0.00/0.00	% Leo-III: Strategy 1 (for '60')
239.52/52.83	% [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
239.52/52.83	% [INFO] 	 Parsing done (310ms). 
239.52/52.83	% [INFO] 	 Running in sequential loop mode. 
239.52/52.83	% [CONFIG] 	 Using configuration: timeout(60) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(10),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)> 
239.52/52.83	% [INFO] 	 eprover registered as external prover. 
239.52/52.83	% [INFO] 	 cvc4 registered as external prover. 
239.52/52.83	% [INFO] 	 Parsing finished. Scanning for conjecture ... 
239.52/52.83	% [INFO] 	 Found a conjecture and 261 axioms. Running axiom selection ... 
239.52/52.83	% [INFO] 	 Axiom selection finished. Selected 242 axioms (removed 19 axioms). 
239.52/52.83	% [INFO] 	 Problem is higher-order (TPTP THF). 
239.52/52.83	% [INFO] 	 Type checking passed. Searching for refutation ... 
239.52/52.83	% External prover 'e' found a proof!
239.52/52.83	% [INFO] 	 Killing All external provers ... 
239.52/52.83	% Time passed: 47155ms (effective reasoning time: 46336ms)
239.52/52.83	% Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(10),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
239.52/52.83	% Axioms used in derivation (242): fact_38_mult__not__zero, fact_105_ord__le__eq__subst, fact_151_subset__iff, fact_31_sum_Oeq__general, fact_160_zero__le, fact_30_sum_Oeq__general__inverses, fact_209_order__less__subst2, fact_244_dual__order_Ostrict__iff__order, fact_74_mult__mono, fact_226_less__zeroE, fact_218_less__imp__le__nat, fact_89_nat__mult__eq__cancel__disj, fact_60_sum__distrib__right, fact_45_bot__nat__0_Oextremum__uniqueI, fact_104_ord__le__eq__subst, fact_113_eq__refl, fact_2_partitionsI, fact_28_le__refl, fact_129_order__trans, fact_189_linorder__cases, fact_162_le__numeral__extra_I3_J, fact_256_order_Oorder__iff__strict, fact_120_antisym__conv, fact_127_order__class_Oorder_Oantisym, fact_94_order__subst1, fact_176_nat__mult__less__cancel__disj, fact_95_order__subst1, fact_207_neqE, fact_53_le__square, fact_102_ord__eq__le__subst, fact_200_less__linear, fact_59_sum__mono, fact_133_linorder__wlog, fact_57_lambda__zero, fact_147_set__eq__subset, fact_202_less__asym_H, fact_208_gt__ex, fact_14_mult__zero__right, fact_136_dual__order_Oeq__iff, fact_237_less__numeral__extra_I4_J, fact_164_subset__CollectI, fact_23_Nat_Oex__has__greatest__nat, fact_15_mult__zero__left, fact_238_less__numeral__extra_I3_J, fact_91_comm__monoid__mult__class_Omult__1, fact_12_mult__cancel__left, fact_4_nat__1__eq__mult__iff, fact_166_prop__restrict, fact_63_atMost__def, fact_112_linear, fact_138_dual__order_Oantisym, fact_33_sum_Oswap, fact_254_order_Ostrict__iff__order, fact_68_mult__nonneg__nonpos, fact_29_sum_Oreindex__bij__witness, fact_108_eq__iff, fact_41_sum_Oneutral, fact_87_order__refl, fact_72_mult__left__mono, fact_0_sum_Oneutral__const, fact_148_subset__trans, fact_139_dual__order_Oantisym, fact_228_infinite__descent0, fact_107_ord__le__eq__subst, fact_84_le__zero__eq, fact_13_mult__eq__0__iff, fact_56_nat__mult__1, fact_227_gr__implies__not0, fact_221_le__neq__implies__less, fact_173_not__gr__zero, fact_171_bot__nat__0_Onot__eq__extremum, fact_61_sum__distrib__left, fact_181_order_Ostrict__implies__not__eq, fact_123_ord__eq__le__trans, fact_65_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_159_Collect__subset, fact_17_le0, fact_215_gr__implies__not__zero, fact_134_dual__order_Otrans, fact_182_not__less__iff__gr__or__eq, fact_51_mult__le__mono1, fact_188_dual__order_Oirrefl, fact_150_subset__refl, fact_225_not__less0, fact_69_mult__nonneg__nonneg, fact_203_less__asym, fact_36_no__zero__divisors, fact_3_partitions__def, fact_260_order_Ostrict__trans1, fact_44_Collect__cong, fact_149_Collect__mono, fact_144_mult_Oleft__commute, fact_25_le__antisym, fact_141_ab__semigroup__mult__class_Omult__ac_I1_J, fact_153_equalityD1, fact_114_eq__refl, fact_67_mult__nonpos__nonneg, fact_222_less__mono__imp__le__mono, fact_78_sum__nonneg, fact_66_mult__nonneg__nonpos2, fact_224_not__gr0, fact_46_bot__nat__0_Oextremum__unique, fact_130_order__trans, fact_155_equalityE, fact_8_atMost__iff, fact_214_not__less__zero, fact_22_bounded__Max__nat, fact_187_order_Ostrict__trans, fact_116_order_Otrans, fact_216_zero__less__iff__neq__zero, fact_248_order_Ostrict__implies__order, fact_191_less__imp__not__eq2, fact_179_nat__mult__le__cancel__disj, fact_186_less__imp__not__less, fact_26_eq__imp__le, fact_100_ord__eq__le__subst, fact_180_dual__order_Ostrict__implies__not__eq, fact_185_exists__least__iff, fact_128_order__class_Oorder_Oantisym, fact_117_order_Otrans, fact_85_subsetI, fact_27_le__trans, fact_193_less__induct, fact_98_order__subst2, fact_62_sum__product, fact_201_less__trans, fact_111_antisym, fact_9_atMost__iff, fact_146_Collect__mono__iff, fact_198_ord__eq__less__trans, fact_99_order__subst2, fact_213_gr__zeroI, fact_1_partitionsE, fact_49_mult__0, fact_86_subset__antisym, fact_35_mult__left__cancel, fact_40_sum_Onot__neutral__contains__not__neutral, fact_204_less__imp__neq, fact_197_ord__less__eq__trans, fact_110_antisym, fact_43_Collect__mem__eq, fact_92_order__subst1, fact_210_order__less__subst1, fact_96_order__subst2, fact_140_zero__reorient, fact_79_mult__eq__self__implies__10, fact_81_mult__le__one, fact_219_le__eq__less__or__eq, fact_39_zero__neq__one, fact_124_ord__eq__le__trans, fact_18_mult__cancel2, fact_70_split__mult__neg__le, fact_142_mult_Oassoc, fact_37_divisors__zero, fact_58_lambda__one, fact_16_bot__nat__0_Oextremum, fact_252_dual__order_Ostrict__trans1, fact_161_le__numeral__extra_I4_J, fact_194_less__not__sym, fact_24_nat__le__linear, fact_165_Collect__restrict, fact_97_order__subst2, fact_196_dual__order_Oasym, fact_121_order__class_Oorder_Oeq__iff, fact_143_mult_Ocommute, fact_131_dual__order_Orefl, fact_6_atMost__subset__iff, fact_220_less__or__eq__imp__le, fact_93_order__subst1, fact_258_order_Ostrict__trans2, fact_240_order_Onot__eq__order__implies__strict, fact_64_atMost__def, fact_109_eq__iff, fact_132_dual__order_Orefl, fact_135_dual__order_Otrans, fact_192_antisym__conv3, fact_34_mult__right__cancel, fact_167_pred__subset__eq, fact_21_mult__is__0, fact_126_ord__le__eq__trans, fact_106_ord__le__eq__subst, fact_206_neq__iff, fact_184_linorder__less__wlog, fact_190_less__imp__triv, fact_195_less__imp__not__eq, fact_174_nat__0__less__mult__iff, fact_77_sum__nonpos, fact_5_nat__mult__eq__1__iff, fact_242_dual__order_Ostrict__implies__order, fact_250_dual__order_Ostrict__trans2, fact_73_mult__mono_H, fact_76_zero__le__one, fact_118_le__cases3, fact_48_less__eq__nat_Osimps_I1_J, fact_20_mult__0__right, fact_10_atMost__eq__iff, fact_170_less__nat__zero__code, fact_101_ord__eq__le__subst, fact_199_less__irrefl, fact_82_mult_Oright__neutral, fact_178_mult__le__cancel2, fact_157_in__mono, fact_90_mult_Ocomm__neutral, fact_54_le__cube, fact_175_mult__less__cancel2, fact_205_order_Oasym, fact_177_less__one, fact_183_dual__order_Ostrict__trans, fact_211_ord__less__eq__subst, fact_125_ord__le__eq__trans, fact_156_subsetD, fact_103_ord__eq__le__subst, fact_55_nat__mult__1__right, fact_122_order__class_Oorder_Oeq__iff, fact_80_mult__left__le, fact_229_bot__nat__0_Oextremum__strict, fact_83_mult_Oleft__neutral, fact_217_nat__less__le, fact_19_mult__cancel1, fact_115_le__cases, fact_47_le__0__eq, fact_158_less__eq__set__def, fact_50_mult__le__mono2, fact_168_conj__subset__def, fact_88_order__refl, fact_145_one__reorient, fact_32_sum_Ocong, fact_42_mem__Collect__eq, fact_152_equalityD2, fact_169_neq0__conv, fact_75_not__one__le__zero, fact_223_gr0I, fact_119_antisym__conv, fact_71_mult__right__mono, fact_163_subset__Collect__iff, fact_52_mult__le__mono, fact_154_subset__eq, fact_212_ord__eq__less__subst, fact_11_mult__cancel__right, fact_137_dual__order_Oeq__iff, fact_7_atMost__subset__iff, fact_246_dual__order_Oorder__iff__strict
239.52/52.83	% No. of inferences in proof: 988
239.52/52.83	% SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 47155 ms resp. 46336 ms w/o parsing
239.52/52.83	% SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
239.52/52.83	thf(set_set_nat_type, type, set_set_nat: $tType).
239.52/52.83	thf(set_nat_type, type, set_nat: $tType).
239.52/52.83	thf(nat_type, type, nat: $tType).
239.52/52.83	thf(one_one_nat_type, type, one_one_nat: nat).
239.52/52.83	thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))).
239.52/52.83	thf(zero_zero_nat_type, type, zero_zero_nat: nat).
239.52/52.83	thf(groups1842438620at_nat_type, type, groups1842438620at_nat: ((nat > nat) > (set_nat > nat))).
239.52/52.83	thf(number1551313001itions_type, type, number1551313001itions: ((nat > nat) > (nat > $o))).
239.52/52.83	thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))).
239.52/52.83	thf(ord_less_eq_nat_o_type, type, ord_less_eq_nat_o: ((nat > $o) > ((nat > $o) > $o))).
239.52/52.83	thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))).
239.52/52.83	thf(ord_less_eq_set_nat_type, type, ord_less_eq_set_nat: (set_nat > (set_nat > $o))).
239.52/52.83	thf(ord_le1613022364et_nat_type, type, ord_le1613022364et_nat: (set_set_nat > (set_set_nat > $o))).
239.52/52.83	thf(collect_nat_type, type, collect_nat: ((nat > $o) > set_nat)).
239.52/52.83	thf(collect_set_nat_type, type, collect_set_nat: ((set_nat > $o) > set_set_nat)).
239.52/52.83	thf(set_ord_atMost_nat_type, type, set_ord_atMost_nat: (nat > set_nat)).
239.52/52.83	thf(set_or1086813439et_nat_type, type, set_or1086813439et_nat: (set_nat > set_set_nat)).
239.52/52.83	thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))).
239.52/52.83	thf(member_set_nat_type, type, member_set_nat: (set_nat > (set_set_nat > $o))).
239.52/52.83	thf(p_type, type, p: (nat > nat)).
239.52/52.83	thf(sk1_type, type, sk1: (set_nat > (set_nat > ((set_nat > set_nat) > (set_nat > set_nat))))).
239.52/52.83	thf(sk2_type, type, sk2: (set_nat > (set_nat > ((set_nat > set_nat) > (set_nat > set_nat))))).
239.52/52.83	thf(sk3_type, type, sk3: (set_nat > (set_nat > ((set_nat > set_nat) > (set_nat > set_nat))))).
239.52/52.83	thf(sk4_type, type, sk4: (set_nat > (set_nat > ((set_nat > set_nat) > (set_nat > set_nat))))).
239.52/52.83	thf(sk5_type, type, sk5: (nat > ((nat > nat) > (nat > (nat > nat))))).
239.52/52.83	thf(sk6_type, type, sk6: (nat > ((nat > nat) > (nat > (nat > nat))))).
239.52/52.83	thf(sk7_type, type, sk7: (set_nat > ((set_nat > set_nat) > (set_nat > (set_nat > set_nat))))).
239.52/52.83	thf(sk8_type, type, sk8: (set_nat > ((set_nat > set_nat) > (set_nat > (set_nat > set_nat))))).
239.52/52.83	thf(sk9_type, type, sk9: (nat > ((nat > nat) > (nat > (nat > nat))))).
239.52/52.83	thf(sk10_type, type, sk10: (nat > ((nat > nat) > (nat > (nat > nat))))).
239.52/52.83	thf(sk11_type, type, sk11: (nat > (nat > ((nat > nat) > (nat > nat))))).
239.52/52.83	thf(sk12_type, type, sk12: (nat > (nat > ((nat > nat) > (nat > nat))))).
239.52/52.83	thf(sk13_type, type, sk13: (nat > (nat > ((nat > nat) > (nat > nat))))).
239.52/52.83	thf(sk14_type, type, sk14: (nat > (nat > ((nat > nat) > (nat > nat))))).
239.52/52.83	thf(sk15_type, type, sk15: ((nat > $o) > nat)).
239.52/52.83	thf(sk16_type, type, sk16: (set_nat > (set_nat > nat))).
239.52/52.83	thf(sk20_type, type, sk20: ((nat > (nat > $o)) > nat)).
239.52/52.83	thf(sk21_type, type, sk21: ((nat > (nat > $o)) > nat)).
239.52/52.83	thf(sk27_type, type, sk27: (nat > nat)).
239.52/52.83	thf(sk38_type, type, sk38: ((nat > $o) > nat)).
239.52/52.83	thf(sk90_type, type, sk90: nat).
239.52/52.83	thf(sk106_type, type, sk106: nat).
239.52/52.83	thf(sk107_type, type, sk107: nat).
239.52/52.83	thf(sk110_type, type, sk110: nat).
239.52/52.83	thf(sk111_type, type, sk111: nat).
239.52/52.83	thf(sk112_type, type, sk112: nat).
239.52/52.83	thf(sk113_type, type, sk113: nat).
239.52/52.83	thf(sk114_type, type, sk114: nat).
239.52/52.83	thf(sk115_type, type, sk115: nat).
239.52/52.83	thf(sk116_type, type, sk116: nat).
239.52/52.83	thf(sk117_type, type, sk117: nat).
239.52/52.83	thf(sk118_type, type, sk118: nat).
239.52/52.83	thf(sk119_type, type, sk119: nat).
239.52/52.83	thf(236,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_order_Ostrict__iff__order)).
239.52/52.83	thf(1089,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
239.52/52.83	thf(1090,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(lifteq,[status(thm)],[1089])).
239.52/52.83	thf(169,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (B != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_dual__order_Ostrict__iff__order)).
239.52/52.83	thf(853,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
239.52/52.83	thf(854,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(lifteq,[status(thm)],[853])).
239.52/52.83	thf(1410,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[1090,854])).
239.52/52.83	thf(1411,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(pattern_uni,[status(thm)],[1410:[]])).
239.52/52.83	thf(30,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((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_211_ord__less__eq__subst)).
239.52/52.83	thf(342,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((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)],[30])).
239.52/52.83	thf(343,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (! [C:(nat > nat),D: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(miniscope,[status(thm)],[342])).
239.52/52.83	thf(344,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (~ ((C @ B) = D)) | (ord_less_nat @ (C @ A) @ D) | (~ (ord_less_nat @ (C @ (sk9 @ D @ (C) @ B @ A)) @ (C @ (sk10 @ D @ (C) @ B @ A)))))),inference(cnf,[status(esa)],[343])).
239.52/52.83	thf(346,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : (((C @ B) != D) | (~ (ord_less_nat @ A @ B)) | (ord_less_nat @ (C @ A) @ D) | (~ (ord_less_nat @ (C @ (sk9 @ D @ (C) @ B @ A)) @ (C @ (sk10 @ D @ (C) @ B @ A)))))),inference(lifteq,[status(thm)],[344])).
239.52/52.83	thf(347,plain,(! [C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (ord_less_nat @ (C @ A) @ (C @ B)) | (~ (ord_less_nat @ (C @ (sk9 @ (C @ B) @ (C) @ B @ A)) @ (C @ (sk10 @ (C @ B) @ (C) @ B @ A)))))),inference(simp,[status(thm)],[346])).
239.52/52.83	thf(79,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_gt__ex)).
239.52/52.83	thf(517,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
239.52/52.83	thf(518,plain,(! [A:nat] : ((ord_less_nat @ A @ (sk27 @ A)))),inference(cnf,[status(esa)],[517])).
239.52/52.83	thf(62,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_less__not__sym)).
239.52/52.83	thf(468,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
239.52/52.83	thf(243,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_137_dual__order_Oeq__iff)).
239.52/52.83	thf(1110,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)],[243])).
239.52/52.83	thf(106,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_bot__nat__0_Oextremum__strict)).
239.52/52.83	thf(628,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
239.52/52.83	thf(3,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_134_dual__order_Otrans)).
239.52/52.83	thf(247,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)],[3])).
239.52/52.83	thf(248,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(miniscope,[status(thm)],[247])).
239.52/52.83	thf(249,plain,(! [C:set_nat,B:set_nat,A:set_nat] : ((~ (ord_less_eq_set_nat @ C @ A)) | (ord_less_eq_set_nat @ C @ B) | (~ (ord_less_eq_set_nat @ A @ B)))),inference(cnf,[status(esa)],[248])).
239.52/52.83	thf(181,axiom,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_zero__le__one)).
239.52/52.83	thf(893,plain,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])).
239.52/52.83	thf(1,conjecture,(((! [A:nat]: (((ord_less_eq_nat @ one_one_nat @ A) & (ord_less_eq_nat @ A @ zero_zero_nat)) <= ((p @ A) != zero_zero_nat)) & ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)) = (p = (^ [A:nat]: (zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
239.52/52.83	thf(2,negated_conjecture,((~ ((! [A:nat]: (((ord_less_eq_nat @ one_one_nat @ A) & (ord_less_eq_nat @ A @ zero_zero_nat)) <= ((p @ A) != zero_zero_nat)) & ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)) = (p = (^ [A:nat]: (zero_zero_nat)))))),inference(neg_conjecture,[status(cth)],[1])).
239.52/52.83	thf(245,plain,((~ ((! [A:nat]: (((ord_less_eq_nat @ one_one_nat @ A) & (ord_less_eq_nat @ A @ zero_zero_nat)) | ((p @ A) = zero_zero_nat)) & ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)) = ((p) = (^ [A:nat]: (zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
239.52/52.83	thf(246,plain,(((! [A:nat]: (((ord_less_eq_nat @ one_one_nat @ A) & (ord_less_eq_nat @ A @ zero_zero_nat)) | ((p @ A) = zero_zero_nat)) & ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)) != ((p) = (^ [A:nat]: (zero_zero_nat))))),inference(lifteq,[status(thm)],[245])).
239.52/52.83	thf(1120,plain,((! [A:nat]: (((ord_less_eq_nat @ one_one_nat @ A) & (ord_less_eq_nat @ A @ zero_zero_nat)) | ((p @ A) = zero_zero_nat)) & ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(bool_ext,[status(thm)],[246])).
239.52/52.83	thf(1123,plain,(((p) = (^ [A:nat]: (zero_zero_nat))) | (! [A:nat]: (((ord_less_eq_nat @ one_one_nat @ A) & (ord_less_eq_nat @ A @ zero_zero_nat)) | ((p @ A) = zero_zero_nat)) & ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat))),inference(lifteq,[status(thm)],[1120])).
239.52/52.83	thf(1130,plain,(! [A:nat] : ((ord_less_eq_nat @ one_one_nat @ A) | ((p @ A) = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))))),inference(cnf,[status(esa)],[1123])).
239.52/52.83	thf(1133,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | (ord_less_eq_nat @ one_one_nat @ A) | ((p) = (^ [B:nat]: (zero_zero_nat))))),inference(lifteq,[status(thm)],[1130])).
239.52/52.83	thf(197,axiom,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_not__one__le__zero)).
239.52/52.83	thf(949,plain,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
239.52/52.83	thf(950,plain,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),inference(polarity_switch,[status(thm)],[949])).
