0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : run_Leo-III %s %d 0.15/0.35 % Computer : n011.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 960 0.15/0.35 % WCLimit : 120 0.15/0.35 % DateTime : Tue Aug 9 05:09:21 EDT 2022 0.15/0.35 % CPUTime : 0.86/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 1.53/1.05 % [INFO] Parsing done (230ms). 1.53/1.06 % [INFO] Running in sequential loop mode. 2.25/1.26 % [INFO] eprover registered as external prover. 2.25/1.26 % [INFO] cvc4 registered as external prover. 2.25/1.26 % [INFO] Scanning for conjecture ... 2.50/1.35 % [INFO] Found a conjecture and 244 axioms. Running axiom selection ... 2.69/1.43 % [INFO] Axiom selection finished. Selected 241 axioms (removed 3 axioms). 3.30/1.58 % [INFO] Problem is higher-order (TPTP THF). 3.30/1.60 % [INFO] Type checking passed. 3.30/1.60 % [CONFIG] Using configuration: timeout(120) with strategy. Searching for refutation ... 11.84/3.66 % External prover 'e' found a proof! 11.84/3.66 % [INFO] Killing All external provers ... 11.84/3.66 % Time passed: 3173ms (effective reasoning time: 2592ms) 11.84/3.66 % Solved by strategy 11.84/3.66 % Axioms used in derivation (241): fact_64_le__zero__eq, fact_39_sum__mono, fact_99_less__eq__nat_Osimps_I1_J, fact_224_less__trans, fact_108_split__mult__neg__le, fact_218_less__imp__not__eq, fact_157_ord__eq__le__subst, fact_188_partitions__remove1__bounds, fact_71_diff__zero, fact_189_nat__mult__eq__cancel__disj, fact_190_le__numeral__extra_I4_J, fact_175_fun__upd__idem__iff, fact_120_mult__eq__self__implies__10, fact_25_diff__le__mono2, fact_213_less__imp__triv, fact_60_lambda__one, fact_97_bot__nat__0_Oextremum__unique, fact_156_ord__le__eq__subst, fact_14_diff__diff__cancel, fact_115_partitions__zero, fact_3__092_060open_062_I_092_060Sum_062i_092_060le_062n_A_N_Ak_O_A_Ip_Ik_A_058_061_Ap_Ak_A_N_A1_J_J_Ai_A_K_Ai_J_A_061_A_I_092_060Sum_062i_092_060le_062n_O_A_Ip_Ik_A_058_061_Ap_Ak_A_N_A1_J_J_Ai_A_K_Ai_J_092_060close_062, fact_18_le__trans, fact_227_less__imp__neq, fact_102_mult__0, fact_40_atMost__def, fact_234_ord__less__eq__subst, fact_197_nat__mult__less__cancel__disj, fact_10_atMost__subset__iff, fact_9_diff__mult__distrib2, fact_56_fun__upd__triv, fact_215_antisym__conv3, fact_128_dual__order_Orefl, fact_85_zero__reorient, fact_26_le__diff__iff_H, fact_22_Nat_Oex__has__greatest__nat, fact_112_mult__mono, fact_237_less__numeral__extra_I4_J, fact_217_less__not__sym, fact_233_order__less__subst1, fact_232_order__less__subst2, fact_8_diff__mult__distrib, fact_162_order__subst2, fact_196_zero__less__diff, fact_178_fun__upd__same, fact_59_order__refl, fact_63_partitionsE, fact_41_atMost__def, fact_89_no__zero__divisors, fact_147_eq__refl, fact_163_order__subst2, fact_131_order__trans, fact_123_dual__order_Oeq__iff, fact_16_nat__1__eq__mult__iff, fact_50_sum_Ocong, fact_214_less__imp__not__eq2, fact_146_eq__refl, fact_38_nat__mult__1, fact_161_order__subst2, fact_171_mult_Ocommute, fact_202_mult__le__cancel2, fact_116_mult__left__le, fact_17_le__refl, fact_210_order_Ostrict__trans, fact_168_order__subst1, fact_138_order__class_Oorder_Oeq__iff, fact_69_mult__cancel__right, fact_113_not__one__le__zero, fact_19_eq__imp__le, fact_240_nat__less__induct, fact_32_mult__le__mono2, fact_226_less__asym, fact_118_sum__nonpos, fact_148_linear, fact_126_dual__order_Otrans, fact_106_mult__nonneg__nonpos, fact_220_ord__less__eq__trans, fact_33_mult__le__mono1, fact_238_linorder__neqE__nat, fact_98_le__0__eq, fact_208_exists__least__iff, fact_127_linorder__wlog, fact_117_mult__le__one, fact_37_nat__mult__1__right, fact_181_fun__upd__def, fact_62_partitionsI, fact_211_dual__order_Oirrefl, fact_72_cancel__comm__monoid__add__class_Odiff__cancel, fact_90_mult__left__cancel, fact_216_less__induct, fact_130_order__trans, fact_221_ord__eq__less__trans, fact_4_calculation, fact_122_dual__order_Oantisym, fact_119_sum__nonneg, fact_223_less__linear, fact_140_antisym__conv, fact_121_dual__order_Oantisym, fact_129_dual__order_Orefl, fact_24_partitions__bounds, fact_207_linorder__less__wlog, fact_109_mult__right__mono, fact_111_mult__mono_H, fact_87_mult__not__zero, fact_15_nat__mult__eq__1__iff, fact_2_atMost__eq__iff, fact_95_sum_Onot__neutral__contains__not__neutral, fact_49_sum_Oeq__general, fact_160_ord__eq__le__subst, fact_166_order__subst1, fact_209_less__imp__not__less, fact_135_ord__le__eq__trans, fact_31_eq__diff__iff, fact_67_mult__eq__0__iff, fact_27_diff__le__self, fact_145_le__cases, fact_192_not__gr__zero, fact_55_fun__upd__upd, fact_79_mult__cancel1, fact_155_ord__le__eq__subst, fact_225_less__asym_H, fact_200_less__one, fact_165_order__subst1, fact_0_partitions, fact_231_gt__ex, fact_150_antisym, fact_170_mult_Oassoc, fact_228_order_Oasym, fact_20_le__antisym, fact_103_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_104_mult__nonneg__nonpos2, fact_93_lambda__zero, fact_70_zero__diff, fact_12_atMost__iff, fact_94_sum_Oneutral, fact_6_sum__distrib__left, fact_66_mult__zero__right, fact_201_nat__mult__le__cancel__disj, fact_68_mult__cancel__left, fact_177_fun__upd__other, fact_184_comm__monoid__mult__class_Omult__1, fact_110_mult__left__mono, fact_74_le0, fact_53_mult_Oright__neutral, fact_125_dual__order_Otrans, fact_75_diff__0__eq__0, fact_107_mult__nonneg__nonneg, fact_154_ord__le__eq__subst, fact_47_sum_Oreindex__bij__witness, fact_205_not__less__iff__gr__or__eq, fact_182_left__diff__distrib_H, fact_132_order__class_Oorder_Oantisym, fact_91_mult__right__cancel, fact_204_order_Ostrict__implies__not__eq, fact_212_linorder__cases, fact_77_mult__is__0, fact_28_diff__le__mono, fact_35_le__square, fact_139_order__class_Oorder_Oeq__iff, fact_84_gr0, fact_57_fun__upd__apply, fact_186_subsetI, fact_124_dual__order_Oeq__iff, fact_61_partitions__def, fact_54_mult_Oleft__neutral, fact_83_diff__is__0__eq, fact_137_ord__eq__le__trans, fact_180_fun__upd__eqD, fact_100_diffs0__imp__equal, fact_101_minus__nat_Odiff__0, fact_194_less__nat__zero__code, fact_230_neqE, fact_172_mult_Oleft__commute, fact_30_le__diff__iff, fact_176_fun__upd__twist, fact_229_neq__iff, fact_45_Collect__mem__eq, fact_78_mult__0__right, fact_152_eq__iff, fact_29_Nat_Odiff__diff__eq, fact_151_eq__iff, fact_82_diff__is__0__eq_H, fact_48_sum_Oeq__general__inverses, fact_36_le__cube, fact_159_ord__eq__le__subst, fact_143_order_Otrans, fact_185_mult_Ocomm__neutral, fact_51_diff__commute, fact_183_right__diff__distrib_H, fact_80_mult__cancel2, fact_81_sum_Oneutral__const, fact_21_nat__le__linear, fact_42_sum__subtractf__nat, fact_198_mult__less__cancel2, fact_23_bounded__Max__nat, fact_76_diff__self__eq__0, fact_114_zero__le__one, fact_219_dual__order_Oasym, fact_136_ord__eq__le__trans, fact_43_partitions__parts__bounded, fact_222_less__irrefl, fact_195_neq0__conv, fact_239_infinite__descent, fact_96_bot__nat__0_Oextremum__uniqueI, fact_13_atMost__iff, fact_164_order__subst2, fact_144_order_Otrans, fact_203_dual__order_Ostrict__implies__not__eq, fact_34_mult__le__mono, fact_187_subset__antisym, fact_1__092_060open_062k_A_092_060le_062_An_092_060close_062, fact_158_ord__eq__le__subst, fact_141_antisym__conv, fact_142_le__cases3, fact_206_dual__order_Ostrict__trans, fact_88_divisors__zero, fact_173_cancel__ab__semigroup__add__class_Odiff__right__commute, fact_65_mult__zero__left, fact_153_ord__le__eq__subst, fact_52_sum_Oswap, fact_92_zero__neq__one, fact_73_bot__nat__0_Oextremum, fact_191_le__numeral__extra_I3_J, fact_5_sum__product, fact_133_order__class_Oorder_Oantisym, fact_86_zero__le, fact_174_one__reorient, fact_167_order__subst1, fact_236_less__numeral__extra_I3_J, fact_11_atMost__subset__iff, fact_169_ab__semigroup__mult__class_Omult__ac_I1_J, fact_134_ord__le__eq__trans, fact_44_mem__Collect__eq, fact_58_order__refl, fact_235_ord__eq__less__subst, fact_179_fun__upd__idem, fact_193_bot__nat__0_Onot__eq__extremum, fact_46_Collect__cong, fact_149_antisym, fact_7_sum__distrib__right, fact_199_nat__0__less__mult__iff, fact_105_mult__nonpos__nonneg 11.84/3.66 % No. of inferences in proof: 486 11.84/3.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3173 ms resp. 2592 ms w/o parsing 12.39/3.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 12.39/3.80 thf(set_set_nat_type, type, set_set_nat: $tType). 12.39/3.80 thf(set_nat_type, type, set_nat: $tType). 12.39/3.80 thf(nat_type, type, nat: $tType). 12.39/3.80 thf(fun_upd_nat_nat_type, type, fun_upd_nat_nat: ((nat > nat) > (nat > (nat > (nat > nat))))). 12.39/3.80 thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))). 12.39/3.80 thf(one_one_nat_type, type, one_one_nat: nat). 12.39/3.80 thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))). 12.39/3.80 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 12.39/3.80 thf(groups1842438620at_nat_type, type, groups1842438620at_nat: ((nat > nat) > (set_nat > nat))). 12.39/3.80 thf(if_nat_type, type, if_nat: ($o > (nat > (nat > nat)))). 12.39/3.80 thf(number1551313001itions_type, type, number1551313001itions: ((nat > nat) > (nat > $o))). 12.39/3.80 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 12.39/3.80 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 12.39/3.80 thf(ord_less_eq_set_nat_type, type, ord_less_eq_set_nat: (set_nat > (set_nat > $o))). 12.39/3.80 thf(ord_le1613022364et_nat_type, type, ord_le1613022364et_nat: (set_set_nat > (set_set_nat > $o))). 12.39/3.80 thf(collect_nat_type, type, collect_nat: ((nat > $o) > set_nat)). 12.39/3.80 thf(collect_set_nat_type, type, collect_set_nat: ((set_nat > $o) > set_set_nat)). 