fact_227_antisym__conv3, fact_92_order__class_Oorder_Oantisym, fact_94_order__trans, fact_230_less__not__sym, fact_146_le__less__linear, fact_49_order__subst1, fact_96_dual__order_Orefl, fact_148_dense__le, fact_206_order_Ostrict__implies__not__eq, fact_282_Pair__inject, fact_255_neq__iff, fact_232_less__imp__not__eq, fact_158_antisym__conv1, fact_20_top__prod__def, fact_34_epigraph__mono, fact_149_dense__ge, fact_204_dual__order_Ostrict__implies__not__eq, fact_12_old_Oprod_Oinject, fact_100_dual__order_Otrans, fact_182_less__le, fact_190_top_Oextremum__uniqueI, fact_1__092_060open_0620_A_060_Ae_092_060close_062, fact_203_dist__pos__lt, fact_122_dual__order_Oorder__iff__strict, fact_186_leI, fact_152_le__less__trans, fact_178_order__le__less__subst1, fact_132_order_Ostrict__iff__order, fact_223_less__imp__triv, fact_162_not__less, fact_257_neqE, fact_238_ord__eq__less__trans, fact_250_less__imp__neq, fact_80_order_Otrans, fact_150_less__le__trans, fact_166_order__less__le__subst2, fact_280_old_Oprod_Oexhaust, fact_118_dual__order_Ostrict__implies__order, fact_134_order_Oorder__iff__strict, fact_16_top__prod__def, fact_124_order_Ostrict__implies__order, fact_188_leD, fact_13_dist__commute__lessI, fact_208_not__less__iff__gr__or__eq, fact_266_order__less__subst1, fact_48_zero__less__dist__iff, fact_22_top__prod__def, fact_62_ord__eq__le__subst, fact_6_iso__tuple__UNIV__I, fact_88_ord__eq__le__trans, fact_110_dual__order_Oantisym, fact_278_old_Oprod_Oinducts, fact_142_less__le__not__le, fact_184_le__less, fact_294_dist__commute, fact_221_linorder__cases, fact_45_dist__eq__0__iff, fact_259_gt__ex, fact_160_le__neq__trans, fact_138_order_Ostrict__trans1, fact_128_dual__order_Ostrict__trans2, fact_342_less__eq__real__def, fact_217_order_Ostrict__trans, fact_126_dense__le__bounded, fact_234_dual__order_Oasym, fact_198_top__greatest, fact_274_ord__eq__less__subst, fact_98_linorder__wlog, fact_3_UNIV__I, fact_174_order__le__less__subst2, fact_219_dual__order_Oirrefl, fact_300_closure__approachable__le, fact_164_not__le, fact_242_less__linear, fact_72_antisym, fact_244_less__trans, fact_66_ord__le__eq__subst, fact_47_dist__le__zero__iff, fact_10_prod_Oinject, conj_0, fact_46_dist__self, fact_74_linear, fact_130_dual__order_Ostrict__trans1, fact_246_less__asym_H, fact_156_antisym__conv2, fact_127_dense__ge__bounded, fact_28_top_Onot__eq__extremum, fact_113_top__set__def, fact_90_ord__le__eq__trans 8.12/6.53 % No. of inferences in proof: 274 8.12/6.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2119 ms resp. 1534 ms w/o parsing 8.12/6.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 8.12/6.53 thf(produc2021989178_set_a_type, type, produc2021989178_set_a: $tType). 8.12/6.53 thf(produc211508562a_real_type, type, produc211508562a_real: $tType). 8.12/6.53 thf(produc1312517202t_real_type, type, produc1312517202t_real: $tType). 8.12/6.53 thf(produc304417648_set_a_type, type, produc304417648_set_a: $tType). 8.12/6.53 thf(produc509513372a_real_type, type, produc509513372a_real: $tType). 8.12/6.53 thf(produc25772804_set_a_type, type, produc25772804_set_a: $tType). 8.12/6.53 thf(set_Pr1158285382l_real_type, type, set_Pr1158285382l_real: $tType). 8.12/6.53 thf(produc792423270l_real_type, type, produc792423270l_real: $tType). 8.12/6.53 thf(produc1931999653t_real_type, type, produc1931999653t_real: $tType). 8.12/6.53 thf(produc232195311t_real_type, type, produc232195311t_real: $tType). 8.12/6.53 thf(produc1350454001_set_a_type, type, produc1350454001_set_a: $tType). 8.12/6.53 thf(set_Pr147102617l_real_type, type, set_Pr147102617l_real: $tType). 8.12/6.53 thf(produc1691597095_set_a_type, type, produc1691597095_set_a: $tType). 8.12/6.53 thf(set_Pr1928503567a_real_type, type, set_Pr1928503567a_real: $tType). 8.12/6.53 thf(produc957004601l_real_type, type, produc957004601l_real: $tType). 8.12/6.53 thf(produc581916509al_nat_type, type, produc581916509al_nat: $tType). 8.12/6.53 thf(produc845587165t_real_type, type, produc845587165t_real: $tType). 8.12/6.53 thf(product_prod_nat_nat_type, type, product_prod_nat_nat: $tType). 8.12/6.53 thf(product_prod_a_real_type, type, product_prod_a_real: $tType). 8.12/6.53 thf(set_real_type, type, set_real: $tType). 8.12/6.53 thf(extended_ereal_type, type, extended_ereal: $tType). 8.12/6.53 thf(set_a_type, type, set_a: $tType). 8.12/6.53 thf(real_type, type, real: $tType). 8.12/6.53 thf(nat_type, type, nat: $tType). 8.12/6.53 thf(a_type, type, a: $tType). 8.12/6.53 thf(elemen1695521870a_real_type, type, elemen1695521870a_real: (set_Pr1928503567a_real > set_Pr1928503567a_real)). 8.12/6.53 thf(elementary_closure_a_type, type, elementary_closure_a: (set_a > set_a)). 8.12/6.53 thf(zero_zero_real_type, type, zero_zero_real: real). 8.12/6.53 thf(lower_930854854raph_a_type, type, lower_930854854raph_a: (set_a > ((a > extended_ereal) > set_Pr1928503567a_real))). 8.12/6.53 thf(ord_less_real_type, type, ord_less_real: (real > (real > $o))). 8.12/6.53 thf(ord_less_set_a_type, type, ord_less_set_a: (set_a > (set_a > $o))). 8.12/6.53 thf(ord_less_eq_real_type, type, ord_less_eq_real: (real > (real > $o))). 8.12/6.53 thf(ord_less_eq_set_a_type, type, ord_less_eq_set_a: (set_a > (set_a > $o))). 8.12/6.53 thf(top_to1567080838real_o_type, type, top_to1567080838real_o: (product_prod_a_real > $o)). 8.12/6.53 thf(top_top_a_o_type, type, top_top_a_o: (a > $o)). 8.12/6.53 thf(top_to345582004_set_a_type, type, top_to345582004_set_a: produc25772804_set_a). 8.12/6.53 thf(top_to1153982881_set_a_type, type, top_to1153982881_set_a: produc1350454001_set_a). 8.12/6.53 thf(top_to724687040_set_a_type, type, top_to724687040_set_a: produc304417648_set_a). 8.12/6.53 thf(top_to829322572a_real_type, type, top_to829322572a_real: produc509513372a_real). 8.12/6.53 thf(top_to35724191t_real_type, type, top_to35724191t_real: produc232195311t_real). 8.12/6.53 thf(top_to1477940855_set_a_type, type, top_to1477940855_set_a: produc1691597095_set_a). 8.12/6.53 thf(top_to2138011583a_real_type, type, top_to2138011583a_real: set_Pr1928503567a_real). 8.12/6.53 thf(top_top_set_real_type, type, top_top_set_real: set_real). 8.12/6.53 thf(top_top_set_a_type, type, top_top_set_a: set_a). 