239.52/52.83	thf(1191,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))) | ((ord_less_eq_nat @ one_one_nat @ A) != (ord_less_eq_nat @ one_one_nat @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[1133,950])).
239.52/52.83	thf(1192,plain,(((p @ zero_zero_nat) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(pattern_uni,[status(thm)],[1191:[bind(A, $thf(zero_zero_nat))]])).
239.52/52.83	thf(1243,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p @ zero_zero_nat) = zero_zero_nat))),inference(func_ext,[status(esa)],[1192])).
239.52/52.83	thf(1266,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p @ zero_zero_nat) != (p @ A)) | (zero_zero_nat != zero_zero_nat))),inference(eqfactor_ordered,[status(thm)],[1243])).
239.52/52.83	thf(1267,plain,(((p @ zero_zero_nat) = zero_zero_nat)),inference(pattern_uni,[status(thm)],[1266:[bind(A, $thf(zero_zero_nat))]])).
239.52/52.83	thf(94,axiom,((! [A:set_nat]: ((groups1842438620at_nat @ (^ [B:nat]: (zero_zero_nat)) @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_sum_Oneutral__const)).
239.52/52.83	thf(580,plain,((! [A:set_nat]: ((groups1842438620at_nat @ (^ [B:nat]: (zero_zero_nat)) @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
239.52/52.83	thf(581,plain,(! [A:set_nat] : (((groups1842438620at_nat @ (^ [B:nat]: (zero_zero_nat)) @ A) = zero_zero_nat))),inference(cnf,[status(esa)],[580])).
239.52/52.83	thf(582,plain,(! [A:set_nat] : (((groups1842438620at_nat @ (^ [B:nat]: (zero_zero_nat)) @ A) = zero_zero_nat))),inference(lifteq,[status(thm)],[581])).
239.52/52.83	thf(1119,plain,((~ (! [A:nat]: (((ord_less_eq_nat @ one_one_nat @ A) & (ord_less_eq_nat @ A @ zero_zero_nat)) | ((p @ A) = zero_zero_nat)) & ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat))) | (~ ((p) = (^ [A:nat]: (zero_zero_nat))))),inference(bool_ext,[status(thm)],[246])).
239.52/52.83	thf(1122,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | (~ (! [A:nat]: (((ord_less_eq_nat @ one_one_nat @ A) & (ord_less_eq_nat @ A @ zero_zero_nat)) | ((p @ A) = zero_zero_nat)) & ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)))),inference(lifteq,[status(thm)],[1119])).
239.52/52.83	thf(1126,plain,((~ ((p @ sk90) = zero_zero_nat)) | (~ ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)) | ((p) != (^ [A:nat]: (zero_zero_nat)))),inference(cnf,[status(esa)],[1122])).
239.52/52.83	thf(1128,plain,(((p @ sk90) != zero_zero_nat) | ((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat)))),inference(lifteq,[status(thm)],[1126])).
239.52/52.83	thf(1740,plain,(! [A:set_nat] : (((p @ sk90) != zero_zero_nat) | ((p) != (^ [B:nat]: (zero_zero_nat))) | ((groups1842438620at_nat @ (^ [B:nat]: (zero_zero_nat)) @ A) != (groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (set_ord_atMost_nat @ zero_zero_nat))))),inference(paramod_ordered,[status(thm)],[582,1128])).
239.52/52.83	thf(1752,plain,(! [A:set_nat] : (((p @ sk90) != zero_zero_nat) | ((p) != (^ [B:nat]: (zero_zero_nat))) | ((^ [B:nat]: (times_times_nat @ (p @ B) @ B)) != (^ [B:nat]: (zero_zero_nat))) | (A != (set_ord_atMost_nat @ zero_zero_nat)))),inference(simp,[status(thm)],[1740])).
239.52/52.83	thf(1757,plain,(((p @ sk90) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (^ [A:nat]: (zero_zero_nat)))),inference(simp,[status(thm)],[1752])).
239.52/52.83	thf(1766,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (^ [A:nat]: (zero_zero_nat))) | ((p @ sk90) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,1757])).
239.52/52.83	thf(1771,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != zero_zero_nat)),inference(simp,[status(thm)],[1766])).
239.52/52.83	thf(1840,plain,(((p @ sk112) != zero_zero_nat) | ((times_times_nat @ (p @ sk113) @ sk113) != zero_zero_nat) | (sk90 != zero_zero_nat)),inference(func_ext,[status(esa)],[1771])).
239.52/52.83	thf(49,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_6_atMost__subset__iff)).
239.52/52.83	thf(408,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)],[49])).
239.52/52.83	thf(212,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((B != zero_zero_nat) => ((times_times_nat @ A @ B) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_no__zero__divisors)).
239.52/52.83	thf(1005,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((~ (B = zero_zero_nat)) => (~ ((times_times_nat @ A @ B) = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])).
239.52/52.83	thf(117,axiom,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_lambda__one)).
239.52/52.83	thf(668,plain,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
239.52/52.83	thf(669,plain,(((times_times_nat @ one_one_nat) = (^ [A:nat]: (A)))),inference(lifteq,[status(thm)],[668])).
239.52/52.83	thf(1129,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(cnf,[status(esa)],[1123])).
239.52/52.83	thf(1132,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(lifteq,[status(thm)],[1129])).
239.52/52.83	thf(1136,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat))),inference(func_ext,[status(esa)],[1132])).
239.52/52.83	thf(1587,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((groups1842438620at_nat @ (^ [B:nat]: (B)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat) | ((^ [B:nat]: (times_times_nat @ (p @ B) @ B)) != (times_times_nat @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[669,1136])).
239.52/52.83	thf(1594,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((groups1842438620at_nat @ (^ [B:nat]: (B)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat) | ((p) != (^ [B:nat]: (one_one_nat))) | ((^ [B:nat]: (B)) != (^ [B:nat]: (B))))),inference(simp,[status(thm)],[1587])).
239.52/52.83	thf(1596,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((groups1842438620at_nat @ (^ [B:nat]: (B)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat) | ((p) != (^ [B:nat]: (one_one_nat))))),inference(simp,[status(thm)],[1594])).
239.52/52.83	thf(123,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)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_mult__right__mono)).
239.52/52.83	thf(683,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)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
239.52/52.83	thf(108,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_mult__0)).
239.52/52.83	thf(634,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
239.52/52.83	thf(635,plain,(! [A:nat] : (((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(cnf,[status(esa)],[634])).
239.52/52.83	thf(636,plain,(! [A:nat] : (((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(lifteq,[status(thm)],[635])).
239.52/52.83	thf(1131,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ zero_zero_nat) | ((p @ A) = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))))),inference(cnf,[status(esa)],[1123])).
239.52/52.83	thf(1134,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | (ord_less_eq_nat @ A @ zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))))),inference(lifteq,[status(thm)],[1131])).
239.52/52.83	thf(1328,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))) | ((ord_less_eq_nat @ A @ zero_zero_nat) != (ord_less_eq_nat @ one_one_nat @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[1134,950])).
239.52/52.83	thf(1329,plain,(((p @ one_one_nat) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(pattern_uni,[status(thm)],[1328:[bind(A, $thf(one_one_nat))]])).
239.52/52.83	thf(1330,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p @ one_one_nat) = zero_zero_nat))),inference(func_ext,[status(esa)],[1329])).
239.52/52.83	thf(1450,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p @ one_one_nat) != (p @ A)) | (zero_zero_nat != zero_zero_nat))),inference(eqfactor_ordered,[status(thm)],[1330])).
239.52/52.83	thf(1451,plain,(((p @ one_one_nat) = zero_zero_nat)),inference(pattern_uni,[status(thm)],[1450:[bind(A, $thf(one_one_nat))]])).
239.52/52.83	thf(1763,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (^ [A:nat]: (zero_zero_nat))) | ((p @ sk90) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,1757])).
239.52/52.83	thf(1770,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != one_one_nat)),inference(simp,[status(thm)],[1763])).
239.52/52.83	thf(1830,plain,(((p @ sk110) != zero_zero_nat) | ((times_times_nat @ (p @ sk111) @ sk111) != zero_zero_nat) | (sk90 != one_one_nat)),inference(func_ext,[status(esa)],[1770])).
239.52/52.83	thf(2072,plain,(! [A:nat] : (((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | ((times_times_nat @ zero_zero_nat @ A) != (times_times_nat @ (p @ sk111) @ sk111)))),inference(paramod_ordered,[status(thm)],[636,1830])).
239.52/52.83	thf(2075,plain,(! [A:nat] : (((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | ((p @ sk111) != zero_zero_nat) | (A != sk111))),inference(simp,[status(thm)],[2072])).
239.52/52.83	thf(2081,plain,(((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | ((p @ sk111) != zero_zero_nat)),inference(simp,[status(thm)],[2075])).
239.52/52.83	thf(2392,plain,(((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | ((p @ sk111) != (p @ sk110)) | (zero_zero_nat != zero_zero_nat)),inference(eqfactor_ordered,[status(thm)],[2081])).
239.52/52.83	thf(2395,plain,(((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | (sk111 != sk110)),inference(simp,[status(thm)],[2392])).
239.52/52.83	thf(232,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)) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_order__subst1)).
239.52/52.83	thf(1073,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) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
239.52/52.83	thf(176,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_61_sum__distrib__left)).
239.52/52.83	thf(873,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)],[176])).
239.52/52.83	thf(77,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ A) @ (collect_nat @ B)) <= (! [C:nat]: ((B @ C) <= (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Collect__mono)).
239.52/52.83	thf(511,plain,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) | ~ (! [C:nat]: ((B @ C) | ~ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
239.52/52.83	thf(121,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nat__mult__1)).
239.52/52.83	thf(677,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
239.52/52.83	thf(27,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) <= (member_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_subset__iff)).
239.52/52.83	thf(329,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
239.52/52.83	thf(330,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A))))),inference(lifteq,[status(thm)],[329])).
239.52/52.83	thf(1426,plain,(! [A:set_nat] : (((ord_less_eq_set_nat @ A) = (^ [B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A)))))),inference(func_ext,[status(esa)],[330])).
239.52/52.83	thf(41,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ A) @ (collect_nat @ B)) = (! [C:nat]: ((A @ C) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Collect__mono__iff)).
239.52/52.83	thf(385,plain,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) = (! [C:nat]: ((A @ C) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
239.52/52.83	thf(40,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_dual__order_Ostrict__trans)).
239.52/52.83	thf(382,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
239.52/52.83	thf(383,plain,((! [A:nat,B:nat]: (! [C:nat]: ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(miniscope,[status(thm)],[382])).
239.52/52.83	thf(384,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_nat @ C @ A)) | (ord_less_nat @ C @ B) | (~ (ord_less_nat @ A @ B)))),inference(cnf,[status(esa)],[383])).
239.52/52.83	thf(1833,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != one_one_nat) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (times_times_nat @ one_one_nat))),inference(paramod_ordered,[status(thm)],[669,1770])).
239.52/52.83	thf(1838,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != one_one_nat) | ((p) != (^ [A:nat]: (one_one_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (A)))),inference(simp,[status(thm)],[1833])).
239.52/52.83	thf(1839,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != one_one_nat) | ((p) != (^ [A:nat]: (one_one_nat)))),inference(simp,[status(thm)],[1838])).
239.52/52.83	thf(1900,plain,(((p @ sk114) != zero_zero_nat) | (sk115 != zero_zero_nat) | ((p @ sk116) != one_one_nat) | (sk90 != one_one_nat)),inference(func_ext,[status(esa)],[1839])).
239.52/52.83	thf(10353,plain,((sk115 != zero_zero_nat) | ((p @ sk116) != one_one_nat) | (sk90 != one_one_nat) | ((p @ sk114) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,1900])).
239.52/52.83	thf(10358,plain,((sk115 != zero_zero_nat) | ((p @ sk116) != one_one_nat) | (sk90 != one_one_nat) | (sk114 != zero_zero_nat)),inference(simp,[status(thm)],[10353])).
239.52/52.83	thf(97,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_infinite__descent0)).
239.52/52.83	thf(588,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
239.52/52.83	thf(589,plain,((! [A:(nat > $o)]: ((A @ zero_zero_nat) => (! [B:nat]: (A @ B) | ~ (! [B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => ((~ (A @ B)) => (? [C:nat]: ((ord_less_nat @ C @ B) & ~ (A @ C)))))))))),inference(miniscope,[status(thm)],[588])).
239.52/52.83	thf(592,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero_zero_nat)) | (A @ B) | (ord_less_nat @ zero_zero_nat @ (sk38 @ (A))))),inference(cnf,[status(esa)],[589])).
239.52/52.83	thf(595,plain,(! [A:nat] : ((~ (zero_zero_nat = zero_zero_nat)) | (zero_zero_nat = A) | (ord_less_nat @ zero_zero_nat @ (sk38 @ (= @ nat @ zero_zero_nat))))),inference(replace_leibeq,[status(thm)],[592:[bind(A, $thf(= @ nat @ zero_zero_nat))]])).
239.52/52.83	thf(600,plain,(! [A:nat] : ((zero_zero_nat != zero_zero_nat) | (zero_zero_nat = A) | (ord_less_nat @ zero_zero_nat @ (sk38 @ (= @ nat @ zero_zero_nat))))),inference(lifteq,[status(thm)],[595])).
239.52/52.83	thf(601,plain,(! [A:nat] : ((zero_zero_nat = A) | (ord_less_nat @ zero_zero_nat @ (sk38 @ (= @ nat @ zero_zero_nat))))),inference(simp,[status(thm)],[600])).
239.52/52.83	thf(629,plain,((~ (? [A:nat]: (ord_less_nat @ A @ zero_zero_nat)))),inference(miniscope,[status(thm)],[628])).
239.52/52.83	thf(630,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ zero_zero_nat)))),inference(cnf,[status(esa)],[629])).
239.52/52.83	thf(3495,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk27 @ A)) != (ord_less_nat @ B @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[518,630])).
239.52/52.83	thf(3504,plain,(! [B:nat,A:nat] : ((A != B) | ((sk27 @ A) != zero_zero_nat))),inference(simp,[status(thm)],[3495])).
239.52/52.83	thf(3506,plain,(! [A:nat] : (((sk27 @ A) != zero_zero_nat))),inference(simp,[status(thm)],[3504])).
239.52/52.83	thf(3893,plain,(! [B:nat,A:nat] : ((ord_less_nat @ zero_zero_nat @ (sk38 @ (= @ nat @ zero_zero_nat))) | (A != (sk27 @ B)))),inference(paramod_ordered,[status(thm)],[601,3506])).
239.52/52.83	thf(3894,plain,((ord_less_nat @ zero_zero_nat @ (sk38 @ (= @ nat @ zero_zero_nat)))),inference(pattern_uni,[status(thm)],[3893:[bind(A, $thf(sk27 @ C)),bind(B, $thf(C))]])).
239.52/52.83	thf(15,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_182_not__less__iff__gr__or__eq)).
239.52/52.83	thf(289,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)],[15])).
239.52/52.83	thf(290,plain,(! [B:nat,A:nat] : (((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),inference(cnf,[status(esa)],[289])).
239.52/52.83	thf(291,plain,(! [B:nat,A:nat] : (((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),inference(lifteq,[status(thm)],[290])).
239.52/52.83	thf(4193,plain,(! [B:nat,A:nat] : ((~ ((ord_less_nat @ B @ A) | (A = B))) | ((ord_less_nat @ zero_zero_nat @ (sk38 @ (= @ nat @ zero_zero_nat))) != (ord_less_nat @ A @ B)))),inference(paramod_ordered,[status(thm)],[3894,291])).
239.52/52.83	thf(4194,plain,((~ ((ord_less_nat @ (sk38 @ (= @ nat @ zero_zero_nat)) @ zero_zero_nat) | (zero_zero_nat = (sk38 @ (= @ nat @ zero_zero_nat)))))),inference(pattern_uni,[status(thm)],[4193:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(sk38 @ (= @ nat @ zero_zero_nat)))]])).
239.52/52.83	thf(4218,plain,((~ (zero_zero_nat = (sk38 @ (= @ nat @ zero_zero_nat))))),inference(cnf,[status(esa)],[4194])).
239.52/52.83	thf(4220,plain,(((sk38 @ (= @ nat @ zero_zero_nat)) != zero_zero_nat)),inference(lifteq,[status(thm)],[4218])).
239.52/52.83	thf(157,axiom,((! [A:(nat > nat),B:nat]: ((~ ((! [C:nat]: (((A @ C) != zero_zero_nat) => ((ord_less_eq_nat @ C @ B) & (ord_less_eq_nat @ one_one_nat @ C)))) => ((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_1_partitionsE)).
239.52/52.83	thf(797,plain,((! [A:(nat > nat),B:nat]: (~ ((! [C:nat]: ((~ ((A @ C) = zero_zero_nat)) => ((ord_less_eq_nat @ C @ B) & (ord_less_eq_nat @ one_one_nat @ C)))) => (~ ((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)],[157])).
239.52/52.83	thf(63,axiom,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Collect__mem__eq)).
239.52/52.83	thf(470,plain,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
239.52/52.83	thf(471,plain,(! [A:set_nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(cnf,[status(esa)],[470])).
239.52/52.83	thf(472,plain,(! [A:set_nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(lifteq,[status(thm)],[471])).
239.52/52.83	thf(187,axiom,((! [A:nat,B:nat]: (((A != zero_zero_nat) & (B != zero_zero_nat)) <= ((times_times_nat @ A @ B) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_mult__not__zero)).
239.52/52.83	thf(910,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat) & ~ (B = zero_zero_nat)) | ((times_times_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])).
239.52/52.83	thf(912,plain,(! [B:nat,A:nat] : ((~ (B = zero_zero_nat)) | ((times_times_nat @ A @ B) = zero_zero_nat))),inference(cnf,[status(esa)],[910])).
239.52/52.83	thf(915,plain,(! [B:nat,A:nat] : ((B != zero_zero_nat) | ((times_times_nat @ A @ B) = zero_zero_nat))),inference(lifteq,[status(thm)],[912])).
239.52/52.83	thf(916,plain,(! [A:nat] : (((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(simp,[status(thm)],[915])).
239.52/52.83	thf(43,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((! [D:nat]: ((A @ D) <= (ord_less_nat @ D @ C))) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__induct)).
239.52/52.83	thf(392,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((! [D:nat]: ((A @ D) | ~ (ord_less_nat @ D @ C))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
239.52/52.83	thf(393,plain,((! [A:(nat > $o)]: (! [B:nat]: (A @ B) | ~ (! [B:nat]: ((! [C:nat]: ((A @ C) | ~ (ord_less_nat @ C @ B))) => (A @ B)))))),inference(miniscope,[status(thm)],[392])).
239.52/52.83	thf(395,plain,(! [B:nat,A:(nat > $o)] : ((A @ B) | (~ (A @ (sk15 @ (A)))))),inference(cnf,[status(esa)],[393])).
239.52/52.83	thf(13948,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ (sk15 @ (A)))) | ((A @ B) != (ord_less_nat @ C @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[395,630])).
239.52/52.83	thf(14250,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ (A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B)))) @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))))),inference(pre_uni,[status(thm)],[13948:[bind(A, $thf(^ [E:nat]: (ord_less_nat @ (D @ E) @ E))),bind(B, $thf(zero_zero_nat)),bind(C, $thf(D @ zero_zero_nat))]])).
239.52/52.83	thf(14455,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ (A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B)))) @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))))),inference(simp,[status(thm)],[14250])).
239.52/52.83	thf(14847,plain,(! [B:(nat > nat),A:nat] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))) | ((times_times_nat @ A @ zero_zero_nat) != (B @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))))),inference(paramod_ordered,[status(thm)],[916,14455])).
239.52/52.83	thf(14909,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ (A @ B) @ zero_zero_nat) @ B))))))),inference(pre_uni,[status(thm)],[14847:[bind(A, $thf(C @ (sk15 @ (^ [D:nat]: (ord_less_nat @ (times_times_nat @ (C @ D) @ zero_zero_nat) @ D))))),bind(B, $thf(^ [D:nat]: (times_times_nat @ (C @ D) @ zero_zero_nat)))]])).
239.52/52.83	thf(14954,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ (A @ B) @ zero_zero_nat) @ B))))))),inference(simp,[status(thm)],[14909])).
239.52/52.83	thf(122,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_bot__nat__0_Onot__eq__extremum)).
239.52/52.83	thf(680,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
239.52/52.83	thf(681,plain,(! [A:nat] : (((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(cnf,[status(esa)],[680])).
239.52/52.83	thf(682,plain,(! [A:nat] : (((ord_less_nat @ zero_zero_nat @ A) = (~ (A = zero_zero_nat))))),inference(lifteq,[status(thm)],[681])).
239.52/52.83	thf(16802,plain,(! [A:(nat > nat)] : ((~ (~ ((sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ (A @ B) @ zero_zero_nat) @ B))) = zero_zero_nat))))),inference(rewrite,[status(thm)],[14954,682])).
