0.00/0.01 % Leo-III: Strategy 1 (for '60') 76.35/20.47 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 76.35/20.47 % [INFO] Parsing done (338ms). 76.35/20.47 % [INFO] Running in sequential loop mode. 76.35/20.47 % [CONFIG] Using configuration: timeout(60) with strategy 76.35/20.47 % [INFO] eprover registered as external prover. 76.35/20.47 % [INFO] cvc4 registered as external prover. 76.35/20.47 % [INFO] Parsing finished. Scanning for conjecture ... 76.35/20.47 % [INFO] Found a conjecture and 351 axioms. Running axiom selection ... 76.35/20.47 % [INFO] Axiom selection finished. Selected 146 axioms (removed 205 axioms). 76.35/20.47 % [INFO] Problem is higher-order (TPTP THF). 76.35/20.47 % [INFO] Type checking passed. Searching for refutation ... 76.35/20.47 % External prover 'e' found a proof! 76.35/20.47 % [INFO] Killing All external provers ... 76.35/20.47 % Time passed: 16038ms (effective reasoning time: 15202ms) 76.35/20.47 % Solved by strategy 76.35/20.47 % Axioms used in derivation (146): fact_61_insert__absorb, fact_7_zero__reorient, fact_9_Zero__hf__def, fact_236_bot__nat__0_Oextremum, fact_238_bot__nat__0_Oextremum__uniqueI, fact_204_le__numeral__extra_I3_J, fact_14_HF__hfset, fact_197_subsetD, fact_203_zero__le, fact_207_bot_Oextremum__unique, fact_269_le__refl, fact_264_Nat_Oex__has__greatest__nat, fact_106_bot__nat__def, fact_215_infinite__super, fact_167_singleton__insert__inj__eq, fact_267_eq__imp__le, fact_130_finite_Oinducts, fact_73_insertI1, fact_177_order__class_Oorder_Oantisym, fact_34_emptyE, fact_43_insert__iff, fact_2_hmem__hempty, fact_175_dual__order_Orefl, fact_88_insert__not__empty, fact_29_hinsert__def, fact_192_order__subst1, fact_117_finite__insert, fact_152_is__singletonI_H, fact_222_subset__insertI2, fact_191_order__subst2, fact_148_is__singletonI, fact_195_subset__iff, fact_144_bot__empty__eq, fact_240_le__0__eq, fact_235_subset__emptyI, fact_165_insert__subset, fact_231_finite__ranking__induct, fact_79_finite__cases, fact_284_zero__diff, fact_136_infinite__finite__induct, fact_265_nat__le__linear, fact_147_is__singleton__the__elem, fact_171_dual__order_Oantisym, fact_210_bot_Oextremum__uniqueI, fact_228_card__eq__0__iff, fact_149_Set_Ois__empty__def, fact_55_insert__commute, fact_179_ord__eq__le__trans, fact_121_finite_Ocases, fact_151_is__singletonE, fact_3_hf__cases, fact_168_card_Oempty, fact_259_card__le__if__inj__on__rel, fact_268_le__trans, fact_209_bot_Oextremum__uniqueI, fact_0_hf__ext, fact_64_insert__ident, fact_85_singleton__inject, fact_102_singleton__iff, fact_160_order__refl, fact_124_finite_Osimps, fact_241_less__eq__nat_Osimps_I1_J, fact_112_ex__in__conv, fact_5_hmem__def, fact_266_le__antisym, fact_31_zero__natural_Orsp, fact_187_antisym, fact_91_doubleton__eq__iff, fact_196_subset__eq, fact_17_empty__iff, fact_189_ord__le__eq__subst, fact_185_eq__refl, fact_174_linorder__wlog, fact_169_card_Oinfinite, fact_158_finite__subset__induct_H, fact_234_insert__subsetI, fact_220_subset__insert, fact_182_le__cases3, fact_282_cancel__comm__monoid__add__class_Odiff__cancel, fact_166_singleton__insert__inj__eq_H, fact_201_infinite__arbitrarily__large, fact_150_is__singleton__def, fact_20_all__not__in__conv, fact_213_finite__subset, fact_37_equals0D, fact_4_hmem__hinsert, fact_186_linear, fact_58_insert__eq__iff, fact_40_insert__absorb2, fact_139_finite_OemptyI, fact_225_subset__singleton__iff, fact_263_bounded__Max__nat, fact_257_obtain__subset__with__card__n, fact_76_insertE, fact_178_ord__le__eq__trans, fact_164_empty__subsetI, fact_180_order__class_Oorder_Oeq__iff, fact_226_subset__singletonD, fact_156_finite__subset__induct, fact_248_card__insert__le, fact_246_card__mono, fact_30_hfset__HF, fact_244_card__seteq, fact_133_finite__ne__induct, fact_11_push__bit__eq__0__iff, fact_127_finite__induct, fact_154_card__0__eq, fact_181_antisym__conv, fact_137_the__elem__eq, fact_161_subsetI, fact_8_Abs__hf__0, fact_49_singletonI, fact_239_bot__nat__0_Oextremum__unique, fact_107_finite__hfset, fact_283_diff__zero, fact_199_card__subset__eq, fact_219_insert__mono, fact_190_ord__eq__le__subst, fact_205_bot_Oextremum, fact_1_hemptyE, fact_46_insertCI, fact_198_in__mono, fact_173_dual__order_Otrans, fact_52_mk__disjoint__insert, fact_221_subset__insertI, fact_188_eq__iff, fact_67_Set_Oset__insert, fact_176_order__trans, fact_242_finite__if__finite__subsets__card__bdd, fact_237_le0, fact_141_infinite__imp__nonempty, fact_208_bot_Oextremum__unique, fact_162_le__zero__eq, fact_6_zero__reorient, fact_217_rev__finite__subset, fact_163_subset__empty, fact_115_equals0I, fact_183_order_Otrans, fact_10_push__bit__of__0, fact_172_dual__order_Oeq__iff, fact_12_drop__bit__of__0, fact_105_singletonD, fact_142_finite_OinsertI, fact_206_bot_Oextremum, fact_70_insertI2, fact_184_le__cases 76.35/20.47 % No. of inferences in proof: 574 76.35/20.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 16038 ms resp. 15202 ms w/o parsing 76.35/20.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 76.35/20.47 thf(set_se933006839lle_hf_type, type, set_se933006839lle_hf: $tType). 76.35/20.47 thf(set_HF_Mirabelle_hf_type, type, set_HF_Mirabelle_hf: $tType). 76.35/20.47 thf(hF_Mirabelle_hf_type, type, hF_Mirabelle_hf: $tType). 76.35/20.47 thf(set_nat_type, type, set_nat: $tType). 76.35/20.47 thf(nat_type, type, nat: $tType). 76.35/20.47 thf(finite1213132899lle_hf_type, type, finite1213132899lle_hf: (set_HF_Mirabelle_hf > nat)). 76.35/20.47 thf(finite586181922lle_hf_type, type, finite586181922lle_hf: (set_HF_Mirabelle_hf > $o)). 76.35/20.47 thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))). 76.35/20.47 thf(zero_z189798548lle_hf_type, type, zero_z189798548lle_hf: hF_Mirabelle_hf). 76.35/20.47 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 76.35/20.47 thf(hF_Mirabelle_HF_type, type, hF_Mirabelle_HF: (set_HF_Mirabelle_hf > hF_Mirabelle_hf)). 76.35/20.47 thf(hF_Mirabelle_Abs_hf_type, type, hF_Mirabelle_Abs_hf: (nat > hF_Mirabelle_hf)). 76.35/20.47 thf(hF_Mirabelle_hfset_type, type, hF_Mirabelle_hfset: (hF_Mirabelle_hf > set_HF_Mirabelle_hf)). 76.35/20.47 thf(hF_Mirabelle_hinsert_type, type, hF_Mirabelle_hinsert: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf))). 76.35/20.47 thf(hF_Mirabelle_hmem_type, type, hF_Mirabelle_hmem: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o))). 76.35/20.47 thf(bot_bo1263054448e_hf_o_type, type, bot_bo1263054448e_hf_o: (hF_Mirabelle_hf > $o)). 76.35/20.47 thf(bot_bot_nat_type, type, bot_bot_nat: nat). 76.35/20.47 thf(bot_bo53200981lle_hf_type, type, bot_bo53200981lle_hf: set_HF_Mirabelle_hf). 76.35/20.47 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 76.35/20.47 thf(ord_le432112161lle_hf_type, type, ord_le432112161lle_hf: (set_HF_Mirabelle_hf > (set_HF_Mirabelle_hf > $o))). 76.35/20.47 thf(semiri2115134414it_nat_type, type, semiri2115134414it_nat: (nat > (nat > nat))). 76.35/20.47 thf(semiri2013084963it_nat_type, type, semiri2013084963it_nat: (nat > (nat > nat))). 76.35/20.47 thf(insert9649339lle_hf_type, type, insert9649339lle_hf: (hF_Mirabelle_hf > (set_HF_Mirabelle_hf > set_HF_Mirabelle_hf))). 76.35/20.47 thf(is_emp566801209lle_hf_type, type, is_emp566801209lle_hf: (set_HF_Mirabelle_hf > $o)). 76.35/20.47 thf(is_sin1448700567lle_hf_type, type, is_sin1448700567lle_hf: (set_HF_Mirabelle_hf > $o)). 76.35/20.47 thf(the_el1104322134lle_hf_type, type, the_el1104322134lle_hf: (set_HF_Mirabelle_hf > hF_Mirabelle_hf)). 76.35/20.47 thf(member1367349282lle_hf_type, type, member1367349282lle_hf: (hF_Mirabelle_hf > (set_HF_Mirabelle_hf > $o))). 76.35/20.47 thf(z_type, type, z: hF_Mirabelle_hf). 76.35/20.47 thf(sk1_type, type, sk1: (nat > (set_HF_Mirabelle_hf > set_HF_Mirabelle_hf))). 76.35/20.47 thf(sk2_type, type, sk2: ((nat > $o) > $o)). 76.35/20.47 thf(sk3_type, type, sk3: (nat > ((nat > $o) > nat))). 76.35/20.47 thf(sk4_type, type, sk4: ((nat > $o) > nat)). 76.35/20.47 thf(sk5_type, type, sk5: (nat > (nat > ((nat > nat) > (nat > nat))))). 76.35/20.47 thf(sk6_type, type, sk6: (nat > (nat > ((nat > nat) > (nat > nat))))). 76.35/20.47 thf(sk7_type, type, sk7: (set_HF_Mirabelle_hf > (nat > set_HF_Mirabelle_hf))). 76.35/20.47 thf(sk8_type, type, sk8: (nat > ((nat > nat) > (nat > (nat > nat))))). 76.35/20.47 thf(sk9_type, type, sk9: (nat > ((nat > nat) > (nat > (nat > nat))))). 76.35/20.47 thf(sk40_type, type, sk40: (set_HF_Mirabelle_hf > (hF_Mirabelle_hf > set_HF_Mirabelle_hf))). 76.35/20.47 thf(sk50_type, type, sk50: (set_HF_Mirabelle_hf > (hF_Mirabelle_hf > set_HF_Mirabelle_hf))). 76.35/20.47 thf(sk59_type, type, sk59: hF_Mirabelle_hf). 76.35/20.47 thf(sk64_type, type, sk64: (hF_Mirabelle_hf > hF_Mirabelle_hf)). 76.35/20.47 thf(sk65_type, type, sk65: (hF_Mirabelle_hf > hF_Mirabelle_hf)). 76.35/20.47 thf(110,axiom,((is_sin1448700567lle_hf = (^ [A:set_HF_Mirabelle_hf]: (A = (insert9649339lle_hf @ (the_el1104322134lle_hf @ A) @ bot_bo53200981lle_hf))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_is__singleton__the__elem)). 76.35/20.47 thf(645,plain,(((is_sin1448700567lle_hf) = (^ [A:set_HF_Mirabelle_hf]: (A = (insert9649339lle_hf @ (the_el1104322134lle_hf @ A) @ bot_bo53200981lle_hf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 76.35/20.47 thf(105,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ B) => ((~ (finite586181922lle_hf @ B)) <= (~ (finite586181922lle_hf @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_infinite__super)). 76.35/20.47 thf(629,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ B) => (~ (finite586181922lle_hf @ B) | (finite586181922lle_hf @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 76.35/20.47 thf(139,axiom,((hF_Mirabelle_hinsert = (^ [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: (hF_Mirabelle_HF @ (insert9649339lle_hf @ A @ (hF_Mirabelle_hfset @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_hinsert__def)). 76.35/20.47 thf(733,plain,(((hF_Mirabelle_hinsert) = (^ [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: (hF_Mirabelle_HF @ (insert9649339lle_hf @ A @ (hF_Mirabelle_hfset @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 76.35/20.47 thf(734,plain,(((hF_Mirabelle_hinsert) = (^ [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: (hF_Mirabelle_HF @ (insert9649339lle_hf @ A @ (hF_Mirabelle_hfset @ B)))))),inference(lifteq,[status(thm)],[733])). 76.35/20.47 thf(846,plain,(! [A:hF_Mirabelle_hf] : (((hF_Mirabelle_hinsert @ A) = (^ [B:hF_Mirabelle_hf]: (hF_Mirabelle_HF @ (insert9649339lle_hf @ A @ (hF_Mirabelle_hfset @ B))))))),inference(func_ext,[status(esa)],[734])). 76.35/20.47 thf(104,axiom,((is_sin1448700567lle_hf = (^ [A:set_HF_Mirabelle_hf]: ? [B:hF_Mirabelle_hf]: (A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_is__singleton__def)). 76.35/20.47 thf(627,plain,(((is_sin1448700567lle_hf) = (^ [A:set_HF_Mirabelle_hf]: ? [B:hF_Mirabelle_hf]: (A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 76.35/20.47 thf(628,plain,(((is_sin1448700567lle_hf) = (^ [A:set_HF_Mirabelle_hf]: ? [B:hF_Mirabelle_hf]: (A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))),inference(lifteq,[status(thm)],[627])). 76.35/20.47 thf(74,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((~ (! [C:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ C) <= (B = (insert9649339lle_hf @ A @ C))))) <= (member1367349282lle_hf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Set_Oset__insert)). 76.35/20.47 thf(468,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: (~ (! [C:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ C) | ~ (B = (insert9649339lle_hf @ A @ C)))) | ~ (member1367349282lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 76.35/20.47 thf(4,axiom,((! [A:nat]: (ord_less_eq_nat @ bot_bot_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_bot_Oextremum)). 76.35/20.47 thf(154,plain,((! [A:nat]: (ord_less_eq_nat @ bot_bot_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 76.35/20.47 thf(155,plain,(! [A:nat] : ((ord_less_eq_nat @ bot_bot_nat @ A))),inference(cnf,[status(esa)],[154])). 76.35/20.47 thf(127,axiom,((bot_bot_nat = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_bot__nat__def)). 76.35/20.47 thf(697,plain,((bot_bot_nat = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 76.35/20.47 thf(698,plain,((bot_bot_nat = zero_zero_nat)),inference(lifteq,[status(thm)],[697])). 76.35/20.47 thf(821,plain,(! [A:nat] : ((ord_less_eq_nat @ zero_zero_nat @ A))),inference(rewrite,[status(thm)],[155,698])). 76.35/20.47 thf(15,axiom,((! [A:nat,B:set_HF_Mirabelle_hf]: ((ord_less_eq_nat @ A @ (finite1213132899lle_hf @ B)) => (~ (! [C:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ C @ B) => (((finite1213132899lle_hf @ C) = A) => (~ (finite586181922lle_hf @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_obtain__subset__with__card__n)). 76.35/20.47 thf(195,plain,((! [A:nat,B:set_HF_Mirabelle_hf]: ((ord_less_eq_nat @ A @ (finite1213132899lle_hf @ B)) => (~ (! [C:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ C @ B) => (((finite1213132899lle_hf @ C) = A) => (~ (finite586181922lle_hf @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 76.35/20.47 thf(197,plain,(! [B:set_HF_Mirabelle_hf,A:nat] : ((~ (ord_less_eq_nat @ A @ (finite1213132899lle_hf @ B))) | ((finite1213132899lle_hf @ (sk7 @ B @ A)) = A))),inference(cnf,[status(esa)],[195])). 76.35/20.47 thf(199,plain,(! [B:set_HF_Mirabelle_hf,A:nat] : (((finite1213132899lle_hf @ (sk7 @ B @ A)) = A) | (~ (ord_less_eq_nat @ A @ (finite1213132899lle_hf @ B))))),inference(lifteq,[status(thm)],[197])). 76.35/20.47 thf(5677,plain,(! [C:set_HF_Mirabelle_hf,B:nat,A:nat] : (((finite1213132899lle_hf @ (sk7 @ C @ B)) = B) | ((ord_less_eq_nat @ zero_zero_nat @ A) != (ord_less_eq_nat @ B @ (finite1213132899lle_hf @ C))))),inference(paramod_ordered,[status(thm)],[821,199])). 76.35/20.47 thf(5678,plain,(! [A:set_HF_Mirabelle_hf] : (((finite1213132899lle_hf @ (sk7 @ A @ zero_zero_nat)) = zero_zero_nat))),inference(pattern_uni,[status(thm)],[5677:[bind(A, $thf(finite1213132899lle_hf @ D)),bind(B, $thf(zero_zero_nat)),bind(C, $thf(D))]])). 76.35/20.47 thf(5778,plain,(! [A:set_HF_Mirabelle_hf] : (((finite1213132899lle_hf @ (sk7 @ A @ zero_zero_nat)) = zero_zero_nat))),inference(simp,[status(thm)],[5678])). 76.35/20.47 thf(117,axiom,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((A = bot_bo53200981lle_hf) => (~ (member1367349282lle_hf @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_equals0D)). 76.35/20.47 thf(666,plain,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((A = bot_bo53200981lle_hf) => (~ (member1367349282lle_hf @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 76.35/20.47 thf(126,axiom,((! [A:hF_Mirabelle_hf]: (member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_singletonI)). 76.35/20.47 thf(695,plain,((! [A:hF_Mirabelle_hf]: (member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 76.35/20.47 thf(696,plain,(! [A:hF_Mirabelle_hf] : ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(cnf,[status(esa)],[695])). 76.35/20.47 thf(107,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ B) => (? [C:set_HF_Mirabelle_hf]: (~ (member1367349282lle_hf @ A @ C) & (B = (insert9649339lle_hf @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_mk__disjoint__insert)). 