8.12/6.53 thf(produc1220567734_set_a_type, type, produc1220567734_set_a: (set_Pr1928503567a_real > (set_a > produc25772804_set_a))). 8.12/6.53 thf(produc190993315_set_a_type, type, produc190993315_set_a: (set_real > (set_a > produc1350454001_set_a))). 8.12/6.53 thf(produc272677600_set_a_type, type, produc272677600_set_a: (set_a > (produc1691597095_set_a > produc304417648_set_a))). 8.12/6.53 thf(produc383769494a_real_type, type, produc383769494a_real: (set_a > (set_Pr1928503567a_real > produc509513372a_real))). 8.12/6.53 thf(produc1266579561t_real_type, type, produc1266579561t_real: (set_a > (set_real > produc232195311t_real))). 8.12/6.53 thf(product_Pair_a_real_type, type, product_Pair_a_real: (a > (real > product_prod_a_real))). 8.12/6.53 thf(real_V404783528a_real_type, type, real_V404783528a_real: (product_prod_a_real > (product_prod_a_real > real))). 8.12/6.53 thf(collec1714955950a_real_type, type, collec1714955950a_real: ((product_prod_a_real > $o) > set_Pr1928503567a_real)). 8.12/6.53 thf(collect_a_type, type, collect_a: ((a > $o) > set_a)). 8.12/6.53 thf(member1103263856a_real_type, type, member1103263856a_real: (product_prod_a_real > (set_Pr1928503567a_real > $o))). 8.12/6.53 thf(e_type, type, e: real). 8.12/6.53 thf(f_type, type, f: (a > extended_ereal)). 8.12/6.53 thf(thesis_type, type, thesis: $o). 8.12/6.53 thf(x_type, type, x: a). 8.12/6.53 thf(y_type, type, y: real). 8.12/6.53 thf(z_type, type, z: real). 8.12/6.53 thf(77,axiom,((! [A:set_a]: ~ (ord_less_set_a @ top_top_set_a @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_top_Oextremum__strict)). 8.12/6.53 thf(385,plain,((! [A:set_a]: ~ (ord_less_set_a @ top_top_set_a @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 8.12/6.53 thf(134,axiom,((top_to724687040_set_a = (produc272677600_set_a @ top_top_set_a @ top_to1477940855_set_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_top__prod__def)). 8.12/6.53 thf(565,plain,((top_to724687040_set_a = (produc272677600_set_a @ top_top_set_a @ top_to1477940855_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 8.12/6.53 thf(82,axiom,(((member1103263856a_real @ (product_Pair_a_real @ x @ y) @ (elemen1695521870a_real @ (lower_930854854raph_a @ top_top_set_a @ f))) & (ord_less_eq_real @ y @ z))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_xy)). 8.12/6.53 thf(397,plain,(((member1103263856a_real @ (product_Pair_a_real @ x @ y) @ (elemen1695521870a_real @ (lower_930854854raph_a @ top_top_set_a @ (f)))) & (ord_less_eq_real @ y @ z))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 8.12/6.53 thf(106,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_gt__ex)). 8.12/6.53 thf(479,plain,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 8.12/6.53 thf(120,axiom,((! [A:real,B:real]: ((B != A) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_dual__order_Ostrict__implies__not__eq)). 8.12/6.53 thf(518,plain,((! [A:real,B:real]: (~ (B = A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 8.12/6.53 thf(102,axiom,((! [A:real,B:real]: ((A != B) = ((ord_less_real @ B @ A) | (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_neq__iff)). 8.12/6.53 thf(468,plain,((! [A:real,B:real]: ((~ (A = B)) = ((ord_less_real @ B @ A) | (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 8.12/6.53 thf(107,axiom,((! [A:set_a]: ((A != top_top_set_a) = (ord_less_set_a @ A @ top_top_set_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_top_Onot__eq__extremum)). 8.12/6.53 thf(481,plain,((! [A:set_a]: ((~ (A = top_top_set_a)) = (ord_less_set_a @ A @ top_top_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 8.12/6.53 thf(75,axiom,((! [A:product_prod_a_real,B:product_prod_a_real,C:real]: ((ord_less_real @ (real_V404783528a_real @ B @ A) @ C) <= (ord_less_real @ (real_V404783528a_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_dist__commute__lessI)). 8.12/6.53 thf(365,plain,((! [A:product_prod_a_real,B:product_prod_a_real,C:real]: ((ord_less_real @ (real_V404783528a_real @ B @ A) @ C) | ~ (ord_less_real @ (real_V404783528a_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 8.12/6.53 thf(1,conjecture,(thesis),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)). 8.12/6.53 thf(2,negated_conjecture,(~ (thesis)),inference(neg_conjecture,[status(cth)],[1])). 8.12/6.53 thf(138,plain,(~ (thesis)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 8.12/6.53 thf(40,axiom,((! [A:real,B:real]: (((A = B) <= (ord_less_eq_real @ B @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_antisym)). 8.12/6.53 thf(247,plain,((! [A:real,B:real]: ((A = B) | ~ (ord_less_eq_real @ B @ A) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 8.12/6.53 thf(26,axiom,((! [A:product_prod_a_real,B:set_Pr1928503567a_real]: ((member1103263856a_real @ A @ (elemen1695521870a_real @ B)) = (! [C:real]: ((ord_less_real @ zero_zero_real @ C) => (? [D:product_prod_a_real]: ((member1103263856a_real @ D @ B) & (ord_less_eq_real @ (real_V404783528a_real @ D @ A) @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_closure__approachable__le)). 8.12/6.53 thf(202,plain,((! [A:product_prod_a_real,B:set_Pr1928503567a_real]: ((member1103263856a_real @ A @ (elemen1695521870a_real @ B)) = (! [C:real]: ((ord_less_real @ zero_zero_real @ C) => (? [D:product_prod_a_real]: ((member1103263856a_real @ D @ B) & (ord_less_eq_real @ (real_V404783528a_real @ D @ A) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 8.12/6.53 thf(19,axiom,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_eq__refl)). 8.12/6.53 thf(184,plain,((! [A:real,B:real]: ((A = B) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 8.12/6.53 thf(72,axiom,((! [A:real,B:real]: (((ord_less_real @ A @ B) <= (A != B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_le__neq__trans)). 8.12/6.53 thf(357,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 8.12/6.53 thf(127,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_less__imp__not__eq)). 8.12/6.53 thf(542,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 8.12/6.53 thf(89,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((((C @ B) = D) => ((ord_less_real @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_real @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_ord__less__eq__subst)). 