239.52/52.83	thf(16803,plain,(! [A:(nat > nat)] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ (A @ B) @ zero_zero_nat) @ B))) = zero_zero_nat))),inference(simp,[status(thm)],[16802])).
239.52/52.83	thf(16804,plain,(! [A:(nat > nat)] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ (A @ B) @ zero_zero_nat) @ B))) = zero_zero_nat))),inference(lifteq,[status(thm)],[16803])).
239.52/52.83	thf(1745,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | ((p @ sk90) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,1128])).
239.52/52.83	thf(1754,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != one_one_nat)),inference(simp,[status(thm)],[1745])).
239.52/52.83	thf(1987,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p) != (^ [B:nat]: (zero_zero_nat))) | (sk90 != one_one_nat) | ((groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (set_ord_atMost_nat @ zero_zero_nat)) != (groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (set_ord_atMost_nat @ zero_zero_nat))))),inference(paramod_ordered,[status(thm)],[1136,1754])).
239.52/52.83	thf(1988,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p) != (^ [B:nat]: (zero_zero_nat))) | (sk90 != one_one_nat))),inference(pattern_uni,[status(thm)],[1987:[]])).
239.52/52.83	thf(118,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_68_mult__nonneg__nonpos)).
239.52/52.83	thf(670,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)],[118])).
239.52/52.83	thf(394,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((A @ B) | (A @ C) | (~ (ord_less_nat @ C @ (sk15 @ (A)))))),inference(cnf,[status(esa)],[393])).
239.52/52.83	thf(13064,plain,(! [A:nat] : ($false | $false | (~ (ord_less_nat @ A @ (sk15 @ (^ [B:nat]: ($false))))))),inference(prim_subst,[status(thm)],[394:[bind(A, $thf(^ [D:nat]: ($false)))]])).
239.52/52.83	thf(13472,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ (sk15 @ (^ [B:nat]: ($false))))))),inference(simp,[status(thm)],[13064])).
239.52/52.83	thf(13710,plain,(! [B:nat,A:nat] : ((A = zero_zero_nat) | ((ord_less_nat @ zero_zero_nat @ A) != (ord_less_nat @ B @ (sk15 @ (^ [C:nat]: ($false))))))),inference(paramod_ordered,[status(thm)],[682,13472])).
239.52/52.83	thf(13711,plain,(((sk15 @ (^ [A:nat]: ($false))) = zero_zero_nat)),inference(pattern_uni,[status(thm)],[13710:[bind(A, $thf(sk15 @ (^ [C:nat]: ($false)))),bind(B, $thf(zero_zero_nat))]])).
239.52/52.83	thf(13736,plain,(((sk15 @ (^ [A:nat]: ($false))) = zero_zero_nat)),inference(lifteq,[status(thm)],[13711])).
239.52/52.83	thf(208,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_dual__order_Oorder__iff__strict)).
239.52/52.83	thf(995,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
239.52/52.83	thf(996,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B))))),inference(lifteq,[status(thm)],[995])).
239.52/52.83	thf(119,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_le__eq__less__or__eq)).
239.52/52.83	thf(673,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
239.52/52.83	thf(674,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(lifteq,[status(thm)],[673])).
239.52/52.83	thf(1310,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B))))),inference(rewrite,[status(thm)],[996,674])).
239.52/52.83	thf(47,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B))) = (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_pred__subset__eq)).
239.52/52.83	thf(402,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B))) = (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
239.52/52.83	thf(403,plain,(! [B:set_nat,A:set_nat] : (((ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B))) = (ord_less_eq_set_nat @ A @ B)))),inference(cnf,[status(esa)],[402])).
239.52/52.83	thf(404,plain,(! [B:set_nat,A:set_nat] : (((ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B))) = (ord_less_eq_set_nat @ A @ B)))),inference(lifteq,[status(thm)],[403])).
239.52/52.83	thf(14,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_less__imp__not__less)).
239.52/52.83	thf(287,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
239.52/52.83	thf(288,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (~ (ord_less_nat @ B @ A)))),inference(cnf,[status(esa)],[287])).
239.52/52.83	thf(3491,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_nat @ C @ B)) | ((ord_less_nat @ A @ (sk27 @ A)) != (ord_less_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[518,288])).
239.52/52.83	thf(3492,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk27 @ A) @ A)))),inference(pattern_uni,[status(thm)],[3491:[bind(A, $thf(D)),bind(B, $thf(D)),bind(C, $thf(sk27 @ D))]])).
239.52/52.83	thf(3508,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk27 @ A) @ A)))),inference(simp,[status(thm)],[3492])).
239.52/52.83	thf(5094,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk27 @ A)) != (ord_less_nat @ (sk27 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[518,3508])).
239.52/52.83	thf(5110,plain,(! [B:nat,A:nat] : ((A != (sk27 @ B)) | ((sk27 @ A) != B))),inference(simp,[status(thm)],[5094])).
239.52/52.83	thf(5123,plain,(! [A:nat] : (((sk27 @ (sk27 @ A)) != A))),inference(simp,[status(thm)],[5110])).
239.52/52.83	thf(13,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_189_linorder__cases)).
239.52/52.83	thf(284,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)],[13])).
239.52/52.83	thf(285,plain,(! [B:nat,A:nat] : ((A = B) | (ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))),inference(cnf,[status(esa)],[284])).
239.52/52.83	thf(286,plain,(! [B:nat,A:nat] : ((A = B) | (ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))),inference(lifteq,[status(thm)],[285])).
239.52/52.83	thf(127,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zero__neq__one)).
239.52/52.83	thf(694,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
239.52/52.83	thf(695,plain,((~ (zero_zero_nat = one_one_nat))),inference(polarity_switch,[status(thm)],[694])).
239.52/52.83	thf(696,plain,((zero_zero_nat != one_one_nat)),inference(lifteq,[status(thm)],[695])).
239.52/52.83	thf(2747,plain,(! [B:nat,A:nat] : ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (B != one_one_nat) | (A != zero_zero_nat))),inference(paramod_ordered,[status(thm)],[286,696])).
239.52/52.83	thf(2748,plain,(! [A:nat] : ((ord_less_nat @ A @ zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A) | (A != one_one_nat))),inference(pattern_uni,[status(thm)],[2747:[bind(A, $thf(zero_zero_nat))]])).
239.52/52.83	thf(2862,plain,((ord_less_nat @ one_one_nat @ zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ one_one_nat)),inference(simp,[status(thm)],[2748])).
239.52/52.83	thf(2936,plain,($false | (ord_less_nat @ zero_zero_nat @ one_one_nat)),inference(rewrite,[status(thm)],[2862,630])).
239.52/52.83	thf(2937,plain,((ord_less_nat @ zero_zero_nat @ one_one_nat)),inference(simp,[status(thm)],[2936])).
239.52/52.83	thf(5095,plain,(! [A:nat] : (((ord_less_nat @ (sk27 @ A) @ A) != (ord_less_nat @ zero_zero_nat @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[2937,3508])).
239.52/52.83	thf(5109,plain,(! [A:nat] : (((sk27 @ A) != zero_zero_nat) | (A != one_one_nat))),inference(simp,[status(thm)],[5095])).
239.52/52.83	thf(5122,plain,(((sk27 @ one_one_nat) != zero_zero_nat)),inference(simp,[status(thm)],[5109])).
239.52/52.83	thf(5129,plain,(! [B:nat,A:nat] : ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (B != zero_zero_nat) | (A != (sk27 @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[286,5122])).
239.52/52.83	thf(5130,plain,(! [A:nat] : ((ord_less_nat @ A @ (sk27 @ one_one_nat)) | (ord_less_nat @ (sk27 @ one_one_nat) @ A) | (A != zero_zero_nat))),inference(pattern_uni,[status(thm)],[5129:[bind(A, $thf(sk27 @ one_one_nat)),bind(B, $thf(B))]])).
239.52/52.83	thf(5137,plain,((ord_less_nat @ zero_zero_nat @ (sk27 @ one_one_nat)) | (ord_less_nat @ (sk27 @ one_one_nat) @ zero_zero_nat)),inference(simp,[status(thm)],[5130])).
239.52/52.83	thf(5241,plain,((ord_less_nat @ zero_zero_nat @ (sk27 @ one_one_nat)) | $false),inference(rewrite,[status(thm)],[5137,630])).
239.52/52.83	thf(5242,plain,((ord_less_nat @ zero_zero_nat @ (sk27 @ one_one_nat))),inference(simp,[status(thm)],[5241])).
239.52/52.83	thf(5248,plain,(! [A:nat] : (((ord_less_nat @ (sk27 @ A) @ A) != (ord_less_nat @ zero_zero_nat @ (sk27 @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[5242,3508])).
239.52/52.83	thf(5277,plain,(! [A:nat] : (((sk27 @ A) != zero_zero_nat) | (A != (sk27 @ one_one_nat)))),inference(simp,[status(thm)],[5248])).
239.52/52.83	thf(5290,plain,(((sk27 @ (sk27 @ one_one_nat)) != zero_zero_nat)),inference(simp,[status(thm)],[5277])).
239.52/52.83	thf(5569,plain,(! [B:nat,A:nat] : ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (B != zero_zero_nat) | (A != (sk27 @ (sk27 @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[286,5290])).
239.52/52.83	thf(5570,plain,(! [A:nat] : ((ord_less_nat @ A @ (sk27 @ (sk27 @ one_one_nat))) | (ord_less_nat @ (sk27 @ (sk27 @ one_one_nat)) @ A) | (A != zero_zero_nat))),inference(pattern_uni,[status(thm)],[5569:[bind(A, $thf(sk27 @ (sk27 @ one_one_nat))),bind(B, $thf(B))]])).
239.52/52.83	thf(5581,plain,((ord_less_nat @ zero_zero_nat @ (sk27 @ (sk27 @ one_one_nat))) | (ord_less_nat @ (sk27 @ (sk27 @ one_one_nat)) @ zero_zero_nat)),inference(simp,[status(thm)],[5570])).
239.52/52.83	thf(5856,plain,((ord_less_nat @ zero_zero_nat @ (sk27 @ (sk27 @ one_one_nat))) | $false),inference(rewrite,[status(thm)],[5581,630])).
239.52/52.83	thf(5857,plain,((ord_less_nat @ zero_zero_nat @ (sk27 @ (sk27 @ one_one_nat)))),inference(simp,[status(thm)],[5856])).
239.52/52.83	thf(5863,plain,(! [A:nat] : (((ord_less_nat @ (sk27 @ A) @ A) != (ord_less_nat @ zero_zero_nat @ (sk27 @ (sk27 @ one_one_nat)))))),inference(paramod_ordered,[status(thm)],[5857,3508])).
239.52/52.83	thf(5895,plain,(! [A:nat] : (((sk27 @ A) != zero_zero_nat) | (A != (sk27 @ (sk27 @ one_one_nat))))),inference(simp,[status(thm)],[5863])).
239.52/52.83	thf(5903,plain,(((sk27 @ (sk27 @ (sk27 @ one_one_nat))) != zero_zero_nat)),inference(simp,[status(thm)],[5895])).
239.52/52.83	thf(14865,plain,(! [B:(nat > nat),A:nat] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))) | ((times_times_nat @ zero_zero_nat @ A) != (B @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))))),inference(paramod_ordered,[status(thm)],[636,14455])).
239.52/52.83	thf(14923,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B)) @ B))))))),inference(pre_uni,[status(thm)],[14865:[bind(A, $thf(D @ (sk15 @ (^ [D:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (D @ D)) @ D))))),bind(B, $thf(^ [D:nat]: (times_times_nat @ zero_zero_nat @ (D @ D))))]])).
239.52/52.83	thf(14962,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B)) @ B))))))),inference(simp,[status(thm)],[14923])).
239.52/52.83	thf(17051,plain,(! [A:(nat > nat)] : ((~ (~ ((sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B)) @ B))) = zero_zero_nat))))),inference(rewrite,[status(thm)],[14962,682])).
239.52/52.83	thf(17052,plain,(! [A:(nat > nat)] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B)) @ B))) = zero_zero_nat))),inference(simp,[status(thm)],[17051])).
239.52/52.83	thf(17053,plain,(! [A:(nat > nat)] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B)) @ B))) = zero_zero_nat))),inference(lifteq,[status(thm)],[17052])).
239.52/52.83	thf(180,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_23_Nat_Oex__has__greatest__nat)).
239.52/52.83	thf(885,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)],[180])).
239.52/52.83	thf(225,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_78_sum__nonneg)).
239.52/52.83	thf(1046,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)],[225])).
239.52/52.83	thf(19,axiom,((! [A:set_nat,B:set_nat]: ((A = B) => (ord_less_eq_set_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_equalityD2)).
239.52/52.83	thf(301,plain,((! [A:set_nat,B:set_nat]: ((A = B) => (ord_less_eq_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
239.52/52.83	thf(2069,plain,(! [A:nat] : (((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | ((times_times_nat @ A @ zero_zero_nat) != (times_times_nat @ (p @ sk111) @ sk111)))),inference(paramod_ordered,[status(thm)],[916,1830])).
239.52/52.83	thf(2077,plain,(! [A:nat] : (((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | (A != (p @ sk111)) | (sk111 != zero_zero_nat))),inference(simp,[status(thm)],[2069])).
239.52/52.83	thf(2082,plain,(((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | (sk111 != zero_zero_nat)),inference(simp,[status(thm)],[2077])).
239.52/52.83	thf(75,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_44_Collect__cong)).
239.52/52.83	thf(504,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)],[75])).
239.52/52.83	thf(192,axiom,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((A = one_one_nat) & (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nat__1__eq__mult__iff)).
239.52/52.83	thf(934,plain,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((A = one_one_nat) & (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
239.52/52.83	thf(59,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_order__refl)).
239.52/52.83	thf(460,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
239.52/52.83	thf(228,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_le__0__eq)).
239.52/52.83	thf(1055,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
239.52/52.83	thf(138,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_bot__nat__0_Oextremum)).
239.52/52.83	thf(724,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
239.52/52.83	thf(69,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: (ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_less__eq__set__def)).
239.52/52.83	thf(485,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: (ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
239.52/52.83	thf(486,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: (ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B)))))),inference(lifteq,[status(thm)],[485])).
239.52/52.83	thf(1428,plain,(((^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A))) = (^ [A:set_nat,B:set_nat]: (ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B))))) | ((ord_less_eq_set_nat) != (ord_less_eq_set_nat))),inference(paramod_ordered,[status(thm)],[330,486])).
239.52/52.83	thf(1429,plain,(((^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A))) = (^ [A:set_nat,B:set_nat]: (ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B)))))),inference(pattern_uni,[status(thm)],[1428:[]])).
239.52/52.83	thf(3195,plain,(! [A:set_nat] : (((^ [B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A))) = (^ [B:set_nat]: (ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B))))))),inference(func_ext,[status(esa)],[1429])).
239.52/52.83	thf(90,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_zero__le)).
239.52/52.83	thf(570,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
239.52/52.83	thf(188,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_comm__monoid__mult__class_Omult__1)).
239.52/52.83	thf(917,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
239.52/52.83	thf(146,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_7_atMost__subset__iff)).
239.52/52.83	thf(751,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)],[146])).
239.52/52.83	thf(17064,plain,(! [B:(nat > nat),A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))) | ((sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ C)) @ C))) != (B @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))))),inference(paramod_ordered,[status(thm)],[17053,14455])).
239.52/52.83	thf(17175,plain,(! [A:(nat > (nat > nat))] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B @ C)) @ C))) @ B))))))),inference(pre_uni,[status(thm)],[17064:[bind(A, $thf(G @ (sk15 @ (^ [D:nat]: (ord_less_nat @ (sk15 @ (^ [E:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (G @ D @ E)) @ E))) @ D))))),bind(B, $thf(^ [D:nat]: (sk15 @ (^ [E:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (G @ D @ E)) @ E)))))]])).
239.52/52.83	thf(17237,plain,(! [A:(nat > (nat > nat))] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B @ C)) @ C))) @ B))))))),inference(simp,[status(thm)],[17175])).
239.52/52.83	thf(17850,plain,(! [A:(nat > (nat > nat))] : ((~ (~ ((sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B @ C)) @ C))) @ B))) = zero_zero_nat))))),inference(rewrite,[status(thm)],[17237,682])).
239.52/52.83	thf(17851,plain,(! [A:(nat > (nat > nat))] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B @ C)) @ C))) @ B))) = zero_zero_nat))),inference(simp,[status(thm)],[17850])).
239.52/52.83	thf(17852,plain,(! [A:(nat > (nat > nat))] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ zero_zero_nat @ (A @ B @ C)) @ C))) @ B))) = zero_zero_nat))),inference(lifteq,[status(thm)],[17851])).
239.52/52.83	thf(200,axiom,((! [A:set_nat,B:(nat > nat),C:set_nat,D:(nat > nat),E:(nat > nat),F:(nat > nat)]: ((! [G:nat]: ((member_nat @ G @ A) => ((member_nat @ (B @ G) @ C) & ((D @ (B @ G)) = G)))) => ((! [G:nat]: ((((B @ (D @ G)) = G) & ((E @ (D @ G)) = (F @ G)) & (member_nat @ (D @ G) @ A)) <= (member_nat @ G @ C))) => ((groups1842438620at_nat @ F @ C) = (groups1842438620at_nat @ E @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_sum_Oeq__general__inverses)).
239.52/52.83	thf(969,plain,((! [A:set_nat,B:(nat > nat),C:set_nat,D:(nat > nat),E:(nat > nat),F:(nat > nat)]: ((! [G:nat]: ((member_nat @ G @ A) => ((member_nat @ (B @ G) @ C) & ((D @ (B @ G)) = G)))) => ((! [G:nat]: ((((B @ (D @ G)) = G) & ((E @ (D @ G)) = (F @ G)) & (member_nat @ (D @ G) @ A)) | ~ (member_nat @ G @ C))) => ((groups1842438620at_nat @ (F) @ C) = (groups1842438620at_nat @ (E) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
239.52/52.83	thf(26,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_order_Ostrict__implies__not__eq)).
239.52/52.83	thf(325,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
239.52/52.83	thf(5188,plain,(! [A:nat] : (((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | ((times_times_nat @ zero_zero_nat @ A) != (times_times_nat @ (p @ sk113) @ sk113)))),inference(paramod_ordered,[status(thm)],[636,1840])).
239.52/52.83	thf(5192,plain,(! [A:nat] : (((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | ((p @ sk113) != zero_zero_nat) | (A != sk113))),inference(simp,[status(thm)],[5188])).
239.52/52.83	thf(5203,plain,(((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | ((p @ sk113) != zero_zero_nat)),inference(simp,[status(thm)],[5192])).
239.52/52.83	thf(5609,plain,(((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | ((p @ sk113) != (p @ sk112)) | (zero_zero_nat != zero_zero_nat)),inference(eqfactor_ordered,[status(thm)],[5203])).
239.52/52.83	thf(5612,plain,(((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | (sk113 != sk112)),inference(simp,[status(thm)],[5609])).
239.52/52.83	thf(5811,plain,((sk90 != zero_zero_nat) | (sk113 != sk112) | ((p @ sk112) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,5612])).
239.52/52.83	thf(5829,plain,((sk90 != zero_zero_nat) | (sk113 != sk112) | (sk112 != one_one_nat)),inference(simp,[status(thm)],[5811])).
239.52/52.83	thf(23,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_dual__order_Oirrefl)).
239.52/52.83	thf(316,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
239.52/52.83	thf(37,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_119_antisym__conv)).
239.52/52.83	thf(374,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)],[37])).
239.52/52.83	thf(375,plain,(! [B:set_nat,A:set_nat] : (((ord_less_eq_set_nat @ B @ A) = (B = A)) | (~ (ord_less_eq_set_nat @ A @ B)))),inference(cnf,[status(esa)],[374])).
239.52/52.83	thf(376,plain,(! [B:set_nat,A:set_nat] : (((ord_less_eq_set_nat @ B @ A) = (B = A)) | (~ (ord_less_eq_set_nat @ A @ B)))),inference(lifteq,[status(thm)],[375])).
239.52/52.83	thf(104,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_9_atMost__iff)).
239.52/52.83	thf(623,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)],[104])).
239.52/52.83	thf(4,axiom,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((ord_less_eq_set_nat @ A @ (B @ D)) <= (! [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 @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_order__subst1)).
239.52/52.83	thf(250,plain,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ C @ D) => ((ord_less_eq_set_nat @ A @ (B @ D)) | ~ (! [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 @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
239.52/52.83	thf(251,plain,((! [A:set_nat,B:(set_nat > set_nat),C:set_nat]: (! [D:set_nat]: ((ord_less_eq_set_nat @ C @ D) => ((ord_less_eq_set_nat @ A @ (B @ D)) | ~ (! [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 @ C))))),inference(miniscope,[status(thm)],[250])).