76.35/20.47 thf(633,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ B) => (? [C:set_HF_Mirabelle_hf]: (~ (member1367349282lle_hf @ A @ C) & (B = (insert9649339lle_hf @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 76.35/20.47 thf(634,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | (~ (member1367349282lle_hf @ A @ (sk50 @ B @ A))))),inference(cnf,[status(esa)],[633])). 76.35/20.47 thf(1005,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | ((member1367349282lle_hf @ A @ (sk50 @ B @ A)) != (member1367349282lle_hf @ A @ B)) | ~ ($true))),inference(eqfactor_ordered,[status(thm)],[634])). 76.35/20.47 thf(1006,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | ((member1367349282lle_hf @ A @ (sk50 @ B @ A)) != (member1367349282lle_hf @ A @ B)))),inference(simp,[status(thm)],[1005])). 76.35/20.47 thf(1093,plain,(! [C:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ B @ C)) | ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) != (member1367349282lle_hf @ B @ (sk50 @ C @ B))))),inference(paramod_ordered,[status(thm)],[696,1006])). 76.35/20.47 thf(1100,plain,(! [C:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ B @ C)) | (A != B) | ((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) != (sk50 @ C @ B)))),inference(simp,[status(thm)],[1093])). 76.35/20.47 thf(1110,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | ((sk50 @ B @ A) != (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(simp,[status(thm)],[1100])). 76.35/20.47 thf(78,axiom,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) = ((A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) | (A = bot_bo53200981lle_hf))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_subset__singleton__iff)). 76.35/20.47 thf(479,plain,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) = ((A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) | (A = bot_bo53200981lle_hf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 76.35/20.47 thf(1007,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | (A != A) | ((sk50 @ B @ A) != B))),inference(simp,[status(thm)],[1005])). 76.35/20.47 thf(1008,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | ((sk50 @ B @ A) != B))),inference(simp,[status(thm)],[1007])). 76.35/20.47 thf(1080,plain,(! [C:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((sk50 @ C @ B) != C) | ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) != (member1367349282lle_hf @ B @ C)))),inference(paramod_ordered,[status(thm)],[696,1008])). 76.35/20.47 thf(1081,plain,(! [A:hF_Mirabelle_hf] : (((sk50 @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf) @ A) != (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(pattern_uni,[status(thm)],[1080:[bind(A, $thf(D)),bind(B, $thf(D)),bind(C, $thf(insert9649339lle_hf @ D @ bot_bo53200981lle_hf))]])). 76.35/20.47 thf(1105,plain,(! [A:hF_Mirabelle_hf] : (((sk50 @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf) @ A) != (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(simp,[status(thm)],[1081])). 76.35/20.47 thf(7,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_le__refl)). 76.35/20.47 thf(161,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 76.35/20.47 thf(162,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ A))),inference(cnf,[status(esa)],[161])). 76.35/20.47 thf(5705,plain,(! [C:set_HF_Mirabelle_hf,B:nat,A:nat] : (((finite1213132899lle_hf @ (sk7 @ C @ B)) = B) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ B @ (finite1213132899lle_hf @ C))))),inference(paramod_ordered,[status(thm)],[162,199])). 76.35/20.47 thf(5706,plain,(! [A:set_HF_Mirabelle_hf] : (((finite1213132899lle_hf @ (sk7 @ A @ (finite1213132899lle_hf @ A))) = (finite1213132899lle_hf @ A)))),inference(pattern_uni,[status(thm)],[5705:[bind(A, $thf(finite1213132899lle_hf @ D)),bind(B, $thf(finite1213132899lle_hf @ D)),bind(C, $thf(D))]])). 76.35/20.47 thf(5751,plain,(! [A:set_HF_Mirabelle_hf] : (((finite1213132899lle_hf @ (sk7 @ A @ (finite1213132899lle_hf @ A))) = (finite1213132899lle_hf @ A)))),inference(simp,[status(thm)],[5706])). 76.35/20.47 thf(198,plain,(! [B:set_HF_Mirabelle_hf,A:nat] : ((~ (ord_less_eq_nat @ A @ (finite1213132899lle_hf @ B))) | (finite586181922lle_hf @ (sk7 @ B @ A)))),inference(cnf,[status(esa)],[195])). 76.35/20.47 thf(5450,plain,(! [C:set_HF_Mirabelle_hf,B:nat,A:nat] : ((finite586181922lle_hf @ (sk7 @ C @ B)) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ B @ (finite1213132899lle_hf @ C))))),inference(paramod_ordered,[status(thm)],[162,198])). 76.35/20.47 thf(5451,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ A @ (finite1213132899lle_hf @ A))))),inference(pattern_uni,[status(thm)],[5450:[bind(A, $thf(finite1213132899lle_hf @ D)),bind(B, $thf(finite1213132899lle_hf @ D)),bind(C, $thf(D))]])). 76.35/20.47 thf(5481,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ A @ (finite1213132899lle_hf @ A))))),inference(simp,[status(thm)],[5451])). 76.35/20.47 thf(6038,plain,(! [B:set_HF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ B @ (finite1213132899lle_hf @ A))) | ((finite1213132899lle_hf @ (sk7 @ A @ (finite1213132899lle_hf @ A))) != (finite1213132899lle_hf @ B)))),inference(paramod_ordered,[status(thm)],[5751,5481])). 76.35/20.47 thf(6039,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ (sk7 @ A @ (finite1213132899lle_hf @ A)) @ (finite1213132899lle_hf @ A))))),inference(pattern_uni,[status(thm)],[6038:[bind(A, $thf(E)),bind(B, $thf(sk7 @ E @ (finite1213132899lle_hf @ E)))]])). 76.35/20.47 thf(6142,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ (sk7 @ A @ (finite1213132899lle_hf @ A)) @ (finite1213132899lle_hf @ A))))),inference(simp,[status(thm)],[6039])). 76.35/20.47 thf(94,axiom,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: (((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ B @ C)) = ((B = A) & (ord_le432112161lle_hf @ C @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_singleton__insert__inj__eq)). 76.35/20.47 thf(582,plain,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: (((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ B @ C)) = ((B = A) & (ord_le432112161lle_hf @ C @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 76.35/20.47 thf(122,axiom,((! [A:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ A @ bot_bo53200981lle_hf))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_empty__iff)). 76.35/20.47 thf(683,plain,((! [A:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ A @ bot_bo53200981lle_hf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 76.35/20.47 thf(138,axiom,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_zero__diff)). 76.35/20.47 thf(730,plain,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 76.35/20.47 thf(118,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_zero__reorient)). 76.35/20.47 thf(671,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 76.35/20.47 thf(672,plain,(! [A:nat] : (((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(cnf,[status(esa)],[671])). 76.35/20.47 thf(673,plain,(! [A:nat] : (((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(lifteq,[status(thm)],[672])). 76.35/20.47 thf(12,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_263_bounded__Max__nat)). 76.35/20.47 thf(177,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)],[12])). 76.35/20.47 thf(178,plain,((! [A:(nat > $o)]: ((? [B:nat]: (A @ B)) => ((? [B:nat]: ! [C:nat]: ((A @ C) => (ord_less_eq_nat @ C @ B))) => (~ (! [B:nat]: ((A @ B) => (~ (! [C:nat]: ((A @ C) => (ord_less_eq_nat @ C @ B))))))))))),inference(miniscope,[status(thm)],[177])). 76.35/20.47 thf(182,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ B)) | (~ (sk2 @ A)) | (A @ (sk4 @ (A))))),inference(cnf,[status(esa)],[178])). 76.35/20.47 thf(2532,plain,(! [C:nat,B:(nat > $o),A:nat] : ((~ (zero_zero_nat = A)) | (~ (sk2 @ (B))) | (B @ (sk4 @ (B))) | ((A = zero_zero_nat) != (B @ C)))),inference(paramod_ordered,[status(thm)],[673,182])). 76.35/20.47 thf(2623,plain,(! [C:nat,B:(nat > $o),A:nat] : ((zero_zero_nat != A) | (~ (sk2 @ (B))) | (B @ (sk4 @ (B))) | ((A = zero_zero_nat) != (B @ C)))),inference(lifteq,[status(thm)],[2532])). 76.35/20.47 thf(2739,plain,(((sk4 @ (^ [A:nat]: (A = zero_zero_nat))) = zero_zero_nat) | (~ (sk2 @ (^ [A:nat]: (A = zero_zero_nat))))),inference(pre_uni,[status(thm)],[2623:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(^ [D:nat]: (D = zero_zero_nat))),bind(C, $thf(zero_zero_nat))]])). 76.35/20.47 thf(2908,plain,(((sk4 @ (^ [A:nat]: (A = zero_zero_nat))) = zero_zero_nat) | (~ (sk2 @ (^ [A:nat]: (A = zero_zero_nat))))),inference(lifteq,[status(thm)],[2739])). 76.35/20.47 thf(142,axiom,((! [A:hF_Mirabelle_hf]: ((zero_z189798548lle_hf = A) = (A = zero_z189798548lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_zero__reorient)). 76.35/20.47 thf(739,plain,((! [A:hF_Mirabelle_hf]: ((zero_z189798548lle_hf = A) = (A = zero_z189798548lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 76.35/20.47 thf(740,plain,(! [A:hF_Mirabelle_hf] : (((zero_z189798548lle_hf = A) = (A = zero_z189798548lle_hf)))),inference(cnf,[status(esa)],[739])). 76.35/20.47 thf(741,plain,(! [A:hF_Mirabelle_hf] : (((zero_z189798548lle_hf = A) = (A = zero_z189798548lle_hf)))),inference(lifteq,[status(thm)],[740])). 76.35/20.47 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_183_order_Otrans)). 76.35/20.47 thf(247,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])). 76.35/20.47 thf(113,axiom,((! [A:nat]: ((semiri2013084963it_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_push__bit__of__0)). 76.35/20.47 thf(655,plain,((! [A:nat]: ((semiri2013084963it_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 76.35/20.47 thf(120,axiom,((! [A:hF_Mirabelle_hf]: ((hF_Mirabelle_HF @ (hF_Mirabelle_hfset @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_HF__hfset)). 76.35/20.47 thf(677,plain,((! [A:hF_Mirabelle_hf]: ((hF_Mirabelle_HF @ (hF_Mirabelle_hfset @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 76.35/20.47 thf(68,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:(set_HF_Mirabelle_hf > $o)]: ((finite586181922lle_hf @ A) => ((((! [D:hF_Mirabelle_hf,E:set_HF_Mirabelle_hf]: (((member1367349282lle_hf @ D @ B) => (((C @ (insert9649339lle_hf @ D @ E)) <= (C @ E)) <= (~ (member1367349282lle_hf @ D @ E)))) <= (finite586181922lle_hf @ E))) => (C @ A)) <= (C @ bot_bo53200981lle_hf)) <= (ord_le432112161lle_hf @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_finite__subset__induct)). 76.35/20.47 thf(408,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:(set_HF_Mirabelle_hf > $o)]: ((finite586181922lle_hf @ A) => (((! [D:hF_Mirabelle_hf,E:set_HF_Mirabelle_hf]: (((member1367349282lle_hf @ D @ B) => ((C @ (insert9649339lle_hf @ D @ E)) | ~ (C @ E) | (member1367349282lle_hf @ D @ E))) | ~ (finite586181922lle_hf @ E))) => (C @ A)) | ~ (C @ bot_bo53200981lle_hf) | ~ (ord_le432112161lle_hf @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 76.35/20.47 thf(9,axiom,((! [A:set_HF_Mirabelle_hf,B:nat]: ((! [C:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ C @ A) => ((finite586181922lle_hf @ C) => (ord_less_eq_nat @ (finite1213132899lle_hf @ C) @ B)))) => ((finite586181922lle_hf @ A) & (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_finite__if__finite__subsets__card__bdd)). 76.35/20.47 thf(166,plain,((! [A:set_HF_Mirabelle_hf,B:nat]: ((! [C:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ C @ A) => ((finite586181922lle_hf @ C) => (ord_less_eq_nat @ (finite1213132899lle_hf @ C) @ B)))) => ((finite586181922lle_hf @ A) & (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 76.35/20.47 thf(170,plain,(! [B:nat,A:set_HF_Mirabelle_hf] : ((ord_le432112161lle_hf @ (sk1 @ B @ A) @ A) | (finite586181922lle_hf @ A))),inference(cnf,[status(esa)],[166])). 76.35/20.47 thf(85,axiom,((! [A:set_HF_Mirabelle_hf]: (((finite1213132899lle_hf @ A) = zero_zero_nat) <= (~ (finite586181922lle_hf @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_card_Oinfinite)). 76.35/20.47 thf(498,plain,((! [A:set_HF_Mirabelle_hf]: (((finite1213132899lle_hf @ A) = zero_zero_nat) | (finite586181922lle_hf @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 76.35/20.47 thf(499,plain,(! [A:set_HF_Mirabelle_hf] : (((finite1213132899lle_hf @ A) = zero_zero_nat) | (finite586181922lle_hf @ A))),inference(cnf,[status(esa)],[498])). 76.35/20.47 thf(500,plain,(! [A:set_HF_Mirabelle_hf] : (((finite1213132899lle_hf @ A) = zero_zero_nat) | (finite586181922lle_hf @ A))),inference(lifteq,[status(thm)],[499])). 76.35/20.47 thf(131,axiom,((! [A:nat]: ((semiri2115134414it_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_drop__bit__of__0)). 76.35/20.47 thf(713,plain,((! [A:nat]: ((semiri2115134414it_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 76.35/20.47 thf(714,plain,(! [A:nat] : (((semiri2115134414it_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(cnf,[status(esa)],[713])). 76.35/20.47 thf(715,plain,(! [A:nat] : (((semiri2115134414it_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(lifteq,[status(thm)],[714])). 76.35/20.47 thf(55,axiom,((! [A:set_HF_Mirabelle_hf]: ((~ (finite586181922lle_hf @ A)) => (A != bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_infinite__imp__nonempty)). 76.35/20.47 thf(353,plain,((! [A:set_HF_Mirabelle_hf]: ((~ (finite586181922lle_hf @ A)) => (~ (A = bot_bo53200981lle_hf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 76.35/20.47 thf(354,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ A) | (~ (A = bot_bo53200981lle_hf)))),inference(cnf,[status(esa)],[353])). 76.35/20.47 thf(355,plain,(! [A:set_HF_Mirabelle_hf] : ((A != bot_bo53200981lle_hf) | (finite586181922lle_hf @ A))),inference(lifteq,[status(thm)],[354])). 76.35/20.47 thf(356,plain,((finite586181922lle_hf @ bot_bo53200981lle_hf)),inference(simp,[status(thm)],[355])). 76.35/20.47 thf(20,axiom,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_card__insert__le)). 76.35/20.47 thf(210,plain,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 76.35/20.47 thf(211,plain,((! [A:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => (! [B:hF_Mirabelle_hf]: (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ B @ A))))))),inference(miniscope,[status(thm)],[210])). 76.35/20.47 thf(212,plain,(! [B:hF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : ((~ (finite586181922lle_hf @ A)) | (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ B @ A))))),inference(cnf,[status(esa)],[211])). 76.35/20.47 thf(6374,plain,(! [B:hF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : ((ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ B @ A))) | ((finite586181922lle_hf @ bot_bo53200981lle_hf) != (finite586181922lle_hf @ A)))),inference(paramod_ordered,[status(thm)],[356,212])). 76.35/20.47 thf(6375,plain,(! [A:hF_Mirabelle_hf] : ((ord_less_eq_nat @ (finite1213132899lle_hf @ bot_bo53200981lle_hf) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf))))),inference(pattern_uni,[status(thm)],[6374:[bind(A, $thf(bot_bo53200981lle_hf))]])). 76.35/20.47 thf(6504,plain,(! [A:hF_Mirabelle_hf] : ((ord_less_eq_nat @ (finite1213132899lle_hf @ bot_bo53200981lle_hf) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf))))),inference(simp,[status(thm)],[6375])). 76.35/20.47 thf(115,axiom,(((finite1213132899lle_hf @ bot_bo53200981lle_hf) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_card_Oempty)). 