8.12/6.53 thf(421,plain,((! [A:real,B:real,C:(real > real),D:real]: ((((C @ B) = D) => ((ord_less_real @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_real @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 8.12/6.53 thf(7,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_less__le__trans)). 8.12/6.53 thf(152,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 8.12/6.53 thf(35,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ A) => (ord_less_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_dual__order_Ostrict__trans1)). 8.12/6.53 thf(228,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ A) => (ord_less_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 8.12/6.53 thf(51,axiom,(((elemen1695521870a_real @ top_to2138011583a_real) = top_to2138011583a_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_closure__UNIV)). 8.12/6.53 thf(289,plain,(((elemen1695521870a_real @ top_to2138011583a_real) = top_to2138011583a_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 8.12/6.53 thf(95,axiom,((! [A:real,B:real]: ((ord_less_real @ B @ A) | (A = B) | (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_less__linear)). 8.12/6.53 thf(448,plain,((! [A:real,B:real]: ((ord_less_real @ B @ A) | (A = B) | (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 8.12/6.53 thf(61,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_le__less)). 8.12/6.53 thf(316,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 8.12/6.53 thf(31,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_order_Oorder__iff__strict)). 8.12/6.53 thf(216,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 8.12/6.53 thf(111,axiom,((ord_less_real @ zero_zero_real @ e)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_0620_A_060_Ae_092_060close_062)). 8.12/6.53 thf(492,plain,((ord_less_real @ zero_zero_real @ e)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 8.12/6.53 thf(42,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ A @ C) <= (ord_less_real @ B @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_order_Ostrict__trans1)). 8.12/6.53 thf(253,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ C) | ~ (ord_less_real @ B @ C) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 8.12/6.53 thf(70,axiom,((? [A:product_prod_a_real]: (member1103263856a_real @ A @ top_to2138011583a_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_UNIV__witness)). 8.12/6.53 thf(353,plain,((? [A:product_prod_a_real]: (member1103263856a_real @ A @ top_to2138011583a_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 8.12/6.53 thf(118,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_less__irrefl)). 8.12/6.53 thf(512,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 8.12/6.53 thf(123,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_dual__order_Oirrefl)). 8.12/6.53 thf(529,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 8.12/6.53 thf(128,axiom,((! [A:(product_prod_a_real > $o),B:product_prod_a_real]: ((A @ B) <= (! [C:a,D:real]: (A @ (product_Pair_a_real @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_prod__cases)). 8.12/6.53 thf(546,plain,((! [A:(product_prod_a_real > $o),B:product_prod_a_real]: ((A @ B) | ~ (! [C:a,D:real]: (A @ (product_Pair_a_real @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 8.12/6.53 thf(33,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_not__le)). 8.12/6.53 thf(220,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 8.12/6.53 thf(64,axiom,((ord_less_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_142_less__le__not__le)). 8.12/6.53 thf(334,plain,(((ord_less_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)],[64])). 8.12/6.53 thf(57,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ A @ C) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_order_Otrans)). 8.12/6.53 thf(302,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ A @ C) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 8.12/6.53 thf(45,axiom,((! [A:real,B:real,C:real]: (((~ (ord_less_eq_real @ B @ C)) <= (ord_less_eq_real @ A @ B)) => (((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 @ A @ B)) <= (ord_less_eq_real @ C @ A))) <= ((~ (ord_less_eq_real @ C @ A)) <= (ord_less_eq_real @ B @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_le__cases3)). 8.12/6.53 thf(260,plain,((! [A:real,B:real,C:real]: ((~ (ord_less_eq_real @ B @ C) | ~ (ord_less_eq_real @ A @ B)) => (((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 @ A @ B) | ~ (ord_less_eq_real @ C @ A)) | ~ (~ (ord_less_eq_real @ C @ A) | ~ (ord_less_eq_real @ B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 8.12/6.53 thf(85,axiom,((! [A:a,B:real,C:(a > extended_ereal),D:real]: ((member1103263856a_real @ (product_Pair_a_real @ A @ D) @ (lower_930854854raph_a @ top_top_set_a @ C)) <= ((ord_less_eq_real @ B @ D) & (member1103263856a_real @ (product_Pair_a_real @ A @ B) @ (lower_930854854raph_a @ top_top_set_a @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_epigraph__mono)). 8.12/6.53 thf(407,plain,((! [A:a,B:real,C:(a > extended_ereal),D:real]: ((member1103263856a_real @ (product_Pair_a_real @ A @ D) @ (lower_930854854raph_a @ top_top_set_a @ (C))) | ~ ((ord_less_eq_real @ B @ D) & (member1103263856a_real @ (product_Pair_a_real @ A @ B) @ (lower_930854854raph_a @ top_top_set_a @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 8.12/6.53 thf(90,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_208_not__less__iff__gr__or__eq)). 8.12/6.53 thf(429,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)],[90])). 8.12/6.53 thf(108,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_less__asym_H)). 8.12/6.53 thf(484,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 8.12/6.53 thf(24,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((B = A) | (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_dual__order_Oorder__iff__strict)). 8.12/6.53 thf(197,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((B = A) | (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 8.12/6.53 thf(121,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ B) <= (ord_less_real @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_dual__order_Ostrict__trans)). 