12.39/3.80 thf(set_ord_atMost_nat_type, type, set_ord_atMost_nat: (nat > set_nat)). 12.39/3.80 thf(set_or1086813439et_nat_type, type, set_or1086813439et_nat: (set_nat > set_set_nat)). 12.39/3.80 thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))). 12.39/3.80 thf(member_set_nat_type, type, member_set_nat: (set_nat > (set_set_nat > $o))). 12.39/3.80 thf(k_type, type, k: nat). 12.39/3.80 thf(n_type, type, n: nat). 12.39/3.80 thf(p_type, type, p: (nat > nat)). 12.39/3.80 thf(226,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_nat__mult__eq__cancel__disj)). 12.39/3.80 thf(1036,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 12.39/3.80 thf(160,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_mult_Ocomm__neutral)). 12.39/3.80 thf(809,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 12.39/3.80 thf(108,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_le__antisym)). 12.39/3.80 thf(629,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 12.39/3.80 thf(143,axiom,((! [A:(nat > nat),B:set_nat,C:(nat > nat),D:set_nat]: ((times_times_nat @ (groups1842438620at_nat @ A @ B) @ (groups1842438620at_nat @ C @ D)) = (groups1842438620at_nat @ (^ [E:nat]: (groups1842438620at_nat @ (^ [F:nat]: (times_times_nat @ (A @ E) @ (C @ F))) @ D)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_sum__product)). 12.39/3.80 thf(760,plain,((! [A:(nat > nat),B:set_nat,C:(nat > nat),D:set_nat]: ((times_times_nat @ (groups1842438620at_nat @ (A) @ B) @ (groups1842438620at_nat @ (C) @ D)) = (groups1842438620at_nat @ (^ [E:nat]: (groups1842438620at_nat @ (^ [F:nat]: (times_times_nat @ (A @ E) @ (C @ F))) @ D)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 12.39/3.80 thf(171,axiom,((! [A:nat,B:nat]: (((B != zero_zero_nat) & (A != zero_zero_nat)) <= ((times_times_nat @ A @ B) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_mult__not__zero)). 12.39/3.80 thf(846,plain,((! [A:nat,B:nat]: ((~ (B = zero_zero_nat) & ~ (A = zero_zero_nat)) | ((times_times_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 12.39/3.80 thf(203,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_mult__right__mono)). 12.39/3.80 thf(962,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 12.39/3.80 thf(196,axiom,((! [A:(nat > (nat > nat)),B:set_nat,C:set_nat]: ((groups1842438620at_nat @ (^ [D:nat]: (groups1842438620at_nat @ (A @ D) @ B)) @ C) = (groups1842438620at_nat @ (^ [D:nat]: (groups1842438620at_nat @ (^ [E:nat]: (A @ E @ D)) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_sum_Oswap)). 12.39/3.80 thf(941,plain,((! [A:(nat > (nat > nat)),B:set_nat,C:set_nat]: ((groups1842438620at_nat @ (^ [D:nat]: (groups1842438620at_nat @ (A @ D) @ B)) @ C) = (groups1842438620at_nat @ (^ [D:nat]: (groups1842438620at_nat @ (^ [E:nat]: (A @ E @ D)) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 12.39/3.80 thf(60,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_less__irrefl)). 12.39/3.80 thf(481,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 12.39/3.80 thf(26,axiom,((! [A:set_nat,B:set_nat]: ((member_set_nat @ A @ (set_or1086813439et_nat @ B)) = (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_atMost__iff)). 12.39/3.80 thf(352,plain,((! [A:set_nat,B:set_nat]: ((member_set_nat @ A @ (set_or1086813439et_nat @ B)) = (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 12.39/3.80 thf(121,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_ord__eq__less__trans)). 12.39/3.80 thf(683,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 12.39/3.80 thf(8,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_21_nat__le__linear)). 12.39/3.80 thf(276,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)],[8])). 12.39/3.80 thf(16,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_148_linear)). 12.39/3.80 thf(308,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)],[16])). 12.39/3.80 thf(138,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_mult__le__cancel2)). 12.39/3.80 thf(741,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 12.39/3.80 thf(179,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_diff__commute)). 12.39/3.80 thf(873,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 12.39/3.80 thf(33,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) <= (~ (ord_less_nat @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_linorder__neqE__nat)). 12.39/3.80 thf(379,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 12.39/3.80 thf(175,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mult__zero__right)). 12.39/3.80 thf(861,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 12.39/3.80 thf(236,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_le__diff__iff_H)). 12.39/3.80 thf(1078,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)) | ~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 12.39/3.80 thf(76,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A) | (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_less__linear)). 12.39/3.80 thf(533,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 12.39/3.80 thf(67,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_order_Otrans)). 12.39/3.80 thf(500,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 12.39/3.80 thf(131,axiom,((! [A:set_nat,B:set_nat]: (((ord_less_eq_set_nat @ B @ A) = (B = A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_antisym__conv)). 12.39/3.80 thf(715,plain,((! [A:set_nat,B:set_nat]: (((ord_less_eq_set_nat @ B @ A) = (B = A)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 12.39/3.80 thf(57,axiom,((! [A:(nat > nat)]: ((number1551313001itions @ A @ zero_zero_nat) = (A = (^ [B:nat]: (zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_partitions__zero)). 12.39/3.80 thf(472,plain,((! [A:(nat > nat)]: ((number1551313001itions @ (A) @ zero_zero_nat) = ((A) = (^ [B:nat]: (zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 12.39/3.80 thf(231,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_diff__diff__cancel)). 12.39/3.80 thf(1063,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 12.39/3.80 thf(192,axiom,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_diff__self__eq__0)). 12.39/3.80 thf(930,plain,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 12.39/3.80 thf(118,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ B @ A)) = (B = A)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_antisym__conv3)). 12.39/3.80 thf(670,plain,((! [A:nat,B:nat]: (((~ (ord_less_nat @ B @ A)) = (B = A)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 12.39/3.80 thf(164,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_nat__mult__1)). 12.39/3.80 thf(829,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 12.39/3.80 thf(43,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_less__eq__nat_Osimps_I1_J)). 12.39/3.80 thf(417,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 12.39/3.80 thf(20,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_144_order_Otrans)). 12.39/3.80 thf(320,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)],[20])). 12.39/3.80 thf(87,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) <= (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_dual__order_Ostrict__trans)). 12.39/3.80 thf(570,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) | ~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 12.39/3.80 thf(167,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_mult_Ocommute)). 12.39/3.80 thf(838,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 12.39/3.80 thf(23,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_order__refl)). 12.39/3.80 thf(344,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 12.39/3.80 thf(172,axiom,((set_ord_atMost_nat = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_atMost__def)). 12.39/3.80 thf(853,plain,(((set_ord_atMost_nat) = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 12.39/3.80 thf(178,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_mult__left__le)). 12.39/3.80 thf(870,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 12.39/3.80 thf(100,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_bot__nat__0_Onot__eq__extremum)). 12.39/3.80 thf(606,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 12.39/3.80 thf(11,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_ord__eq__le__trans)). 12.39/3.80 thf(284,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 12.39/3.80 thf(12,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((~ (! [D:nat]: ((A @ D) => (~ (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D))))))) <= (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_bounded__Max__nat)). 12.39/3.80 thf(289,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => (~ (! [D:nat]: ((A @ D) => (~ (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))))) | ~ (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 12.39/3.80 thf(19,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_less__imp__neq)). 12.39/3.80 thf(316,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 12.39/3.80 thf(154,axiom,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (fun_upd_nat_nat @ p @ k @ (minus_minus_nat @ (p @ k) @ one_one_nat) @ A) @ A)) @ (set_ord_atMost_nat @ (minus_minus_nat @ n @ k))) = (minus_minus_nat @ (groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ n)) @ k))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_calculation)). 