239.52/52.83	thf(253,plain,(! [D:set_nat,C:set_nat,B:(set_nat > set_nat),A:set_nat] : ((~ (ord_less_eq_set_nat @ C @ D)) | (ord_less_eq_set_nat @ A @ (B @ D)) | (~ (ord_less_eq_set_nat @ (B @ (sk1 @ D @ C @ (B) @ A)) @ (B @ (sk2 @ D @ C @ (B) @ A)))) | (~ (ord_less_eq_set_nat @ A @ (B @ C))))),inference(cnf,[status(esa)],[251])).
239.52/52.83	thf(13960,plain,(! [C:nat,B:(nat > $o),A:nat] : ((~ (A = zero_zero_nat)) | (~ (B @ (sk15 @ (B)))) | ((ord_less_nat @ zero_zero_nat @ A) != (B @ C)))),inference(paramod_ordered,[status(thm)],[682,395])).
239.52/52.83	thf(14078,plain,(! [C:nat,B:(nat > $o),A:nat] : ((A != zero_zero_nat) | (~ (B @ (sk15 @ (B)))) | ((ord_less_nat @ zero_zero_nat @ A) != (B @ C)))),inference(lifteq,[status(thm)],[13960])).
239.52/52.83	thf(14110,plain,((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat))))),inference(pre_uni,[status(thm)],[14078:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(ord_less_nat @ zero_zero_nat)),bind(C, $thf(zero_zero_nat))]])).
239.52/52.83	thf(14545,plain,((~ (~ ((sk15 @ (ord_less_nat @ zero_zero_nat)) = zero_zero_nat)))),inference(rewrite,[status(thm)],[14110,682])).
239.52/52.83	thf(14546,plain,(((sk15 @ (ord_less_nat @ zero_zero_nat)) = zero_zero_nat)),inference(simp,[status(thm)],[14545])).
239.52/52.83	thf(14547,plain,(((sk15 @ (ord_less_nat @ zero_zero_nat)) = zero_zero_nat)),inference(lifteq,[status(thm)],[14546])).
239.52/52.83	thf(78,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((A = B) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_order__class_Oorder_Oantisym)).
239.52/52.83	thf(514,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
239.52/52.83	thf(193,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_order__trans)).
239.52/52.83	thf(937,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
239.52/52.83	thf(32,axiom,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_less__imp__triv)).
239.52/52.83	thf(353,plain,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
239.52/52.83	thf(65,axiom,((('?' @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: ((~ (A @ C)) <= (ord_less_nat @ C @ B)) & (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_exists__least__iff)).
239.52/52.83	thf(475,plain,((('?' @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: (~ (A @ C) | ~ (ord_less_nat @ C @ B)) & (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
239.52/52.83	thf(2394,plain,(((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | ((p @ sk111) != (p @ sk110))),inference(simp,[status(thm)],[2392])).
239.52/52.83	thf(3292,plain,((sk90 != one_one_nat) | ((p @ sk111) != (p @ sk110)) | ((p @ sk110) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,2394])).
239.52/52.83	thf(3322,plain,((sk90 != one_one_nat) | ((p @ sk111) != (p @ sk110)) | (sk110 != one_one_nat)),inference(simp,[status(thm)],[3292])).
239.52/52.83	thf(223,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_5_nat__mult__eq__1__iff)).
239.52/52.83	thf(1040,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)],[223])).
239.52/52.83	thf(91,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_64_atMost__def)).
239.52/52.83	thf(572,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)],[91])).
239.52/52.83	thf(573,plain,(((set_ord_atMost_nat) = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(lifteq,[status(thm)],[572])).
239.52/52.83	thf(1118,plain,(! [A:nat] : (((set_ord_atMost_nat @ A) = (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(func_ext,[status(esa)],[573])).
239.52/52.83	thf(6701,plain,(! [B:nat,A:set_nat] : (((collect_nat @ (^ [C:nat]: (member_nat @ C @ A))) = (set_ord_atMost_nat @ B)) | (A != (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ B)))))),inference(paramod_ordered,[status(thm)],[472,1118])).
239.52/52.83	thf(6702,plain,(! [A:nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ A)))))) = (set_ord_atMost_nat @ A)))),inference(pattern_uni,[status(thm)],[6701:[bind(A, $thf(collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ B)))),bind(B, $thf(B))]])).
239.52/52.83	thf(6895,plain,(! [A:nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ A)))))) = (set_ord_atMost_nat @ A)))),inference(simp,[status(thm)],[6702])).
239.52/52.83	thf(217,axiom,((! [A:(nat > nat),B:set_nat]: ((~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = zero_zero_nat)))) <= ((groups1842438620at_nat @ A @ B) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_sum_Onot__neutral__contains__not__neutral)).
239.52/52.83	thf(1020,plain,((! [A:(nat > nat),B:set_nat]: (~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = zero_zero_nat))) | ((groups1842438620at_nat @ (A) @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])).
239.52/52.83	thf(92,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_18_mult__cancel2)).
239.52/52.83	thf(574,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)],[92])).
239.52/52.83	thf(1742,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p @ sk90) != zero_zero_nat) | ((p) != (^ [B:nat]: (zero_zero_nat))) | ((groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (set_ord_atMost_nat @ zero_zero_nat)) != (groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (set_ord_atMost_nat @ zero_zero_nat))))),inference(paramod_ordered,[status(thm)],[1136,1128])).
239.52/52.83	thf(1743,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p @ sk90) != zero_zero_nat) | ((p) != (^ [B:nat]: (zero_zero_nat))))),inference(pattern_uni,[status(thm)],[1742:[]])).
239.52/52.83	thf(2014,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p) != (^ [B:nat]: (zero_zero_nat))) | ((p @ sk90) != (p @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[1267,1743])).
239.52/52.83	thf(2017,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((p) != (^ [B:nat]: (zero_zero_nat))) | (sk90 != zero_zero_nat))),inference(simp,[status(thm)],[2014])).
239.52/52.83	thf(67,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_200_less__linear)).
239.52/52.83	thf(480,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)],[67])).
239.52/52.83	thf(11,axiom,((! [A:set_nat,B:set_nat,C:nat]: (((member_nat @ C @ A) => (member_nat @ C @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_in__mono)).
239.52/52.83	thf(278,plain,((! [A:set_nat,B:set_nat,C:nat]: (((member_nat @ C @ A) => (member_nat @ C @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
239.52/52.83	thf(279,plain,((! [A:set_nat,B:set_nat]: (! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(miniscope,[status(thm)],[278])).
239.52/52.83	thf(280,plain,(! [C:nat,B:set_nat,A:set_nat] : ((~ (member_nat @ C @ A)) | (member_nat @ C @ B) | (~ (ord_less_eq_set_nat @ A @ B)))),inference(cnf,[status(esa)],[279])).
239.52/52.83	thf(173,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_122_order__class_Oorder_Oeq__iff)).
239.52/52.83	thf(866,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)],[173])).
239.52/52.83	thf(44,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_less__asym_H)).
239.52/52.83	thf(396,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
239.52/52.83	thf(50,axiom,((! [A:set_nat,B:set_nat]: ((A = B) => (~ ((~ (ord_less_eq_set_nat @ B @ A)) <= (ord_less_eq_set_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_equalityE)).
239.52/52.83	thf(411,plain,((! [A:set_nat,B:set_nat]: ((A = B) => (~ (~ (ord_less_eq_set_nat @ B @ A) | ~ (ord_less_eq_set_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
239.52/52.83	thf(105,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_nat__less__le)).
239.52/52.83	thf(626,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
239.52/52.83	thf(627,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(lifteq,[status(thm)],[626])).
239.52/52.83	thf(1404,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[1090,627])).
239.52/52.83	thf(1405,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(pattern_uni,[status(thm)],[1404:[]])).
239.52/52.83	thf(2152,plain,((sk90 != one_one_nat) | (sk111 != zero_zero_nat) | ((p @ sk110) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,2082])).
239.52/52.83	thf(2154,plain,((sk90 != one_one_nat) | (sk111 != zero_zero_nat) | (sk110 != zero_zero_nat)),inference(simp,[status(thm)],[2152])).
239.52/52.83	thf(76,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_equalityD1)).
239.52/52.83	thf(507,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
239.52/52.83	thf(98,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_bot__nat__0_Oextremum__unique)).
239.52/52.83	thf(602,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
239.52/52.83	thf(203,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_order__refl)).
239.52/52.83	thf(981,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
239.52/52.83	thf(150,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) <= (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_dual__order_Ostrict__trans2)).
239.52/52.83	thf(766,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
239.52/52.83	thf(241,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ A @ C) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_mult__less__cancel2)).
239.52/52.83	thf(1104,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ A @ C) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
239.52/52.83	thf(7,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 @ E @ F) => (ord_less_eq_set_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_nat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ord__eq__le__subst)).
239.52/52.83	thf(260,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 @ E @ F) => (ord_less_eq_set_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_nat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
239.52/52.83	thf(261,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 @ E @ F) => (ord_less_eq_set_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_nat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(miniscope,[status(thm)],[260])).
239.52/52.83	thf(262,plain,(! [D:set_nat,C:set_nat,B:(set_nat > set_nat),A:set_nat] : ((~ (ord_less_eq_set_nat @ C @ D)) | (ord_less_eq_set_nat @ (sk3 @ D @ C @ (B) @ A) @ (sk4 @ D @ C @ (B) @ A)) | (ord_less_eq_set_nat @ A @ (B @ D)) | (~ (A = (B @ C))))),inference(cnf,[status(esa)],[261])).
239.52/52.83	thf(264,plain,(! [D:set_nat,C:set_nat,B:(set_nat > set_nat),A:set_nat] : ((A != (B @ C)) | (~ (ord_less_eq_set_nat @ C @ D)) | (ord_less_eq_set_nat @ (sk3 @ D @ C @ (B) @ A) @ (sk4 @ D @ C @ (B) @ A)) | (ord_less_eq_set_nat @ A @ (B @ D)))),inference(lifteq,[status(thm)],[262])).
239.52/52.83	thf(265,plain,(! [C:set_nat,B:set_nat,A:(set_nat > set_nat)] : ((~ (ord_less_eq_set_nat @ B @ C)) | (ord_less_eq_set_nat @ (sk3 @ C @ B @ (A) @ (A @ B)) @ (sk4 @ C @ B @ (A) @ (A @ B))) | (ord_less_eq_set_nat @ (A @ B) @ (A @ C)))),inference(simp,[status(thm)],[264])).
239.52/52.83	thf(21,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_less__imp__neq)).
239.52/52.83	thf(307,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
239.52/52.83	thf(16,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_136_dual__order_Oeq__iff)).
239.52/52.83	thf(292,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)],[16])).
239.52/52.83	thf(189,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_66_mult__nonneg__nonpos2)).
239.52/52.83	thf(920,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)],[189])).
239.52/52.83	thf(39,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_108_eq__iff)).
239.52/52.83	thf(380,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)],[39])).
239.52/52.83	thf(115,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_gr__implies__not__zero)).
239.52/52.83	thf(661,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
239.52/52.83	thf(155,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_dual__order_Orefl)).
239.52/52.83	thf(792,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
239.52/52.83	thf(793,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ A))),inference(cnf,[status(esa)],[792])).
239.52/52.83	thf(867,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = (= @ nat))),inference(lifteq,[status(thm)],[866])).
239.52/52.83	thf(1306,plain,(! [A:nat] : (((^ [B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = (= @ nat @ A)))),inference(func_ext,[status(esa)],[867])).
239.52/52.83	thf(3314,plain,((sk90 != one_one_nat) | ((p @ sk111) != (p @ sk110)) | ((p @ sk110) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,2394])).
239.52/52.83	thf(3318,plain,((sk90 != one_one_nat) | ((p @ sk111) != (p @ sk110)) | (sk110 != zero_zero_nat)),inference(simp,[status(thm)],[3314])).
239.52/52.83	thf(34,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_ord__eq__less__subst)).
239.52/52.83	thf(359,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
239.52/52.83	thf(360,plain,((! [A:nat,B:(nat > nat),C:nat]: ((A = (B @ C)) => (! [D:nat]: ((ord_less_nat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))))))))),inference(miniscope,[status(thm)],[359])).
239.52/52.83	thf(362,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((~ (A = (B @ C))) | (~ (ord_less_nat @ C @ D)) | (ord_less_nat @ A @ (B @ D)) | (~ (ord_less_nat @ (B @ (sk11 @ D @ C @ (B) @ A)) @ (B @ (sk12 @ D @ C @ (B) @ A)))))),inference(cnf,[status(esa)],[360])).
239.52/52.83	thf(365,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((A != (B @ C)) | (~ (ord_less_nat @ C @ D)) | (ord_less_nat @ A @ (B @ D)) | (~ (ord_less_nat @ (B @ (sk11 @ D @ C @ (B) @ A)) @ (B @ (sk12 @ D @ C @ (B) @ A)))))),inference(lifteq,[status(thm)],[362])).
239.52/52.83	thf(366,plain,(! [C:nat,B:nat,A:(nat > nat)] : ((~ (ord_less_nat @ B @ C)) | (ord_less_nat @ (A @ B) @ (A @ C)) | (~ (ord_less_nat @ (A @ (sk11 @ C @ B @ (A) @ (A @ B))) @ (A @ (sk12 @ C @ B @ (A) @ (A @ B))))))),inference(simp,[status(thm)],[365])).
239.52/52.83	thf(1989,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != one_one_nat) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (times_times_nat @ one_one_nat))),inference(paramod_ordered,[status(thm)],[669,1754])).
239.52/52.83	thf(1997,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != one_one_nat) | ((p) != (^ [A:nat]: (one_one_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (A)))),inference(simp,[status(thm)],[1989])).
239.52/52.83	thf(2000,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != one_one_nat) | ((p) != (^ [A:nat]: (one_one_nat)))),inference(simp,[status(thm)],[1997])).
239.52/52.83	thf(57,axiom,((! [A:set_nat,B:set_nat,C:nat]: (((member_nat @ C @ B) <= (member_nat @ C @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_subsetD)).
239.52/52.83	thf(439,plain,((! [A:set_nat,B:set_nat,C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
239.52/52.83	thf(2891,plain,((sk90 != one_one_nat) | (sk111 != sk110) | ((p @ sk110) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,2395])).
239.52/52.83	thf(2910,plain,((sk90 != one_one_nat) | (sk111 != sk110) | (sk110 != one_one_nat)),inference(simp,[status(thm)],[2891])).
239.52/52.83	thf(83,axiom,((! [A:nat,B:nat,C:nat]: (((((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => ((~ ((~ (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ C @ A))) <= ((~ (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ 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_118_le__cases3)).
239.52/52.83	thf(529,plain,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => (~ (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ A)) | ~ (~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ 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)],[83])).
239.52/52.83	thf(1843,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != zero_zero_nat) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (times_times_nat @ one_one_nat))),inference(paramod_ordered,[status(thm)],[669,1771])).
239.52/52.83	thf(1848,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != zero_zero_nat) | ((p) != (^ [A:nat]: (one_one_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (A)))),inference(simp,[status(thm)],[1843])).
239.52/52.83	thf(1849,plain,(((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != zero_zero_nat) | ((p) != (^ [A:nat]: (one_one_nat)))),inference(simp,[status(thm)],[1848])).
239.52/52.83	thf(1913,plain,(((p @ sk117) != zero_zero_nat) | (sk118 != zero_zero_nat) | ((p @ sk119) != one_one_nat) | (sk90 != zero_zero_nat)),inference(func_ext,[status(esa)],[1849])).
239.52/52.83	thf(10737,plain,((sk118 != zero_zero_nat) | ((p @ sk119) != one_one_nat) | (sk90 != zero_zero_nat) | ((p @ sk117) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,1913])).
239.52/52.83	thf(10742,plain,((sk118 != zero_zero_nat) | ((p @ sk119) != one_one_nat) | (sk90 != zero_zero_nat) | (sk117 != zero_zero_nat)),inference(simp,[status(thm)],[10737])).
239.52/52.83	thf(6699,plain,(! [B:nat,A:set_nat] : (((collect_nat @ (^ [C:nat]: (member_nat @ C @ A))) = (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ B)))) | (A != (set_ord_atMost_nat @ B)))),inference(paramod_ordered,[status(thm)],[472,1118])).
239.52/52.83	thf(6700,plain,(! [A:nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ (set_ord_atMost_nat @ A)))) = (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(pattern_uni,[status(thm)],[6699:[bind(A, $thf(set_ord_atMost_nat @ C)),bind(B, $thf(C))]])).
239.52/52.83	thf(6893,plain,(! [A:nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ (set_ord_atMost_nat @ A)))) = (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(simp,[status(thm)],[6700])).
239.52/52.83	thf(9040,plain,(! [B:nat,A:nat] : (((collect_nat @ (^ [C:nat]: (member_nat @ C @ (collect_nat @ (^ [D:nat]: (member_nat @ D @ (collect_nat @ (^ [E:nat]: (ord_less_eq_nat @ E @ A))))))))) = (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ B)))) | ((set_ord_atMost_nat @ A) != (set_ord_atMost_nat @ B)))),inference(paramod_ordered,[status(thm)],[6895,6893])).
239.52/52.83	thf(9041,plain,(! [A:nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (member_nat @ C @ (collect_nat @ (^ [D:nat]: (ord_less_eq_nat @ D @ A))))))))) = (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(pattern_uni,[status(thm)],[9040:[bind(A, $thf(A)),bind(B, $thf(A))]])).
239.52/52.83	thf(134,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_neq0__conv)).
239.52/52.83	thf(714,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
239.52/52.83	thf(182,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ 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 @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mult__mono)).
239.52/52.83	thf(894,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ 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 @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
239.52/52.83	thf(14829,plain,(! [B:(nat > nat),A:nat] : (((ord_less_nat @ A @ (sk27 @ A)) != (ord_less_nat @ (B @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C)))) @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))))),inference(paramod_ordered,[status(thm)],[518,14455])).
239.52/52.83	thf(14884,plain,(! [B:(nat > nat),A:nat] : ((A != (B @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))) | ((sk27 @ A) != (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C)))))),inference(simp,[status(thm)],[14829])).
239.52/52.83	thf(14943,plain,(! [A:(nat > nat)] : (((sk27 @ (A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))) != (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B)))))),inference(simp,[status(thm)],[14884])).
239.52/52.83	thf(293,plain,(((^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))) = (= @ set_nat))),inference(lifteq,[status(thm)],[292])).
239.52/52.83	thf(1174,plain,(! [A:set_nat] : (((^ [B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))) = (= @ set_nat @ A)))),inference(func_ext,[status(esa)],[293])).
239.52/52.83	thf(14838,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))) | ((sk15 @ (ord_less_nat @ zero_zero_nat)) != (A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))))),inference(paramod_ordered,[status(thm)],[14547,14455])).
239.52/52.83	thf(14929,plain,((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat))))))),inference(pre_uni,[status(thm)],[14838:[bind(A, $thf(^ [B:nat]: (sk15 @ (ord_less_nat @ zero_zero_nat))))]])).
239.52/52.83	thf(15762,plain,((~ (~ ((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat)))) = zero_zero_nat)))),inference(rewrite,[status(thm)],[14929,682])).
239.52/52.83	thf(15763,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat)))) = zero_zero_nat)),inference(simp,[status(thm)],[15762])).
239.52/52.83	thf(15764,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat)))) = zero_zero_nat)),inference(lifteq,[status(thm)],[15763])).
239.52/52.83	thf(15772,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))) | ((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat)))) != (A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))))),inference(paramod_ordered,[status(thm)],[15764,14455])).
239.52/52.83	thf(15864,plain,((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat))))))))),inference(pre_uni,[status(thm)],[15772:[bind(A, $thf(^ [B:nat]: (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat))))))]])).
239.52/52.83	thf(16384,plain,((~ (~ ((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat)))))) = zero_zero_nat)))),inference(rewrite,[status(thm)],[15864,682])).
239.52/52.83	thf(16385,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat)))))) = zero_zero_nat)),inference(simp,[status(thm)],[16384])).
239.52/52.83	thf(16386,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ zero_zero_nat)))))) = zero_zero_nat)),inference(lifteq,[status(thm)],[16385])).
239.52/52.83	thf(18,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_209_order__less__subst2)).
239.52/52.83	thf(297,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)],[18])).
239.52/52.83	thf(53,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_ord__less__eq__trans)).
239.52/52.83	thf(424,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
239.52/52.83	thf(54,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_206_neq__iff)).
239.52/52.83	thf(429,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)],[54])).
239.52/52.83	thf(160,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_zero__reorient)).
239.52/52.83	thf(813,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
239.52/52.83	thf(814,plain,(! [A:nat] : (((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(cnf,[status(esa)],[813])).
239.52/52.83	thf(815,plain,(! [A:nat] : (((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(lifteq,[status(thm)],[814])).
239.52/52.83	thf(140,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_174_nat__0__less__mult__iff)).
239.52/52.83	thf(729,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)],[140])).
239.52/52.83	thf(1386,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[854,627])).
239.52/52.83	thf(1387,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(pattern_uni,[status(thm)],[1386:[]])).