8.12/6.53 thf(522,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ B) | ~ (ord_less_real @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 8.12/6.53 thf(112,axiom,((! [A:product_prod_a_real,B:set_Pr1928503567a_real,C:product_prod_a_real]: ((((A = C) = (! [D:product_prod_a_real]: (((real_V404783528a_real @ A @ D) = (real_V404783528a_real @ C @ D)) <= (member1103263856a_real @ D @ B)))) <= (member1103263856a_real @ C @ B)) <= (member1103263856a_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_metric__eq__thm)). 8.12/6.53 thf(493,plain,((! [A:product_prod_a_real,B:set_Pr1928503567a_real,C:product_prod_a_real]: (((A = C) = (! [D:product_prod_a_real]: (((real_V404783528a_real @ A @ D) = (real_V404783528a_real @ C @ D)) | ~ (member1103263856a_real @ D @ B)))) | ~ (member1103263856a_real @ C @ B) | ~ (member1103263856a_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 8.12/6.53 thf(20,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_78_le__cases)). 8.12/6.53 thf(188,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)],[20])). 8.12/6.53 thf(78,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_lt__ex)). 8.12/6.53 thf(388,plain,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 8.12/6.53 thf(4,axiom,((! [A:real,B:real]: (((A = B) | (ord_less_real @ A @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_le__imp__less__or__eq)). 8.12/6.53 thf(141,plain,((! [A:real,B:real]: ((A = B) | (ord_less_real @ A @ B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 8.12/6.53 thf(114,axiom,((! [A:product_prod_a_real,B:(product_prod_a_real > $o)]: ((member1103263856a_real @ A @ (collec1714955950a_real @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_mem__Collect__eq)). 8.12/6.53 thf(499,plain,((! [A:product_prod_a_real,B:(product_prod_a_real > $o)]: ((member1103263856a_real @ A @ (collec1714955950a_real @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 8.12/6.53 thf(66,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_real @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_order__less__le__subst2)). 8.12/6.53 thf(339,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_real @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 8.12/6.53 thf(110,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_257_neqE)). 8.12/6.53 thf(489,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)],[110])). 8.12/6.53 thf(103,axiom,((! [A:set_a]: (ord_less_eq_set_a @ A @ top_top_set_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_top__greatest)). 8.12/6.53 thf(471,plain,((! [A:set_a]: (ord_less_eq_set_a @ A @ top_top_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 8.12/6.53 thf(43,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_not__le__imp__less)). 8.12/6.53 thf(256,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 8.12/6.53 thf(22,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_order_Ostrict__implies__order)). 8.12/6.53 thf(193,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 8.12/6.53 thf(126,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_ord__less__eq__trans)). 8.12/6.53 thf(537,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 8.12/6.53 thf(80,axiom,((top_to829322572a_real = (produc383769494a_real @ top_top_set_a @ top_to2138011583a_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_top__prod__def)). 8.12/6.53 thf(393,plain,((top_to829322572a_real = (produc383769494a_real @ top_top_set_a @ top_to2138011583a_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 8.12/6.53 thf(119,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (ord_less_real @ A @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_order_Ostrict__trans)). 8.12/6.53 thf(515,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (ord_less_real @ A @ C)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 8.12/6.53 thf(98,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_order_Oasym)). 8.12/6.53 thf(457,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 8.12/6.53 thf(15,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((~ (ord_less_real @ A @ B)) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_antisym__conv2)). 8.12/6.53 thf(173,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((~ (ord_less_real @ A @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 8.12/6.53 thf(136,axiom,((! [A:real,B:real]: ((A != B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_order_Ostrict__implies__not__eq)). 8.12/6.53 thf(569,plain,((! [A:real,B:real]: (~ (A = B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 8.12/6.53 thf(67,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) => (B = A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_dual__order_Oantisym)). 8.12/6.53 thf(343,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) => (B = A)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 8.12/6.53 thf(39,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_not__less)). 8.12/6.53 thf(244,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 8.12/6.53 thf(73,axiom,((top_top_set_a = (collect_a @ top_top_a_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_top__set__def)). 8.12/6.53 thf(360,plain,((top_top_set_a = (collect_a @ (top_top_a_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 8.12/6.53 thf(27,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_order__refl)). 8.12/6.53 thf(205,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 8.12/6.53 thf(117,axiom,((! [A:product_prod_a_real]: ~ (! [B:a,C:real]: (A != (product_Pair_a_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_old_Oprod_Oexhaust)). 8.12/6.53 thf(508,plain,((! [A:product_prod_a_real]: ~ (! [B:a,C:real]: ~ (A = (product_Pair_a_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 8.12/6.53 thf(55,axiom,((! [A:product_prod_a_real]: (member1103263856a_real @ A @ top_to2138011583a_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_UNIV__I)). 