12.39/3.80 thf(789,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (fun_upd_nat_nat @ p @ k @ (minus_minus_nat @ (p @ k) @ one_one_nat) @ A) @ A)) @ (set_ord_atMost_nat @ (minus_minus_nat @ n @ k))) = (minus_minus_nat @ (groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ n)) @ k))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 12.39/3.80 thf(52,axiom,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_order__class_Oorder_Oeq__iff)). 12.39/3.80 thf(443,plain,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 12.39/3.80 thf(113,axiom,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ A @ (B @ C)) => (((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_set_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_nat @ A @ (B @ D))) <= (ord_less_eq_set_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_order__subst1)). 12.39/3.80 thf(646,plain,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ A @ (B @ C)) => (((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_set_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_nat @ A @ (B @ D))) | ~ (ord_less_eq_set_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 12.39/3.80 thf(221,axiom,((! [A:(nat > nat),B:set_nat,C:nat]: ((times_times_nat @ (groups1842438620at_nat @ A @ B) @ C) = (groups1842438620at_nat @ (^ [D:nat]: (times_times_nat @ (A @ D) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_sum__distrib__right)). 12.39/3.80 thf(1020,plain,((! [A:(nat > nat),B:set_nat,C:nat]: ((times_times_nat @ (groups1842438620at_nat @ (A) @ B) @ C) = (groups1842438620at_nat @ (^ [D:nat]: (times_times_nat @ (A @ D) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 12.39/3.80 thf(159,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_mult__nonneg__nonpos2)). 12.39/3.80 thf(806,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 12.39/3.80 thf(58,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((number1551313001itions @ A @ B) => (ord_less_eq_nat @ (A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_partitions__bounds)). 12.39/3.80 thf(475,plain,((! [A:(nat > nat),B:nat,C:nat]: ((number1551313001itions @ (A) @ B) => (ord_less_eq_nat @ (A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 12.39/3.80 thf(190,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D)))) => (ord_less_eq_nat @ (groups1842438620at_nat @ B @ A) @ (groups1842438620at_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_sum__mono)). 12.39/3.80 thf(924,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D)))) => (ord_less_eq_nat @ (groups1842438620at_nat @ (B) @ A) @ (groups1842438620at_nat @ (C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 12.39/3.80 thf(123,axiom,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_not__one__le__zero)). 12.39/3.80 thf(692,plain,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 12.39/3.80 thf(201,axiom,((! [A:set_nat,B:(nat > nat)]: ((ord_less_eq_nat @ zero_zero_nat @ (groups1842438620at_nat @ B @ A)) <= (! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ zero_zero_nat @ (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_sum__nonneg)). 12.39/3.80 thf(956,plain,((! [A:set_nat,B:(nat > nat)]: ((ord_less_eq_nat @ zero_zero_nat @ (groups1842438620at_nat @ (B) @ A)) | ~ (! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ zero_zero_nat @ (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 12.39/3.80 thf(234,axiom,((! [A:nat,B:nat]: (((B = one_one_nat) | (A = zero_zero_nat)) <= (A = (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_mult__eq__self__implies__10)). 12.39/3.80 thf(1072,plain,((! [A:nat,B:nat]: ((B = one_one_nat) | (A = zero_zero_nat) | ~ (A = (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 12.39/3.80 thf(243,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_zero__less__diff)). 12.39/3.80 thf(1104,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 12.39/3.80 thf(98,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_152_eq__iff)). 12.39/3.80 thf(602,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)],[98])). 12.39/3.80 thf(145,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mult__cancel__right)). 12.39/3.80 thf(766,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 12.39/3.80 thf(156,axiom,((! [A:(nat > nat),B:nat]: ((~ ((! [C:nat]: (((ord_less_eq_nat @ C @ B) & (ord_less_eq_nat @ one_one_nat @ C)) <= ((A @ C) != zero_zero_nat))) => ((groups1842438620at_nat @ (^ [C:nat]: (times_times_nat @ (A @ C) @ C)) @ (set_ord_atMost_nat @ B)) != B))) <= (number1551313001itions @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_partitionsE)). 12.39/3.80 thf(793,plain,((! [A:(nat > nat),B:nat]: (~ ((! [C:nat]: (((ord_less_eq_nat @ C @ B) & (ord_less_eq_nat @ one_one_nat @ C)) | ((A @ C) = zero_zero_nat))) => (~ ((groups1842438620at_nat @ (^ [C:nat]: (times_times_nat @ (A @ C) @ C)) @ (set_ord_atMost_nat @ B)) = B))) | ~ (number1551313001itions @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 12.39/3.80 thf(130,axiom,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_le__numeral__extra_I3_J)). 12.39/3.80 thf(714,plain,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 12.39/3.80 thf(229,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_mult__le__mono2)). 12.39/3.80 thf(1057,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 12.39/3.80 thf(185,axiom,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_zero__diff)). 12.39/3.80 thf(894,plain,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 12.39/3.80 thf(150,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mult__is__0)). 12.39/3.80 thf(778,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 12.39/3.80 thf(228,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat),E:(nat > nat)]: ((! [F:nat]: ((? [G:nat]: ((member_nat @ G @ B) & ((C @ G) = F) & ! [H:nat]: ((H = G) <= ((member_nat @ H @ B) & ((C @ H) = F))))) <= (member_nat @ F @ A))) => ((! [F:nat]: ((member_nat @ F @ B) => (((D @ (C @ F)) = (E @ F)) & (member_nat @ (C @ F) @ A)))) => ((groups1842438620at_nat @ E @ B) = (groups1842438620at_nat @ D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_sum_Oeq__general)). 12.39/3.80 thf(1042,plain,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat),E:(nat > nat)]: ((! [F:nat]: (? [G:nat]: ((member_nat @ G @ B) & ((C @ G) = F) & ! [H:nat]: ((H = G) | ~ ((member_nat @ H @ B) & ((C @ H) = F)))) | ~ (member_nat @ F @ A))) => ((! [F:nat]: ((member_nat @ F @ B) => (((D @ (C @ F)) = (E @ F)) & (member_nat @ (C @ F) @ A)))) => ((groups1842438620at_nat @ (E) @ B) = (groups1842438620at_nat @ (D) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 12.39/3.80 thf(84,axiom,((! [A:(nat > nat),B:nat]: ((fun_upd_nat_nat @ A @ B @ (A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_fun__upd__triv)). 12.39/3.80 thf(561,plain,((! [A:(nat > nat),B:nat]: ((fun_upd_nat_nat @ A @ B @ (A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 12.39/3.80 thf(13,axiom,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_zero__le__one)). 12.39/3.80 thf(297,plain,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 12.39/3.80 thf(6,axiom,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_less_eq_set_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_ord__le__eq__subst)). 12.39/3.80 thf(260,plain,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_less_eq_set_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 12.39/3.80 thf(25,axiom,((! [A:set_nat,B:set_nat]: ((ord_le1613022364et_nat @ (set_or1086813439et_nat @ A) @ (set_or1086813439et_nat @ B)) = (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_atMost__subset__iff)). 12.39/3.80 thf(349,plain,((! [A:set_nat,B:set_nat]: ((ord_le1613022364et_nat @ (set_or1086813439et_nat @ A) @ (set_or1086813439et_nat @ B)) = (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 12.39/3.80 thf(61,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_order_Ostrict__implies__not__eq)). 12.39/3.80 thf(484,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 12.39/3.80 thf(29,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_139_order__class_Oorder_Oeq__iff)). 12.39/3.80 thf(361,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)],[29])). 12.39/3.80 thf(181,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: (((groups1842438620at_nat @ (^ [D:nat]: (minus_minus_nat @ (C @ D) @ (B @ D))) @ A) = (minus_minus_nat @ (groups1842438620at_nat @ C @ A) @ (groups1842438620at_nat @ B @ A))) <= (! [D:nat]: ((ord_less_eq_nat @ (B @ D) @ (C @ D)) <= (member_nat @ D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_sum__subtractf__nat)). 12.39/3.80 thf(879,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: (((groups1842438620at_nat @ (^ [D:nat]: (minus_minus_nat @ (C @ D) @ (B @ D))) @ A) = (minus_minus_nat @ (groups1842438620at_nat @ (C) @ A) @ (groups1842438620at_nat @ (B) @ A))) | ~ (! [D:nat]: ((ord_less_eq_nat @ (B @ D) @ (C @ D)) | ~ (member_nat @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 12.39/3.80 thf(49,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_not__less__iff__gr__or__eq)). 12.39/3.80 thf(435,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 12.39/3.80 thf(92,axiom,((! [A:(nat > nat),B:nat,C:nat,D:(nat > nat),E:nat]: ((C = E) <= ((fun_upd_nat_nat @ A @ B @ C) = (fun_upd_nat_nat @ D @ B @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_fun__upd__eqD)). 12.39/3.80 thf(583,plain,((! [A:(nat > nat),B:nat,C:nat,D:(nat > nat),E:nat]: ((C = E) | ~ ((fun_upd_nat_nat @ A @ B @ C) = (fun_upd_nat_nat @ D @ B @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 12.39/3.80 thf(64,axiom,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_le__numeral__extra_I4_J)). 