76.35/20.47 thf(661,plain,(((finite1213132899lle_hf @ bot_bo53200981lle_hf) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 76.35/20.47 thf(662,plain,(((finite1213132899lle_hf @ bot_bo53200981lle_hf) = zero_zero_nat)),inference(lifteq,[status(thm)],[661])). 76.35/20.47 thf(6515,plain,(! [A:hF_Mirabelle_hf] : ((ord_less_eq_nat @ zero_zero_nat @ (finite1213132899lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf))))),inference(rewrite,[status(thm)],[6504,662])). 76.35/20.47 thf(144,axiom,((! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_hmem__hempty)). 76.35/20.47 thf(747,plain,((! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 76.35/20.47 thf(51,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_bot__nat__0_Oextremum__uniqueI)). 76.35/20.47 thf(340,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 76.35/20.47 thf(667,plain,((! [A:set_HF_Mirabelle_hf]: ((A = bot_bo53200981lle_hf) => (~ (? [B:hF_Mirabelle_hf]: (member1367349282lle_hf @ B @ A)))))),inference(miniscope,[status(thm)],[666])). 76.35/20.47 thf(668,plain,(! [B:hF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : ((~ (A = bot_bo53200981lle_hf)) | (~ (member1367349282lle_hf @ B @ A)))),inference(cnf,[status(esa)],[667])). 76.35/20.47 thf(669,plain,(! [B:hF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : ((A != bot_bo53200981lle_hf) | (~ (member1367349282lle_hf @ B @ A)))),inference(lifteq,[status(thm)],[668])). 76.35/20.47 thf(670,plain,(! [A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ bot_bo53200981lle_hf)))),inference(simp,[status(thm)],[669])). 76.35/20.47 thf(72,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: (member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_insertI1)). 76.35/20.47 thf(463,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: (member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 76.35/20.47 thf(464,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ B)))),inference(cnf,[status(esa)],[463])). 76.35/20.47 thf(469,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ (sk40 @ B @ A))) | (~ (member1367349282lle_hf @ A @ B)))),inference(cnf,[status(esa)],[468])). 76.35/20.47 thf(949,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | ((member1367349282lle_hf @ A @ (sk40 @ B @ A)) != (member1367349282lle_hf @ A @ B)) | ~ ($true))),inference(eqfactor_ordered,[status(thm)],[469])). 76.35/20.47 thf(950,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | ((member1367349282lle_hf @ A @ (sk40 @ B @ A)) != (member1367349282lle_hf @ A @ B)))),inference(simp,[status(thm)],[949])). 76.35/20.47 thf(1096,plain,(! [C:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ B @ C)) | ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) != (member1367349282lle_hf @ B @ (sk40 @ C @ B))))),inference(paramod_ordered,[status(thm)],[696,950])). 76.35/20.47 thf(1097,plain,(! [C:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ B @ C)) | (A != B) | ((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) != (sk40 @ C @ B)))),inference(simp,[status(thm)],[1096])). 76.35/20.47 thf(1106,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | ((sk40 @ B @ A) != (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(simp,[status(thm)],[1097])). 76.35/20.47 thf(2407,plain,(! [D:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((sk40 @ D @ C) != (insert9649339lle_hf @ C @ bot_bo53200981lle_hf)) | ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ B)) != (member1367349282lle_hf @ C @ D)))),inference(paramod_ordered,[status(thm)],[464,1106])). 76.35/20.47 thf(2408,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((sk40 @ (insert9649339lle_hf @ A @ B) @ A) != (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(pattern_uni,[status(thm)],[2407:[bind(A, $thf(E)),bind(B, $thf(F)),bind(C, $thf(E)),bind(D, $thf(insert9649339lle_hf @ E @ F))]])). 76.35/20.47 thf(2434,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((sk40 @ (insert9649339lle_hf @ A @ B) @ A) != (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(simp,[status(thm)],[2408])). 76.35/20.47 thf(75,axiom,((ord_le432112161lle_hf = (^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_subset__eq)). 76.35/20.47 thf(472,plain,(((ord_le432112161lle_hf) = (^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 76.35/20.47 thf(5,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_180_order__class_Oorder_Oeq__iff)). 76.35/20.47 thf(156,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)],[5])). 76.35/20.47 thf(157,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = (= @ nat))),inference(lifteq,[status(thm)],[156])). 76.35/20.47 thf(829,plain,(! [A:nat] : (((^ [B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = (= @ nat @ A)))),inference(func_ext,[status(esa)],[157])). 76.35/20.47 thf(2402,plain,(! [D:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ C @ (sk50 @ D @ C))) | ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ B)) != (member1367349282lle_hf @ C @ D)))),inference(paramod_ordered,[status(thm)],[464,634])). 76.35/20.47 thf(2403,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ (sk50 @ (insert9649339lle_hf @ A @ B) @ A))))),inference(pattern_uni,[status(thm)],[2402:[bind(A, $thf(E)),bind(B, $thf(F)),bind(C, $thf(E)),bind(D, $thf(insert9649339lle_hf @ E @ F))]])). 76.35/20.47 thf(2432,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ (sk50 @ (insert9649339lle_hf @ A @ B) @ A))))),inference(simp,[status(thm)],[2403])). 76.35/20.47 thf(41,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_nat__le__linear)). 76.35/20.47 thf(288,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 76.35/20.47 thf(32,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_zero__le)). 76.35/20.47 thf(257,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 76.35/20.47 thf(136,axiom,((! [A:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => ((hF_Mirabelle_hfset @ (hF_Mirabelle_HF @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_hfset__HF)). 76.35/20.47 thf(724,plain,((! [A:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => ((hF_Mirabelle_hfset @ (hF_Mirabelle_HF @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 76.35/20.47 thf(13,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_ord__eq__le__subst)). 76.35/20.47 thf(184,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 76.35/20.47 thf(95,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ (insert9649339lle_hf @ A @ B)) = (finite586181922lle_hf @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_finite__insert)). 76.35/20.47 thf(585,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ (insert9649339lle_hf @ A @ B)) = (finite586181922lle_hf @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 76.35/20.47 thf(586,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((finite586181922lle_hf @ (insert9649339lle_hf @ A @ B)) = (finite586181922lle_hf @ B)))),inference(cnf,[status(esa)],[585])). 76.35/20.47 thf(587,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((finite586181922lle_hf @ (insert9649339lle_hf @ A @ B)) = (finite586181922lle_hf @ B)))),inference(lifteq,[status(thm)],[586])). 76.35/20.47 thf(56,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: (((insert9649339lle_hf @ A @ B) = (insert9649339lle_hf @ C @ bot_bo53200981lle_hf)) = ((A = C) & (ord_le432112161lle_hf @ B @ (insert9649339lle_hf @ C @ bot_bo53200981lle_hf)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_singleton__insert__inj__eq_H)). 76.35/20.47 thf(357,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: (((insert9649339lle_hf @ A @ B) = (insert9649339lle_hf @ C @ bot_bo53200981lle_hf)) = ((A = C) & (ord_le432112161lle_hf @ B @ (insert9649339lle_hf @ C @ bot_bo53200981lle_hf)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 76.35/20.47 thf(196,plain,(! [B:set_HF_Mirabelle_hf,A:nat] : ((~ (ord_less_eq_nat @ A @ (finite1213132899lle_hf @ B))) | (ord_le432112161lle_hf @ (sk7 @ B @ A) @ B))),inference(cnf,[status(esa)],[195])). 76.35/20.47 thf(678,plain,(! [A:hF_Mirabelle_hf] : (((hF_Mirabelle_HF @ (hF_Mirabelle_hfset @ A)) = A))),inference(cnf,[status(esa)],[677])). 76.35/20.47 thf(679,plain,(! [A:hF_Mirabelle_hf] : (((hF_Mirabelle_HF @ (hF_Mirabelle_hfset @ A)) = A))),inference(lifteq,[status(thm)],[678])). 76.35/20.47 thf(140,axiom,((zero_z189798548lle_hf = (hF_Mirabelle_HF @ bot_bo53200981lle_hf))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Zero__hf__def)). 76.35/20.47 thf(735,plain,((zero_z189798548lle_hf = (hF_Mirabelle_HF @ bot_bo53200981lle_hf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 76.35/20.47 thf(736,plain,(((hF_Mirabelle_HF @ bot_bo53200981lle_hf) = zero_z189798548lle_hf)),inference(lifteq,[status(thm)],[735])). 76.35/20.47 thf(1038,plain,(! [A:hF_Mirabelle_hf] : ((A = zero_z189798548lle_hf) | ((hF_Mirabelle_HF @ (hF_Mirabelle_hfset @ A)) != (hF_Mirabelle_HF @ bot_bo53200981lle_hf)))),inference(paramod_ordered,[status(thm)],[679,736])). 76.35/20.47 thf(1040,plain,(! [A:hF_Mirabelle_hf] : ((A = zero_z189798548lle_hf) | ((hF_Mirabelle_hfset @ A) != bot_bo53200981lle_hf))),inference(simp,[status(thm)],[1038])). 76.35/20.47 thf(1,conjecture,(((z = zero_z189798548lle_hf) = (! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ z)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 76.35/20.47 thf(2,negated_conjecture,((~ ((z = zero_z189798548lle_hf) = (! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ z))))),inference(neg_conjecture,[status(cth)],[1])). 76.35/20.47 thf(149,plain,((~ ((z = zero_z189798548lle_hf) = (! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ z))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 76.35/20.47 thf(150,plain,(((z = zero_z189798548lle_hf) != (! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ z)))),inference(lifteq,[status(thm)],[149])). 76.35/20.47 thf(761,plain,((~ (z = zero_z189798548lle_hf)) | (~ (! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ z)))),inference(bool_ext,[status(thm)],[150])). 76.35/20.47 thf(763,plain,((z != zero_z189798548lle_hf) | (~ (! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ z)))),inference(lifteq,[status(thm)],[761])). 76.35/20.47 thf(765,plain,((hF_Mirabelle_hmem @ sk59 @ z) | (z != zero_z189798548lle_hf)),inference(cnf,[status(esa)],[763])). 76.35/20.47 thf(748,plain,((~ (? [A:hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf)))),inference(miniscope,[status(thm)],[747])). 76.35/20.47 thf(749,plain,(! [A:hF_Mirabelle_hf] : ((~ (hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf)))),inference(cnf,[status(esa)],[748])). 76.35/20.47 thf(840,plain,(! [A:hF_Mirabelle_hf] : ((z != zero_z189798548lle_hf) | ((hF_Mirabelle_hmem @ sk59 @ z) != (hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf)))),inference(paramod_ordered,[status(thm)],[765,749])). 76.35/20.47 thf(842,plain,(! [A:hF_Mirabelle_hf] : ((z != zero_z189798548lle_hf) | (sk59 != A) | (z != zero_z189798548lle_hf))),inference(simp,[status(thm)],[840])). 76.35/20.47 thf(844,plain,((z != zero_z189798548lle_hf)),inference(simp,[status(thm)],[842])). 76.35/20.47 thf(1510,plain,(! [A:hF_Mirabelle_hf] : (((hF_Mirabelle_hfset @ A) != bot_bo53200981lle_hf) | (A != z))),inference(paramod_ordered,[status(thm)],[1040,844])). 76.35/20.47 thf(1511,plain,(((hF_Mirabelle_hfset @ z) != bot_bo53200981lle_hf)),inference(pattern_uni,[status(thm)],[1510:[bind(A, $thf(z))]])). 76.35/20.47 thf(145,axiom,(((= @ hF_Mirabelle_hf) = (^ [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ C @ A) = (hF_Mirabelle_hmem @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hf__ext)). 76.35/20.47 thf(750,plain,(((= @ hF_Mirabelle_hf) = (^ [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ C @ A) = (hF_Mirabelle_hmem @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 76.35/20.47 thf(751,plain,(((= @ hF_Mirabelle_hf) = (^ [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ C @ A) = (hF_Mirabelle_hmem @ C @ B))))),inference(lifteq,[status(thm)],[750])). 76.35/20.47 thf(89,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((insert9649339lle_hf @ A @ B) != bot_bo53200981lle_hf))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_insert__not__empty)). 76.35/20.47 thf(542,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ~ ((insert9649339lle_hf @ A @ B) = bot_bo53200981lle_hf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 76.35/20.47 thf(71,axiom,((! [A:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf) => (A = bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_bot_Oextremum__uniqueI)). 76.35/20.47 thf(460,plain,((! [A:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf) => (A = bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 76.35/20.47 thf(185,plain,((! [A:nat,B:(nat > nat),C:nat]: (! [D:nat]: ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(miniscope,[status(thm)],[184])). 76.35/20.47 thf(186,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((~ (ord_less_eq_nat @ C @ D)) | (ord_less_eq_nat @ A @ (B @ D)) | (ord_less_eq_nat @ (sk5 @ D @ C @ (B) @ A) @ (sk6 @ D @ C @ (B) @ A)) | (~ (A = (B @ C))))),inference(cnf,[status(esa)],[185])). 76.35/20.47 thf(188,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((A != (B @ C)) | (~ (ord_less_eq_nat @ C @ D)) | (ord_less_eq_nat @ A @ (B @ D)) | (ord_less_eq_nat @ (sk5 @ D @ C @ (B) @ A) @ (sk6 @ D @ C @ (B) @ A)))),inference(lifteq,[status(thm)],[186])). 76.35/20.47 thf(189,plain,(! [C:nat,B:nat,A:(nat > nat)] : ((~ (ord_less_eq_nat @ B @ C)) | (ord_less_eq_nat @ (A @ B) @ (A @ C)) | (ord_less_eq_nat @ (sk5 @ C @ B @ (A) @ (A @ B)) @ (sk6 @ C @ B @ (A) @ (A @ B))))),inference(simp,[status(thm)],[188])). 76.35/20.47 thf(40,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => (((! [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))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_order__subst1)). 76.35/20.47 thf(284,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => (((! [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))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 76.35/20.47 thf(26,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_le__0__eq)). 76.35/20.47 thf(228,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 76.35/20.47 thf(70,axiom,((! [A:set_HF_Mirabelle_hf,B:(set_HF_Mirabelle_hf > $o)]: (((A != bot_bo53200981lle_hf) => ((! [C:hF_Mirabelle_hf]: (B @ (insert9649339lle_hf @ C @ bot_bo53200981lle_hf))) => ((B @ A) <= (! [C:hF_Mirabelle_hf,D:set_HF_Mirabelle_hf]: (((((B @ (insert9649339lle_hf @ C @ D)) <= (B @ D)) <= (~ (member1367349282lle_hf @ C @ D))) <= (D != bot_bo53200981lle_hf)) <= (finite586181922lle_hf @ D)))))) <= (finite586181922lle_hf @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_finite__ne__induct)). 