8.12/6.53 thf(298,plain,((! [A:product_prod_a_real]: (member1103263856a_real @ A @ top_to2138011583a_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 8.12/6.53 thf(87,axiom,((! [A:a,B:real,C:a,D:real]: ((~ ((A = C) => (B != D))) <= ((product_Pair_a_real @ A @ B) = (product_Pair_a_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_Pair__inject)). 8.12/6.53 thf(412,plain,((! [A:a,B:real,C:a,D:real]: (~ ((A = C) => (~ (B = D))) | ~ ((product_Pair_a_real @ A @ B) = (product_Pair_a_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 8.12/6.53 thf(12,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_leI)). 8.12/6.53 thf(166,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 8.12/6.53 thf(6,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_order__le__less__subst2)). 8.12/6.53 thf(148,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 8.12/6.53 thf(10,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_86_order__class_Oorder_Oeq__iff)). 8.12/6.53 thf(161,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)],[10])). 8.12/6.53 thf(137,axiom,((! [A:a,B:real]: (((member1103263856a_real @ (product_Pair_a_real @ A @ B) @ (lower_930854854raph_a @ top_top_set_a @ f)) & (ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ A @ B) @ (product_Pair_a_real @ x @ y)) @ e)) => (thesis)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 8.12/6.53 thf(573,plain,((! [A:a,B:real]: (((member1103263856a_real @ (product_Pair_a_real @ A @ B) @ (lower_930854854raph_a @ top_top_set_a @ (f))) & (ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ A @ B) @ (product_Pair_a_real @ x @ y)) @ e)) => (thesis)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 8.12/6.53 thf(54,axiom,((! [A:product_prod_a_real,B:product_prod_a_real]: (ord_less_eq_real @ zero_zero_real @ (real_V404783528a_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_zero__le__dist)). 8.12/6.53 thf(296,plain,((! [A:product_prod_a_real,B:product_prod_a_real]: (ord_less_eq_real @ zero_zero_real @ (real_V404783528a_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 8.12/6.53 thf(133,axiom,((! [A:set_a]: ((ord_less_eq_set_a @ top_top_set_a @ A) = (A = top_top_set_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_top_Oextremum__unique)). 8.12/6.53 thf(562,plain,((! [A:set_a]: ((ord_less_eq_set_a @ top_top_set_a @ A) = (A = top_top_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 8.12/6.53 thf(16,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_leD)). 8.12/6.53 thf(176,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 8.12/6.53 thf(84,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_238_ord__eq__less__trans)). 8.12/6.53 thf(402,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)],[84])). 8.12/6.53 thf(52,axiom,((! [A:real,B:real]: ((! [C:real]: ((ord_less_real @ A @ C) => (ord_less_eq_real @ B @ C))) => (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_dense__ge)). 8.12/6.53 thf(291,plain,((! [A:real,B:real]: ((! [C:real]: ((ord_less_real @ A @ C) => (ord_less_eq_real @ B @ C))) => (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 8.12/6.53 thf(48,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_less__imp__le)). 8.12/6.53 thf(281,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 8.12/6.53 thf(94,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (? [C:real]: ((ord_less_real @ C @ B) & (ord_less_real @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_dense)). 8.12/6.53 thf(445,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (? [C:real]: ((ord_less_real @ C @ B) & (ord_less_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 8.12/6.53 thf(60,axiom,((! [A:set_Pr1928503567a_real]: ((top_to2138011583a_real = A) <= (! [B:product_prod_a_real]: (member1103263856a_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_UNIV__eq__I)). 8.12/6.53 thf(313,plain,((! [A:set_Pr1928503567a_real]: ((top_to2138011583a_real = A) | ~ (! [B:product_prod_a_real]: (member1103263856a_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 8.12/6.53 thf(5,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((ord_less_real @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_order__less__le__subst1)). 8.12/6.53 thf(144,plain,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_eq_real @ C @ D) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 8.12/6.53 thf(18,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (! [C:real]: ((ord_less_eq_real @ C @ B) <= (ord_less_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_dense__le)). 8.12/6.53 thf(181,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (! [C:real]: ((ord_less_eq_real @ C @ B) | ~ (ord_less_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 8.12/6.53 thf(46,axiom,((! [A:product_prod_a_real,B:product_prod_a_real]: ((ord_less_eq_real @ (real_V404783528a_real @ A @ B) @ zero_zero_real) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_dist__le__zero__iff)). 8.12/6.53 thf(274,plain,((! [A:product_prod_a_real,B:product_prod_a_real]: ((ord_less_eq_real @ (real_V404783528a_real @ A @ B) @ zero_zero_real) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 8.12/6.53 thf(88,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_dual__order_Oasym)). 8.12/6.53 thf(419,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 8.12/6.53 thf(62,axiom,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_ord__eq__le__subst)). 8.12/6.53 thf(318,plain,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_eq_real @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 8.12/6.53 thf(92,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_244_less__trans)). 8.12/6.53 thf(434,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)],[92])). 8.12/6.53 thf(74,axiom,((! [A:product_prod_a_real,B:product_prod_a_real]: ((A != B) => (ord_less_real @ zero_zero_real @ (real_V404783528a_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_dist__pos__lt)). 8.12/6.53 thf(362,plain,((! [A:product_prod_a_real,B:product_prod_a_real]: ((~ (A = B)) => (ord_less_real @ zero_zero_real @ (real_V404783528a_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 8.12/6.53 thf(96,axiom,((! [A:(product_prod_a_real > $o),B:product_prod_a_real]: ((! [C:a,D:real]: (A @ (product_Pair_a_real @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_old_Oprod_Oinducts)). 