239.52/52.83	thf(5611,plain,(((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | ((p @ sk113) != (p @ sk112))),inference(simp,[status(thm)],[5609])).
239.52/52.83	thf(237,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 @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_mult__le__mono1)).
239.52/52.83	thf(1091,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 @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
239.52/52.83	thf(345,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (~ ((C @ B) = D)) | (ord_less_nat @ (C @ A) @ D) | (ord_less_nat @ (sk9 @ D @ (C) @ B @ A) @ (sk10 @ D @ (C) @ B @ A)))),inference(cnf,[status(esa)],[343])).
239.52/52.83	thf(348,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : (((C @ B) != D) | (~ (ord_less_nat @ A @ B)) | (ord_less_nat @ (C @ A) @ D) | (ord_less_nat @ (sk9 @ D @ (C) @ B @ A) @ (sk10 @ D @ (C) @ B @ A)))),inference(lifteq,[status(thm)],[345])).
239.52/52.83	thf(349,plain,(! [C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (ord_less_nat @ (C @ A) @ (C @ B)) | (ord_less_nat @ (sk9 @ (C @ B) @ (C) @ B @ A) @ (sk10 @ (C @ B) @ (C) @ B @ A)))),inference(simp,[status(thm)],[348])).
239.52/52.83	thf(14868,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))) | ((A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B)))) != (p @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[1267,14455])).
239.52/52.83	thf(14928,plain,((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (ord_less_nat @ (p @ zero_zero_nat)))))),inference(pre_uni,[status(thm)],[14868:[bind(A, $thf(^ [B:nat]: (p @ zero_zero_nat)))]])).
239.52/52.83	thf(15154,plain,((~ (~ ((sk15 @ (ord_less_nat @ (p @ zero_zero_nat))) = zero_zero_nat)))),inference(rewrite,[status(thm)],[14928,682])).
239.52/52.83	thf(15155,plain,(((sk15 @ (ord_less_nat @ (p @ zero_zero_nat))) = zero_zero_nat)),inference(simp,[status(thm)],[15154])).
239.52/52.83	thf(15156,plain,(((sk15 @ (ord_less_nat @ (p @ zero_zero_nat))) = zero_zero_nat)),inference(lifteq,[status(thm)],[15155])).
239.52/52.83	thf(15163,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))) | ((sk15 @ (ord_less_nat @ (p @ zero_zero_nat))) != (A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))))),inference(paramod_ordered,[status(thm)],[15156,14455])).
239.52/52.83	thf(15232,plain,((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (p @ zero_zero_nat)))))))),inference(pre_uni,[status(thm)],[15163:[bind(A, $thf(^ [B:nat]: (sk15 @ (ord_less_nat @ (p @ zero_zero_nat)))))]])).
239.52/52.83	thf(16070,plain,((~ (~ ((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (p @ zero_zero_nat))))) = zero_zero_nat)))),inference(rewrite,[status(thm)],[15232,682])).
239.52/52.83	thf(16071,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (p @ zero_zero_nat))))) = zero_zero_nat)),inference(simp,[status(thm)],[16070])).
239.52/52.83	thf(16072,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (p @ zero_zero_nat))))) = zero_zero_nat)),inference(lifteq,[status(thm)],[16071])).
239.52/52.83	thf(89,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((((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)))) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_order__subst1)).
239.52/52.83	thf(566,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((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))) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
239.52/52.83	thf(178,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_not__less0)).
239.52/52.83	thf(879,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
239.52/52.83	thf(56,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_dual__order_Ostrict__implies__not__eq)).
239.52/52.83	thf(435,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
239.52/52.83	thf(116,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_order_Otrans)).
239.52/52.83	thf(665,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
239.52/52.83	thf(95,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_115_le__cases)).
239.52/52.83	thf(583,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)],[95])).
239.52/52.83	thf(148,axiom,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_le__numeral__extra_I4_J)).
239.52/52.83	thf(757,plain,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
239.52/52.83	thf(133,axiom,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: ((ord_less_eq_set_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_set_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_order__subst1)).
239.52/52.83	thf(710,plain,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: ((ord_less_eq_set_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_set_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_set_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
239.52/52.83	thf(165,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)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_ordered__comm__semiring__class_Ocomm__mult__left__mono)).
239.52/52.83	thf(842,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)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
239.52/52.83	thf(25,axiom,((! [A:nat,B:set_nat,C:set_nat,D:(nat > $o)]: (((ord_less_eq_set_nat @ B @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ C))))) => (D @ A)) <= (member_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_prop__restrict)).
239.52/52.83	thf(322,plain,((! [A:nat,B:set_nat,C:set_nat,D:(nat > $o)]: (((ord_less_eq_set_nat @ B @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ C))))) => (D @ A)) | ~ (member_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
239.52/52.83	thf(323,plain,((! [A:nat,B:set_nat]: (! [C:set_nat,D:(nat > $o)]: ((ord_less_eq_set_nat @ B @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ C))))) => (D @ A)) | ~ (member_nat @ A @ B)))),inference(miniscope,[status(thm)],[322])).
239.52/52.83	thf(324,plain,(! [D:(nat > $o),C:set_nat,B:set_nat,A:nat] : ((~ (ord_less_eq_set_nat @ B @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ C)))))) | (D @ A) | (~ (member_nat @ A @ B)))),inference(cnf,[status(esa)],[323])).
239.52/52.83	thf(214,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_eq_nat @ A @ C) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_mult__le__cancel2)).
239.52/52.83	thf(1012,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_eq_nat @ A @ C) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
239.52/52.83	thf(7278,plain,((sk90 != zero_zero_nat) | ((p @ sk113) != (p @ sk112)) | ((p @ sk112) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,5611])).
239.52/52.83	thf(7308,plain,((sk90 != zero_zero_nat) | ((p @ sk113) != (p @ sk112)) | (sk112 != one_one_nat)),inference(simp,[status(thm)],[7278])).
239.52/52.83	thf(220,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_mult__zero__left)).
239.52/52.83	thf(1032,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])).
239.52/52.83	thf(252,plain,(! [D:set_nat,C:set_nat,B:(set_nat > set_nat),A:set_nat] : ((~ (ord_less_eq_set_nat @ C @ D)) | (ord_less_eq_set_nat @ A @ (B @ D)) | (ord_less_eq_set_nat @ (sk1 @ D @ C @ (B) @ A) @ (sk2 @ D @ C @ (B) @ A)) | (~ (ord_less_eq_set_nat @ A @ (B @ C))))),inference(cnf,[status(esa)],[251])).
239.52/52.83	thf(1759,plain,(((p @ sk106) != zero_zero_nat) | ((times_times_nat @ (p @ sk107) @ sk107) != zero_zero_nat) | ((p @ sk90) != zero_zero_nat)),inference(func_ext,[status(esa)],[1757])).
239.52/52.83	thf(22662,plain,(! [A:nat] : (((p @ sk106) != zero_zero_nat) | ((p @ sk90) != zero_zero_nat) | ((times_times_nat @ A @ zero_zero_nat) != (times_times_nat @ (p @ sk107) @ sk107)))),inference(paramod_ordered,[status(thm)],[916,1759])).
239.52/52.83	thf(22712,plain,(! [A:nat] : (((p @ sk106) != zero_zero_nat) | ((p @ sk90) != zero_zero_nat) | (A != (p @ sk107)) | (sk107 != zero_zero_nat))),inference(simp,[status(thm)],[22662])).
239.52/52.83	thf(22728,plain,(((p @ sk106) != zero_zero_nat) | ((p @ sk90) != zero_zero_nat) | (sk107 != zero_zero_nat)),inference(simp,[status(thm)],[22712])).
239.52/52.83	thf(22752,plain,(((p @ sk106) != zero_zero_nat) | (sk107 != zero_zero_nat) | ((p @ sk90) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,22728])).
239.52/52.83	thf(22754,plain,(((p @ sk106) != zero_zero_nat) | (sk107 != zero_zero_nat) | (sk90 != zero_zero_nat)),inference(simp,[status(thm)],[22752])).
239.52/52.83	thf(5158,plain,(((times_times_nat @ (p @ sk113) @ sk113) != zero_zero_nat) | (sk90 != zero_zero_nat) | ((p @ sk112) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,1840])).
239.52/52.83	thf(5201,plain,(((times_times_nat @ (p @ sk113) @ sk113) != zero_zero_nat) | (sk90 != zero_zero_nat) | (sk112 != one_one_nat)),inference(simp,[status(thm)],[5158])).
239.52/52.83	thf(85,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_mult_Ocommute)).
239.52/52.83	thf(551,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
239.52/52.83	thf(80,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) <= (B = C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_ord__le__eq__trans)).
239.52/52.83	thf(519,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (B = C) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
239.52/52.83	thf(5607,plain,((sk90 != zero_zero_nat) | ((p @ sk113) != zero_zero_nat) | ((p @ sk112) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,5203])).
239.52/52.83	thf(5615,plain,((sk90 != zero_zero_nat) | ((p @ sk113) != zero_zero_nat) | (sk112 != zero_zero_nat)),inference(simp,[status(thm)],[5607])).
239.52/52.83	thf(202,axiom,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_le__numeral__extra_I3_J)).
239.52/52.83	thf(980,plain,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
239.52/52.83	thf(42,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_order__less__subst1)).
239.52/52.83	thf(388,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
239.52/52.83	thf(33,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_less__trans)).
239.52/52.83	thf(356,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
239.52/52.83	thf(14833,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))) | ((A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B)))) != (sk15 @ (^ [B:nat]: ($false)))))),inference(paramod_ordered,[status(thm)],[13736,14455])).
239.52/52.83	thf(14899,plain,((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (^ [A:nat]: ($false)))))))),inference(pre_uni,[status(thm)],[14833:[bind(A, $thf(^ [B:nat]: (sk15 @ (^ [C:nat]: ($false)))))]])).
239.52/52.83	thf(14972,plain,((~ (~ ((sk15 @ (ord_less_nat @ (sk15 @ (^ [A:nat]: ($false))))) = zero_zero_nat)))),inference(rewrite,[status(thm)],[14899,682])).
239.52/52.83	thf(14973,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (^ [A:nat]: ($false))))) = zero_zero_nat)),inference(simp,[status(thm)],[14972])).
239.52/52.83	thf(14974,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (^ [A:nat]: ($false))))) = zero_zero_nat)),inference(lifteq,[status(thm)],[14973])).
239.52/52.83	thf(14983,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))) | ((sk15 @ (ord_less_nat @ (sk15 @ (^ [B:nat]: ($false))))) != (A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))))),inference(paramod_ordered,[status(thm)],[14974,14455])).
239.52/52.83	thf(15079,plain,((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (^ [A:nat]: ($false)))))))))),inference(pre_uni,[status(thm)],[14983:[bind(A, $thf(^ [B:nat]: (sk15 @ (ord_less_nat @ (sk15 @ (^ [C:nat]: ($false)))))))]])).
239.52/52.83	thf(15928,plain,((~ (~ ((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (^ [A:nat]: ($false))))))) = zero_zero_nat)))),inference(rewrite,[status(thm)],[15079,682])).
239.52/52.83	thf(15929,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (^ [A:nat]: ($false))))))) = zero_zero_nat)),inference(simp,[status(thm)],[15928])).
239.52/52.83	thf(15930,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (^ [A:nat]: ($false))))))) = zero_zero_nat)),inference(lifteq,[status(thm)],[15929])).
239.52/52.83	thf(206,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_52_mult__le__mono)).
239.52/52.83	thf(989,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)],[206])).
239.52/52.83	thf(128,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_50_mult__le__mono2)).
239.52/52.83	thf(697,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)],[128])).
239.52/52.83	thf(1762,plain,(((p @ sk90) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (times_times_nat @ one_one_nat))),inference(paramod_ordered,[status(thm)],[669,1757])).
239.52/52.83	thf(1769,plain,(((p @ sk90) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (zero_zero_nat))) | ((p) != (^ [A:nat]: (one_one_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (A)))),inference(simp,[status(thm)],[1762])).
239.52/52.83	thf(1772,plain,(((p @ sk90) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (zero_zero_nat))) | ((p) != (^ [A:nat]: (one_one_nat)))),inference(simp,[status(thm)],[1769])).
239.52/52.83	thf(2390,plain,((sk90 != one_one_nat) | ((p @ sk111) != zero_zero_nat) | ((p @ sk110) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,2081])).
239.52/52.83	thf(2397,plain,((sk90 != one_one_nat) | ((p @ sk111) != zero_zero_nat) | (sk110 != zero_zero_nat)),inference(simp,[status(thm)],[2390])).
239.52/52.83	thf(2972,plain,((sk90 != one_one_nat) | (sk110 != zero_zero_nat) | ((p @ sk111) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,2397])).
239.52/52.83	thf(2990,plain,((sk90 != one_one_nat) | (sk110 != zero_zero_nat) | (sk111 != one_one_nat)),inference(simp,[status(thm)],[2972])).
239.52/52.83	thf(100,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_12_mult__cancel__left)).
239.52/52.83	thf(610,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)],[100])).
239.52/52.83	thf(1748,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | ((p @ sk90) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,1128])).
239.52/52.83	thf(1755,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != zero_zero_nat)),inference(simp,[status(thm)],[1748])).
239.52/52.83	thf(5156,plain,(! [A:nat] : (((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | ((times_times_nat @ A @ zero_zero_nat) != (times_times_nat @ (p @ sk113) @ sk113)))),inference(paramod_ordered,[status(thm)],[916,1840])).
239.52/52.83	thf(5193,plain,(! [A:nat] : (((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | (A != (p @ sk113)) | (sk113 != zero_zero_nat))),inference(simp,[status(thm)],[5156])).
239.52/52.83	thf(5204,plain,(((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | (sk113 != zero_zero_nat)),inference(simp,[status(thm)],[5193])).
239.52/52.83	thf(5214,plain,((sk90 != zero_zero_nat) | (sk113 != zero_zero_nat) | ((p @ sk112) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,5204])).
239.52/52.83	thf(5233,plain,((sk90 != zero_zero_nat) | (sk113 != zero_zero_nat) | (sk112 != one_one_nat)),inference(simp,[status(thm)],[5214])).
239.52/52.83	thf(6,axiom,((! [A:set_nat,B:set_nat,C:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ B) & (C @ D))))) = (! [D:nat]: ((member_nat @ D @ A) => (C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_subset__Collect__iff)).
239.52/52.83	thf(256,plain,((! [A:set_nat,B:set_nat,C:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ B) & (C @ D))))) = (! [D:nat]: ((member_nat @ D @ A) => (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
239.52/52.83	thf(5828,plain,((sk90 != zero_zero_nat) | (sk113 != sk112) | ((p @ sk112) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,5612])).
239.52/52.83	thf(5830,plain,((sk90 != zero_zero_nat) | (sk113 != sk112) | (sk112 != zero_zero_nat)),inference(simp,[status(thm)],[5828])).
239.52/52.83	thf(219,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_eq__imp__le)).
239.52/52.83	thf(1028,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
239.52/52.83	thf(29,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_subset__trans)).
239.52/52.83	thf(339,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
239.52/52.83	thf(82,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_less__irrefl)).
239.52/52.83	thf(526,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
239.52/52.83	thf(109,axiom,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_less__one)).
239.52/52.83	thf(637,plain,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
239.52/52.83	thf(678,plain,(! [A:nat] : (((times_times_nat @ one_one_nat @ A) = A))),inference(cnf,[status(esa)],[677])).
239.52/52.83	thf(679,plain,(! [A:nat] : (((times_times_nat @ one_one_nat @ A) = A))),inference(lifteq,[status(thm)],[678])).
239.52/52.83	thf(131,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_112_linear)).
239.52/52.83	thf(706,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)],[131])).
239.52/52.83	thf(124,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_62_sum__product)).
239.52/52.83	thf(686,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)],[124])).
239.52/52.83	thf(476,plain,(((^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: (~ (A @ C) | ~ (ord_less_nat @ C @ B)) & (A @ B))) = ('?' @ nat))),inference(lifteq,[status(thm)],[475])).
239.52/52.83	thf(552,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(lifteq,[status(thm)],[551])).
239.52/52.83	thf(1114,plain,(! [A:nat] : (((times_times_nat @ A) = (^ [B:nat]: (times_times_nat @ B @ A))))),inference(func_ext,[status(esa)],[552])).
239.52/52.83	thf(209,axiom,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_less__numeral__extra_I4_J)).
239.52/52.83	thf(997,plain,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
239.52/52.83	thf(2151,plain,((sk90 != one_one_nat) | (sk111 != zero_zero_nat) | ((p @ sk110) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,2082])).
239.52/52.83	thf(2153,plain,((sk90 != one_one_nat) | (sk111 != zero_zero_nat) | (sk110 != one_one_nat)),inference(simp,[status(thm)],[2151])).
239.52/52.83	thf(211,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nat__mult__1__right)).
239.52/52.83	thf(1002,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])).
239.52/52.83	thf(99,axiom,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: (((B @ C) = zero_zero_nat) <= (member_nat @ C @ A))) => ((groups1842438620at_nat @ B @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_sum_Oneutral)).
239.52/52.83	thf(605,plain,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: (((B @ C) = zero_zero_nat) | ~ (member_nat @ C @ A))) => ((groups1842438620at_nat @ (B) @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])).
239.52/52.83	thf(1241,plain,(! [A:nat] : (((ord_less_eq_nat @ A) = (^ [B:nat]: ((ord_less_nat @ A @ B) | (A = B)))))),inference(func_ext,[status(esa)],[674])).
239.52/52.83	thf(2073,plain,(((times_times_nat @ (p @ sk111) @ sk111) != zero_zero_nat) | (sk90 != one_one_nat) | ((p @ sk110) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,1830])).
239.52/52.83	thf(2076,plain,(((times_times_nat @ (p @ sk111) @ sk111) != zero_zero_nat) | (sk90 != one_one_nat) | (sk110 != zero_zero_nat)),inference(simp,[status(thm)],[2073])).
239.52/52.83	thf(88,axiom,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: ((A = (B @ C)) => ((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))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_ord__eq__le__subst)).
239.52/52.83	thf(558,plain,((! [A:set_nat,B:(nat > set_nat),C:nat,D:nat]: ((A = (B @ C)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
239.52/52.83	thf(5096,plain,(! [A:nat] : (((ord_less_nat @ (sk27 @ A) @ A) != (ord_less_nat @ zero_zero_nat @ (sk38 @ (= @ nat @ zero_zero_nat)))))),inference(paramod_ordered,[status(thm)],[3894,3508])).
239.52/52.83	thf(5113,plain,(! [A:nat] : (((sk27 @ A) != zero_zero_nat) | (A != (sk38 @ (= @ nat @ zero_zero_nat))))),inference(simp,[status(thm)],[5096])).
239.52/52.83	thf(5126,plain,(((sk27 @ (sk38 @ (= @ nat @ zero_zero_nat))) != zero_zero_nat)),inference(simp,[status(thm)],[5113])).
239.52/52.83	thf(156,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_33_sum_Oswap)).
239.52/52.83	thf(794,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)],[156])).
239.52/52.83	thf(2908,plain,((sk90 != one_one_nat) | (sk111 != sk110) | ((p @ sk110) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,2395])).
239.52/52.83	thf(2909,plain,((sk90 != one_one_nat) | (sk111 != sk110) | (sk110 != zero_zero_nat)),inference(simp,[status(thm)],[2908])).
239.52/52.83	thf(14830,plain,(! [B:(nat > nat),A:set_nat] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))) | ((groups1842438620at_nat @ (^ [C:nat]: (zero_zero_nat)) @ A) != (B @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))))),inference(paramod_ordered,[status(thm)],[582,14455])).
239.52/52.83	thf(14886,plain,(! [A:(nat > set_nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [C:nat]: (zero_zero_nat)) @ (A @ B)) @ B))))))),inference(pre_uni,[status(thm)],[14830:[bind(A, $thf(D @ (sk15 @ (^ [D:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [E:nat]: (zero_zero_nat)) @ (D @ D)) @ D))))),bind(B, $thf(^ [D:nat]: (groups1842438620at_nat @ (^ [E:nat]: (zero_zero_nat)) @ (D @ D))))]])).
239.52/52.83	thf(14944,plain,(! [A:(nat > set_nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [C:nat]: (zero_zero_nat)) @ (A @ B)) @ B))))))),inference(simp,[status(thm)],[14886])).
239.52/52.83	thf(16546,plain,(! [A:(nat > set_nat)] : ((~ (~ ((sk15 @ (^ [B:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [C:nat]: (zero_zero_nat)) @ (A @ B)) @ B))) = zero_zero_nat))))),inference(rewrite,[status(thm)],[14944,682])).
239.52/52.83	thf(16547,plain,(! [A:(nat > set_nat)] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [C:nat]: (zero_zero_nat)) @ (A @ B)) @ B))) = zero_zero_nat))),inference(simp,[status(thm)],[16546])).