12.39/3.80 thf(493,plain,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 12.39/3.80 thf(142,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_comm__monoid__mult__class_Omult__1)). 12.39/3.80 thf(757,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 12.39/3.80 thf(169,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_mult__mono)). 12.39/3.80 thf(842,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 12.39/3.80 thf(218,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_diff__le__self)). 12.39/3.80 thf(1012,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 12.39/3.80 thf(90,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_less__asym)). 12.39/3.80 thf(578,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 12.39/3.80 thf(114,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_eq__refl)). 12.39/3.80 thf(650,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 12.39/3.80 thf(134,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_less__nat__zero__code)). 12.39/3.80 thf(725,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 12.39/3.80 thf(39,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_less__not__sym)). 12.39/3.80 thf(403,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 12.39/3.80 thf(241,axiom,((! [A:(nat > nat),B:nat]: ((! [C:nat]: (((A @ C) != zero_zero_nat) => ((ord_less_eq_nat @ one_one_nat @ C) & (ord_less_eq_nat @ C @ B)))) => ((number1551313001itions @ A @ B) <= ((groups1842438620at_nat @ (^ [C:nat]: (times_times_nat @ (A @ C) @ C)) @ (set_ord_atMost_nat @ B)) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_partitionsI)). 12.39/3.80 thf(1096,plain,((! [A:(nat > nat),B:nat]: ((! [C:nat]: ((~ ((A @ C) = zero_zero_nat)) => ((ord_less_eq_nat @ one_one_nat @ C) & (ord_less_eq_nat @ C @ B)))) => ((number1551313001itions @ (A) @ B) | ~ ((groups1842438620at_nat @ (^ [C:nat]: (times_times_nat @ (A @ C) @ C)) @ (set_ord_atMost_nat @ B)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 12.39/3.80 thf(216,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_cancel__ab__semigroup__add__class_Odiff__right__commute)). 12.39/3.80 thf(1006,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 12.39/3.80 thf(95,axiom,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_eq__iff)). 12.39/3.80 thf(593,plain,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 12.39/3.80 thf(182,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_diff__is__0__eq)). 12.39/3.80 thf(884,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 12.39/3.80 thf(237,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_left__diff__distrib_H)). 12.39/3.80 thf(1082,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 12.39/3.80 thf(62,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((A = B) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_antisym)). 12.39/3.80 thf(488,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 12.39/3.80 thf(193,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_diff__mult__distrib)). 12.39/3.80 thf(933,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 12.39/3.80 thf(82,axiom,((set_or1086813439et_nat = (^ [A:set_nat]: (collect_set_nat @ (^ [B:set_nat]: (ord_less_eq_set_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_atMost__def)). 12.39/3.80 thf(554,plain,(((set_or1086813439et_nat) = (^ [A:set_nat]: (collect_set_nat @ (^ [B:set_nat]: (ord_less_eq_set_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 12.39/3.80 thf(235,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_mult_Oright__neutral)). 12.39/3.80 thf(1075,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 12.39/3.80 thf(73,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_dual__order_Oasym)). 12.39/3.80 thf(526,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 12.39/3.80 thf(227,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (((ord_less_eq_nat @ B @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ A)) | ((ord_less_eq_nat @ zero_zero_nat @ B) & (ord_less_eq_nat @ A @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_split__mult__neg__le)). 12.39/3.80 thf(1039,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (((ord_less_eq_nat @ B @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ A)) | ((ord_less_eq_nat @ zero_zero_nat @ B) & (ord_less_eq_nat @ A @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 12.39/3.80 thf(79,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_124_dual__order_Oeq__iff)). 12.39/3.80 thf(547,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)],[79])). 12.39/3.80 thf(128,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((A @ C) <= (! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_less__induct)). 12.39/3.80 thf(706,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((A @ C) | ~ (! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 12.39/3.80 thf(37,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_ord__eq__le__subst)). 12.39/3.80 thf(393,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 12.39/3.80 thf(115,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_less__imp__not__less)). 12.39/3.80 thf(654,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 12.39/3.80 thf(230,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_mult__le__mono1)). 12.39/3.80 thf(1060,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 12.39/3.80 thf(68,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_le0)). 12.39/3.80 thf(503,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 12.39/3.80 thf(1,conjecture,(((minus_minus_nat @ (groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ n)) @ k) = (minus_minus_nat @ n @ k))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 12.39/3.80 thf(2,negated_conjecture,((~ ((minus_minus_nat @ (groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ n)) @ k) = (minus_minus_nat @ n @ k)))),inference(neg_conjecture,[status(cth)],[1])). 12.39/3.80 thf(244,plain,((~ ((minus_minus_nat @ (groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ n)) @ k) = (minus_minus_nat @ n @ k)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 12.39/3.80 thf(189,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ B @ C) & (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_nat__mult__less__cancel__disj)). 12.39/3.80 thf(921,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ B @ C) & (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 12.39/3.80 thf(223,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_mult__left__mono)). 12.39/3.80 thf(1026,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 12.39/3.80 thf(200,axiom,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_diff__zero)). 12.39/3.80 thf(953,plain,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 12.39/3.80 thf(93,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_not__gr__zero)). 12.39/3.80 thf(586,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 12.39/3.80 thf(117,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: ((((ord_less_eq_set_nat @ (C @ A) @ D) <= (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_nat @ E @ F)))) <= ((C @ B) = D)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_ord__le__eq__subst)). 12.39/3.80 thf(662,plain,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: ((ord_less_eq_set_nat @ (C @ A) @ D) | ~ (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 12.39/3.80 thf(132,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((A != B) => ((fun_upd_nat_nat @ C @ B @ D @ A) = (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_fun__upd__other)). 12.39/3.80 thf(718,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((~ (A = B)) => ((fun_upd_nat_nat @ (C) @ B @ D @ A) = (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 12.39/3.80 thf(14,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((C @ B) = D) => ((ord_less_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_ord__less__eq__subst)). 12.39/3.80 thf(298,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((C @ B) = D) => ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 12.39/3.80 thf(42,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C))) <= (~ (A @ C)))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_infinite__descent)). 12.39/3.80 thf(412,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C)) | (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 12.39/3.80 thf(204,axiom,((! [A:nat,B:nat]: ((member_nat @ A @ (set_ord_atMost_nat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_atMost__iff)). 12.39/3.80 thf(965,plain,((! [A:nat,B:nat]: ((member_nat @ A @ (set_ord_atMost_nat @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 12.39/3.80 thf(104,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_order__class_Oorder_Oantisym)). 12.39/3.80 thf(618,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 12.39/3.80 thf(46,axiom,((fun_upd_nat_nat = (^ [A:(nat > nat),B:nat,C:nat,D:nat]: (if_nat @ (D = B) @ C @ (A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_fun__upd__apply)). 12.39/3.80 thf(425,plain,(((fun_upd_nat_nat) = (^ [A:(nat > nat),B:nat,C:nat,D:nat]: (if_nat @ (D = B) @ C @ (A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 12.39/3.80 thf(71,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((? [D:nat]: ((A @ D) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E)))) <= (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Nat_Oex__has__greatest__nat)). 