8.12/6.53 thf(451,plain,((! [A:(product_prod_a_real > $o),B:product_prod_a_real]: ((! [C:a,D:real]: (A @ (product_Pair_a_real @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 8.12/6.53 thf(135,axiom,((top_to345582004_set_a = (produc1220567734_set_a @ top_to2138011583a_real @ top_top_set_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_top__prod__def)). 8.12/6.53 thf(567,plain,((top_to345582004_set_a = (produc1220567734_set_a @ top_to2138011583a_real @ top_top_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 8.12/6.53 thf(105,axiom,((top_to1153982881_set_a = (produc190993315_set_a @ top_top_set_real @ top_top_set_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_top__prod__def)). 8.12/6.53 thf(477,plain,((top_to1153982881_set_a = (produc190993315_set_a @ top_top_set_real @ top_top_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 8.12/6.53 thf(76,axiom,((! [A:(real > (real > $o)),B:real,C:real]: ((((A @ B @ C) <= (! [D:real,E:real]: ((A @ D @ E) <= (A @ E @ D)))) <= (! [D:real]: (A @ D @ D))) <= (! [D:real,E:real]: ((A @ D @ E) <= (ord_less_real @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_linorder__less__wlog)). 8.12/6.53 thf(367,plain,((! [A:(real > (real > $o)),B:real,C:real]: ((A @ B @ C) | ~ (! [D:real,E:real]: ((A @ D @ E) | ~ (A @ E @ D))) | ~ (! [D:real]: (A @ D @ D)) | ~ (! [D:real,E:real]: ((A @ D @ E) | ~ (ord_less_real @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 8.12/6.53 thf(125,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_less__asym)). 8.12/6.53 thf(535,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 8.12/6.53 thf(8,axiom,((! [A:real,B:real]: ((A != B) => ((ord_less_eq_real @ A @ B) => (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_order_Onot__eq__order__implies__strict)). 8.12/6.53 thf(155,plain,((! [A:real,B:real]: ((~ (A = B)) => ((ord_less_eq_real @ A @ B) => (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 8.12/6.53 thf(100,axiom,((! [A:product_prod_a_real]: ? [B:a,C:real]: (A = (product_Pair_a_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_surj__pair)). 8.12/6.53 thf(462,plain,((! [A:product_prod_a_real]: ? [B:a,C:real]: (A = (product_Pair_a_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 8.12/6.53 thf(34,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ C) <= (B = C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_ord__le__eq__trans)). 8.12/6.53 thf(223,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ C) | ~ (B = C) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 8.12/6.53 thf(116,axiom,((! [A:a,B:real,C:a,D:real]: (((product_Pair_a_real @ A @ B) = (product_Pair_a_real @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_prod_Oinject)). 8.12/6.53 thf(505,plain,((! [A:a,B:real,C:a,D:real]: (((product_Pair_a_real @ A @ B) = (product_Pair_a_real @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 8.12/6.53 thf(38,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((ord_less_eq_real @ A @ B) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_antisym__conv1)). 8.12/6.53 thf(241,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((ord_less_eq_real @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 8.12/6.53 thf(104,axiom,((! [A:real,B:real]: ((B != A) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_less__imp__not__eq2)). 8.12/6.53 thf(473,plain,((! [A:real,B:real]: (~ (B = A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 8.12/6.53 thf(29,axiom,((! [A:real,B:real,C:real]: (((! [D:real]: ((ord_less_real @ A @ D) => ((ord_less_eq_real @ D @ C) <= (ord_less_real @ D @ B)))) => (ord_less_eq_real @ B @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_dense__le__bounded)). 8.12/6.53 thf(209,plain,((! [A:real,B:real,C:real]: (((! [D:real]: ((ord_less_real @ A @ D) => ((ord_less_eq_real @ D @ C) | ~ (ord_less_real @ D @ B)))) => (ord_less_eq_real @ B @ C)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 8.12/6.53 thf(71,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_108_dual__order_Oeq__iff)). 8.12/6.53 thf(355,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)],[71])). 8.12/6.53 thf(130,axiom,((! [A:set_a]: ((ord_less_eq_set_a @ top_top_set_a @ A) => (A = top_top_set_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_top_Oextremum__uniqueI)). 8.12/6.53 thf(553,plain,((! [A:set_a]: ((ord_less_eq_set_a @ top_top_set_a @ A) => (A = top_top_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 8.12/6.53 thf(122,axiom,((! [A:real,B:real]: ((A != B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_less__imp__neq)). 8.12/6.53 thf(525,plain,((! [A:real,B:real]: (~ (A = B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 8.12/6.53 thf(86,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_227_antisym__conv3)). 8.12/6.53 thf(409,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)],[86])). 8.12/6.53 thf(59,axiom,((! [A:product_prod_a_real,B:product_prod_a_real]: (((real_V404783528a_real @ A @ B) = zero_zero_real) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_dist__eq__0__iff)). 8.12/6.53 thf(310,plain,((! [A:product_prod_a_real,B:product_prod_a_real]: (((real_V404783528a_real @ A @ B) = zero_zero_real) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 8.12/6.53 thf(25,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ C @ A) => (ord_less_real @ C @ B)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_dual__order_Ostrict__trans2)). 8.12/6.53 thf(199,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ C @ A) => (ord_less_real @ C @ B)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 8.12/6.53 thf(115,axiom,((? [A:product_prod_a_real]: ((member1103263856a_real @ A @ (lower_930854854raph_a @ top_top_set_a @ f)) & (ord_less_real @ (real_V404783528a_real @ A @ (product_Pair_a_real @ x @ y)) @ e)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062)). 8.12/6.53 thf(502,plain,((? [A:product_prod_a_real]: ((member1103263856a_real @ A @ (lower_930854854raph_a @ top_top_set_a @ (f))) & (ord_less_real @ (real_V404783528a_real @ A @ (product_Pair_a_real @ x @ y)) @ e)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 8.12/6.53 thf(65,axiom,((! [A:product_prod_a_real]: ((real_V404783528a_real @ A @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_dist__self)). 