76.35/20.47 thf(448,plain,((! [A:set_HF_Mirabelle_hf,B:(set_HF_Mirabelle_hf > $o)]: (((~ (A = bot_bo53200981lle_hf)) => ((! [C:hF_Mirabelle_hf]: (B @ (insert9649339lle_hf @ C @ bot_bo53200981lle_hf))) => ((B @ A) | ~ (! [C:hF_Mirabelle_hf,D:set_HF_Mirabelle_hf]: ((B @ (insert9649339lle_hf @ C @ D)) | ~ (B @ D) | (member1367349282lle_hf @ C @ D) | (D = bot_bo53200981lle_hf) | ~ (finite586181922lle_hf @ D)))))) | ~ (finite586181922lle_hf @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 76.35/20.47 thf(47,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:(hF_Mirabelle_hf > (hF_Mirabelle_hf > $o))]: ((finite586181922lle_hf @ A) => ((! [D:hF_Mirabelle_hf]: ((? [E:hF_Mirabelle_hf]: ((C @ D @ E) & (member1367349282lle_hf @ E @ A))) <= (member1367349282lle_hf @ D @ B))) => ((! [D:hF_Mirabelle_hf,E:hF_Mirabelle_hf,F:hF_Mirabelle_hf]: ((member1367349282lle_hf @ D @ B) => (((((C @ E @ F) => (D = E)) <= (C @ D @ F)) <= (member1367349282lle_hf @ F @ A)) <= (member1367349282lle_hf @ E @ B)))) => (ord_less_eq_nat @ (finite1213132899lle_hf @ B) @ (finite1213132899lle_hf @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_card__le__if__inj__on__rel)). 76.35/20.47 thf(316,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:(hF_Mirabelle_hf > (hF_Mirabelle_hf > $o))]: ((finite586181922lle_hf @ A) => ((! [D:hF_Mirabelle_hf]: (? [E:hF_Mirabelle_hf]: ((C @ D @ E) & (member1367349282lle_hf @ E @ A)) | ~ (member1367349282lle_hf @ D @ B))) => ((! [D:hF_Mirabelle_hf,E:hF_Mirabelle_hf,F:hF_Mirabelle_hf]: ((member1367349282lle_hf @ D @ B) => (((C @ E @ F) => (D = E)) | ~ (C @ D @ F) | ~ (member1367349282lle_hf @ F @ A) | ~ (member1367349282lle_hf @ E @ B)))) => (ord_less_eq_nat @ (finite1213132899lle_hf @ B) @ (finite1213132899lle_hf @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 76.35/20.47 thf(34,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_linorder__wlog)). 76.35/20.47 thf(261,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 76.35/20.47 thf(130,axiom,((! [A:hF_Mirabelle_hf]: (finite586181922lle_hf @ (hF_Mirabelle_hfset @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_finite__hfset)). 76.35/20.47 thf(711,plain,((! [A:hF_Mirabelle_hf]: (finite586181922lle_hf @ (hF_Mirabelle_hfset @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 76.35/20.47 thf(712,plain,(! [A:hF_Mirabelle_hf] : ((finite586181922lle_hf @ (hF_Mirabelle_hfset @ A)))),inference(cnf,[status(esa)],[711])). 76.35/20.47 thf(6341,plain,(! [C:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((ord_less_eq_nat @ (finite1213132899lle_hf @ B) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ C @ B))) | ((finite586181922lle_hf @ (hF_Mirabelle_hfset @ A)) != (finite586181922lle_hf @ B)))),inference(paramod_ordered,[status(thm)],[712,212])). 76.35/20.47 thf(6342,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((ord_less_eq_nat @ (finite1213132899lle_hf @ (hF_Mirabelle_hfset @ B)) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ A @ (hF_Mirabelle_hfset @ B)))))),inference(pattern_uni,[status(thm)],[6341:[bind(A, $thf(D)),bind(B, $thf(hF_Mirabelle_hfset @ D))]])). 76.35/20.47 thf(6490,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((ord_less_eq_nat @ (finite1213132899lle_hf @ (hF_Mirabelle_hfset @ B)) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ A @ (hF_Mirabelle_hfset @ B)))))),inference(simp,[status(thm)],[6342])). 76.35/20.47 thf(7133,plain,(! [D:set_HF_Mirabelle_hf,C:nat,B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ D @ C)) | ((ord_less_eq_nat @ (finite1213132899lle_hf @ (hF_Mirabelle_hfset @ B)) @ (finite1213132899lle_hf @ (insert9649339lle_hf @ A @ (hF_Mirabelle_hfset @ B)))) != (ord_less_eq_nat @ C @ (finite1213132899lle_hf @ D))))),inference(paramod_ordered,[status(thm)],[6490,198])). 76.35/20.47 thf(7134,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ (insert9649339lle_hf @ A @ (hF_Mirabelle_hfset @ B)) @ (finite1213132899lle_hf @ (hF_Mirabelle_hfset @ B)))))),inference(pattern_uni,[status(thm)],[7133:[bind(A, $thf(G)),bind(B, $thf(I)),bind(C, $thf(finite1213132899lle_hf @ (hF_Mirabelle_hfset @ I))),bind(D, $thf(insert9649339lle_hf @ G @ (hF_Mirabelle_hfset @ I)))]])). 76.35/20.47 thf(7236,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ (insert9649339lle_hf @ A @ (hF_Mirabelle_hfset @ B)) @ (finite1213132899lle_hf @ (hF_Mirabelle_hfset @ B)))))),inference(simp,[status(thm)],[7134])). 76.35/20.47 thf(22,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_eq__refl)). 76.35/20.47 thf(216,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 76.35/20.47 thf(76,axiom,((! [A:hF_Mirabelle_hf]: (is_sin1448700567lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_is__singletonI)). 76.35/20.47 thf(474,plain,((! [A:hF_Mirabelle_hf]: (is_sin1448700567lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 76.35/20.47 thf(475,plain,(! [A:hF_Mirabelle_hf] : ((is_sin1448700567lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(cnf,[status(esa)],[474])). 76.35/20.47 thf(179,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (~ (ord_less_eq_nat @ (sk3 @ C @ (A)) @ C)) | (sk2 @ A))),inference(cnf,[status(esa)],[178])). 76.35/20.47 thf(97,axiom,((finite586181922lle_hf = (^ [A:set_HF_Mirabelle_hf]: ((A = bot_bo53200981lle_hf) | ? [B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((A = (insert9649339lle_hf @ C @ B)) & (finite586181922lle_hf @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_finite_Osimps)). 76.35/20.47 thf(591,plain,(((finite586181922lle_hf) = (^ [A:set_HF_Mirabelle_hf]: ((A = bot_bo53200981lle_hf) | ? [B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((A = (insert9649339lle_hf @ C @ B)) & (finite586181922lle_hf @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 76.35/20.47 thf(180,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (A @ (sk3 @ C @ (A))) | (sk2 @ A))),inference(cnf,[status(esa)],[178])). 76.35/20.47 thf(1941,plain,(! [D:nat,C:nat,B:(nat > $o),A:nat] : ((~ (zero_zero_nat = A)) | (B @ (sk3 @ D @ (B))) | (sk2 @ (B)) | ((A = zero_zero_nat) != (B @ C)))),inference(paramod_ordered,[status(thm)],[673,180])). 76.35/20.47 thf(2025,plain,(! [D:nat,C:nat,B:(nat > $o),A:nat] : ((zero_zero_nat != A) | (B @ (sk3 @ D @ (B))) | (sk2 @ (B)) | ((A = zero_zero_nat) != (B @ C)))),inference(lifteq,[status(thm)],[1941])). 76.35/20.47 thf(2116,plain,(! [A:nat] : ((sk2 @ (= @ nat @ zero_zero_nat)) | (zero_zero_nat = (sk3 @ A @ (= @ nat @ zero_zero_nat))))),inference(pre_uni,[status(thm)],[2025:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(= @ nat @ zero_zero_nat)),bind(C, $thf(zero_zero_nat)),bind(D, $thf(D))]])). 76.35/20.47 thf(2235,plain,(! [A:nat] : (((sk3 @ A @ (= @ nat @ zero_zero_nat)) = zero_zero_nat) | (sk2 @ (= @ nat @ zero_zero_nat)))),inference(lifteq,[status(thm)],[2116])). 76.35/20.47 thf(2236,plain,(! [A:nat] : (((sk3 @ A @ (= @ nat @ zero_zero_nat)) = zero_zero_nat) | (sk2 @ (= @ nat @ zero_zero_nat)))),inference(simp,[status(thm)],[2235])). 76.35/20.47 thf(646,plain,(((is_sin1448700567lle_hf) = (^ [A:set_HF_Mirabelle_hf]: (A = (insert9649339lle_hf @ (the_el1104322134lle_hf @ A) @ bot_bo53200981lle_hf))))),inference(lifteq,[status(thm)],[645])). 76.35/20.47 thf(27,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_ord__le__eq__subst)). 76.35/20.47 thf(231,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 76.35/20.47 thf(232,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:(nat > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ ((C @ B) = D)))))),inference(miniscope,[status(thm)],[231])). 76.35/20.47 thf(234,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ (C @ A) @ D) | (ord_less_eq_nat @ (sk8 @ D @ (C) @ B @ A) @ (sk9 @ D @ (C) @ B @ A)) | (~ ((C @ B) = D)))),inference(cnf,[status(esa)],[232])). 76.35/20.47 thf(237,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : (((C @ B) != D) | (~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ (C @ A) @ D) | (ord_less_eq_nat @ (sk8 @ D @ (C) @ B @ A) @ (sk9 @ D @ (C) @ B @ A)))),inference(lifteq,[status(thm)],[234])). 76.35/20.47 thf(238,plain,(! [C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ (C @ A) @ (C @ B)) | (ord_less_eq_nat @ (sk8 @ (C @ B) @ (C) @ B @ A) @ (sk9 @ (C @ B) @ (C) @ B @ A)))),inference(simp,[status(thm)],[237])). 76.35/20.47 thf(101,axiom,((! [A:set_HF_Mirabelle_hf,B:(set_HF_Mirabelle_hf > $o)]: ((finite586181922lle_hf @ A) => (((! [C:hF_Mirabelle_hf,D:set_HF_Mirabelle_hf]: (((~ (member1367349282lle_hf @ C @ D)) => ((B @ D) => (B @ (insert9649339lle_hf @ C @ D)))) <= (finite586181922lle_hf @ D))) => (B @ A)) <= (B @ bot_bo53200981lle_hf))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_finite__induct)). 76.35/20.47 thf(602,plain,((! [A:set_HF_Mirabelle_hf,B:(set_HF_Mirabelle_hf > $o)]: ((finite586181922lle_hf @ A) => (((! [C:hF_Mirabelle_hf,D:set_HF_Mirabelle_hf]: (((~ (member1367349282lle_hf @ C @ D)) => ((B @ D) => (B @ (insert9649339lle_hf @ C @ D)))) | ~ (finite586181922lle_hf @ D))) => (B @ A)) | ~ (B @ bot_bo53200981lle_hf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 76.35/20.47 thf(39,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((! [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)) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_order__subst2)). 76.35/20.47 thf(280,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((! [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)) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 76.35/20.47 thf(125,axiom,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_singletonD)). 76.35/20.47 thf(692,plain,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 76.35/20.47 thf(43,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_bot__nat__0_Oextremum__unique)). 76.35/20.47 thf(293,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 76.35/20.47 thf(64,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: (((ord_le432112161lle_hf @ C @ B) => (ord_le432112161lle_hf @ (insert9649339lle_hf @ A @ C) @ B)) <= (member1367349282lle_hf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_insert__subsetI)). 76.35/20.47 thf(396,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: (((ord_le432112161lle_hf @ C @ B) => (ord_le432112161lle_hf @ (insert9649339lle_hf @ A @ C) @ B)) | ~ (member1367349282lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 76.35/20.47 thf(114,axiom,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_diff__zero)). 76.35/20.47 thf(658,plain,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 76.35/20.47 thf(659,plain,(! [A:nat] : (((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(cnf,[status(esa)],[658])). 76.35/20.47 thf(660,plain,(! [A:nat] : (((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(lifteq,[status(thm)],[659])). 76.35/20.47 thf(46,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((((B = A) <= (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ (finite1213132899lle_hf @ B))) <= (ord_le432112161lle_hf @ B @ A)) <= (finite586181922lle_hf @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_card__seteq)). 76.35/20.47 thf(312,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((B = A) | ~ (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ (finite1213132899lle_hf @ B)) | ~ (ord_le432112161lle_hf @ B @ A) | ~ (finite586181922lle_hf @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 76.35/20.47 thf(18,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_less__eq__nat_Osimps_I1_J)). 76.35/20.47 thf(206,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 76.35/20.47 thf(60,axiom,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:hF_Mirabelle_hf,D:hF_Mirabelle_hf]: (((insert9649339lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) = (insert9649339lle_hf @ C @ (insert9649339lle_hf @ D @ bot_bo53200981lle_hf))) = (((A = D) & (B = C)) | ((A = C) & (B = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_doubleton__eq__iff)). 76.35/20.47 thf(380,plain,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:hF_Mirabelle_hf,D:hF_Mirabelle_hf]: (((insert9649339lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) = (insert9649339lle_hf @ C @ (insert9649339lle_hf @ D @ bot_bo53200981lle_hf))) = (((A = D) & (B = C)) | ((A = C) & (B = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 76.35/20.47 thf(36,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_dual__order_Oantisym)). 76.35/20.47 thf(270,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 76.35/20.47 thf(90,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:(set_HF_Mirabelle_hf > $o)]: ((((C @ bot_bo53200981lle_hf) => ((! [D:hF_Mirabelle_hf,E:set_HF_Mirabelle_hf]: (((member1367349282lle_hf @ D @ B) => ((ord_le432112161lle_hf @ E @ B) => ((~ (member1367349282lle_hf @ D @ E)) => ((C @ (insert9649339lle_hf @ D @ E)) <= (C @ E))))) <= (finite586181922lle_hf @ E))) => (C @ A))) <= (ord_le432112161lle_hf @ A @ B)) <= (finite586181922lle_hf @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_finite__subset__induct_H)). 76.35/20.47 thf(546,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:(set_HF_Mirabelle_hf > $o)]: (((C @ bot_bo53200981lle_hf) => ((! [D:hF_Mirabelle_hf,E:set_HF_Mirabelle_hf]: (((member1367349282lle_hf @ D @ B) => ((ord_le432112161lle_hf @ E @ B) => ((~ (member1367349282lle_hf @ D @ E)) => ((C @ (insert9649339lle_hf @ D @ E)) | ~ (C @ E))))) | ~ (finite586181922lle_hf @ E))) => (C @ A))) | ~ (ord_le432112161lle_hf @ A @ B) | ~ (finite586181922lle_hf @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 76.35/20.47 thf(23,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) <= (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_dual__order_Otrans)). 76.35/20.47 thf(220,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 76.35/20.47 thf(894,plain,(! [A:set_HF_Mirabelle_hf] : (((is_sin1448700567lle_hf @ A) = (? [B:hF_Mirabelle_hf]: (A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)))))),inference(func_ext,[status(esa)],[628])). 76.35/20.47 thf(951,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | (A != A) | ((sk40 @ B @ A) != B))),inference(simp,[status(thm)],[949])). 76.35/20.47 thf(952,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ B)) | ((sk40 @ B @ A) != B))),inference(simp,[status(thm)],[951])). 76.35/20.47 thf(54,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: (((ord_le432112161lle_hf @ B @ (insert9649339lle_hf @ A @ C)) = (ord_le432112161lle_hf @ B @ C)) <= (~ (member1367349282lle_hf @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subset__insert)). 76.35/20.47 thf(349,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: (((ord_le432112161lle_hf @ B @ (insert9649339lle_hf @ A @ C)) = (ord_le432112161lle_hf @ B @ C)) | (member1367349282lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 76.35/20.47 thf(6,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_order__class_Oorder_Oantisym)). 76.35/20.47 thf(158,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 76.35/20.47 thf(159,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ B @ A)) | (A = B) | (~ (ord_less_eq_nat @ A @ B)))),inference(cnf,[status(esa)],[158])). 76.35/20.47 thf(160,plain,(! [B:nat,A:nat] : ((A = B) | (~ (ord_less_eq_nat @ B @ A)) | (~ (ord_less_eq_nat @ A @ B)))),inference(lifteq,[status(thm)],[159])). 76.35/20.47 thf(132,axiom,((is_emp566801209lle_hf = (^ [A:set_HF_Mirabelle_hf]: (A = bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Set_Ois__empty__def)). 76.35/20.47 thf(716,plain,(((is_emp566801209lle_hf) = (^ [A:set_HF_Mirabelle_hf]: (A = bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 76.35/20.47 thf(717,plain,(((is_emp566801209lle_hf) = (^ [A:set_HF_Mirabelle_hf]: (A = bot_bo53200981lle_hf)))),inference(lifteq,[status(thm)],[716])). 76.35/20.47 thf(788,plain,(! [A:set_HF_Mirabelle_hf] : (((is_emp566801209lle_hf @ A) = (A = bot_bo53200981lle_hf)))),inference(func_ext,[status(esa)],[717])). 