239.52/52.83	thf(16548,plain,(! [A:(nat > set_nat)] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [C:nat]: (zero_zero_nat)) @ (A @ B)) @ B))) = zero_zero_nat))),inference(lifteq,[status(thm)],[16547])).
239.52/52.83	thf(22,axiom,((! [A:set_nat,B:set_nat,C: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_123_ord__eq__le__trans)).
239.52/52.83	thf(311,plain,((! [A:set_nat,B:set_nat,C: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)],[22])).
239.52/52.83	thf(45,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_less__asym)).
239.52/52.83	thf(398,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
239.52/52.83	thf(221,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) <= (ord_less_eq_nat @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_order_Onot__eq__order__implies__strict)).
239.52/52.83	thf(1035,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_eq_nat @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
239.52/52.83	thf(125,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_54_le__cube)).
239.52/52.83	thf(689,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)],[125])).
239.52/52.83	thf(58,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ D @ D)) => ((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ D @ E) <= (A @ E @ D))))) <= (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_linorder__less__wlog)).
239.52/52.83	thf(442,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ D @ D)) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ D @ E) | ~ (A @ E @ D))))) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
239.52/52.83	thf(443,plain,((! [A:(nat > (nat > $o))]: (((! [B:nat]: (A @ B @ B)) => (! [B:nat,C:nat]: (A @ B @ C) | ~ (! [B:nat,C:nat]: ((A @ B @ C) | ~ (A @ C @ B))))) | ~ (! [B:nat,C:nat]: ((ord_less_nat @ B @ C) => (A @ B @ C)))))),inference(miniscope,[status(thm)],[442])).
239.52/52.83	thf(444,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((~ (A @ (sk17 @ (A)) @ (sk17 @ (A)))) | (A @ B @ C) | (~ (A @ (sk18 @ (A)) @ (sk19 @ (A)))) | (ord_less_nat @ (sk20 @ (A)) @ (sk21 @ (A))))),inference(cnf,[status(esa)],[443])).
239.52/52.83	thf(141,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)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_mult__left__mono)).
239.52/52.83	thf(732,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)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
239.52/52.83	thf(152,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((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_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_order__subst2)).
239.52/52.83	thf(772,plain,((! [A:set_nat,B:set_nat,C:(set_nat > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((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_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
239.52/52.83	thf(145,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat)]: (((! [E:nat]: ((member_nat @ E @ B) => ((C @ E) = (D @ E)))) => ((groups1842438620at_nat @ C @ A) = (groups1842438620at_nat @ D @ B))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_sum_Ocong)).
239.52/52.83	thf(743,plain,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat)]: (((! [E:nat]: ((member_nat @ E @ B) => ((C @ E) = (D @ E)))) => ((groups1842438620at_nat @ (C) @ A) = (groups1842438620at_nat @ (D) @ B))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
239.52/52.83	thf(2389,plain,(((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | ((p @ sk111) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,2081])).
239.52/52.83	thf(2398,plain,(((p @ sk110) != zero_zero_nat) | (sk90 != one_one_nat) | (sk111 != one_one_nat)),inference(simp,[status(thm)],[2389])).
239.52/52.83	thf(12,axiom,((! [A:set_nat,B:set_nat]: (((ord_less_eq_set_nat @ B @ A) => (A = B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_subset__antisym)).
239.52/52.83	thf(281,plain,((! [A:set_nat,B:set_nat]: (((ord_less_eq_set_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
239.52/52.83	thf(257,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (! [C:(nat > $o)]: ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ B) & (C @ D))))) = (! [D:nat]: ((member_nat @ D @ A) => (C @ D)))))))),inference(miniscope,[status(thm)],[256])).
239.52/52.83	thf(258,plain,(! [C:(nat > $o),B:set_nat,A:set_nat] : ((~ (ord_less_eq_set_nat @ A @ B)) | ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ B) & (C @ D))))) = (! [D:nat]: ((member_nat @ D @ A) => (C @ D)))))),inference(cnf,[status(esa)],[257])).
239.52/52.83	thf(259,plain,(! [C:(nat > $o),B:set_nat,A:set_nat] : (((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ B) & (C @ D))))) = (! [D:nat]: ((member_nat @ D @ A) => (C @ D)))) | (~ (ord_less_eq_set_nat @ A @ B)))),inference(lifteq,[status(thm)],[258])).
239.52/52.83	thf(185,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_order_Ostrict__trans2)).
239.52/52.83	thf(904,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
239.52/52.83	thf(2388,plain,((sk90 != one_one_nat) | ((p @ sk111) != zero_zero_nat) | ((p @ sk110) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,2081])).
239.52/52.83	thf(2393,plain,((sk90 != one_one_nat) | ((p @ sk111) != zero_zero_nat) | (sk110 != one_one_nat)),inference(simp,[status(thm)],[2388])).
239.52/52.83	thf(93,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_one__reorient)).
239.52/52.83	thf(577,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
239.52/52.83	thf(578,plain,(! [A:nat] : (((one_one_nat = A) = (A = one_one_nat)))),inference(cnf,[status(esa)],[577])).
239.52/52.83	thf(579,plain,(! [A:nat] : (((one_one_nat = A) = (A = one_one_nat)))),inference(lifteq,[status(thm)],[578])).
239.52/52.83	thf(389,plain,((! [A:nat,B:(nat > nat),C:nat]: ((ord_less_nat @ A @ (B @ C)) => (! [D:nat]: (((! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))) | ~ (ord_less_nat @ C @ D)))))),inference(miniscope,[status(thm)],[388])).
239.52/52.83	thf(391,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((~ (ord_less_nat @ A @ (B @ C))) | (ord_less_nat @ (sk13 @ D @ C @ (B) @ A) @ (sk14 @ D @ C @ (B) @ A)) | (ord_less_nat @ A @ (B @ D)) | (~ (ord_less_nat @ C @ D)))),inference(cnf,[status(esa)],[389])).
239.52/52.83	thf(445,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((~ (A @ (sk17 @ (A)) @ (sk17 @ (A)))) | (A @ B @ C) | (~ (A @ (sk18 @ (A)) @ (sk19 @ (A)))) | (~ (A @ (sk20 @ (A)) @ (sk21 @ (A)))))),inference(cnf,[status(esa)],[443])).
239.52/52.83	thf(158,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_120_antisym__conv)).
239.52/52.83	thf(804,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)],[158])).
239.52/52.83	thf(31,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_order__trans)).
239.52/52.83	thf(350,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
239.52/52.83	thf(229,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_103_ord__eq__le__subst)).
239.52/52.83	thf(1058,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)],[229])).
239.52/52.83	thf(242,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_mult__zero__right)).
239.52/52.83	thf(1107,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
239.52/52.83	thf(603,plain,(! [A:nat] : (((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(cnf,[status(esa)],[602])).
239.52/52.83	thf(604,plain,(! [A:nat] : (((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(lifteq,[status(thm)],[603])).
239.52/52.83	thf(2070,plain,(((times_times_nat @ (p @ sk111) @ sk111) != zero_zero_nat) | (sk90 != one_one_nat) | ((p @ sk110) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,1830])).
239.52/52.83	thf(2079,plain,(((times_times_nat @ (p @ sk111) @ sk111) != zero_zero_nat) | (sk90 != one_one_nat) | (sk110 != one_one_nat)),inference(simp,[status(thm)],[2070])).
239.52/52.83	thf(184,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_gr__implies__not0)).
239.52/52.83	thf(900,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
239.52/52.83	thf(10,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_less__imp__not__eq2)).
239.52/52.83	thf(274,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
239.52/52.83	thf(22768,plain,((sk107 != zero_zero_nat) | (sk90 != zero_zero_nat) | ((p @ sk106) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,22754])).
239.52/52.83	thf(22786,plain,((sk107 != zero_zero_nat) | (sk90 != zero_zero_nat) | (sk106 != one_one_nat)),inference(simp,[status(thm)],[22768])).
239.52/52.83	thf(38,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_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_116_order_Otrans)).
239.52/52.83	thf(377,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_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)],[38])).
239.52/52.83	thf(8,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_eq__refl)).
239.52/52.83	thf(268,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
239.52/52.83	thf(269,plain,(! [B:set_nat,A:set_nat] : ((ord_less_eq_set_nat @ A @ B) | (~ (A = B)))),inference(cnf,[status(esa)],[268])).
239.52/52.83	thf(270,plain,(! [B:set_nat,A:set_nat] : ((A != B) | (ord_less_eq_set_nat @ A @ B))),inference(lifteq,[status(thm)],[269])).
239.52/52.83	thf(271,plain,(! [A:set_nat] : ((ord_less_eq_set_nat @ A @ A))),inference(simp,[status(thm)],[270])).
239.52/52.83	thf(172,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult_Ocomm__neutral)).
239.52/52.83	thf(863,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
239.52/52.83	thf(154,axiom,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ (C @ A) @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_ord__le__eq__subst)).
239.52/52.83	thf(784,plain,((! [A:nat,B:nat,C:(nat > set_nat),D:set_nat]: ((((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ (C @ A) @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
239.52/52.83	thf(20,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_63_atMost__def)).
239.52/52.83	thf(305,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)],[20])).
239.52/52.83	thf(306,plain,(((set_or1086813439et_nat) = (^ [A:set_nat]: (collect_set_nat @ (^ [B:set_nat]: (ord_less_eq_set_nat @ B @ A)))))),inference(lifteq,[status(thm)],[305])).
239.52/52.83	thf(1117,plain,(! [A:set_nat] : (((set_or1086813439et_nat @ A) = (collect_set_nat @ (^ [B:set_nat]: (ord_less_eq_set_nat @ B @ A)))))),inference(func_ext,[status(esa)],[306])).
239.52/52.83	thf(5585,plain,((sk90 != zero_zero_nat) | ((p @ sk113) != zero_zero_nat) | ((p @ sk112) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,5203])).
239.52/52.83	thf(5610,plain,((sk90 != zero_zero_nat) | ((p @ sk113) != zero_zero_nat) | (sk112 != one_one_nat)),inference(simp,[status(thm)],[5585])).
239.52/52.83	thf(143,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_89_nat__mult__eq__cancel__disj)).
239.52/52.83	thf(737,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)],[143])).
239.52/52.83	thf(224,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_not__gr0)).
239.52/52.83	thf(1043,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
239.52/52.83	thf(55,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_85_subsetI)).
239.52/52.83	thf(432,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)],[55])).
239.52/52.83	thf(434,plain,(! [B:set_nat,A:set_nat] : ((ord_less_eq_set_nat @ A @ B) | (~ (member_nat @ (sk16 @ B @ A) @ B)))),inference(cnf,[status(esa)],[432])).
239.52/52.83	thf(66,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_192_antisym__conv3)).
239.52/52.83	thf(477,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)],[66])).
239.52/52.83	thf(386,plain,(! [B:(nat > $o),A:(nat > $o)] : (((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) = (! [C:nat]: ((A @ C) => (B @ C)))))),inference(cnf,[status(esa)],[385])).
239.52/52.83	thf(387,plain,(! [B:(nat > $o),A:(nat > $o)] : (((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) = (! [C:nat]: ((A @ C) => (B @ C)))))),inference(lifteq,[status(thm)],[386])).
239.52/52.83	thf(72,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_147_set__eq__subset)).
239.52/52.83	thf(494,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)],[72])).
239.52/52.83	thf(107,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_141_ab__semigroup__mult__class_Omult__ac_I1_J)).
239.52/52.83	thf(631,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)],[107])).
239.52/52.83	thf(149,axiom,((! [A:nat,B:nat,C:(nat > nat),D: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)))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_ord__le__eq__subst)).
239.52/52.83	thf(758,plain,((! [A:nat,B:nat,C:(nat > nat),D: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)))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
239.52/52.83	thf(161,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_dual__order_Ostrict__implies__order)).
239.52/52.83	thf(816,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
239.52/52.83	thf(8959,plain,(! [A:nat] : (((groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ A))))))) = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))) | ((set_ord_atMost_nat @ A) != (set_ord_atMost_nat @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[6895,1132])).
239.52/52.83	thf(8960,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (collect_nat @ (^ [A:nat]: (member_nat @ A @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ zero_zero_nat))))))) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(pattern_uni,[status(thm)],[8959:[bind(A, $thf(zero_zero_nat))]])).
239.52/52.83	thf(9275,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (collect_nat @ (^ [A:nat]: (member_nat @ A @ (collect_nat @ (^ [B:nat]: (B = zero_zero_nat))))))) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(rewrite,[status(thm)],[8960,604])).
239.52/52.83	thf(139,axiom,((! [A:nat,B: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))) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_split__mult__neg__le)).
239.52/52.83	thf(726,plain,((! [A:nat,B: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))) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
239.52/52.83	thf(6709,plain,(! [B:nat,A:nat] : (((p @ B) = zero_zero_nat) | ((groups1842438620at_nat @ (^ [C:nat]: (times_times_nat @ (p @ C) @ C)) @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ A)))) = zero_zero_nat) | ((set_ord_atMost_nat @ A) != (set_ord_atMost_nat @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[1118,1136])).
239.52/52.83	thf(6710,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ zero_zero_nat)))) = zero_zero_nat))),inference(pattern_uni,[status(thm)],[6709:[bind(A, $thf(zero_zero_nat))]])).
239.52/52.83	thf(6900,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ zero_zero_nat)))) = zero_zero_nat))),inference(simp,[status(thm)],[6710])).
239.52/52.83	thf(20298,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | ((groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (collect_nat @ (^ [B:nat]: (B = zero_zero_nat)))) = zero_zero_nat))),inference(rewrite,[status(thm)],[6900,604])).
239.52/52.83	thf(68,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) <= (member_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_subset__eq)).
239.52/52.83	thf(483,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
239.52/52.83	thf(151,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__nonpos__nonneg)).
239.52/52.83	thf(769,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
239.52/52.83	thf(195,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_60_sum__distrib__right)).
239.52/52.83	thf(943,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)],[195])).
239.52/52.83	thf(60,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_187_order_Ostrict__trans)).
239.52/52.83	thf(462,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)],[60])).
239.52/52.83	thf(244,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__square)).
239.52/52.83	thf(1112,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
239.52/52.83	thf(35,axiom,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (B @ C)))) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Collect__subset)).
239.52/52.83	thf(367,plain,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (B @ C)))) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
239.52/52.83	thf(167,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_le__refl)).
239.52/52.83	thf(848,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
239.52/52.83	thf(129,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ B) <= (ord_less_eq_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_mult__left__le)).
239.52/52.83	thf(700,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
239.52/52.83	thf(204,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_zero__less__iff__neq__zero)).
239.52/52.83	thf(983,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
239.52/52.83	thf(2399,plain,((sk90 != one_one_nat) | (sk110 != one_one_nat) | ((p @ sk111) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,2393])).
239.52/52.83	thf(2401,plain,((sk90 != one_one_nat) | (sk110 != one_one_nat) | (sk111 != one_one_nat)),inference(simp,[status(thm)],[2399])).
239.52/52.83	thf(215,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_179_nat__mult__le__cancel__disj)).
239.52/52.83	thf(1015,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)],[215])).
239.52/52.83	thf(1113,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(cnf,[status(esa)],[1112])).
239.52/52.83	thf(298,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (! [C:(nat > nat),D:nat]: ((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(miniscope,[status(thm)],[297])).
239.52/52.83	thf(299,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (~ (ord_less_nat @ (C @ B) @ D)) | (ord_less_nat @ (C @ A) @ D) | (~ (ord_less_nat @ (C @ (sk5 @ D @ (C) @ B @ A)) @ (C @ (sk6 @ D @ (C) @ B @ A)))))),inference(cnf,[status(esa)],[298])).
239.52/52.83	thf(263,plain,(! [D:set_nat,C:set_nat,B:(set_nat > set_nat),A:set_nat] : ((~ (ord_less_eq_set_nat @ C @ D)) | (~ (ord_less_eq_set_nat @ (B @ (sk3 @ D @ C @ (B) @ A)) @ (B @ (sk4 @ D @ C @ (B) @ A)))) | (ord_less_eq_set_nat @ A @ (B @ D)) | (~ (A = (B @ C))))),inference(cnf,[status(esa)],[261])).
239.52/52.83	thf(266,plain,(! [D:set_nat,C:set_nat,B:(set_nat > set_nat),A:set_nat] : ((A != (B @ C)) | (~ (ord_less_eq_set_nat @ C @ D)) | (~ (ord_less_eq_set_nat @ (B @ (sk3 @ D @ C @ (B) @ A)) @ (B @ (sk4 @ D @ C @ (B) @ A)))) | (ord_less_eq_set_nat @ A @ (B @ D)))),inference(lifteq,[status(thm)],[263])).
239.52/52.83	thf(267,plain,(! [C:set_nat,B:set_nat,A:(set_nat > set_nat)] : ((~ (ord_less_eq_set_nat @ B @ C)) | (~ (ord_less_eq_set_nat @ (A @ (sk3 @ C @ B @ (A) @ (A @ B))) @ (A @ (sk4 @ C @ B @ (A) @ (A @ B))))) | (ord_less_eq_set_nat @ (A @ B) @ (A @ C)))),inference(simp,[status(thm)],[266])).
239.52/52.83	thf(430,plain,(! [B:nat,A:nat] : (((~ (A = B)) = ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))))),inference(cnf,[status(esa)],[429])).
239.52/52.83	thf(431,plain,(! [B:nat,A:nat] : ((((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B)) = (~ (A = B))))),inference(lifteq,[status(thm)],[430])).
239.52/52.83	thf(113,axiom,((! [A:(nat > nat),B:nat]: (((number1551313001itions @ A @ B) <= ((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 @ C @ B) & (ord_less_eq_nat @ one_one_nat @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_partitionsI)).
239.52/52.83	thf(653,plain,((! [A:(nat > nat),B:nat]: ((number1551313001itions @ (A) @ B) | ~ ((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 @ C @ B) & (ord_less_eq_nat @ one_one_nat @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
239.52/52.83	thf(114,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_19_mult__cancel1)).
239.52/52.83	thf(658,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)],[114])).
239.52/52.83	thf(230,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) => ((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_order__subst2)).
239.52/52.83	thf(1066,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) => ((! [E:nat,F:nat]: ((ord_less_eq_set_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_set_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
239.52/52.83	thf(174,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_less__zeroE)).
239.52/52.83	thf(868,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
239.52/52.83	thf(205,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_79_mult__eq__self__implies__10)).
239.52/52.83	thf(986,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)],[205])).
239.52/52.83	thf(64,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_order_Oasym)).
239.52/52.83	thf(473,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
239.52/52.83	thf(137,axiom,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_less__numeral__extra_I3_J)).
239.52/52.83	thf(722,plain,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
239.52/52.83	thf(136,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_109_eq__iff)).
239.52/52.83	thf(720,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)],[136])).
239.52/52.83	thf(721,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = (= @ nat))),inference(lifteq,[status(thm)],[720])).
239.52/52.83	thf(1304,plain,(! [A:nat] : (((^ [B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = (= @ nat @ A)))),inference(func_ext,[status(esa)],[721])).
239.52/52.83	thf(1744,plain,(((p @ sk90) != zero_zero_nat) | ((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (times_times_nat @ one_one_nat))),inference(paramod_ordered,[status(thm)],[669,1128])).
239.52/52.83	thf(1753,plain,(((p @ sk90) != zero_zero_nat) | ((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | ((p) != (^ [A:nat]: (one_one_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (A)))),inference(simp,[status(thm)],[1744])).
239.52/52.83	thf(1758,plain,(((p @ sk90) != zero_zero_nat) | ((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | ((p) != (^ [A:nat]: (one_one_nat)))),inference(simp,[status(thm)],[1753])).
239.52/52.83	thf(5,axiom,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((B @ C) & (member_nat @ C @ A)))) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Collect__restrict)).
239.52/52.83	thf(254,plain,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((B @ C) & (member_nat @ C @ A)))) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
239.52/52.83	thf(255,plain,(! [B:(nat > $o),A:set_nat] : ((ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((B @ C) & (member_nat @ C @ A)))) @ A))),inference(cnf,[status(esa)],[254])).
239.52/52.83	thf(234,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_35_mult__left__cancel)).
239.52/52.83	thf(1081,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)],[234])).
239.52/52.83	thf(102,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_10_atMost__eq__iff)).
239.52/52.83	thf(617,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)],[102])).
239.52/52.83	thf(216,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_order_Oorder__iff__strict)).
239.52/52.83	thf(1018,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
239.52/52.83	thf(147,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_less__nat__zero__code)).
239.52/52.83	thf(754,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
239.52/52.83	thf(86,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mult__nonneg__nonneg)).
239.52/52.83	thf(553,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
239.52/52.83	thf(163,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_le__antisym)).
239.52/52.83	thf(836,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
239.52/52.83	thf(226,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_mult_Oright__neutral)).
239.52/52.83	thf(1049,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
239.52/52.83	thf(71,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: (((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))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_order__subst2)).