12.39/3.80 thf(513,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E))) | ~ (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 12.39/3.80 thf(88,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_le__trans)). 12.39/3.80 thf(573,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 12.39/3.80 thf(32,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_less__imp__not__eq)). 12.39/3.80 thf(375,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 12.39/3.80 thf(163,axiom,((! [A:set_nat,B:(nat > nat),C:set_nat,D:(nat > nat),E:(nat > nat),F:(nat > nat)]: ((! [G:nat]: ((((D @ (B @ G)) = G) & (member_nat @ (B @ G) @ C)) <= (member_nat @ G @ A))) => ((! [G:nat]: (((member_nat @ (D @ G) @ A) & ((E @ (D @ G)) = (F @ G)) & ((B @ (D @ G)) = G)) <= (member_nat @ G @ C))) => ((groups1842438620at_nat @ F @ C) = (groups1842438620at_nat @ E @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_sum_Oeq__general__inverses)). 12.39/3.80 thf(819,plain,((! [A:set_nat,B:(nat > nat),C:set_nat,D:(nat > nat),E:(nat > nat),F:(nat > nat)]: ((! [G:nat]: ((((D @ (B @ G)) = G) & (member_nat @ (B @ G) @ C)) | ~ (member_nat @ G @ A))) => ((! [G:nat]: (((member_nat @ (D @ G) @ A) & ((E @ (D @ G)) = (F @ G)) & ((B @ (D @ G)) = G)) | ~ (member_nat @ G @ C))) => ((groups1842438620at_nat @ (F) @ C) = (groups1842438620at_nat @ (E) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 12.39/3.80 thf(207,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult__left__cancel)). 12.39/3.80 thf(975,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 12.39/3.80 thf(124,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_dual__order_Orefl)). 12.39/3.80 thf(694,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 12.39/3.80 thf(136,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_order__subst2)). 12.39/3.80 thf(732,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 12.39/3.80 thf(148,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_mult__nonneg__nonneg)). 12.39/3.80 thf(772,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 12.39/3.80 thf(129,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_subsetI)). 12.39/3.80 thf(711,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 12.39/3.80 thf(10,axiom,((! [A:set_nat,B:set_nat]: (((B = A) <= (ord_less_eq_set_nat @ B @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_dual__order_Oantisym)). 12.39/3.80 thf(281,plain,((! [A:set_nat,B:set_nat]: ((B = A) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 12.39/3.80 thf(34,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_ord__le__eq__trans)). 12.39/3.80 thf(382,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 12.39/3.80 thf(153,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_le__cube)). 12.39/3.80 thf(787,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 12.39/3.80 thf(239,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_nat__0__less__mult__iff)). 12.39/3.80 thf(1090,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 12.39/3.80 thf(198,axiom,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_minus__nat_Odiff__0)). 12.39/3.80 thf(947,plain,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 12.39/3.80 thf(53,axiom,((! [A:nat,B:nat,C:nat]: ((((((~ ((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 @ B @ A)))) <= ((~ (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ C))) <= ((~ (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ B @ A))) <= ((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_le__cases3)). 12.39/3.80 thf(445,plain,((! [A:nat,B:nat,C:nat]: (~ ((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 @ B @ A))) | ~ (~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ A @ C)) | ~ (~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ A)) | ~ (~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 12.39/3.80 thf(194,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_eq_nat @ B @ C) <= (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_nat__mult__le__cancel__disj)). 12.39/3.80 thf(936,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_eq_nat @ B @ C) | ~ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 12.39/3.80 thf(187,axiom,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_diff__0__eq__0)). 12.39/3.80 thf(900,plain,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 12.39/3.80 thf(120,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_order_Oasym)). 12.39/3.80 thf(681,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 12.39/3.80 thf(152,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_mult__nonpos__nonneg)). 12.39/3.80 thf(784,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 12.39/3.80 thf(44,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ A) => (ord_less_eq_set_nat @ C @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_dual__order_Otrans)). 12.39/3.80 thf(419,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ A) => (ord_less_eq_set_nat @ C @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 12.39/3.80 thf(137,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_ord__eq__le__trans)). 12.39/3.80 thf(736,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 12.39/3.80 thf(212,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_mult__nonneg__nonpos)). 12.39/3.80 thf(996,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 12.39/3.80 thf(86,axiom,((! [A:nat,B:nat]: ((A != B) => ((ord_less_nat @ B @ A) <= (~ (ord_less_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_neqE)). 12.39/3.80 thf(567,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 12.39/3.80 thf(70,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => (((ord_less_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F)))) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_order__less__subst1)). 12.39/3.80 thf(509,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 12.39/3.80 thf(103,axiom,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_less__numeral__extra_I4_J)). 12.39/3.80 thf(616,plain,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 12.39/3.80 thf(97,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) <= (A != B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_linorder__cases)). 12.39/3.80 thf(599,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (A = B) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 12.39/3.80 thf(208,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) & (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_nat__mult__eq__1__iff)). 12.39/3.80 thf(979,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((A = one_one_nat) & (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 12.39/3.80 thf(99,axiom,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_dual__order_Oeq__iff)). 12.39/3.80 thf(604,plain,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 12.39/3.80 thf(184,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_eq__diff__iff)). 12.39/3.80 thf(890,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 12.39/3.80 thf(35,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_le__zero__eq)). 12.39/3.80 thf(387,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 12.39/3.80 thf(65,axiom,((! [A:nat,B:nat]: (((B = A) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_dual__order_Oantisym)). 12.39/3.80 thf(494,plain,((! [A:nat,B:nat]: ((B = A) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 12.39/3.80 thf(162,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_diff__le__mono)). 12.39/3.80 thf(816,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 12.39/3.80 thf(101,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_nat @ (C @ E) @ (C @ F)) <= (ord_less_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_order__less__subst2)). 12.39/3.80 thf(609,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 12.39/3.80 thf(21,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((fun_upd_nat_nat @ A @ B @ C) = A) = ((A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_fun__upd__idem__iff)). 12.39/3.80 thf(323,plain,((! [A:(nat > nat),B:nat,C:nat]: (((fun_upd_nat_nat @ A @ B @ C) = (A)) = ((A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 12.39/3.80 thf(105,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_bot__nat__0_Oextremum__unique)). 12.39/3.80 thf(621,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 12.39/3.80 thf(224,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_le__diff__iff)). 12.39/3.80 thf(1029,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 12.39/3.80 thf(107,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_order_Ostrict__trans)). 12.39/3.80 thf(626,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 12.39/3.80 thf(146,axiom,((number1551313001itions = (^ [A:(nat > nat),B:nat]: (((groups1842438620at_nat @ (^ [C:nat]: (times_times_nat @ (A @ C) @ C)) @ (set_ord_atMost_nat @ B)) = B) & ! [C:nat]: (((A @ C) != zero_zero_nat) => ((ord_less_eq_nat @ one_one_nat @ C) & (ord_less_eq_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_partitions__def)). 12.39/3.80 thf(769,plain,(((number1551313001itions) = (^ [A:(nat > nat),B:nat]: (((groups1842438620at_nat @ (^ [C:nat]: (times_times_nat @ (A @ C) @ C)) @ (set_ord_atMost_nat @ B)) = B) & ! [C:nat]: ((~ ((A @ C) = zero_zero_nat)) => ((ord_less_eq_nat @ one_one_nat @ C) & (ord_less_eq_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 12.39/3.80 thf(55,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_ord__le__eq__subst)). 