76.35/20.47 thf(8,axiom,((! [A:hF_Mirabelle_hf]: ((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_the__elem__eq)). 76.35/20.47 thf(163,plain,((! [A:hF_Mirabelle_hf]: ((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 76.35/20.47 thf(164,plain,(! [A:hF_Mirabelle_hf] : (((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = A))),inference(cnf,[status(esa)],[163])). 76.35/20.47 thf(165,plain,(! [A:hF_Mirabelle_hf] : (((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = A))),inference(lifteq,[status(thm)],[164])). 76.35/20.47 thf(14,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_le__trans)). 76.35/20.47 thf(192,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 76.35/20.47 thf(67,axiom,((! [A:set_HF_Mirabelle_hf]: (ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_empty__subsetI)). 76.35/20.47 thf(406,plain,((! [A:set_HF_Mirabelle_hf]: (ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 76.35/20.47 thf(407,plain,(! [A:set_HF_Mirabelle_hf] : ((ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A))),inference(cnf,[status(esa)],[406])). 76.35/20.47 thf(80,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ B) <= (! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_subsetI)). 76.35/20.47 thf(484,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ B) | ~ (! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 76.35/20.47 thf(83,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((ord_le432112161lle_hf @ (insert9649339lle_hf @ C @ A) @ (insert9649339lle_hf @ C @ B)) <= (ord_le432112161lle_hf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_insert__mono)). 76.35/20.47 thf(493,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((ord_le432112161lle_hf @ (insert9649339lle_hf @ C @ A) @ (insert9649339lle_hf @ C @ B)) | ~ (ord_le432112161lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 76.35/20.47 thf(148,axiom,((! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_hemptyE)). 76.35/20.47 thf(757,plain,((! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ zero_z189798548lle_hf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 76.35/20.47 thf(121,axiom,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_singleton__iff)). 76.35/20.47 thf(680,plain,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 76.35/20.47 thf(681,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) = (A = B)))),inference(cnf,[status(esa)],[680])). 76.35/20.47 thf(682,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) = (A = B)))),inference(lifteq,[status(thm)],[681])). 76.35/20.47 thf(6196,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ (sk7 @ A @ zero_zero_nat) @ (finite1213132899lle_hf @ A))) | ((finite1213132899lle_hf @ bot_bo53200981lle_hf) != (finite1213132899lle_hf @ A)))),inference(paramod_ordered,[status(thm)],[662,6142])). 76.35/20.47 thf(6197,plain,((finite586181922lle_hf @ (sk7 @ (sk7 @ bot_bo53200981lle_hf @ zero_zero_nat) @ (finite1213132899lle_hf @ bot_bo53200981lle_hf)))),inference(pattern_uni,[status(thm)],[6196:[bind(A, $thf(bot_bo53200981lle_hf))]])). 76.35/20.47 thf(5195,plain,(! [C:set_HF_Mirabelle_hf,B:nat,A:nat] : ((ord_le432112161lle_hf @ (sk7 @ C @ B) @ C) | ((ord_less_eq_nat @ zero_zero_nat @ A) != (ord_less_eq_nat @ B @ (finite1213132899lle_hf @ C))))),inference(paramod_ordered,[status(thm)],[821,196])). 76.35/20.47 thf(5196,plain,(! [A:set_HF_Mirabelle_hf] : ((ord_le432112161lle_hf @ (sk7 @ A @ zero_zero_nat) @ A))),inference(pattern_uni,[status(thm)],[5195:[bind(A, $thf(finite1213132899lle_hf @ D)),bind(B, $thf(zero_zero_nat)),bind(C, $thf(D))]])). 76.35/20.47 thf(5243,plain,(! [A:set_HF_Mirabelle_hf] : ((ord_le432112161lle_hf @ (sk7 @ A @ zero_zero_nat) @ A))),inference(simp,[status(thm)],[5196])). 76.35/20.47 thf(52,axiom,((! [A:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf) = (A = bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_bot_Oextremum__unique)). 76.35/20.47 thf(343,plain,((! [A:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf) = (A = bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 76.35/20.47 thf(344,plain,(! [A:set_HF_Mirabelle_hf] : (((ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf) = (A = bot_bo53200981lle_hf)))),inference(cnf,[status(esa)],[343])). 76.35/20.47 thf(345,plain,(! [A:set_HF_Mirabelle_hf] : (((ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf) = (A = bot_bo53200981lle_hf)))),inference(lifteq,[status(thm)],[344])). 76.35/20.47 thf(5271,plain,(! [B:set_HF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : ((B = bot_bo53200981lle_hf) | ((ord_le432112161lle_hf @ (sk7 @ A @ zero_zero_nat) @ A) != (ord_le432112161lle_hf @ B @ bot_bo53200981lle_hf)))),inference(paramod_ordered,[status(thm)],[5243,345])). 76.35/20.47 thf(5272,plain,(((sk7 @ bot_bo53200981lle_hf @ zero_zero_nat) = bot_bo53200981lle_hf)),inference(pattern_uni,[status(thm)],[5271:[bind(A, $thf(bot_bo53200981lle_hf)),bind(B, $thf(sk7 @ bot_bo53200981lle_hf @ zero_zero_nat))]])). 76.35/20.47 thf(5282,plain,(((sk7 @ bot_bo53200981lle_hf @ zero_zero_nat) = bot_bo53200981lle_hf)),inference(lifteq,[status(thm)],[5272])). 76.35/20.47 thf(6292,plain,((finite586181922lle_hf @ (sk7 @ bot_bo53200981lle_hf @ zero_zero_nat))),inference(rewrite,[status(thm)],[6197,5282,662])). 76.35/20.47 thf(116,axiom,((! [A:set_HF_Mirabelle_hf]: ((! [B:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ B @ A)) = (A = bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_all__not__in__conv)). 76.35/20.47 thf(663,plain,((! [A:set_HF_Mirabelle_hf]: ((! [B:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ B @ A)) = (A = bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 76.35/20.47 thf(664,plain,(! [A:set_HF_Mirabelle_hf] : (((! [B:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ B @ A)) = (A = bot_bo53200981lle_hf)))),inference(cnf,[status(esa)],[663])). 76.35/20.47 thf(665,plain,(! [A:set_HF_Mirabelle_hf] : (((! [B:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ B @ A)) = (A = bot_bo53200981lle_hf)))),inference(lifteq,[status(thm)],[664])). 76.35/20.47 thf(66,axiom,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: ((insert9649339lle_hf @ A @ (insert9649339lle_hf @ B @ C)) = (insert9649339lle_hf @ B @ (insert9649339lle_hf @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_insert__commute)). 76.35/20.47 thf(403,plain,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: ((insert9649339lle_hf @ A @ (insert9649339lle_hf @ B @ C)) = (insert9649339lle_hf @ B @ (insert9649339lle_hf @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 76.35/20.47 thf(169,plain,(! [B:nat,A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk1 @ B @ A)) | (finite586181922lle_hf @ A))),inference(cnf,[status(esa)],[166])). 76.35/20.47 thf(98,axiom,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: (((A = bot_bo53200981lle_hf) | (A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))) <= (ord_le432112161lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_subset__singletonD)). 76.35/20.47 thf(593,plain,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((A = bot_bo53200981lle_hf) | (A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) | ~ (ord_le432112161lle_hf @ A @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 76.35/20.47 thf(5437,plain,(! [C:set_HF_Mirabelle_hf,B:nat,A:nat] : ((finite586181922lle_hf @ (sk7 @ C @ B)) | ((ord_less_eq_nat @ zero_zero_nat @ A) != (ord_less_eq_nat @ B @ (finite1213132899lle_hf @ C))))),inference(paramod_ordered,[status(thm)],[821,198])). 76.35/20.47 thf(5438,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ A @ zero_zero_nat)))),inference(pattern_uni,[status(thm)],[5437:[bind(A, $thf(finite1213132899lle_hf @ D)),bind(B, $thf(zero_zero_nat)),bind(C, $thf(D))]])). 76.35/20.47 thf(5497,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ A @ zero_zero_nat)))),inference(simp,[status(thm)],[5438])). 76.35/20.47 thf(143,axiom,((! [A:hF_Mirabelle_hf]: ((A != zero_z189798548lle_hf) => (~ (! [B:hF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ B @ C) <= (A = (hF_Mirabelle_hinsert @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_hf__cases)). 76.35/20.47 thf(742,plain,((! [A:hF_Mirabelle_hf]: ((~ (A = zero_z189798548lle_hf)) => (~ (! [B:hF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ B @ C) | ~ (A = (hF_Mirabelle_hinsert @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 76.35/20.47 thf(6177,plain,(! [B:set_HF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ (sk7 @ B @ zero_zero_nat) @ (finite1213132899lle_hf @ B))) | ((finite1213132899lle_hf @ (sk7 @ A @ zero_zero_nat)) != (finite1213132899lle_hf @ B)))),inference(paramod_ordered,[status(thm)],[5778,6142])). 76.35/20.47 thf(6178,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ (sk7 @ (sk7 @ A @ zero_zero_nat) @ zero_zero_nat) @ (finite1213132899lle_hf @ (sk7 @ A @ zero_zero_nat)))))),inference(pattern_uni,[status(thm)],[6177:[bind(A, $thf(C)),bind(B, $thf(sk7 @ C @ zero_zero_nat))]])). 76.35/20.47 thf(6273,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ (sk7 @ (sk7 @ A @ zero_zero_nat) @ zero_zero_nat) @ (finite1213132899lle_hf @ (sk7 @ A @ zero_zero_nat)))))),inference(simp,[status(thm)],[6178])). 76.35/20.47 thf(6748,plain,(! [A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk7 @ (sk7 @ (sk7 @ A @ zero_zero_nat) @ zero_zero_nat) @ zero_zero_nat)))),inference(rewrite,[status(thm)],[6273,5778])). 76.35/20.47 thf(92,axiom,((ord_le432112161lle_hf = (^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ B) <= (member1367349282lle_hf @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_subset__iff)). 76.35/20.47 thf(577,plain,(((ord_le432112161lle_hf) = (^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ B) | ~ (member1367349282lle_hf @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 76.35/20.47 thf(578,plain,(((ord_le432112161lle_hf) = (^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ B) | ~ (member1367349282lle_hf @ C @ A))))),inference(lifteq,[status(thm)],[577])). 76.35/20.47 thf(25,axiom,((! [A:nat]: ((A = bot_bot_nat) <= (ord_less_eq_nat @ A @ bot_bot_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_bot_Oextremum__uniqueI)). 76.35/20.47 thf(225,plain,((! [A:nat]: ((A = bot_bot_nat) | ~ (ord_less_eq_nat @ A @ bot_bot_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 76.35/20.47 thf(146,axiom,(((hF_Mirabelle_Abs_hf @ zero_zero_nat) = zero_z189798548lle_hf)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Abs__hf__0)). 76.35/20.47 thf(752,plain,(((hF_Mirabelle_Abs_hf @ zero_zero_nat) = zero_z189798548lle_hf)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 76.35/20.47 thf(753,plain,(((hF_Mirabelle_Abs_hf @ zero_zero_nat) = zero_z189798548lle_hf)),inference(lifteq,[status(thm)],[752])). 76.35/20.47 thf(108,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: (((~ (member1367349282lle_hf @ A @ C)) => (((insert9649339lle_hf @ A @ B) = (insert9649339lle_hf @ A @ C)) = (B = C))) <= (~ (member1367349282lle_hf @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_insert__ident)). 76.35/20.47 thf(637,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: (((~ (member1367349282lle_hf @ A @ C)) => (((insert9649339lle_hf @ A @ B) = (insert9649339lle_hf @ A @ C)) = (B = C))) | (member1367349282lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 76.35/20.47 thf(123,axiom,((! [A:nat,B:nat]: (((semiri2013084963it_nat @ A @ B) = zero_zero_nat) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_push__bit__eq__0__iff)). 76.35/20.47 thf(686,plain,((! [A:nat,B:nat]: (((semiri2013084963it_nat @ A @ B) = zero_zero_nat) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 76.35/20.47 thf(77,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ B) => ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_subsetD)). 76.35/20.47 thf(476,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ B) => ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 76.35/20.47 thf(63,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ (insert9649339lle_hf @ A @ B) @ C) = ((ord_le432112161lle_hf @ B @ C) & (member1367349282lle_hf @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_insert__subset)). 76.35/20.47 thf(393,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ (insert9649339lle_hf @ A @ B) @ C) = ((ord_le432112161lle_hf @ B @ C) & (member1367349282lle_hf @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 76.35/20.47 thf(111,axiom,((! [A:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => ((~ (! [B:set_HF_Mirabelle_hf]: ((~ (finite586181922lle_hf @ B)) <= (? [C:hF_Mirabelle_hf]: (A = (insert9649339lle_hf @ C @ B)))))) <= (A != bot_bo53200981lle_hf))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_finite_Ocases)). 76.35/20.47 thf(647,plain,((! [A:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => (~ (! [B:set_HF_Mirabelle_hf]: (~ (finite586181922lle_hf @ B) | ~ (? [C:hF_Mirabelle_hf]: (A = (insert9649339lle_hf @ C @ B))))) | (A = bot_bo53200981lle_hf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 76.35/20.47 thf(10,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_181_antisym__conv)). 76.35/20.47 thf(173,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)],[10])). 76.35/20.47 thf(134,axiom,((bot_bo1263054448e_hf_o = (^ [A:hF_Mirabelle_hf]: (member1367349282lle_hf @ A @ bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_bot__empty__eq)). 76.35/20.47 thf(721,plain,(((bot_bo1263054448e_hf_o) = (^ [A:hF_Mirabelle_hf]: (member1367349282lle_hf @ A @ bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 76.35/20.47 thf(181,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (~ (sk2 @ A)) | (~ (A @ C)) | (ord_less_eq_nat @ C @ (sk4 @ (A))))),inference(cnf,[status(esa)],[178])). 76.35/20.47 thf(183,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (~ (sk2 @ A)) | (~ (A @ C)) | (ord_less_eq_nat @ C @ (sk4 @ (A))))),inference(simp,[status(thm)],[181])). 76.35/20.47 thf(3136,plain,(! [D:nat,C:nat,B:(nat > $o),A:nat] : ((~ (A = zero_zero_nat)) | (~ (sk2 @ (B))) | (~ (B @ D)) | (ord_less_eq_nat @ D @ (sk4 @ (B))) | ((zero_zero_nat = A) != (B @ C)))),inference(paramod_ordered,[status(thm)],[673,183])). 76.35/20.47 thf(3228,plain,(! [D:nat,C:nat,B:(nat > $o),A:nat] : ((A != zero_zero_nat) | (~ (sk2 @ (B))) | (~ (B @ D)) | (ord_less_eq_nat @ D @ (sk4 @ (B))) | ((zero_zero_nat = A) != (B @ C)))),inference(lifteq,[status(thm)],[3136])). 76.35/20.47 thf(3328,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ (sk4 @ (^ [B:nat]: (zero_zero_nat = zero_zero_nat)))) | (~ (zero_zero_nat = zero_zero_nat)) | (~ (sk2 @ (^ [B:nat]: (zero_zero_nat = zero_zero_nat)))))),inference(pre_uni,[status(thm)],[3228:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(^ [E:nat]: (zero_zero_nat = zero_zero_nat))),bind(C, $thf(C)),bind(D, $thf(D))]])). 76.35/20.47 thf(3363,plain,(! [A:nat] : ((zero_zero_nat != zero_zero_nat) | (ord_less_eq_nat @ A @ (sk4 @ (^ [B:nat]: (zero_zero_nat = zero_zero_nat)))) | (~ (sk2 @ (^ [B:nat]: (zero_zero_nat = zero_zero_nat)))))),inference(lifteq,[status(thm)],[3328])). 76.35/20.47 thf(3364,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ (sk4 @ (^ [B:nat]: ($true)))) | (~ (sk2 @ (^ [B:nat]: ($true)))))),inference(simp,[status(thm)],[3363])). 