239.52/52.83	thf(490,plain,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: (((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))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
239.52/52.83	thf(120,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]: (((ord_less_eq_nat @ one_one_nat @ C) & (ord_less_eq_nat @ C @ B)) <= ((A @ C) != zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_partitions__def)).
239.52/52.83	thf(675,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]: (((ord_less_eq_nat @ one_one_nat @ C) & (ord_less_eq_nat @ C @ B)) | ((A @ C) = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
239.52/52.83	thf(112,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_124_ord__eq__le__trans)).
239.52/52.83	thf(648,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)],[112])).
239.52/52.83	thf(70,axiom,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mem__Collect__eq)).
239.52/52.83	thf(487,plain,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
239.52/52.83	thf(153,axiom,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: ((A = (B @ C)) => ((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_ord__eq__le__subst)).
239.52/52.83	thf(776,plain,((! [A:nat,B:(set_nat > nat),C:set_nat,D:set_nat]: ((A = (B @ C)) => ((ord_less_eq_set_nat @ C @ D) => ((! [E:set_nat,F:set_nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_set_nat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
239.52/52.83	thf(110,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_antisym)).
239.52/52.83	thf(640,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
239.52/52.83	thf(231,axiom,((! [A:nat]: ((A != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_gr0I)).
239.52/52.83	thf(1070,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])).
239.52/52.83	thf(199,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat),E:(nat > nat)]: ((! [F:nat]: ((? [G:nat]: (((C @ G) = F) & ! [H:nat]: ((H = G) <= (((C @ H) = F) & (member_nat @ H @ B))) & (member_nat @ G @ B))) <= (member_nat @ F @ A))) => ((! [F:nat]: ((((D @ (C @ F)) = (E @ F)) & (member_nat @ (C @ F) @ A)) <= (member_nat @ F @ B))) => ((groups1842438620at_nat @ E @ B) = (groups1842438620at_nat @ D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_sum_Oeq__general)).
239.52/52.83	thf(954,plain,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat),E:(nat > nat)]: ((! [F:nat]: (? [G:nat]: (((C @ G) = F) & ! [H:nat]: ((H = G) | ~ (((C @ H) = F) & (member_nat @ H @ B))) & (member_nat @ G @ B)) | ~ (member_nat @ F @ A))) => ((! [F:nat]: ((((D @ (C @ F)) = (E @ F)) & (member_nat @ (C @ F) @ A)) | ~ (member_nat @ F @ B))) => ((groups1842438620at_nat @ (E) @ B) = (groups1842438620at_nat @ (D) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])).
239.52/52.83	thf(87,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_less__eq__nat_Osimps_I1_J)).
239.52/52.83	thf(556,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
239.52/52.83	thf(557,plain,(! [A:nat] : ((ord_less_eq_nat @ zero_zero_nat @ A))),inference(cnf,[status(esa)],[556])).
239.52/52.83	thf(170,axiom,((! [A:nat,B:nat]: (((A = B) | (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_less__or__eq__imp__le)).
239.52/52.83	thf(855,plain,((! [A:nat,B:nat]: (((A = B) | (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
239.52/52.83	thf(218,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_mult__0__right)).
239.52/52.83	thf(1025,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
239.52/52.83	thf(275,plain,(! [B:nat,A:nat] : ((~ (B = A)) | (~ (ord_less_nat @ A @ B)))),inference(cnf,[status(esa)],[274])).
239.52/52.83	thf(276,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ A @ B)))),inference(lifteq,[status(thm)],[275])).
239.52/52.83	thf(277,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ A)))),inference(simp,[status(thm)],[276])).
239.52/52.83	thf(3490,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk27 @ A)) != (ord_less_nat @ B @ B)))),inference(paramod_ordered,[status(thm)],[518,277])).
239.52/52.83	thf(3505,plain,(! [B:nat,A:nat] : ((A != B) | ((sk27 @ A) != B))),inference(simp,[status(thm)],[3490])).
239.52/52.83	thf(3507,plain,(! [A:nat] : (((sk27 @ A) != A))),inference(simp,[status(thm)],[3505])).
239.52/52.83	thf(28,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (((C @ B) = D) => ((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)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ord__le__eq__subst)).
239.52/52.83	thf(331,plain,((! [A:set_nat,B:set_nat,C:(set_nat > set_nat),D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (((C @ B) = D) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
239.52/52.83	thf(135,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_not__less__zero)).
239.52/52.83	thf(717,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])).
239.52/52.83	thf(14849,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))) | ((A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B)))) != (p @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1451,14455])).
239.52/52.83	thf(14931,plain,((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (ord_less_nat @ (p @ one_one_nat)))))),inference(pre_uni,[status(thm)],[14849:[bind(A, $thf(^ [B:nat]: (p @ one_one_nat)))]])).
239.52/52.83	thf(15554,plain,((~ (~ ((sk15 @ (ord_less_nat @ (p @ one_one_nat))) = zero_zero_nat)))),inference(rewrite,[status(thm)],[14931,682])).
239.52/52.83	thf(15555,plain,(((sk15 @ (ord_less_nat @ (p @ one_one_nat))) = zero_zero_nat)),inference(simp,[status(thm)],[15554])).
239.52/52.83	thf(15556,plain,(((sk15 @ (ord_less_nat @ (p @ one_one_nat))) = zero_zero_nat)),inference(lifteq,[status(thm)],[15555])).
239.52/52.83	thf(332,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (! [C:(set_nat > set_nat),D:set_nat]: (((C @ B) = D) => ((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))))))))),inference(miniscope,[status(thm)],[331])).
239.52/52.83	thf(334,plain,(! [D:set_nat,C:(set_nat > set_nat),B:set_nat,A:set_nat] : ((~ (ord_less_eq_set_nat @ A @ B)) | (~ ((C @ B) = D)) | (ord_less_eq_set_nat @ (C @ A) @ D) | (ord_less_eq_set_nat @ (sk7 @ D @ (C) @ B @ A) @ (sk8 @ D @ (C) @ B @ A)))),inference(cnf,[status(esa)],[332])).
239.52/52.83	thf(337,plain,(! [D:set_nat,C:(set_nat > set_nat),B:set_nat,A:set_nat] : (((C @ B) != D) | (~ (ord_less_eq_set_nat @ A @ B)) | (ord_less_eq_set_nat @ (C @ A) @ D) | (ord_less_eq_set_nat @ (sk7 @ D @ (C) @ B @ A) @ (sk8 @ D @ (C) @ B @ A)))),inference(lifteq,[status(thm)],[334])).
239.52/52.83	thf(338,plain,(! [C:(set_nat > set_nat),B:set_nat,A:set_nat] : ((~ (ord_less_eq_set_nat @ A @ B)) | (ord_less_eq_set_nat @ (C @ A) @ (C @ B)) | (ord_less_eq_set_nat @ (sk7 @ (C @ B) @ (C) @ B @ A) @ (sk8 @ (C @ B) @ (C) @ B @ A)))),inference(simp,[status(thm)],[337])).
239.52/52.83	thf(198,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_13_mult__eq__0__iff)).
239.52/52.83	thf(951,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)],[198])).
239.52/52.83	thf(10711,plain,((sk118 != zero_zero_nat) | ((p @ sk119) != one_one_nat) | (sk90 != zero_zero_nat) | ((p @ sk117) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,1913])).
239.52/52.83	thf(10739,plain,((sk118 != zero_zero_nat) | ((p @ sk119) != one_one_nat) | (sk90 != zero_zero_nat) | (sk117 != one_one_nat)),inference(simp,[status(thm)],[10711])).
239.52/52.83	thf(111,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (B = C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_ord__le__eq__trans)).
239.52/52.83	thf(643,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (B = C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
239.52/52.83	thf(222,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_24_nat__le__linear)).
239.52/52.83	thf(1038,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)],[222])).
239.52/52.83	thf(96,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_73_mult__mono_H)).
239.52/52.83	thf(585,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)],[96])).
239.52/52.83	thf(5586,plain,(((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | ((p @ sk113) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,5203])).
239.52/52.83	thf(5613,plain,(((p @ sk112) != zero_zero_nat) | (sk90 != zero_zero_nat) | (sk113 != one_one_nat)),inference(simp,[status(thm)],[5586])).
239.52/52.83	thf(5947,plain,((sk90 != zero_zero_nat) | (sk113 != one_one_nat) | ((p @ sk112) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,5613])).
239.52/52.83	thf(5948,plain,((sk90 != zero_zero_nat) | (sk113 != one_one_nat) | (sk112 != zero_zero_nat)),inference(simp,[status(thm)],[5947])).
239.52/52.83	thf(1235,plain,(! [A:set_nat] : (((ord_less_eq_set_nat @ A) = (^ [B:set_nat]: (ord_less_eq_nat_o @ (^ [C:nat]: (member_nat @ C @ A)) @ (^ [C:nat]: (member_nat @ C @ B))))))),inference(func_ext,[status(esa)],[486])).
239.52/52.83	thf(235,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_34_mult__right__cancel)).
239.52/52.83	thf(1085,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)],[235])).
239.52/52.83	thf(6986,plain,(! [A:nat] : (((p @ A) = zero_zero_nat) | (A = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))))),inference(rewrite,[status(thm)],[1134,604])).
239.52/52.83	thf(7009,plain,(! [A:nat] : ((A = zero_zero_nat) | ((p @ A) = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))))),inference(lifteq,[status(thm)],[6986])).
239.52/52.83	thf(6693,plain,(! [A:nat] : (((groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))) = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))) | ((set_ord_atMost_nat @ A) != (set_ord_atMost_nat @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[1118,1132])).
239.52/52.83	thf(6694,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (collect_nat @ (^ [A:nat]: (ord_less_eq_nat @ A @ zero_zero_nat)))) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(pattern_uni,[status(thm)],[6693:[bind(A, $thf(zero_zero_nat))]])).
239.52/52.83	thf(7319,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (collect_nat @ (^ [A:nat]: (A = zero_zero_nat)))) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(rewrite,[status(thm)],[6694,604])).
239.52/52.83	thf(186,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_21_mult__is__0)).
239.52/52.83	thf(907,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)],[186])).
239.52/52.83	thf(15563,plain,(! [A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))) | ((sk15 @ (ord_less_nat @ (p @ one_one_nat))) != (A @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (A @ B) @ B))))))),inference(paramod_ordered,[status(thm)],[15556,14455])).
239.52/52.83	thf(15649,plain,((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (p @ one_one_nat)))))))),inference(pre_uni,[status(thm)],[15563:[bind(A, $thf(^ [B:nat]: (sk15 @ (ord_less_nat @ (p @ one_one_nat)))))]])).
239.52/52.83	thf(16204,plain,((~ (~ ((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (p @ one_one_nat))))) = zero_zero_nat)))),inference(rewrite,[status(thm)],[15649,682])).
239.52/52.83	thf(16205,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (p @ one_one_nat))))) = zero_zero_nat)),inference(simp,[status(thm)],[16204])).
239.52/52.83	thf(16206,plain,(((sk15 @ (ord_less_nat @ (sk15 @ (ord_less_nat @ (p @ one_one_nat))))) = zero_zero_nat)),inference(lifteq,[status(thm)],[16205])).
239.52/52.83	thf(333,plain,(! [D:set_nat,C:(set_nat > set_nat),B:set_nat,A:set_nat] : ((~ (ord_less_eq_set_nat @ A @ B)) | (~ ((C @ B) = D)) | (ord_less_eq_set_nat @ (C @ A) @ D) | (~ (ord_less_eq_set_nat @ (C @ (sk7 @ D @ (C) @ B @ A)) @ (C @ (sk8 @ D @ (C) @ B @ A)))))),inference(cnf,[status(esa)],[332])).
239.52/52.83	thf(335,plain,(! [D:set_nat,C:(set_nat > set_nat),B:set_nat,A:set_nat] : (((C @ B) != D) | (~ (ord_less_eq_set_nat @ A @ B)) | (ord_less_eq_set_nat @ (C @ A) @ D) | (~ (ord_less_eq_set_nat @ (C @ (sk7 @ D @ (C) @ B @ A)) @ (C @ (sk8 @ D @ (C) @ B @ A)))))),inference(lifteq,[status(thm)],[333])).
239.52/52.83	thf(336,plain,(! [C:(set_nat > set_nat),B:set_nat,A:set_nat] : ((~ (ord_less_eq_set_nat @ A @ B)) | (ord_less_eq_set_nat @ (C @ A) @ (C @ B)) | (~ (ord_less_eq_set_nat @ (C @ (sk7 @ (C @ B) @ (C) @ B @ A)) @ (C @ (sk8 @ (C @ B) @ (C) @ B @ A)))))),inference(simp,[status(thm)],[335])).
239.52/52.83	thf(130,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_37_divisors__zero)).
239.52/52.83	thf(703,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)],[130])).
239.52/52.83	thf(1137,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat))) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (times_times_nat @ one_one_nat))),inference(paramod_ordered,[status(thm)],[669,1132])).
239.52/52.83	thf(1140,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat))) | ((p) != (^ [A:nat]: (one_one_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (A)))),inference(simp,[status(thm)],[1137])).
239.52/52.83	thf(1141,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat))) | ((p) != (^ [A:nat]: (one_one_nat)))),inference(simp,[status(thm)],[1140])).
239.52/52.83	thf(101,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) <= (ord_less_eq_nat @ (C @ B) @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_order__subst2)).
239.52/52.83	thf(613,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ (ord_less_eq_nat @ (C @ B) @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
239.52/52.83	thf(227,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_139_dual__order_Oantisym)).
239.52/52.83	thf(1052,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)],[227])).
239.52/52.83	thf(7300,plain,((sk90 != zero_zero_nat) | ((p @ sk113) != (p @ sk112)) | ((p @ sk112) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,5611])).
239.52/52.83	thf(7303,plain,((sk90 != zero_zero_nat) | ((p @ sk113) != (p @ sk112)) | (sk112 != zero_zero_nat)),inference(simp,[status(thm)],[7300])).
239.52/52.83	thf(446,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((~ (A @ (sk17 @ (A)) @ (sk17 @ (A)))) | (A @ B @ C) | (A @ (sk19 @ (A)) @ (sk18 @ (A))) | (ord_less_nat @ (sk20 @ (A)) @ (sk21 @ (A))))),inference(cnf,[status(esa)],[443])).
239.52/52.83	thf(177,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_order__class_Oorder_Oantisym)).
239.52/52.83	thf(876,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])).
239.52/52.83	thf(238,axiom,((! [A:set_nat,B:(nat > nat)]: ((ord_less_eq_nat @ (groups1842438620at_nat @ B @ A) @ zero_zero_nat) <= (! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ (B @ C) @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_sum__nonpos)).
239.52/52.83	thf(1094,plain,((! [A:set_nat,B:(nat > nat)]: ((ord_less_eq_nat @ (groups1842438620at_nat @ (B) @ A) @ zero_zero_nat) | ~ (! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ (B @ C) @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
239.52/52.83	thf(201,axiom,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_lambda__zero)).
239.52/52.83	thf(978,plain,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
239.52/52.83	thf(166,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_order_Ostrict__trans1)).
239.52/52.83	thf(845,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
239.52/52.83	thf(2567,plain,(! [B:nat,A:nat] : ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (B != one_one_nat) | (sk111 != zero_zero_nat) | (sk110 != one_one_nat) | (A != sk90))),inference(paramod_ordered,[status(thm)],[286,2153])).
239.52/52.83	thf(2568,plain,(! [A:nat] : ((ord_less_nat @ A @ sk90) | (ord_less_nat @ sk90 @ A) | (A != one_one_nat) | (sk111 != zero_zero_nat) | (sk110 != one_one_nat))),inference(pattern_uni,[status(thm)],[2567:[bind(A, $thf(sk90))]])).
239.52/52.83	thf(2755,plain,((ord_less_nat @ one_one_nat @ sk90) | (ord_less_nat @ sk90 @ one_one_nat) | (sk111 != zero_zero_nat) | (sk110 != one_one_nat)),inference(simp,[status(thm)],[2568])).
239.52/52.83	thf(638,plain,(! [A:nat] : (((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),inference(cnf,[status(esa)],[637])).
239.52/52.83	thf(639,plain,(! [A:nat] : (((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),inference(lifteq,[status(thm)],[638])).
239.52/52.83	thf(11122,plain,((ord_less_nat @ one_one_nat @ sk90) | (sk90 = zero_zero_nat) | (sk111 != zero_zero_nat) | (sk110 != one_one_nat)),inference(rewrite,[status(thm)],[2755,639])).
239.52/52.83	thf(11123,plain,((sk90 = zero_zero_nat) | (ord_less_nat @ one_one_nat @ sk90) | (sk111 != zero_zero_nat) | (sk110 != one_one_nat)),inference(lifteq,[status(thm)],[11122])).
239.52/52.83	thf(8969,plain,(! [B:nat,A:set_nat] : (((collect_nat @ (^ [C:nat]: (member_nat @ C @ (collect_nat @ (^ [D:nat]: (member_nat @ D @ A)))))) = (set_ord_atMost_nat @ B)) | (A != (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ B)))))),inference(paramod_ordered,[status(thm)],[472,6895])).
239.52/52.83	thf(8970,plain,(! [A:nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (member_nat @ C @ (collect_nat @ (^ [D:nat]: (ord_less_eq_nat @ D @ A))))))))) = (set_ord_atMost_nat @ A)))),inference(pattern_uni,[status(thm)],[8969:[bind(A, $thf(collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ B)))),bind(B, $thf(B))]])).
239.52/52.83	thf(9192,plain,(! [A:nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (member_nat @ C @ (collect_nat @ (^ [D:nat]: (ord_less_eq_nat @ D @ A))))))))) = (set_ord_atMost_nat @ A)))),inference(simp,[status(thm)],[8970])).
239.52/52.83	thf(10440,plain,(! [A:nat] : (((groups1842438620at_nat @ (^ [B:nat]: (times_times_nat @ (p @ B) @ B)) @ (collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (member_nat @ C @ (collect_nat @ (^ [D:nat]: (ord_less_eq_nat @ D @ A)))))))))) = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))) | ((set_ord_atMost_nat @ A) != (set_ord_atMost_nat @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[9192,1132])).
239.52/52.83	thf(10441,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (collect_nat @ (^ [A:nat]: (member_nat @ A @ (collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ zero_zero_nat)))))))))) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(pattern_uni,[status(thm)],[10440:[bind(A, $thf(zero_zero_nat))]])).
239.52/52.83	thf(18061,plain,(((groups1842438620at_nat @ (^ [A:nat]: (times_times_nat @ (p @ A) @ A)) @ (collect_nat @ (^ [A:nat]: (member_nat @ A @ (collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (C = zero_zero_nat)))))))))) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat)))),inference(rewrite,[status(thm)],[10441,604])).
239.52/52.83	thf(81,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_subset__refl)).
239.52/52.83	thf(524,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
239.52/52.83	thf(368,plain,(! [B:(nat > $o),A:set_nat] : ((ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (B @ C)))) @ A))),inference(cnf,[status(esa)],[367])).
239.52/52.83	thf(61,axiom,((! [A:set_nat,B:(nat > $o),C:(nat > $o)]: ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((C @ D) & (B @ D))))) = ((ord_less_eq_set_nat @ A @ (collect_nat @ B)) & (ord_less_eq_set_nat @ A @ (collect_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_conj__subset__def)).
239.52/52.83	thf(465,plain,((! [A:set_nat,B:(nat > $o),C:(nat > $o)]: ((ord_less_eq_set_nat @ A @ (collect_nat @ (^ [D:nat]: ((C @ D) & (B @ D))))) = ((ord_less_eq_set_nat @ A @ (collect_nat @ (B))) & (ord_less_eq_set_nat @ A @ (collect_nat @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
239.52/52.83	thf(16555,plain,(! [B:(nat > nat),A:(nat > set_nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))) | ((sk15 @ (^ [C:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [D:nat]: (zero_zero_nat)) @ (A @ C)) @ C))) != (B @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))))),inference(paramod_ordered,[status(thm)],[16548,14455])).
239.52/52.83	thf(16649,plain,(! [A:(nat > (nat > set_nat))] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [D:nat]: (zero_zero_nat)) @ (A @ B @ C)) @ C))) @ B))))))),inference(pre_uni,[status(thm)],[16555:[bind(A, $thf(G @ (sk15 @ (^ [D:nat]: (ord_less_nat @ (sk15 @ (^ [E:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [F:nat]: (zero_zero_nat)) @ (G @ D @ E)) @ E))) @ D))))),bind(B, $thf(^ [D:nat]: (sk15 @ (^ [E:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [F:nat]: (zero_zero_nat)) @ (G @ D @ E)) @ E)))))]])).
239.52/52.83	thf(16715,plain,(! [A:(nat > (nat > set_nat))] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [D:nat]: (zero_zero_nat)) @ (A @ B @ C)) @ C))) @ B))))))),inference(simp,[status(thm)],[16649])).