8.12/6.53 thf(336,plain,((! [A:product_prod_a_real]: ((real_V404783528a_real @ A @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 8.12/6.53 thf(113,axiom,((real_V404783528a_real = (^ [A:product_prod_a_real,B:product_prod_a_real]: (real_V404783528a_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_dist__commute)). 8.12/6.53 thf(497,plain,(((real_V404783528a_real) = (^ [A:product_prod_a_real,B:product_prod_a_real]: (real_V404783528a_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 8.12/6.53 thf(131,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((((ord_less_real @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F))))) <= (ord_less_real @ (C @ B) @ D)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_order__less__subst2)). 8.12/6.53 thf(556,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) | ~ (ord_less_real @ (C @ B) @ D) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 8.12/6.53 thf(32,axiom,((! [A:real]: (ord_less_eq_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_dual__order_Orefl)). 8.12/6.53 thf(218,plain,((! [A:real]: (ord_less_eq_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 8.12/6.53 thf(41,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_92_order__class_Oorder_Oantisym)). 8.12/6.53 thf(250,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)],[41])). 8.12/6.53 thf(101,axiom,((! [A:product_prod_a_real,B:product_prod_a_real]: ((ord_less_real @ zero_zero_real @ (real_V404783528a_real @ A @ B)) = (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_zero__less__dist__iff)). 8.12/6.53 thf(465,plain,((! [A:product_prod_a_real,B:product_prod_a_real]: ((ord_less_real @ zero_zero_real @ (real_V404783528a_real @ A @ B)) = (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 8.12/6.53 thf(36,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_eq_real @ A @ (B @ C)) => (((ord_less_eq_real @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_real @ E @ F)))) <= (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_order__subst1)). 8.12/6.53 thf(231,plain,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_eq_real @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_real @ E @ F))) | ~ (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 8.12/6.53 thf(44,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_70_eq__iff)). 8.12/6.53 thf(258,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)],[44])). 8.12/6.53 thf(79,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_221_linorder__cases)). 8.12/6.53 thf(390,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)],[79])). 8.12/6.53 thf(14,axiom,((! [A:product_prod_a_real]: (member1103263856a_real @ A @ top_to2138011583a_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_iso__tuple__UNIV__I)). 8.12/6.53 thf(171,plain,((! [A:product_prod_a_real]: (member1103263856a_real @ A @ top_to2138011583a_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 8.12/6.53 thf(3,axiom,((ord_less_real = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_order_Ostrict__iff__order)). 8.12/6.53 thf(139,plain,(((ord_less_real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 8.12/6.53 thf(9,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_order_Ostrict__trans2)). 8.12/6.53 thf(158,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 8.12/6.53 thf(69,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) | (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_linear)). 8.12/6.53 thf(351,plain,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) | (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 8.12/6.53 thf(37,axiom,((! [A:(real > (real > $o)),B:real,C:real]: ((! [D:real,E:real]: ((ord_less_eq_real @ D @ E) => (A @ D @ E))) => ((A @ B @ C) <= (! [D:real,E:real]: ((A @ D @ E) <= (A @ E @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_linorder__wlog)). 8.12/6.53 thf(235,plain,((! [A:(real > (real > $o)),B:real,C:real]: ((! [D:real,E:real]: ((ord_less_eq_real @ D @ E) => (A @ D @ E))) => ((A @ B @ C) | ~ (! [D:real,E:real]: ((A @ D @ E) | ~ (A @ E @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 8.12/6.53 thf(28,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_less__eq__real__def)). 8.12/6.53 thf(207,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 8.12/6.53 thf(68,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_88_ord__eq__le__trans)). 8.12/6.53 thf(346,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)],[68])). 8.12/6.53 thf(129,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((((ord_less_real @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F)))) <= (ord_less_real @ C @ D)) <= (ord_less_real @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_order__less__subst1)). 8.12/6.53 thf(549,plain,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_real @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))) | ~ (ord_less_real @ C @ D) | ~ (ord_less_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 8.12/6.53 thf(30,axiom,((top_to2138011583a_real = (collec1714955950a_real @ top_to1567080838real_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_top__set__def)). 8.12/6.53 thf(214,plain,((top_to2138011583a_real = (collec1714955950a_real @ (top_to1567080838real_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 8.12/6.53 thf(50,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_dual__order_Ostrict__implies__order)). 8.12/6.53 thf(287,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 8.12/6.53 thf(56,axiom,((ord_less_real = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (B != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_dual__order_Ostrict__iff__order)). 8.12/6.53 thf(300,plain,(((ord_less_real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 8.12/6.53 thf(91,axiom,(((elementary_closure_a @ top_top_set_a) = top_top_set_a)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_closure__UNIV)). 