76.35/20.47 thf(141,axiom,((hF_Mirabelle_hmem = (^ [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: (member1367349282lle_hf @ A @ (hF_Mirabelle_hfset @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_hmem__def)). 76.35/20.47 thf(737,plain,(((hF_Mirabelle_hmem) = (^ [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: (member1367349282lle_hf @ A @ (hF_Mirabelle_hfset @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 76.35/20.47 thf(738,plain,(((^ [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: (member1367349282lle_hf @ A @ (hF_Mirabelle_hfset @ B))) = (hF_Mirabelle_hmem))),inference(lifteq,[status(thm)],[737])). 76.35/20.47 thf(792,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((member1367349282lle_hf @ A @ (hF_Mirabelle_hfset @ B)) = (hF_Mirabelle_hmem @ A @ B)))),inference(func_ext,[status(esa)],[738])). 76.35/20.47 thf(88,axiom,((! [A:(set_HF_Mirabelle_hf > $o),B:set_HF_Mirabelle_hf]: ((! [C:set_HF_Mirabelle_hf]: ((A @ C) <= (~ (finite586181922lle_hf @ C)))) => ((A @ bot_bo53200981lle_hf) => ((! [C:hF_Mirabelle_hf,D:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ D) => ((~ (member1367349282lle_hf @ C @ D)) => ((A @ (insert9649339lle_hf @ C @ D)) <= (A @ D))))) => (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_infinite__finite__induct)). 76.35/20.47 thf(508,plain,((! [A:(set_HF_Mirabelle_hf > $o),B:set_HF_Mirabelle_hf]: ((! [C:set_HF_Mirabelle_hf]: ((A @ C) | (finite586181922lle_hf @ C))) => ((A @ bot_bo53200981lle_hf) => ((! [C:hF_Mirabelle_hf,D:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ D) => ((~ (member1367349282lle_hf @ C @ D)) => ((A @ (insert9649339lle_hf @ C @ D)) | ~ (A @ D))))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 76.35/20.47 thf(656,plain,(! [A:nat] : (((semiri2013084963it_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(cnf,[status(esa)],[655])). 76.35/20.47 thf(657,plain,(! [A:nat] : (((semiri2013084963it_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(lifteq,[status(thm)],[656])). 76.35/20.47 thf(119,axiom,((! [A:set_HF_Mirabelle_hf]: ((? [B:hF_Mirabelle_hf]: (member1367349282lle_hf @ B @ A)) = (A != bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_ex__in__conv)). 76.35/20.47 thf(674,plain,((! [A:set_HF_Mirabelle_hf]: ((? [B:hF_Mirabelle_hf]: (member1367349282lle_hf @ B @ A)) = (~ (A = bot_bo53200981lle_hf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 76.35/20.47 thf(2740,plain,((zero_zero_nat = (sk4 @ (= @ nat @ zero_zero_nat))) | (~ (sk2 @ (= @ nat @ zero_zero_nat)))),inference(pre_uni,[status(thm)],[2623:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(= @ nat @ zero_zero_nat)),bind(C, $thf(zero_zero_nat))]])). 76.35/20.47 thf(2909,plain,(((sk4 @ (= @ nat @ zero_zero_nat)) = zero_zero_nat) | (~ (sk2 @ (= @ nat @ zero_zero_nat)))),inference(lifteq,[status(thm)],[2740])). 76.35/20.47 thf(57,axiom,((! [A:set_HF_Mirabelle_hf,B:(set_HF_Mirabelle_hf > $o)]: ((((B @ A) <= (! [C:set_HF_Mirabelle_hf,D:hF_Mirabelle_hf]: (((B @ C) => (B @ (insert9649339lle_hf @ D @ C))) <= (finite586181922lle_hf @ C)))) <= (B @ bot_bo53200981lle_hf)) <= (finite586181922lle_hf @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_finite_Oinducts)). 76.35/20.47 thf(360,plain,((! [A:set_HF_Mirabelle_hf,B:(set_HF_Mirabelle_hf > $o)]: ((B @ A) | ~ (! [C:set_HF_Mirabelle_hf,D:hF_Mirabelle_hf]: (((B @ C) => (B @ (insert9649339lle_hf @ D @ C))) | ~ (finite586181922lle_hf @ C))) | ~ (B @ bot_bo53200981lle_hf) | ~ (finite586181922lle_hf @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 76.35/20.47 thf(133,axiom,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_cancel__comm__monoid__add__class_Odiff__cancel)). 76.35/20.47 thf(718,plain,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 76.35/20.47 thf(69,axiom,((! [A:set_HF_Mirabelle_hf,B:(set_HF_Mirabelle_hf > $o),C:(hF_Mirabelle_hf > nat)]: ((finite586181922lle_hf @ A) => (((B @ A) <= (! [D:hF_Mirabelle_hf,E:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ E) => ((! [F:hF_Mirabelle_hf]: ((member1367349282lle_hf @ F @ E) => (ord_less_eq_nat @ (C @ F) @ (C @ D)))) => ((B @ (insert9649339lle_hf @ D @ E)) <= (B @ E)))))) <= (B @ bot_bo53200981lle_hf))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_finite__ranking__induct)). 76.35/20.47 thf(430,plain,((! [A:set_HF_Mirabelle_hf,B:(set_HF_Mirabelle_hf > $o),C:(hF_Mirabelle_hf > nat)]: ((finite586181922lle_hf @ A) => ((B @ A) | ~ (! [D:hF_Mirabelle_hf,E:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ E) => ((! [F:hF_Mirabelle_hf]: ((member1367349282lle_hf @ F @ E) => (ord_less_eq_nat @ (C @ F) @ (C @ D)))) => ((B @ (insert9649339lle_hf @ D @ E)) | ~ (B @ E))))) | ~ (B @ bot_bo53200981lle_hf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 76.35/20.47 thf(124,axiom,((! [A:set_HF_Mirabelle_hf]: ((! [B:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ B @ A)) => (ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_subset__emptyI)). 76.35/20.47 thf(689,plain,((! [A:set_HF_Mirabelle_hf]: ((! [B:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ B @ A)) => (ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 76.35/20.47 thf(44,axiom,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)) => (((~ (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ B @ A)) => ((((~ (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ C @ B)) => ((~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B)))) <= ((~ (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)))) <= ((~ (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_le__cases3)). 76.35/20.47 thf(296,plain,((! [A:nat,B:nat,C:nat]: ((~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)) => ((~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ A)) => (((~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ C @ B)) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))) | ~ (~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ C)))) | ~ (~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 76.35/20.47 thf(3,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ bot_bot_nat) = (A = bot_bot_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_bot_Oextremum__unique)). 76.35/20.47 thf(151,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ bot_bot_nat) = (A = bot_bot_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 76.35/20.47 thf(152,plain,(! [A:nat] : (((ord_less_eq_nat @ A @ bot_bot_nat) = (A = bot_bot_nat)))),inference(cnf,[status(esa)],[151])). 76.35/20.47 thf(153,plain,(! [A:nat] : (((ord_less_eq_nat @ A @ bot_bot_nat) = (A = bot_bot_nat)))),inference(lifteq,[status(thm)],[152])). 76.35/20.47 thf(780,plain,(! [A:nat] : (((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(rewrite,[status(thm)],[153,698])). 76.35/20.47 thf(1931,plain,(! [D:nat,C:nat,B:(nat > $o),A:nat] : ((~ (A = zero_zero_nat)) | (B @ (sk3 @ D @ (B))) | (sk2 @ (B)) | ((ord_less_eq_nat @ A @ zero_zero_nat) != (B @ C)))),inference(paramod_ordered,[status(thm)],[780,180])). 76.35/20.47 thf(2006,plain,(! [D:nat,C:nat,B:(nat > $o),A:nat] : ((A != zero_zero_nat) | (B @ (sk3 @ D @ (B))) | (sk2 @ (B)) | ((ord_less_eq_nat @ A @ zero_zero_nat) != (B @ C)))),inference(lifteq,[status(thm)],[1931])). 76.35/20.47 thf(2094,plain,(! [A:nat] : ((sk2 @ (^ [B:nat]: (ord_less_eq_nat @ B @ zero_zero_nat))) | (ord_less_eq_nat @ (sk3 @ A @ (^ [B:nat]: (ord_less_eq_nat @ B @ zero_zero_nat))) @ zero_zero_nat))),inference(pre_uni,[status(thm)],[2006:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(^ [E:nat]: (ord_less_eq_nat @ E @ zero_zero_nat))),bind(C, $thf(zero_zero_nat)),bind(D, $thf(D))]])). 76.35/20.47 thf(2210,plain,(! [A:nat] : ((sk2 @ (^ [B:nat]: (ord_less_eq_nat @ B @ zero_zero_nat))) | (ord_less_eq_nat @ (sk3 @ A @ (^ [B:nat]: (ord_less_eq_nat @ B @ zero_zero_nat))) @ zero_zero_nat))),inference(simp,[status(thm)],[2094])). 76.35/20.47 thf(7859,plain,(! [A:nat] : ((sk2 @ (^ [B:nat]: (B = zero_zero_nat))) | ((sk3 @ A @ (^ [B:nat]: (ord_less_eq_nat @ B @ zero_zero_nat))) = zero_zero_nat))),inference(rewrite,[status(thm)],[2210,780])). 76.35/20.47 thf(7860,plain,(! [A:nat] : (((sk3 @ A @ (^ [B:nat]: (ord_less_eq_nat @ B @ zero_zero_nat))) = zero_zero_nat) | (sk2 @ (^ [B:nat]: (B = zero_zero_nat))))),inference(lifteq,[status(thm)],[7859])). 76.35/20.47 thf(904,plain,(! [A:set_HF_Mirabelle_hf] : (((ord_le432112161lle_hf @ A) = (^ [B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ B) | ~ (member1367349282lle_hf @ C @ A)))))),inference(func_ext,[status(esa)],[578])). 76.35/20.47 thf(11,axiom,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_le__numeral__extra_I3_J)). 76.35/20.47 thf(176,plain,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 76.35/20.47 thf(187,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((~ (ord_less_eq_nat @ C @ D)) | (ord_less_eq_nat @ A @ (B @ D)) | (~ (ord_less_eq_nat @ (B @ (sk5 @ D @ C @ (B) @ A)) @ (B @ (sk6 @ D @ C @ (B) @ A)))) | (~ (A = (B @ C))))),inference(cnf,[status(esa)],[185])). 76.35/20.47 thf(190,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((A != (B @ C)) | (~ (ord_less_eq_nat @ C @ D)) | (ord_less_eq_nat @ A @ (B @ D)) | (~ (ord_less_eq_nat @ (B @ (sk5 @ D @ C @ (B) @ A)) @ (B @ (sk6 @ D @ C @ (B) @ A)))))),inference(lifteq,[status(thm)],[187])). 76.35/20.47 thf(191,plain,(! [C:nat,B:nat,A:(nat > nat)] : ((~ (ord_less_eq_nat @ B @ C)) | (ord_less_eq_nat @ (A @ B) @ (A @ C)) | (~ (ord_less_eq_nat @ (A @ (sk5 @ C @ B @ (A) @ (A @ B))) @ (A @ (sk6 @ C @ B @ (A) @ (A @ B))))))),inference(simp,[status(thm)],[190])). 76.35/20.47 thf(731,plain,(! [A:nat] : (((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(cnf,[status(esa)],[730])). 76.35/20.47 thf(732,plain,(! [A:nat] : (((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(lifteq,[status(thm)],[731])). 76.35/20.47 thf(93,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ C @ B)) <= (member1367349282lle_hf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_insertI2)). 76.35/20.47 thf(579,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ C @ B)) | ~ (member1367349282lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 76.35/20.47 thf(17,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_172_dual__order_Oeq__iff)). 76.35/20.47 thf(204,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)],[17])). 76.35/20.47 thf(543,plain,((~ (? [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((insert9649339lle_hf @ A @ B) = bot_bo53200981lle_hf)))),inference(miniscope,[status(thm)],[542])). 76.35/20.47 thf(544,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ ((insert9649339lle_hf @ A @ B) = bot_bo53200981lle_hf)))),inference(cnf,[status(esa)],[543])). 76.35/20.47 thf(545,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((insert9649339lle_hf @ A @ B) != bot_bo53200981lle_hf))),inference(lifteq,[status(thm)],[544])). 76.35/20.47 thf(33,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_le0)). 76.35/20.47 thf(259,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 76.35/20.47 thf(109,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => ((((finite1213132899lle_hf @ B) = (finite1213132899lle_hf @ A)) => (B = A)) <= (ord_le432112161lle_hf @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_card__subset__eq)). 76.35/20.47 thf(641,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => ((((finite1213132899lle_hf @ B) = (finite1213132899lle_hf @ A)) => (B = A)) | ~ (ord_le432112161lle_hf @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 76.35/20.47 thf(91,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: (((A = C) <= (~ (member1367349282lle_hf @ A @ B))) => (member1367349282lle_hf @ A @ (insert9649339lle_hf @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_insertCI)). 76.35/20.47 thf(572,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: (((A = C) | (member1367349282lle_hf @ A @ B)) => (member1367349282lle_hf @ A @ (insert9649339lle_hf @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 76.35/20.47 thf(2399,plain,(! [C:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ B)) != (member1367349282lle_hf @ C @ bot_bo53200981lle_hf)))),inference(paramod_ordered,[status(thm)],[464,670])). 76.35/20.47 thf(2425,plain,(! [C:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((A != C) | ((insert9649339lle_hf @ A @ B) != bot_bo53200981lle_hf))),inference(simp,[status(thm)],[2399])). 76.35/20.47 thf(2442,plain,(! [B:hF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : (((insert9649339lle_hf @ B @ A) != bot_bo53200981lle_hf))),inference(simp,[status(thm)],[2425])). 76.35/20.47 thf(49,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_dual__order_Orefl)). 76.35/20.47 thf(335,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 76.35/20.47 thf(233,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ (C @ A) @ D) | (~ (ord_less_eq_nat @ (C @ (sk8 @ D @ (C) @ B @ A)) @ (C @ (sk9 @ D @ (C) @ B @ A)))) | (~ ((C @ B) = D)))),inference(cnf,[status(esa)],[232])). 76.35/20.47 thf(235,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : (((C @ B) != D) | (~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ (C @ A) @ D) | (~ (ord_less_eq_nat @ (C @ (sk8 @ D @ (C) @ B @ A)) @ (C @ (sk9 @ D @ (C) @ B @ A)))))),inference(lifteq,[status(thm)],[233])). 76.35/20.47 thf(236,plain,(! [C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ (C @ A) @ (C @ B)) | (~ (ord_less_eq_nat @ (C @ (sk8 @ (C @ B) @ (C) @ B @ A)) @ (C @ (sk9 @ (C @ B) @ (C) @ B @ A)))))),inference(simp,[status(thm)],[235])). 76.35/20.47 thf(1467,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((? [C:hF_Mirabelle_hf]: (B = (insert9649339lle_hf @ C @ bot_bo53200981lle_hf))) | ((is_sin1448700567lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) != (is_sin1448700567lle_hf @ B)))),inference(paramod_ordered,[status(thm)],[475,894])). 76.35/20.47 thf(1468,plain,(! [A:hF_Mirabelle_hf] : ((? [B:hF_Mirabelle_hf]: ((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))),inference(pattern_uni,[status(thm)],[1467:[bind(A, $thf(C)),bind(B, $thf(insert9649339lle_hf @ C @ bot_bo53200981lle_hf))]])). 76.35/20.47 thf(1481,plain,(! [A:hF_Mirabelle_hf] : (((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ (sk65 @ A) @ bot_bo53200981lle_hf)))),inference(cnf,[status(esa)],[1468])). 76.35/20.47 thf(1482,plain,(! [A:hF_Mirabelle_hf] : (((insert9649339lle_hf @ (sk65 @ A) @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(lifteq,[status(thm)],[1481])). 76.35/20.47 thf(1483,plain,(! [A:hF_Mirabelle_hf] : (((insert9649339lle_hf @ (sk65 @ A) @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(simp,[status(thm)],[1482])). 76.35/20.47 thf(1842,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = B) | ((insert9649339lle_hf @ (sk65 @ A) @ bot_bo53200981lle_hf) != (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)))),inference(paramod_ordered,[status(thm)],[1483,165])). 76.35/20.47 thf(1843,plain,(! [A:hF_Mirabelle_hf] : (((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = (sk65 @ A)))),inference(pattern_uni,[status(thm)],[1842:[bind(A, $thf(C)),bind(B, $thf(sk65 @ C))]])). 76.35/20.47 thf(1855,plain,(! [A:hF_Mirabelle_hf] : (((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = (sk65 @ A)))),inference(simp,[status(thm)],[1843])). 76.35/20.47 thf(1865,plain,(! [A:hF_Mirabelle_hf] : (((sk65 @ A) = A))),inference(rewrite,[status(thm)],[1855,165])). 