12.39/3.80 thf(462,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 12.39/3.80 thf(174,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_mult__0)). 12.39/3.80 thf(858,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 12.39/3.80 thf(31,axiom,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_ord__eq__le__subst)). 12.39/3.80 thf(367,plain,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 12.39/3.80 thf(81,axiom,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_less__numeral__extra_I3_J)). 12.39/3.80 thf(552,plain,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 12.39/3.80 thf(72,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((A @ C) <= (! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_nat__less__induct)). 12.39/3.80 thf(521,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((A @ C) | ~ (! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 12.39/3.80 thf(202,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_mult__0__right)). 12.39/3.80 thf(959,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 12.39/3.80 thf(15,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_le__refl)). 12.39/3.80 thf(306,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 12.39/3.80 thf(214,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_mult_Oleft__neutral)). 12.39/3.80 thf(1000,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 12.39/3.80 thf(232,axiom,((! [A:set_nat]: ((groups1842438620at_nat @ (^ [B:nat]: (zero_zero_nat)) @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_sum_Oneutral__const)). 12.39/3.80 thf(1066,plain,((! [A:set_nat]: ((groups1842438620at_nat @ (^ [B:nat]: (zero_zero_nat)) @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 12.39/3.80 thf(9,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_one__reorient)). 12.39/3.80 thf(278,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 12.39/3.80 thf(69,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)))))) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_order__subst1)). 12.39/3.80 thf(505,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)))))) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 12.39/3.80 thf(50,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zero__reorient)). 12.39/3.80 thf(438,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 12.39/3.80 thf(133,axiom,((! [A:nat,B:nat,C:$o]: (((C) <= (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_less__imp__triv)). 12.39/3.80 thf(722,plain,((! [A:nat,B:nat,C:$o]: ((C) | ~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 12.39/3.80 thf(94,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: ((((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_nat @ E @ F)))) <= (ord_less_eq_nat @ (C @ B) @ D)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_order__subst2)). 12.39/3.80 thf(589,plain,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) | ~ (ord_less_eq_nat @ (C @ B) @ D) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 12.39/3.80 thf(191,axiom,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ (B @ C) @ zero_zero_nat))) => (ord_less_eq_nat @ (groups1842438620at_nat @ B @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_sum__nonpos)). 12.39/3.80 thf(927,plain,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ (B @ C) @ zero_zero_nat))) => (ord_less_eq_nat @ (groups1842438620at_nat @ (B) @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 12.39/3.80 thf(161,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_mult__right__cancel)). 12.39/3.80 thf(812,plain,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 12.39/3.80 thf(195,axiom,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_lambda__zero)). 12.39/3.80 thf(939,plain,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 12.39/3.80 thf(220,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_le__square)). 12.39/3.80 thf(1018,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 12.39/3.80 thf(27,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_neq0__conv)). 12.39/3.80 thf(355,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 12.39/3.80 thf(141,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_diff__is__0__eq_H)). 12.39/3.80 thf(754,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 12.39/3.80 thf(205,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_diff__le__mono2)). 12.39/3.80 thf(968,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 12.39/3.80 thf(75,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_bot__nat__0_Oextremum)). 12.39/3.80 thf(531,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 12.39/3.80 thf(197,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_right__diff__distrib_H)). 12.39/3.80 thf(944,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 12.39/3.80 thf(215,axiom,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_cancel__comm__monoid__add__class_Odiff__cancel)). 12.39/3.80 thf(1003,plain,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 12.39/3.80 thf(183,axiom,((! [A:nat,B:(nat > nat),C:set_nat]: ((times_times_nat @ A @ (groups1842438620at_nat @ B @ C)) = (groups1842438620at_nat @ (^ [D:nat]: (times_times_nat @ A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_sum__distrib__left)). 12.39/3.80 thf(887,plain,((! [A:nat,B:(nat > nat),C:set_nat]: ((times_times_nat @ A @ (groups1842438620at_nat @ (B) @ C)) = (groups1842438620at_nat @ (^ [D:nat]: (times_times_nat @ A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 12.39/3.80 thf(206,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => (((times_times_nat @ A @ B) != zero_zero_nat) <= (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_no__zero__divisors)). 12.39/3.80 thf(971,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => (~ ((times_times_nat @ A @ B) = zero_zero_nat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 12.39/3.80 thf(41,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) = (B = A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_antisym__conv)). 12.39/3.80 thf(409,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) = (B = A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 12.39/3.80 thf(17,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_dual__order_Ostrict__implies__not__eq)). 12.39/3.80 thf(310,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 12.39/3.80 thf(211,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ B @ one_one_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat))) <= (ord_less_eq_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_mult__le__one)). 12.39/3.80 thf(993,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ B @ one_one_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat))) | ~ (ord_less_eq_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 12.39/3.80 thf(91,axiom,((! [A:(nat > $o),B:(nat > $o)]: (((collect_nat @ A) = (collect_nat @ B)) <= (! [C:nat]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__cong)). 12.39/3.80 thf(580,plain,((! [A:(nat > $o),B:(nat > $o)]: (((collect_nat @ (A)) = (collect_nat @ (B))) | ~ (! [C:nat]: ((A @ C) = (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 12.39/3.80 thf(173,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_mult__zero__left)). 12.39/3.80 thf(855,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 12.39/3.80 thf(119,axiom,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: ((((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))) <= (ord_less_eq_set_nat @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_ord__eq__le__subst)). 12.39/3.80 thf(673,plain,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_set_nat @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 12.39/3.80 thf(155,axiom,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_lambda__one)). 12.39/3.80 thf(791,plain,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 12.39/3.80 thf(51,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_less__asym_H)). 12.39/3.80 thf(441,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 12.39/3.80 thf(168,axiom,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (fun_upd_nat_nat @ p @ k @ (minus_minus_nat @ (p @ k) @ one_one_nat) @ A) @ A)) @ (set_ord_atMost_nat @ (minus_minus_nat @ n @ k))) = (groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (fun_upd_nat_nat @ p @ k @ (minus_minus_nat @ (p @ k) @ one_one_nat) @ A) @ A)) @ (set_ord_atMost_nat @ n)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062_I_092_060Sum_062i_092_060le_062n_A_N_Ak_O_A_Ip_Ik_A_058_061_Ap_Ak_A_N_A1_J_J_Ai_A_K_Ai_J_A_061_A_I_092_060Sum_062i_092_060le_062n_O_A_Ip_Ik_A_058_061_Ap_Ak_A_N_A1_J_J_Ai_A_K_Ai_J_092_060close_062)). 12.39/3.80 thf(840,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (fun_upd_nat_nat @ p @ k @ (minus_minus_nat @ (p @ k) @ one_one_nat) @ A) @ A)) @ (set_ord_atMost_nat @ (minus_minus_nat @ n @ k))) = (groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (fun_upd_nat_nat @ p @ k @ (minus_minus_nat @ (p @ k) @ one_one_nat) @ A) @ A)) @ (set_ord_atMost_nat @ n)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 12.39/3.80 thf(112,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_subset__antisym)). 12.39/3.80 thf(643,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 12.39/3.80 thf(238,axiom,((! [A:set_nat,B:(nat > nat)]: (((groups1842438620at_nat @ B @ A) = zero_zero_nat) <= (! [C:nat]: ((member_nat @ C @ A) => ((B @ C) = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_sum_Oneutral)). 