8.12/6.53 thf(432,plain,(((elementary_closure_a @ top_top_set_a) = top_top_set_a)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 8.12/6.53 thf(13,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ A @ C) <= (ord_less_real @ B @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_le__less__trans)). 8.12/6.53 thf(168,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ C) | ~ (ord_less_real @ B @ C) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 8.12/6.53 thf(21,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_84_antisym__conv)). 8.12/6.53 thf(190,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)],[21])). 8.12/6.53 thf(58,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((! [D:real]: ((ord_less_real @ A @ D) => ((ord_less_eq_real @ C @ D) <= (ord_less_real @ D @ B)))) => (ord_less_eq_real @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_dense__ge__bounded)). 8.12/6.53 thf(305,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((! [D:real]: ((ord_less_real @ A @ D) => ((ord_less_eq_real @ C @ D) | ~ (ord_less_real @ D @ B)))) => (ord_less_eq_real @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 8.12/6.53 thf(63,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_66_ord__le__eq__subst)). 8.12/6.53 thf(326,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)],[63])). 8.12/6.53 thf(53,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_le__less__linear)). 8.12/6.54 thf(294,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 8.12/6.54 thf(23,axiom,((ord_less_real = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_less__le)). 8.12/6.54 thf(195,plain,(((ord_less_real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 8.12/6.54 thf(93,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((A = (B @ C)) => ((ord_less_real @ C @ D) => ((ord_less_real @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_ord__eq__less__subst)). 8.12/6.54 thf(437,plain,((! [A:real,B:(real > real),C:real,D:real]: ((A = (B @ C)) => ((ord_less_real @ C @ D) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 8.12/6.54 thf(83,axiom,((top_to35724191t_real = (produc1266579561t_real @ top_top_set_a @ top_top_set_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_top__prod__def)). 8.12/6.54 thf(400,plain,((top_to35724191t_real = (produc1266579561t_real @ top_top_set_a @ top_top_set_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 8.12/6.54 thf(124,axiom,((! [A:product_prod_a_real,B:product_prod_a_real]: ~ (ord_less_real @ (real_V404783528a_real @ A @ B) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_dist__not__less__zero)). 8.12/6.54 thf(532,plain,((! [A:product_prod_a_real,B:product_prod_a_real]: ~ (ord_less_real @ (real_V404783528a_real @ A @ B) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 8.12/6.54 thf(49,axiom,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F))) => (ord_less_real @ A @ (B @ D)))) <= (ord_less_eq_real @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_order__le__less__subst1)). 8.12/6.54 thf(283,plain,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_real @ C @ D) => ((! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))) => (ord_less_real @ A @ (B @ D)))) | ~ (ord_less_eq_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 8.12/6.54 thf(81,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_less__imp__not__less)). 8.12/6.54 thf(395,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 8.12/6.54 thf(99,axiom,((! [A:real,B:real,C:$o]: (((C) <= (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_less__imp__triv)). 8.12/6.54 thf(459,plain,((! [A:real,B:real,C:$o]: ((C) | ~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 8.12/6.54 thf(11,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ A @ C) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_order__trans)). 8.12/6.54 thf(163,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ A @ C) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 8.12/6.54 thf(17,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_100_dual__order_Otrans)). 8.12/6.54 thf(178,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)],[17])). 8.12/6.54 thf(47,axiom,((! [A:real,B:real,C:(real > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_order__subst2)). 8.12/6.54 thf(277,plain,((! [A:real,B:real,C:(real > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_real @ E @ F))) => (ord_less_eq_real @ (C @ A) @ D))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 8.12/6.54 thf(109,axiom,((! [A:a,B:real,C:a,D:real]: (((product_Pair_a_real @ A @ B) = (product_Pair_a_real @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_old_Oprod_Oinject)). 8.12/6.54 thf(486,plain,((! [A:a,B:real,C:a,D:real]: (((product_Pair_a_real @ A @ B) = (product_Pair_a_real @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 8.12/6.54 thf(132,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_less__not__sym)). 8.12/6.54 thf(560,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 8.12/6.54 thf(97,axiom,((! [A:set_Pr1928503567a_real]: ((collec1714955950a_real @ (^ [B:product_prod_a_real]: (member1103263856a_real @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Collect__mem__eq)). 8.12/6.54 thf(454,plain,((! [A:set_Pr1928503567a_real]: ((collec1714955950a_real @ (^ [B:product_prod_a_real]: (member1103263856a_real @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 8.12/6.54 thf(578,plain,($false),inference(e,[status(thm)],[385,565,397,479,518,468,481,365,138,247,202,184,357,542,421,152,228,289,448,316,216,492,253,353,512,529,546,220,334,302,260,407,429,484,197,522,493,188,388,141,499,339,489,471,256,193,537,393,515,457,173,569,343,244,360,205,508,298,412,166,148,161,573,296,562,176,402,291,281,445,313,144,181,274,419,318,434,362,451,567,477,367,535,155,462,223,505,241,473,209,355,553,525,409,310,199,502,336,497,556,218,250,465,231,258,390,171,139,158,351,235,207,346,549,214,287,300,432,168,190,305,326,294,195,437,400,532,283,395,459,163,178,277,486,560,454])). 8.12/6.54 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 8.12/6.54 % [INFO] Killing All external provers ... 8.12/6.54 FINAL WATCH: 8.0 CPU 2.4 WC 8.12/6.54 Killed 1 orphans 8.12/6.54 Killed 2 orphans 8.12/6.54 Killed 1 orphans 8.12/6.54 EOF