76.35/20.47 thf(59,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ B) => ((insert9649339lle_hf @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_insert__absorb)). 76.35/20.47 thf(377,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ B) => ((insert9649339lle_hf @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 76.35/20.47 thf(19,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)). 76.35/20.47 thf(208,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)],[19])). 76.35/20.47 thf(100,axiom,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: (((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_singleton__inject)). 76.35/20.47 thf(599,plain,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf]: (((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 76.35/20.47 thf(900,plain,(! [A:hF_Mirabelle_hf] : (((= @ hF_Mirabelle_hf @ A) = (^ [B:hF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ C @ A) = (hF_Mirabelle_hmem @ C @ B)))))),inference(func_ext,[status(esa)],[751])). 76.35/20.47 thf(172,plain,(! [B:nat,A:set_HF_Mirabelle_hf] : ((~ (ord_less_eq_nat @ (finite1213132899lle_hf @ (sk1 @ B @ A)) @ B)) | (finite586181922lle_hf @ A))),inference(cnf,[status(esa)],[166])). 76.35/20.47 thf(205,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = (= @ nat))),inference(lifteq,[status(thm)],[204])). 76.35/20.47 thf(831,plain,(! [A:nat] : (((^ [B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = (= @ nat @ A)))),inference(func_ext,[status(esa)],[205])). 76.35/20.47 thf(106,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ B) => ((finite586181922lle_hf @ A) <= (finite586181922lle_hf @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_finite__subset)). 76.35/20.47 thf(631,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ B) => ((finite586181922lle_hf @ A) | ~ (finite586181922lle_hf @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 76.35/20.47 thf(21,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_le__antisym)). 76.35/20.47 thf(213,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 76.35/20.47 thf(103,axiom,((! [A:set_HF_Mirabelle_hf,B:nat]: ((~ (finite586181922lle_hf @ A)) => (? [C:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ C) & ((finite1213132899lle_hf @ C) = B) & (ord_le432112161lle_hf @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_infinite__arbitrarily__large)). 76.35/20.47 thf(621,plain,((! [A:set_HF_Mirabelle_hf,B:nat]: ((~ (finite586181922lle_hf @ A)) => (? [C:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ C) & ((finite1213132899lle_hf @ C) = B) & (ord_le432112161lle_hf @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 76.35/20.47 thf(762,plain,((z = zero_z189798548lle_hf) | (! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ z))),inference(bool_ext,[status(thm)],[150])). 76.35/20.47 thf(764,plain,((z = zero_z189798548lle_hf) | (! [A:hF_Mirabelle_hf]: ~ (hF_Mirabelle_hmem @ A @ z))),inference(lifteq,[status(thm)],[762])). 76.35/20.47 thf(766,plain,(! [A:hF_Mirabelle_hf] : ((~ (hF_Mirabelle_hmem @ A @ z)) | (z = zero_z189798548lle_hf))),inference(cnf,[status(esa)],[764])). 76.35/20.47 thf(848,plain,(! [A:hF_Mirabelle_hf] : ((~ (hF_Mirabelle_hmem @ A @ z)))),inference(simplifyReflect,[status(thm)],[766,844])). 76.35/20.47 thf(895,plain,(! [A:set_HF_Mirabelle_hf] : (((is_sin1448700567lle_hf @ A) = (A = (insert9649339lle_hf @ (the_el1104322134lle_hf @ A) @ bot_bo53200981lle_hf))))),inference(func_ext,[status(esa)],[646])). 76.35/20.47 thf(65,axiom,((! [A:set_HF_Mirabelle_hf]: ((is_sin1448700567lle_hf @ A) => (~ (! [B:hF_Mirabelle_hf]: (A != (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_is__singletonE)). 76.35/20.47 thf(399,plain,((! [A:set_HF_Mirabelle_hf]: ((is_sin1448700567lle_hf @ A) => (~ (! [B:hF_Mirabelle_hf]: ~ (A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 76.35/20.47 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_184_le__cases)). 76.35/20.47 thf(278,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])). 76.35/20.47 thf(24,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_188_eq__iff)). 76.35/20.47 thf(223,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)],[24])). 76.35/20.47 thf(87,axiom,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ C)) => ((A != B) => (member1367349282lle_hf @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_insertE)). 76.35/20.47 thf(505,plain,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ C)) => ((~ (A = B)) => (member1367349282lle_hf @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 76.35/20.47 thf(167,plain,(! [B:nat,A:set_HF_Mirabelle_hf] : ((finite586181922lle_hf @ (sk1 @ B @ A)) | (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ B))),inference(cnf,[status(esa)],[166])). 76.35/20.47 thf(35,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_antisym)). 76.35/20.47 thf(267,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 76.35/20.47 thf(1089,plain,(! [C:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((sk40 @ C @ B) != C) | ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) != (member1367349282lle_hf @ B @ C)))),inference(paramod_ordered,[status(thm)],[696,952])). 76.35/20.47 thf(1090,plain,(! [A:hF_Mirabelle_hf] : (((sk40 @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf) @ A) != (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(pattern_uni,[status(thm)],[1089:[bind(A, $thf(D)),bind(B, $thf(D)),bind(C, $thf(insert9649339lle_hf @ D @ bot_bo53200981lle_hf))]])). 76.35/20.47 thf(1102,plain,(! [A:hF_Mirabelle_hf] : (((sk40 @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf) @ A) != (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(simp,[status(thm)],[1090])). 76.35/20.47 thf(82,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: (((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B)) <= (ord_le432112161lle_hf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_in__mono)). 76.35/20.47 thf(490,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: (((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B)) | ~ (ord_le432112161lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 76.35/20.47 thf(58,axiom,((! [A:set_HF_Mirabelle_hf]: (((finite1213132899lle_hf @ A) = zero_zero_nat) = ((A = bot_bo53200981lle_hf) | ~ (finite586181922lle_hf @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_card__eq__0__iff)). 76.35/20.47 thf(374,plain,((! [A:set_HF_Mirabelle_hf]: (((finite1213132899lle_hf @ A) = zero_zero_nat) = ((A = bot_bo53200981lle_hf) | ~ (finite586181922lle_hf @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 76.35/20.47 thf(31,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_order__refl)). 76.35/20.47 thf(255,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 76.35/20.47 thf(2115,plain,(! [A:nat] : ((sk2 @ (^ [B:nat]: (B = zero_zero_nat))) | ((sk3 @ A @ (^ [B:nat]: (B = zero_zero_nat))) = zero_zero_nat))),inference(pre_uni,[status(thm)],[2025:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(^ [E:nat]: (E = zero_zero_nat))),bind(C, $thf(zero_zero_nat)),bind(D, $thf(D))]])). 76.35/20.47 thf(2233,plain,(! [A:nat] : (((sk3 @ A @ (^ [B:nat]: (B = zero_zero_nat))) = zero_zero_nat) | (sk2 @ (^ [B:nat]: (B = zero_zero_nat))))),inference(lifteq,[status(thm)],[2115])). 76.35/20.47 thf(2234,plain,(! [A:nat] : (((sk3 @ A @ (^ [B:nat]: (B = zero_zero_nat))) = zero_zero_nat) | (sk2 @ (^ [B:nat]: (B = zero_zero_nat))))),inference(simp,[status(thm)],[2233])). 76.35/20.47 thf(1508,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((hF_Mirabelle_hfset @ A) != bot_bo53200981lle_hf) | (~ (hF_Mirabelle_hmem @ B @ A)) | (zero_z189798548lle_hf != zero_z189798548lle_hf))),inference(paramod_ordered,[status(thm)],[1040,749])). 76.35/20.47 thf(1509,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((hF_Mirabelle_hfset @ A) != bot_bo53200981lle_hf) | (~ (hF_Mirabelle_hmem @ B @ A)))),inference(pattern_uni,[status(thm)],[1508:[]])). 76.35/20.47 thf(147,axiom,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ A @ (hF_Mirabelle_hinsert @ B @ C)) = ((hF_Mirabelle_hmem @ A @ C) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_hmem__hinsert)). 76.35/20.47 thf(754,plain,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ A @ (hF_Mirabelle_hinsert @ B @ C)) = ((hF_Mirabelle_hmem @ A @ C) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 76.35/20.47 thf(6663,plain,(! [C:nat,B:set_HF_Mirabelle_hf,A:nat] : ((~ (sk2 @ (^ [D:nat]: ($true)))) | (finite586181922lle_hf @ B) | ((ord_less_eq_nat @ A @ (sk4 @ (^ [D:nat]: ($true)))) != (ord_less_eq_nat @ (finite1213132899lle_hf @ (sk1 @ C @ B)) @ C)))),inference(paramod_ordered,[status(thm)],[3364,172])). 76.35/20.47 thf(6664,plain,(! [A:set_HF_Mirabelle_hf] : ((~ (sk2 @ (^ [B:nat]: ($true)))) | (finite586181922lle_hf @ A))),inference(pattern_uni,[status(thm)],[6663:[bind(A, $thf(finite1213132899lle_hf @ (sk1 @ (sk4 @ (^ [E:nat]: ($true))) @ F))),bind(B, $thf(F)),bind(C, $thf(sk4 @ (^ [D:nat]: ($true))))]])). 76.35/20.47 thf(6719,plain,(! [A:set_HF_Mirabelle_hf] : ((~ (sk2 @ (^ [B:nat]: ($true)))) | (finite586181922lle_hf @ A))),inference(simp,[status(thm)],[6664])). 76.35/20.47 thf(193,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C)))))),inference(miniscope,[status(thm)],[192])). 76.35/20.47 thf(194,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ A @ C) | (~ (ord_less_eq_nat @ B @ C)))),inference(cnf,[status(esa)],[193])). 76.35/20.47 thf(209,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A))),inference(cnf,[status(esa)],[208])). 76.35/20.47 thf(81,axiom,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => (finite586181922lle_hf @ (insert9649339lle_hf @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_finite_OinsertI)). 76.35/20.47 thf(487,plain,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => (finite586181922lle_hf @ (insert9649339lle_hf @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 76.35/20.47 thf(45,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_bot__nat__0_Oextremum)). 76.35/20.47 thf(310,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 76.35/20.47 thf(473,plain,(((ord_le432112161lle_hf) = (^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B))))),inference(lifteq,[status(thm)],[472])). 76.35/20.47 thf(906,plain,(((^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B))) = (^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ B) | ~ (member1367349282lle_hf @ C @ A)))) | ((ord_le432112161lle_hf) != (ord_le432112161lle_hf))),inference(paramod_ordered,[status(thm)],[578,473])). 76.35/20.47 thf(907,plain,(((^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B))) = (^ [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ B) | ~ (member1367349282lle_hf @ C @ A))))),inference(pattern_uni,[status(thm)],[906:[]])). 76.35/20.47 thf(1053,plain,(! [A:set_HF_Mirabelle_hf] : (((^ [B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ A) => (member1367349282lle_hf @ C @ B))) = (^ [B:set_HF_Mirabelle_hf]: ! [C:hF_Mirabelle_hf]: ((member1367349282lle_hf @ C @ B) | ~ (member1367349282lle_hf @ C @ A)))))),inference(func_ext,[status(esa)],[907])). 76.35/20.47 thf(226,plain,(! [A:nat] : ((A = bot_bot_nat) | (~ (ord_less_eq_nat @ A @ bot_bot_nat)))),inference(cnf,[status(esa)],[225])). 76.35/20.47 thf(227,plain,(! [A:nat] : ((A = bot_bot_nat) | (~ (ord_less_eq_nat @ A @ bot_bot_nat)))),inference(lifteq,[status(thm)],[226])). 76.35/20.47 thf(1130,plain,(! [A:nat] : ((A = zero_zero_nat) | (~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(rewrite,[status(thm)],[227,698])). 76.35/20.47 thf(129,axiom,((! [A:set_HF_Mirabelle_hf]: (((is_sin1448700567lle_hf @ A) <= (! [B:hF_Mirabelle_hf,C:hF_Mirabelle_hf]: (((B = C) <= (member1367349282lle_hf @ C @ A)) <= (member1367349282lle_hf @ B @ A)))) <= (A != bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_is__singletonI_H)). 76.35/20.47 thf(703,plain,((! [A:set_HF_Mirabelle_hf]: ((is_sin1448700567lle_hf @ A) | ~ (! [B:hF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((B = C) | ~ (member1367349282lle_hf @ C @ A) | ~ (member1367349282lle_hf @ B @ A))) | (A = bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 76.35/20.47 thf(137,axiom,((! [A:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ A @ bot_bo53200981lle_hf))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_emptyE)). 76.35/20.47 thf(727,plain,((! [A:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ A @ bot_bo53200981lle_hf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 76.35/20.47 thf(84,axiom,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: (ord_le432112161lle_hf @ A @ (insert9649339lle_hf @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_subset__insertI)). 76.35/20.47 thf(496,plain,((! [A:set_HF_Mirabelle_hf,B:hF_Mirabelle_hf]: (ord_le432112161lle_hf @ A @ (insert9649339lle_hf @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 76.35/20.47 thf(497,plain,(! [B:hF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : ((ord_le432112161lle_hf @ A @ (insert9649339lle_hf @ B @ A)))),inference(cnf,[status(esa)],[496])). 76.35/20.47 thf(174,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | ((ord_less_eq_nat @ B @ A) = (B = A)))),inference(cnf,[status(esa)],[173])). 76.35/20.47 thf(175,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ B @ A) = (B = A)) | (~ (ord_less_eq_nat @ A @ B)))),inference(lifteq,[status(thm)],[174])). 76.35/20.47 thf(62,axiom,((! [A:set_HF_Mirabelle_hf]: (((~ (! [B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((A = (insert9649339lle_hf @ C @ B)) => ((~ (member1367349282lle_hf @ C @ B)) => (~ (finite586181922lle_hf @ B)))))) <= (A != bot_bo53200981lle_hf)) <= (finite586181922lle_hf @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_finite__cases)). 76.35/20.47 thf(386,plain,((! [A:set_HF_Mirabelle_hf]: (~ (! [B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((A = (insert9649339lle_hf @ C @ B)) => ((~ (member1367349282lle_hf @ C @ B)) => (~ (finite586181922lle_hf @ B))))) | (A = bot_bo53200981lle_hf) | ~ (finite586181922lle_hf @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 76.35/20.47 thf(79,axiom,((! [A:set_HF_Mirabelle_hf]: (ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_bot_Oextremum)). 76.35/20.47 thf(482,plain,((! [A:set_HF_Mirabelle_hf]: (ord_le432112161lle_hf @ bot_bo53200981lle_hf @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 76.35/20.47 thf(687,plain,(! [B:nat,A:nat] : ((((semiri2013084963it_nat @ A @ B) = zero_zero_nat) = (B = zero_zero_nat)))),inference(cnf,[status(esa)],[686])). 76.35/20.47 thf(688,plain,(! [B:nat,A:nat] : ((((semiri2013084963it_nat @ A @ B) = zero_zero_nat) = (B = zero_zero_nat)))),inference(lifteq,[status(thm)],[687])). 76.35/20.47 thf(1085,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) != (member1367349282lle_hf @ B @ bot_bo53200981lle_hf)))),inference(paramod_ordered,[status(thm)],[696,670])). 76.35/20.47 thf(1099,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((A != B) | ((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) != bot_bo53200981lle_hf))),inference(simp,[status(thm)],[1085])). 76.35/20.47 thf(1108,plain,(! [A:hF_Mirabelle_hf] : (((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) != bot_bo53200981lle_hf))),inference(simp,[status(thm)],[1099])). 