12.39/3.80 thf(1085,plain,((! [A:set_nat,B:(nat > nat)]: (((groups1842438620at_nat @ (B) @ A) = zero_zero_nat) | ~ (! [C:nat]: ((member_nat @ C @ A) => ((B @ C) = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 12.39/3.80 thf(56,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_order__refl)). 12.39/3.80 thf(470,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 12.39/3.80 thf(89,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_gt__ex)). 12.39/3.80 thf(576,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 12.39/3.80 thf(139,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat)]: (((! [E:nat]: (((C @ E) = (D @ E)) <= (member_nat @ E @ B))) => ((groups1842438620at_nat @ C @ A) = (groups1842438620at_nat @ D @ B))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_sum_Ocong)). 12.39/3.80 thf(744,plain,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat)]: (((! [E:nat]: (((C @ E) = (D @ E)) | ~ (member_nat @ E @ B))) => ((groups1842438620at_nat @ (C) @ A) = (groups1842438620at_nat @ (D) @ B))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 12.39/3.80 thf(127,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_less__trans)). 12.39/3.80 thf(703,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 12.39/3.80 thf(102,axiom,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq)). 12.39/3.80 thf(613,plain,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 12.39/3.80 thf(176,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__eq__0__iff)). 12.39/3.80 thf(864,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 12.39/3.80 thf(18,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_zero__le)). 12.39/3.80 thf(314,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 12.39/3.80 thf(96,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_eq__refl)). 12.39/3.80 thf(595,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 12.39/3.80 thf(116,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) <= (ord_less_eq_nat @ D @ E))) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_linorder__wlog)). 12.39/3.80 thf(656,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) | ~ (ord_less_eq_nat @ D @ E))) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 12.39/3.80 thf(222,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_nat__mult__1__right)). 12.39/3.80 thf(1023,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 12.39/3.80 thf(66,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_zero__neq__one)). 12.39/3.80 thf(497,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 12.39/3.80 thf(180,axiom,((! [A:nat,B:nat]: (((set_ord_atMost_nat @ A) = (set_ord_atMost_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_atMost__eq__iff)). 12.39/3.80 thf(876,plain,((! [A:nat,B:nat]: (((set_ord_atMost_nat @ A) = (set_ord_atMost_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 12.39/3.80 thf(170,axiom,((ord_less_eq_nat @ k @ n)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062k_A_092_060le_062_An_092_060close_062)). 12.39/3.80 thf(845,plain,((ord_less_eq_nat @ k @ n)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 12.39/3.80 thf(4,axiom,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_ord__eq__le__subst)). 12.39/3.80 thf(250,plain,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_set_nat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 12.39/3.80 thf(78,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_ord__eq__less__subst)). 12.39/3.80 thf(539,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 12.39/3.80 thf(147,axiom,((ord_less_nat @ zero_zero_nat @ (p @ k))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_gr0)). 12.39/3.80 thf(771,plain,((ord_less_nat @ zero_zero_nat @ (p @ k))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 12.39/3.80 thf(30,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat,E:nat]: (((fun_upd_nat_nat @ (fun_upd_nat_nat @ C @ A @ D) @ B @ E) = (fun_upd_nat_nat @ (fun_upd_nat_nat @ C @ B @ E) @ A @ D)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_fun__upd__twist)). 12.39/3.80 thf(363,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat,E:nat]: (((fun_upd_nat_nat @ (fun_upd_nat_nat @ C @ A @ D) @ B @ E) = (fun_upd_nat_nat @ (fun_upd_nat_nat @ C @ B @ E) @ A @ D)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 12.39/3.80 thf(83,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((B = C) => (ord_less_eq_set_nat @ A @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_ord__le__eq__trans)). 12.39/3.80 thf(556,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((B = C) => (ord_less_eq_set_nat @ A @ C)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 12.39/3.80 thf(122,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_eq__imp__le)). 12.39/3.80 thf(688,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 12.39/3.80 thf(188,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat),D:set_nat,E:(nat > nat),F:(nat > nat)]: ((((! [G:nat]: ((member_nat @ G @ D) => ((C @ (B @ G)) = G))) => ((! [G:nat]: ((member_nat @ G @ D) => (member_nat @ (B @ G) @ A))) => (((groups1842438620at_nat @ F @ A) = (groups1842438620at_nat @ E @ D)) <= (! [G:nat]: ((member_nat @ G @ A) => ((E @ (C @ G)) = (F @ G))))))) <= (! [G:nat]: ((member_nat @ (C @ G) @ D) <= (member_nat @ G @ A)))) <= (! [G:nat]: ((member_nat @ G @ A) => ((B @ (C @ G)) = G)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_sum_Oreindex__bij__witness)). 12.39/3.80 thf(903,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat),D:set_nat,E:(nat > nat),F:(nat > nat)]: (((! [G:nat]: ((member_nat @ G @ D) => ((C @ (B @ G)) = G))) => ((! [G:nat]: ((member_nat @ G @ D) => (member_nat @ (B @ G) @ A))) => (((groups1842438620at_nat @ (F) @ A) = (groups1842438620at_nat @ (E) @ D)) | ~ (! [G:nat]: ((member_nat @ G @ A) => ((E @ (C @ G)) = (F @ G))))))) | ~ (! [G:nat]: ((member_nat @ (C @ G) @ D) | ~ (member_nat @ G @ A))) | ~ (! [G:nat]: ((member_nat @ G @ A) => ((B @ (C @ G)) = G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 12.39/3.80 thf(126,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (C @ B) @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_set_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_order__subst2)). 12.39/3.80 thf(699,plain,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (C @ B) @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_set_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 12.39/3.80 thf(36,axiom,((! [A:(nat > nat),B:nat,C:nat,D:nat]: ((fun_upd_nat_nat @ (fun_upd_nat_nat @ A @ B @ C) @ B @ D) = (fun_upd_nat_nat @ A @ B @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_fun__upd__upd)). 12.39/3.80 thf(390,plain,((! [A:(nat > nat),B:nat,C:nat,D:nat]: ((fun_upd_nat_nat @ (fun_upd_nat_nat @ A @ B @ C) @ B @ D) = (fun_upd_nat_nat @ A @ B @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 12.39/3.80 thf(109,axiom,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_less__one)). 12.39/3.80 thf(632,plain,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 12.39/3.80 thf(38,axiom,((fun_upd_nat_nat = (^ [A:(nat > nat),B:nat,C:nat,D:nat]: (if_nat @ (D = B) @ C @ (A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_fun__upd__def)). 12.39/3.80 thf(401,plain,(((fun_upd_nat_nat) = (^ [A:(nat > nat),B:nat,C:nat,D:nat]: (if_nat @ (D = B) @ C @ (A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 12.39/3.80 thf(151,axiom,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (set_ord_atMost_nat @ A) @ (set_ord_atMost_nat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_atMost__subset__iff)). 12.39/3.80 thf(781,plain,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (set_ord_atMost_nat @ A) @ (set_ord_atMost_nat @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 12.39/3.80 thf(242,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) => ((A = B) <= ((minus_minus_nat @ B @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_diffs0__imp__equal)). 12.39/3.80 thf(1101,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) => ((A = B) | ~ ((minus_minus_nat @ B @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 12.39/3.80 thf(5,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_dual__order_Orefl)). 12.39/3.80 thf(258,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 12.39/3.80 thf(3,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_less__imp__not__eq2)). 12.39/3.80 thf(246,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 12.39/3.80 thf(59,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((fun_upd_nat_nat @ A @ B @ C @ B) = C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_fun__upd__same)). 12.39/3.80 thf(478,plain,((! [A:(nat > nat),B:nat,C:nat]: ((fun_upd_nat_nat @ (A) @ B @ C @ B) = C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 12.39/3.80 thf(144,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_mult_Oleft__commute)). 12.39/3.80 thf(763,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 12.39/3.80 thf(165,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_mult__le__mono)). 12.39/3.80 thf(832,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 12.39/3.80 thf(24,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_order__class_Oorder_Oantisym)). 12.39/3.80 thf(346,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 12.39/3.80 thf(80,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_neq__iff)). 12.39/3.80 thf(549,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 12.39/3.80 thf(77,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_order__trans)). 