76.35/20.47 thf(30,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (B = C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_ord__le__eq__trans)). 76.35/20.47 thf(250,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (B = C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 76.35/20.47 thf(73,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => ((finite586181922lle_hf @ B) <= (ord_le432112161lle_hf @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_rev__finite__subset)). 76.35/20.47 thf(465,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((finite586181922lle_hf @ A) => ((finite586181922lle_hf @ B) | ~ (ord_le432112161lle_hf @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 76.35/20.47 thf(675,plain,(! [A:set_HF_Mirabelle_hf] : (((? [B:hF_Mirabelle_hf]: (member1367349282lle_hf @ B @ A)) = (~ (A = bot_bo53200981lle_hf))))),inference(cnf,[status(esa)],[674])). 76.35/20.47 thf(676,plain,(! [A:set_HF_Mirabelle_hf] : (((? [B:hF_Mirabelle_hf]: (member1367349282lle_hf @ B @ A)) = (~ (A = bot_bo53200981lle_hf))))),inference(lifteq,[status(thm)],[675])). 76.35/20.47 thf(1452,plain,(! [B:set_HF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : (((~ (! [C:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ C @ A))) = (? [C:hF_Mirabelle_hf]: (member1367349282lle_hf @ C @ B))) | ((A = bot_bo53200981lle_hf) != (B = bot_bo53200981lle_hf)))),inference(paramod_ordered,[status(thm)],[665,676])). 76.35/20.47 thf(1453,plain,(! [A:set_HF_Mirabelle_hf] : (((~ (! [B:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ B @ A))) = (? [B:hF_Mirabelle_hf]: (member1367349282lle_hf @ B @ A))))),inference(pattern_uni,[status(thm)],[1452:[bind(A, $thf(A)),bind(B, $thf(A))]])). 76.35/20.47 thf(171,plain,(! [B:nat,A:set_HF_Mirabelle_hf] : ((~ (ord_less_eq_nat @ (finite1213132899lle_hf @ (sk1 @ B @ A)) @ B)) | (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ B))),inference(cnf,[status(esa)],[166])). 76.35/20.47 thf(96,axiom,((! [A:set_HF_Mirabelle_hf]: ((((finite1213132899lle_hf @ A) = zero_zero_nat) = (A = bot_bo53200981lle_hf)) <= (finite586181922lle_hf @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_card__0__eq)). 76.35/20.47 thf(588,plain,((! [A:set_HF_Mirabelle_hf]: ((((finite1213132899lle_hf @ A) = zero_zero_nat) = (A = bot_bo53200981lle_hf)) | ~ (finite586181922lle_hf @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 76.35/20.47 thf(128,axiom,((! [A:set_HF_Mirabelle_hf]: ((! [B:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ B @ A)) => (A = bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_equals0I)). 76.35/20.47 thf(699,plain,((! [A:set_HF_Mirabelle_hf]: ((! [B:hF_Mirabelle_hf]: ~ (member1367349282lle_hf @ B @ A)) => (A = bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 76.35/20.47 thf(112,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((insert9649339lle_hf @ A @ (insert9649339lle_hf @ A @ B)) = (insert9649339lle_hf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_insert__absorb2)). 76.35/20.47 thf(652,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((insert9649339lle_hf @ A @ (insert9649339lle_hf @ A @ B)) = (insert9649339lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 76.35/20.47 thf(42,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_le__zero__eq)). 76.35/20.47 thf(290,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 76.35/20.47 thf(61,axiom,((! [A:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf) = (A = bot_bo53200981lle_hf)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_subset__empty)). 76.35/20.47 thf(383,plain,((! [A:set_HF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ bot_bo53200981lle_hf) = (A = bot_bo53200981lle_hf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 76.35/20.47 thf(53,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ (insert9649339lle_hf @ C @ B)) <= (ord_le432112161lle_hf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_subset__insertI2)). 76.35/20.47 thf(346,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((ord_le432112161lle_hf @ A @ (insert9649339lle_hf @ C @ B)) | ~ (ord_le432112161lle_hf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 76.35/20.47 thf(102,axiom,((finite586181922lle_hf @ bot_bo53200981lle_hf)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_finite_OemptyI)). 76.35/20.47 thf(620,plain,((finite586181922lle_hf @ bot_bo53200981lle_hf)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 76.35/20.47 thf(37,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_179_ord__eq__le__trans)). 76.35/20.47 thf(273,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)],[37])). 76.35/20.47 thf(5210,plain,(! [C:set_HF_Mirabelle_hf,B:nat,A:nat] : ((ord_le432112161lle_hf @ (sk7 @ C @ B) @ C) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ B @ (finite1213132899lle_hf @ C))))),inference(paramod_ordered,[status(thm)],[162,196])). 76.35/20.47 thf(5211,plain,(! [A:set_HF_Mirabelle_hf] : ((ord_le432112161lle_hf @ (sk7 @ A @ (finite1213132899lle_hf @ A)) @ A))),inference(pattern_uni,[status(thm)],[5210:[bind(A, $thf(finite1213132899lle_hf @ D)),bind(B, $thf(finite1213132899lle_hf @ D)),bind(C, $thf(D))]])). 76.35/20.47 thf(5247,plain,(! [A:set_HF_Mirabelle_hf] : ((ord_le432112161lle_hf @ (sk7 @ A @ (finite1213132899lle_hf @ A)) @ A))),inference(simp,[status(thm)],[5211])). 76.35/20.47 thf(168,plain,(! [B:nat,A:set_HF_Mirabelle_hf] : ((ord_le432112161lle_hf @ (sk1 @ B @ A) @ A) | (ord_less_eq_nat @ (finite1213132899lle_hf @ A) @ B))),inference(cnf,[status(esa)],[166])). 76.35/20.47 thf(722,plain,(((^ [A:hF_Mirabelle_hf]: (member1367349282lle_hf @ A @ bot_bo53200981lle_hf)) = (bot_bo1263054448e_hf_o))),inference(lifteq,[status(thm)],[721])). 76.35/20.47 thf(789,plain,(((bot_bo1263054448e_hf_o) = (^ [A:hF_Mirabelle_hf]: ($false)))),inference(rewrite,[status(thm)],[722,670])). 76.35/20.47 thf(790,plain,(! [A:hF_Mirabelle_hf] : ((~ (bot_bo1263054448e_hf_o @ A)))),inference(func_ext,[status(esa)],[789])). 76.35/20.47 thf(28,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)) & (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_Nat_Oex__has__greatest__nat)). 76.35/20.47 thf(239,plain,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)) & (A @ D)))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 76.35/20.47 thf(3643,plain,(! [C:nat,B:nat,A:nat] : (((B = zero_zero_nat) = (zero_zero_nat = C)) | (((semiri2013084963it_nat @ A @ B) = zero_zero_nat) != (C = zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[688,673])). 76.35/20.47 thf(3644,plain,(! [B:nat,A:nat] : (((zero_zero_nat = (semiri2013084963it_nat @ A @ B)) = (B = zero_zero_nat)))),inference(pattern_uni,[status(thm)],[3643:[bind(A, $thf(D)),bind(B, $thf(E)),bind(C, $thf(semiri2013084963it_nat @ D @ E))]])). 76.35/20.47 thf(3765,plain,(! [B:nat,A:nat] : (((zero_zero_nat = (semiri2013084963it_nat @ A @ B)) = (B = zero_zero_nat)))),inference(simp,[status(thm)],[3644])). 76.35/20.47 thf(719,plain,(! [A:nat] : (((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(cnf,[status(esa)],[718])). 76.35/20.47 thf(720,plain,(! [A:nat] : (((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(lifteq,[status(thm)],[719])). 76.35/20.47 thf(896,plain,(((^ [A:set_HF_Mirabelle_hf]: (A = (insert9649339lle_hf @ (the_el1104322134lle_hf @ A) @ bot_bo53200981lle_hf))) = (^ [A:set_HF_Mirabelle_hf]: ? [B:hF_Mirabelle_hf]: (A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)))) | ((is_sin1448700567lle_hf) != (is_sin1448700567lle_hf))),inference(paramod_ordered,[status(thm)],[646,628])). 76.35/20.47 thf(897,plain,(((^ [A:set_HF_Mirabelle_hf]: (A = (insert9649339lle_hf @ (the_el1104322134lle_hf @ A) @ bot_bo53200981lle_hf))) = (^ [A:set_HF_Mirabelle_hf]: ? [B:hF_Mirabelle_hf]: (A = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))),inference(pattern_uni,[status(thm)],[896:[]])). 76.35/20.47 thf(48,axiom,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: (((ord_less_eq_nat @ (finite1213132899lle_hf @ B) @ (finite1213132899lle_hf @ A)) <= (ord_le432112161lle_hf @ B @ A)) <= (finite586181922lle_hf @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_card__mono)). 76.35/20.47 thf(332,plain,((! [A:set_HF_Mirabelle_hf,B:set_HF_Mirabelle_hf]: ((ord_less_eq_nat @ (finite1213132899lle_hf @ B) @ (finite1213132899lle_hf @ A)) | ~ (ord_le432112161lle_hf @ B @ A) | ~ (finite586181922lle_hf @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 76.35/20.47 thf(1465,plain,(! [B:hF_Mirabelle_hf,A:set_HF_Mirabelle_hf] : ((? [C:hF_Mirabelle_hf]: (A = (insert9649339lle_hf @ C @ bot_bo53200981lle_hf))) | ((is_sin1448700567lle_hf @ A) != (is_sin1448700567lle_hf @ (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))),inference(paramod_ordered,[status(thm)],[894,475])). 76.35/20.47 thf(1466,plain,(! [A:hF_Mirabelle_hf] : ((? [B:hF_Mirabelle_hf]: ((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ B @ bot_bo53200981lle_hf))))),inference(pattern_uni,[status(thm)],[1465:[bind(A, $thf(insert9649339lle_hf @ C @ bot_bo53200981lle_hf)),bind(B, $thf(C))]])). 76.35/20.47 thf(1478,plain,(! [A:hF_Mirabelle_hf] : (((insert9649339lle_hf @ A @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ (sk64 @ A) @ bot_bo53200981lle_hf)))),inference(cnf,[status(esa)],[1466])). 76.35/20.47 thf(1479,plain,(! [A:hF_Mirabelle_hf] : (((insert9649339lle_hf @ (sk64 @ A) @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(lifteq,[status(thm)],[1478])). 76.35/20.47 thf(1480,plain,(! [A:hF_Mirabelle_hf] : (((insert9649339lle_hf @ (sk64 @ A) @ bot_bo53200981lle_hf) = (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)))),inference(simp,[status(thm)],[1479])). 76.35/20.47 thf(1750,plain,(! [B:hF_Mirabelle_hf,A:hF_Mirabelle_hf] : (((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = B) | ((insert9649339lle_hf @ (sk64 @ A) @ bot_bo53200981lle_hf) != (insert9649339lle_hf @ B @ bot_bo53200981lle_hf)))),inference(paramod_ordered,[status(thm)],[1480,165])). 76.35/20.47 thf(1751,plain,(! [A:hF_Mirabelle_hf] : (((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = (sk64 @ A)))),inference(pattern_uni,[status(thm)],[1750:[bind(A, $thf(C)),bind(B, $thf(sk64 @ C))]])). 76.35/20.47 thf(1766,plain,(! [A:hF_Mirabelle_hf] : (((the_el1104322134lle_hf @ (insert9649339lle_hf @ A @ bot_bo53200981lle_hf)) = (sk64 @ A)))),inference(simp,[status(thm)],[1751])). 76.35/20.47 thf(1827,plain,(! [A:hF_Mirabelle_hf] : (((sk64 @ A) = A))),inference(rewrite,[status(thm)],[1766,165])). 76.35/20.47 thf(99,axiom,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ C)) = ((A = B) | (member1367349282lle_hf @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_insert__iff)). 76.35/20.47 thf(596,plain,((! [A:hF_Mirabelle_hf,B:hF_Mirabelle_hf,C:set_HF_Mirabelle_hf]: ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ B @ C)) = ((A = B) | (member1367349282lle_hf @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 76.35/20.47 thf(135,axiom,((zero_zero_nat = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zero__natural_Orsp)). 76.35/20.47 thf(723,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 76.35/20.47 thf(86,axiom,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf,D:set_HF_Mirabelle_hf]: ((~ (member1367349282lle_hf @ A @ B)) => ((~ (member1367349282lle_hf @ C @ D)) => (((insert9649339lle_hf @ A @ B) = (insert9649339lle_hf @ C @ D)) = (((? [E:set_HF_Mirabelle_hf]: (~ (member1367349282lle_hf @ C @ E) & ~ (member1367349282lle_hf @ A @ E) & (D = (insert9649339lle_hf @ A @ E)) & (B = (insert9649339lle_hf @ C @ E)))) <= (A != C)) & ((A = C) => (B = D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_insert__eq__iff)). 76.35/20.47 thf(501,plain,((! [A:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf,D:set_HF_Mirabelle_hf]: ((~ (member1367349282lle_hf @ A @ B)) => ((~ (member1367349282lle_hf @ C @ D)) => (((insert9649339lle_hf @ A @ B) = (insert9649339lle_hf @ C @ D)) = ((? [E:set_HF_Mirabelle_hf]: (~ (member1367349282lle_hf @ C @ E) & ~ (member1367349282lle_hf @ A @ E) & (D = (insert9649339lle_hf @ A @ E)) & (B = (insert9649339lle_hf @ C @ E))) | (A = C)) & ((A = C) => (B = D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 76.35/20.47 thf(16,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_eq__imp__le)). 76.35/20.47 thf(200,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 76.35/20.47 thf(50,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_176_order__trans)). 76.35/20.47 thf(337,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)],[50])). 76.35/20.47 thf(2419,plain,(! [D:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf,B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ C @ (sk40 @ D @ C))) | ((member1367349282lle_hf @ A @ (insert9649339lle_hf @ A @ B)) != (member1367349282lle_hf @ C @ D)))),inference(paramod_ordered,[status(thm)],[464,469])). 76.35/20.47 thf(2420,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ (sk40 @ (insert9649339lle_hf @ A @ B) @ A))))),inference(pattern_uni,[status(thm)],[2419:[bind(A, $thf(E)),bind(B, $thf(F)),bind(C, $thf(E)),bind(D, $thf(insert9649339lle_hf @ E @ F))]])). 76.35/20.47 thf(2438,plain,(! [B:set_HF_Mirabelle_hf,A:hF_Mirabelle_hf] : ((~ (member1367349282lle_hf @ A @ (sk40 @ (insert9649339lle_hf @ A @ B) @ A))))),inference(simp,[status(thm)],[2420])). 76.35/20.47 thf(221,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:nat]: ((ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A)))))),inference(miniscope,[status(thm)],[220])). 76.35/20.47 thf(222,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ C @ B) | (~ (ord_less_eq_nat @ C @ A)))),inference(cnf,[status(esa)],[221])). 76.35/20.47 thf(592,plain,(((^ [A:set_HF_Mirabelle_hf]: ((A = bot_bo53200981lle_hf) | ? [B:set_HF_Mirabelle_hf,C:hF_Mirabelle_hf]: ((A = (insert9649339lle_hf @ C @ B)) & (finite586181922lle_hf @ B)))) = (finite586181922lle_hf))),inference(lifteq,[status(thm)],[591])). 76.35/20.47 thf(9848,plain,($false),inference(e,[status(thm)],[645,629,846,628,468,5778,666,1110,479,1105,6142,582,683,730,2908,741,247,655,677,408,170,500,715,6515,698,747,340,670,2434,472,829,2432,288,257,724,184,587,357,196,1511,751,542,460,189,284,228,448,316,261,7236,216,475,179,591,1040,2236,646,238,353,821,602,280,634,692,734,293,396,660,312,206,380,5751,270,661,546,220,894,952,349,160,788,165,192,407,484,493,757,682,1106,6292,665,697,156,403,1006,356,169,593,5497,742,6748,578,225,753,637,679,212,686,476,393,647,5481,173,721,3364,343,792,508,657,674,2909,633,360,662,718,750,430,166,161,149,733,180,689,296,7860,904,176,191,732,579,204,545,259,577,711,641,572,2442,335,236,1865,498,5282,713,736,377,737,208,599,900,406,172,831,631,345,213,621,848,895,198,399,695,278,780,223,505,167,658,267,1102,490,162,680,663,374,255,2234,1509,749,754,6719,194,209,487,712,739,310,1053,585,463,1130,199,673,177,182,703,154,727,1008,497,175,386,627,482,671,688,1108,250,465,231,844,1453,171,5243,588,699,158,652,290,383,346,716,151,620,752,183,273,5247,735,950,168,790,6490,210,239,195,3765,720,897,474,464,332,1827,596,723,501,163,200,337,469,2438,676,222,592,496])). 76.35/20.47 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 76.35/20.47 % [INFO] Killing All external provers ... 76.35/20.47 FINAL WATCH: 56.4 CPU 16.4 WC 76.35/20.47 Killed 2 orphans 76.35/20.47 Killed 2 orphans 76.35/20.47 EOF