12.39/3.80 thf(536,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 12.39/3.80 thf(157,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mult__cancel__left)). 12.39/3.80 thf(800,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 12.39/3.80 thf(213,axiom,((number1551313001itions @ p @ n)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_partitions)). 12.39/3.80 thf(999,plain,((number1551313001itions @ (p) @ n)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 12.39/3.80 thf(140,axiom,((! [A:(nat > nat),B:nat]: ((number1551313001itions @ A @ B) => (ord_less_eq_nat @ (groups1842438620at_nat @ A @ (set_ord_atMost_nat @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_partitions__parts__bounded)). 12.39/3.80 thf(752,plain,((! [A:(nat > nat),B:nat]: ((number1551313001itions @ (A) @ B) => (ord_less_eq_nat @ (groups1842438620at_nat @ (A) @ (set_ord_atMost_nat @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 12.39/3.80 thf(48,axiom,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq)). 12.39/3.80 thf(432,plain,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 12.39/3.80 thf(40,axiom,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: ((ord_less_eq_set_nat @ A @ (B @ C)) => (((ord_less_eq_set_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_order__subst1)). 12.39/3.80 thf(405,plain,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: ((ord_less_eq_set_nat @ A @ (B @ C)) => ((ord_less_eq_set_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 12.39/3.80 thf(45,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_dual__order_Otrans)). 12.39/3.80 thf(422,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 12.39/3.80 thf(177,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_mult_Oassoc)). 12.39/3.80 thf(867,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 12.39/3.80 thf(199,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_diff__mult__distrib2)). 12.39/3.80 thf(950,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 12.39/3.80 thf(166,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_mult__cancel2)). 12.39/3.80 thf(835,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 12.39/3.80 thf(85,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_dual__order_Oirrefl)). 12.39/3.80 thf(564,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 12.39/3.80 thf(22,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E)))) <= (! [D:nat]: (A @ D @ D))) <= (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_linorder__less__wlog)). 12.39/3.80 thf(326,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) | ~ (! [D:nat]: (A @ D @ D)) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 12.39/3.80 thf(7,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: ((ord_less_eq_set_nat @ A @ B) => (((! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_ord__le__eq__subst)). 12.39/3.80 thf(268,plain,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: ((ord_less_eq_set_nat @ A @ B) => (((! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 12.39/3.80 thf(28,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_order__trans)). 12.39/3.80 thf(358,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 12.39/3.80 thf(186,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_mult__less__cancel2)). 12.39/3.80 thf(897,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 12.39/3.80 thf(225,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 12.39/3.80 thf(1033,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 12.39/3.80 thf(110,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((fun_upd_nat_nat @ A @ B @ C) = A) <= ((A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_fun__upd__idem)). 12.39/3.80 thf(635,plain,((! [A:(nat > nat),B:nat,C:nat]: (((fun_upd_nat_nat @ A @ B @ C) = (A)) | ~ ((A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 12.39/3.80 thf(125,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_150_antisym)). 12.39/3.80 thf(696,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)],[125])). 12.39/3.80 thf(135,axiom,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_set_nat @ (C @ B) @ D) => ((ord_less_eq_set_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_order__subst2)). 12.39/3.80 thf(728,plain,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_set_nat @ (C @ B) @ D) => ((ord_less_eq_set_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 12.39/3.80 thf(210,axiom,((! [A:(nat > nat),B:nat,C:nat,D:nat]: (((((ord_less_eq_nat @ one_one_nat @ D) & (ord_less_eq_nat @ D @ (minus_minus_nat @ B @ C))) <= ((fun_upd_nat_nat @ A @ C @ (minus_minus_nat @ (A @ C) @ one_one_nat) @ D) != zero_zero_nat)) <= (ord_less_nat @ zero_zero_nat @ (A @ C))) <= (number1551313001itions @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_partitions__remove1__bounds)). 12.39/3.80 thf(987,plain,((! [A:(nat > nat),B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ one_one_nat @ D) & (ord_less_eq_nat @ D @ (minus_minus_nat @ B @ C))) | ((fun_upd_nat_nat @ (A) @ C @ (minus_minus_nat @ (A @ C) @ one_one_nat) @ D) = zero_zero_nat) | ~ (ord_less_nat @ zero_zero_nat @ (A @ C)) | ~ (number1551313001itions @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 12.39/3.80 thf(47,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (B = C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_ord__less__eq__trans)). 12.39/3.80 thf(427,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (B = C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 12.39/3.80 thf(74,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_le__0__eq)). 12.39/3.80 thf(528,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 12.39/3.80 thf(54,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_bot__nat__0_Oextremum__uniqueI)). 12.39/3.80 thf(459,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 12.39/3.80 thf(209,axiom,((! [A:(nat > nat),B:set_nat]: (((groups1842438620at_nat @ A @ B) != zero_zero_nat) => (~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_sum_Onot__neutral__contains__not__neutral)). 12.39/3.80 thf(982,plain,((! [A:(nat > nat),B:set_nat]: ((~ ((groups1842438620at_nat @ (A) @ B) = zero_zero_nat)) => (~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 12.39/3.80 thf(240,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_mult__mono_H)). 12.39/3.80 thf(1093,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 12.39/3.80 thf(106,axiom,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))) & (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_exists__least__iff)). 12.39/3.80 thf(624,plain,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))) & (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 12.39/3.80 thf(158,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_mult__cancel1)). 12.39/3.80 thf(803,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 12.39/3.80 thf(217,axiom,((! [A:nat,B:nat]: (((B = zero_zero_nat) | (A = zero_zero_nat)) <= ((times_times_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_divisors__zero)). 12.39/3.80 thf(1009,plain,((! [A:nat,B:nat]: ((B = zero_zero_nat) | (A = zero_zero_nat) | ~ ((times_times_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 12.39/3.80 thf(149,axiom,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((B = one_one_nat) & (A = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_nat__1__eq__mult__iff)). 12.39/3.80 thf(775,plain,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((B = one_one_nat) & (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 12.39/3.80 thf(111,axiom,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_order__subst1)). 12.39/3.80 thf(639,plain,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:set_nat,F:set_nat]: ((ord_less_eq_set_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 12.39/3.80 thf(63,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_145_le__cases)). 12.39/3.80 thf(491,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)],[63])). 12.39/3.80 thf(233,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_ab__semigroup__mult__class_Omult__ac_I1_J)). 12.39/3.80 thf(1069,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 12.39/3.80 thf(219,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Nat_Odiff__diff__eq)). 12.39/3.80 thf(1014,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 12.39/3.80 thf(1107,plain,(($false)),inference(e,[status(thm)],[1036,809,629,760,846,962,941,481,352,683,276,308,741,873,379,861,1078,533,500,715,472,1063,930,670,829,417,320,570,838,344,853,870,606,284,289,316,789,443,646,1020,806,475,924,692,956,1072,1104,602,766,793,714,1057,894,778,1042,561,297,260,349,484,361,879,435,583,493,757,842,1012,578,650,725,403,1096,1006,593,884,1082,488,933,554,1075,526,1039,547,706,393,654,1060,503,244,921,1026,953,586,662,718,298,412,965,618,425,513,573,375,819,975,694,732,772,711,281,382,787,1090,947,445,936,900,681,784,419,736,996,567,509,616,599,979,604,890,387,494,816,609,323,621,1029,626,769,462,858,367,552,521,959,306,1000,1066,278,505,438,722,589,927,812,939,1018,355,754,968,531,944,1003,887,971,409,310,993,580,855,673,791,441,840,643,1085,470,576,744,703,613,864,314,595,656,1023,497,876,845,250,539,771,363,556,688,903,699,390,632,401,781,1101,258,246,478,763,832,346,549,536,800,999,752,432,405,422,867,950,835,564,326,268,358,897,1033,635,696,728,987,427,528,459,982,1093,624,803,1009,775,639,491,1069,1014])). 12.39/3.80 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 12.39/3.80 % [INFO] Killing All external provers ... 12.79/3.86 EOF