239.52/52.83	thf(17551,plain,(! [A:(nat > (nat > set_nat))] : ((~ (~ ((sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [D:nat]: (zero_zero_nat)) @ (A @ B @ C)) @ C))) @ B))) = zero_zero_nat))))),inference(rewrite,[status(thm)],[16715,682])).
239.52/52.83	thf(17552,plain,(! [A:(nat > (nat > set_nat))] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [D:nat]: (zero_zero_nat)) @ (A @ B @ C)) @ C))) @ B))) = zero_zero_nat))),inference(simp,[status(thm)],[17551])).
239.52/52.83	thf(17553,plain,(! [A:(nat > (nat > set_nat))] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (groups1842438620at_nat @ (^ [D:nat]: (zero_zero_nat)) @ (A @ B @ C)) @ C))) @ B))) = zero_zero_nat))),inference(lifteq,[status(thm)],[17552])).
239.52/52.83	thf(7699,plain,(! [B:nat,A:nat] : ((~ (B = zero_zero_nat)) | ((ord_less_nat @ A @ (sk27 @ A)) != (ord_less_nat @ zero_zero_nat @ B)))),inference(paramod_ordered,[status(thm)],[518,682])).
239.52/52.83	thf(7700,plain,((~ ((sk27 @ zero_zero_nat) = zero_zero_nat))),inference(pattern_uni,[status(thm)],[7699:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(sk27 @ zero_zero_nat))]])).
239.52/52.83	thf(7764,plain,(((sk27 @ zero_zero_nat) != zero_zero_nat)),inference(lifteq,[status(thm)],[7700])).
239.52/52.83	thf(191,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_gr__zeroI)).
239.52/52.83	thf(931,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])).
239.52/52.83	thf(24,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_207_neqE)).
239.52/52.83	thf(319,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)],[24])).
239.52/52.83	thf(390,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((~ (ord_less_nat @ A @ (B @ C))) | (~ (ord_less_nat @ (B @ (sk13 @ D @ C @ (B) @ A)) @ (B @ (sk14 @ D @ C @ (B) @ A)))) | (ord_less_nat @ A @ (B @ D)) | (~ (ord_less_nat @ C @ D)))),inference(cnf,[status(esa)],[389])).
239.52/52.83	thf(51,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_less__imp__not__eq)).
239.52/52.83	thf(418,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
239.52/52.83	thf(196,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_mult_Oleft__neutral)).
239.52/52.83	thf(946,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
239.52/52.83	thf(240,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_le__zero__eq)).
239.52/52.83	thf(1101,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
239.52/52.83	thf(11143,plain,(! [A:nat] : ((sk90 = zero_zero_nat) | (sk111 != zero_zero_nat) | (sk110 != one_one_nat) | ((ord_less_nat @ (sk27 @ A) @ A) != (ord_less_nat @ one_one_nat @ sk90)))),inference(paramod_ordered,[status(thm)],[11123,3508])).
239.52/52.83	thf(11185,plain,(! [A:nat] : ((sk90 = zero_zero_nat) | (sk111 != zero_zero_nat) | (sk110 != one_one_nat) | ((sk27 @ A) != one_one_nat) | (A != sk90))),inference(simp,[status(thm)],[11143])).
239.52/52.83	thf(11210,plain,((sk90 = zero_zero_nat) | (sk111 != zero_zero_nat) | (sk110 != one_one_nat) | ((sk27 @ sk90) != one_one_nat)),inference(simp,[status(thm)],[11185])).
239.52/52.83	thf(433,plain,(! [B:set_nat,A:set_nat] : ((ord_less_eq_set_nat @ A @ B) | (member_nat @ (sk16 @ B @ A) @ A))),inference(cnf,[status(esa)],[432])).
239.52/52.83	thf(2057,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != zero_zero_nat) | ((^ [A:nat]: (times_times_nat @ (p @ A) @ A)) != (times_times_nat @ one_one_nat))),inference(paramod_ordered,[status(thm)],[669,1755])).
239.52/52.83	thf(2064,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != zero_zero_nat) | ((p) != (^ [A:nat]: (one_one_nat))) | ((^ [A:nat]: (A)) != (^ [A:nat]: (A)))),inference(simp,[status(thm)],[2057])).
239.52/52.83	thf(2066,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (set_ord_atMost_nat @ zero_zero_nat)) != zero_zero_nat) | ((p) != (^ [A:nat]: (zero_zero_nat))) | (sk90 != zero_zero_nat) | ((p) != (^ [A:nat]: (one_one_nat)))),inference(simp,[status(thm)],[2064])).
239.52/52.83	thf(233,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C)) <= (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_less__mono__imp__le__mono)).
239.52/52.83	thf(1077,plain,((! [A:(nat > nat),B:nat,C:nat]: ((ord_less_eq_nat @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
239.52/52.83	thf(8792,plain,(! [B:nat,A:nat] : (((collect_nat @ (^ [C:nat]: (member_nat @ C @ (collect_nat @ (^ [D:nat]: (ord_less_eq_nat @ D @ A)))))) = (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ B)))) | ((set_ord_atMost_nat @ A) != (set_ord_atMost_nat @ B)))),inference(paramod_ordered,[status(thm)],[1118,6893])).
239.52/52.83	thf(8793,plain,(! [A:nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ C @ A)))))) = (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(pattern_uni,[status(thm)],[8792:[bind(A, $thf(A)),bind(B, $thf(A))]])).
239.52/52.83	thf(9,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_dual__order_Orefl)).
239.52/52.83	thf(272,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
239.52/52.83	thf(2571,plain,(! [B:nat,A:nat] : ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (sk90 != one_one_nat) | (sk111 != zero_zero_nat) | (B != one_one_nat) | (A != sk110))),inference(paramod_ordered,[status(thm)],[286,2153])).
239.52/52.83	thf(2572,plain,(! [A:nat] : ((ord_less_nat @ A @ sk110) | (ord_less_nat @ sk110 @ A) | (sk90 != one_one_nat) | (sk111 != zero_zero_nat) | (A != one_one_nat))),inference(pattern_uni,[status(thm)],[2571:[bind(A, $thf(sk110))]])).
239.52/52.83	thf(2757,plain,((ord_less_nat @ one_one_nat @ sk110) | (ord_less_nat @ sk110 @ one_one_nat) | (sk90 != one_one_nat) | (sk111 != zero_zero_nat)),inference(simp,[status(thm)],[2572])).
239.52/52.83	thf(14699,plain,((ord_less_nat @ one_one_nat @ sk110) | (sk110 = zero_zero_nat) | (sk90 != one_one_nat) | (sk111 != zero_zero_nat)),inference(rewrite,[status(thm)],[2757,639])).
239.52/52.83	thf(14700,plain,((sk110 = zero_zero_nat) | (ord_less_nat @ one_one_nat @ sk110) | (sk90 != one_one_nat) | (sk111 != zero_zero_nat)),inference(lifteq,[status(thm)],[14699])).
239.52/52.83	thf(5189,plain,(((times_times_nat @ (p @ sk113) @ sk113) != zero_zero_nat) | (sk90 != zero_zero_nat) | ((p @ sk112) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,1840])).
239.52/52.83	thf(5194,plain,(((times_times_nat @ (p @ sk113) @ sk113) != zero_zero_nat) | (sk90 != zero_zero_nat) | (sk112 != zero_zero_nat)),inference(simp,[status(thm)],[5189])).
239.52/52.83	thf(6756,plain,(! [A:nat] : (((groups1842438620at_nat @ (^ [B:nat]: (B)) @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))) = zero_zero_nat) | ((p) = (^ [B:nat]: (zero_zero_nat))) | ((p) != (^ [B:nat]: (one_one_nat))) | ((set_ord_atMost_nat @ A) != (set_ord_atMost_nat @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[1118,1141])).
239.52/52.83	thf(6757,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (collect_nat @ (^ [A:nat]: (ord_less_eq_nat @ A @ zero_zero_nat)))) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat))) | ((p) != (^ [A:nat]: (one_one_nat)))),inference(pattern_uni,[status(thm)],[6756:[bind(A, $thf(zero_zero_nat))]])).
239.52/52.83	thf(9542,plain,(((groups1842438620at_nat @ (^ [A:nat]: (A)) @ (collect_nat @ (^ [A:nat]: (A = zero_zero_nat)))) = zero_zero_nat) | ((p) = (^ [A:nat]: (zero_zero_nat))) | ((p) != (^ [A:nat]: (one_one_nat)))),inference(rewrite,[status(thm)],[6757,604])).
239.52/52.83	thf(300,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (~ (ord_less_nat @ (C @ B) @ D)) | (ord_less_nat @ (C @ A) @ D) | (ord_less_nat @ (sk5 @ D @ (C) @ B @ A) @ (sk6 @ D @ (C) @ B @ A)))),inference(cnf,[status(esa)],[298])).
239.52/52.83	thf(409,plain,(! [B:set_nat,A:set_nat] : (((ord_le1613022364et_nat @ (set_or1086813439et_nat @ A) @ (set_or1086813439et_nat @ B)) = (ord_less_eq_set_nat @ A @ B)))),inference(cnf,[status(esa)],[408])).
239.52/52.83	thf(410,plain,(! [B:set_nat,A:set_nat] : (((ord_le1613022364et_nat @ (set_or1086813439et_nat @ A) @ (set_or1086813439et_nat @ B)) = (ord_less_eq_set_nat @ A @ B)))),inference(lifteq,[status(thm)],[409])).
239.52/52.83	thf(239,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_eq__refl)).
239.52/52.83	thf(1097,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
239.52/52.83	thf(5231,plain,((sk90 != zero_zero_nat) | (sk113 != zero_zero_nat) | ((p @ sk112) != (p @ zero_zero_nat))),inference(paramod_ordered,[status(thm)],[1267,5204])).
239.52/52.83	thf(5232,plain,((sk90 != zero_zero_nat) | (sk113 != zero_zero_nat) | (sk112 != zero_zero_nat)),inference(simp,[status(thm)],[5231])).
239.52/52.83	thf(162,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat),D:set_nat,E:(nat > nat),F:(nat > nat)]: (((! [G:nat]: ((member_nat @ (C @ G) @ D) <= (member_nat @ G @ A))) => ((! [G:nat]: (((C @ (B @ G)) = G) <= (member_nat @ G @ D))) => (((! [G:nat]: ((member_nat @ G @ A) => ((E @ (C @ G)) = (F @ G)))) => ((groups1842438620at_nat @ F @ A) = (groups1842438620at_nat @ E @ D))) <= (! [G:nat]: ((member_nat @ G @ D) => (member_nat @ (B @ G) @ A)))))) <= (! [G:nat]: (((B @ (C @ G)) = G) <= (member_nat @ G @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_sum_Oreindex__bij__witness)).
239.52/52.83	thf(818,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat),D:set_nat,E:(nat > nat),F:(nat > nat)]: (((! [G:nat]: ((member_nat @ (C @ G) @ D) | ~ (member_nat @ G @ A))) => ((! [G:nat]: (((C @ (B @ G)) = G) | ~ (member_nat @ G @ D))) => (((! [G:nat]: ((member_nat @ G @ A) => ((E @ (C @ G)) = (F @ G)))) => ((groups1842438620at_nat @ (F) @ A) = (groups1842438620at_nat @ (E) @ D))) | ~ (! [G:nat]: ((member_nat @ G @ D) => (member_nat @ (B @ G) @ A)))))) | ~ (! [G:nat]: (((B @ (C @ G)) = G) | ~ (member_nat @ G @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
239.52/52.83	thf(48,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_138_dual__order_Oantisym)).
239.52/52.83	thf(405,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)],[48])).
239.52/52.83	thf(52,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_dual__order_Oasym)).
239.52/52.83	thf(422,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
239.52/52.83	thf(864,plain,(! [A:nat] : (((times_times_nat @ A @ one_one_nat) = A))),inference(cnf,[status(esa)],[863])).
239.52/52.83	thf(865,plain,(! [A:nat] : (((times_times_nat @ A @ one_one_nat) = A))),inference(lifteq,[status(thm)],[864])).
239.52/52.83	thf(142,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_less__imp__le__nat)).
239.52/52.83	thf(735,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
239.52/52.83	thf(210,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_142_mult_Oassoc)).
239.52/52.83	thf(999,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)],[210])).
239.52/52.83	thf(103,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_144_mult_Oleft__commute)).
239.52/52.83	thf(620,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)],[103])).
239.52/52.83	thf(17,axiom,((! [A:set_nat,B:set_nat]: (((A = B) <= (ord_less_eq_set_nat @ B @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_antisym)).
239.52/52.83	thf(294,plain,((! [A:set_nat,B:set_nat]: ((A = B) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
239.52/52.83	thf(340,plain,((! [A:set_nat,B:set_nat]: (! [C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(miniscope,[status(thm)],[339])).
239.52/52.83	thf(341,plain,(! [C:set_nat,B:set_nat,A:set_nat] : ((ord_less_eq_set_nat @ A @ C) | (~ (ord_less_eq_set_nat @ B @ C)) | (~ (ord_less_eq_set_nat @ A @ B)))),inference(cnf,[status(esa)],[340])).
239.52/52.83	thf(183,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) <= (A != B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_le__neq__implies__less)).
239.52/52.83	thf(897,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
239.52/52.83	thf(46,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_121_order__class_Oorder_Oeq__iff)).
239.52/52.83	thf(400,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)],[46])).
239.52/52.83	thf(10327,plain,((sk115 != zero_zero_nat) | ((p @ sk116) != one_one_nat) | (sk90 != one_one_nat) | ((p @ sk114) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,1900])).
239.52/52.83	thf(10355,plain,((sk115 != zero_zero_nat) | ((p @ sk116) != one_one_nat) | (sk90 != one_one_nat) | (sk114 != one_one_nat)),inference(simp,[status(thm)],[10327])).
239.52/52.83	thf(282,plain,(! [B:set_nat,A:set_nat] : ((~ (ord_less_eq_set_nat @ B @ A)) | (A = B) | (~ (ord_less_eq_set_nat @ A @ B)))),inference(cnf,[status(esa)],[281])).
239.52/52.83	thf(283,plain,(! [B:set_nat,A:set_nat] : ((A = B) | (~ (ord_less_eq_set_nat @ B @ A)) | (~ (ord_less_eq_set_nat @ A @ B)))),inference(lifteq,[status(thm)],[282])).
239.52/52.83	thf(357,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))))),inference(miniscope,[status(thm)],[356])).
239.52/52.83	thf(358,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (~ (ord_less_nat @ B @ C)) | (ord_less_nat @ A @ C))),inference(cnf,[status(esa)],[357])).
239.52/52.83	thf(159,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((A @ D @ E) <= (A @ E @ D))) => (A @ B @ C)) <= (! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_linorder__wlog)).
239.52/52.83	thf(807,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((A @ D @ E) | ~ (A @ E @ D))) => (A @ B @ C)) | ~ (! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
239.52/52.83	thf(144,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ B) <= (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_dual__order_Ostrict__trans1)).
239.52/52.83	thf(740,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ B) | ~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
239.52/52.83	thf(171,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_27_le__trans)).
239.52/52.83	thf(860,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)],[171])).
239.52/52.83	thf(207,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((ord_less_eq_nat @ (groups1842438620at_nat @ B @ A) @ (groups1842438620at_nat @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_sum__mono)).
239.52/52.83	thf(992,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((ord_less_eq_nat @ (groups1842438620at_nat @ (B) @ A) @ (groups1842438620at_nat @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
239.52/52.83	thf(16811,plain,(! [B:(nat > nat),A:(nat > nat)] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))) | ((sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ (A @ C) @ zero_zero_nat) @ C))) != (B @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (B @ C) @ C))))))),inference(paramod_ordered,[status(thm)],[16804,14455])).
239.52/52.83	thf(16899,plain,(! [A:(nat > (nat > nat))] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ (A @ B @ C) @ zero_zero_nat) @ C))) @ B))))))),inference(pre_uni,[status(thm)],[16811:[bind(A, $thf(F @ (sk15 @ (^ [D:nat]: (ord_less_nat @ (sk15 @ (^ [E:nat]: (ord_less_nat @ (times_times_nat @ (F @ D @ E) @ zero_zero_nat) @ E))) @ D))))),bind(B, $thf(^ [D:nat]: (sk15 @ (^ [E:nat]: (ord_less_nat @ (times_times_nat @ (F @ D @ E) @ zero_zero_nat) @ E)))))]])).
239.52/52.83	thf(16970,plain,(! [A:(nat > (nat > nat))] : ((~ (ord_less_nat @ zero_zero_nat @ (sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ (A @ B @ C) @ zero_zero_nat) @ C))) @ B))))))),inference(simp,[status(thm)],[16899])).
239.52/52.83	thf(17678,plain,(! [A:(nat > (nat > nat))] : ((~ (~ ((sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ (A @ B @ C) @ zero_zero_nat) @ C))) @ B))) = zero_zero_nat))))),inference(rewrite,[status(thm)],[16970,682])).
239.52/52.83	thf(17679,plain,(! [A:(nat > (nat > nat))] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ (A @ B @ C) @ zero_zero_nat) @ C))) @ B))) = zero_zero_nat))),inference(simp,[status(thm)],[17678])).
239.52/52.83	thf(17680,plain,(! [A:(nat > (nat > nat))] : (((sk15 @ (^ [B:nat]: (ord_less_nat @ (sk15 @ (^ [C:nat]: (ord_less_nat @ (times_times_nat @ (A @ B @ C) @ zero_zero_nat) @ C))) @ B))) = zero_zero_nat))),inference(lifteq,[status(thm)],[17679])).
239.52/52.83	thf(168,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_176_nat__mult__less__cancel__disj)).
239.52/52.83	thf(850,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)],[168])).
239.52/52.83	thf(74,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_8_atMost__iff)).
239.52/52.83	thf(501,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)],[74])).
239.52/52.83	thf(36,axiom,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_ord__eq__less__trans)).
239.52/52.83	thf(369,plain,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
239.52/52.83	thf(164,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_not__gr__zero)).
239.52/52.83	thf(839,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
239.52/52.83	thf(126,axiom,((! [A:nat]: ((A = zero_zero_nat) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_bot__nat__0_Oextremum__uniqueI)).
239.52/52.83	thf(691,plain,((! [A:nat]: ((A = zero_zero_nat) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
239.52/52.83	thf(5626,plain,((sk90 != zero_zero_nat) | (sk112 != one_one_nat) | ((p @ sk113) != (p @ one_one_nat))),inference(paramod_ordered,[status(thm)],[1451,5610])).
239.52/52.83	thf(5645,plain,((sk90 != zero_zero_nat) | (sk112 != one_one_nat) | (sk113 != one_one_nat)),inference(simp,[status(thm)],[5626])).
239.52/52.83	thf(175,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_order_Ostrict__implies__order)).
239.52/52.83	thf(871,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
239.52/52.83	thf(194,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((A = C) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_mult__cancel__right)).
239.52/52.83	thf(940,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((A = C) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
239.52/52.83	thf(15411,plain,(! [C:set_nat,B:set_nat,A:set_nat] : ((ord_less_eq_nat_o @ (^ [D:nat]: (member_nat @ D @ B)) @ (^ [D:nat]: (member_nat @ D @ C))) | ((ord_less_eq_set_nat @ A @ A) != (ord_less_eq_set_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[271,404])).
239.52/52.83	thf(15412,plain,(! [A:set_nat] : ((ord_less_eq_nat_o @ (^ [B:nat]: (member_nat @ B @ A)) @ (^ [B:nat]: (member_nat @ B @ A))))),inference(pattern_uni,[status(thm)],[15411:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(A))]])).
239.52/52.83	thf(213,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => (((ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat) <= (ord_less_eq_nat @ B @ one_one_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_mult__le__one)).
239.52/52.83	thf(1009,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat) | ~ (ord_less_eq_nat @ B @ one_one_nat) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
239.52/52.83	thf(190,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_bounded__Max__nat)).
239.52/52.83	thf(923,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)],[190])).
239.52/52.83	thf(84,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_set_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))) <= ((C @ B) = D)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_ord__le__eq__subst)).
239.52/52.83	thf(543,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_set_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
239.52/52.83	thf(676,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]: (((ord_less_eq_nat @ one_one_nat @ C) & (ord_less_eq_nat @ C @ B)) | ((A @ C) = zero_zero_nat)))))),inference(lifteq,[status(thm)],[675])).
239.52/52.83	thf(73,axiom,((! [A:set_nat,B:set_nat,C:(nat > $o),D:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (collect_nat @ (^ [E:nat]: ((member_nat @ E @ A) & (C @ E)))) @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ B))))) <= (! [E:nat]: ((member_nat @ E @ A) => ((C @ E) => (D @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_subset__CollectI)).
239.52/52.83	thf(496,plain,((! [A:set_nat,B:set_nat,C:(nat > $o),D:(nat > $o)]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (collect_nat @ (^ [E:nat]: ((member_nat @ E @ A) & (C @ E)))) @ (collect_nat @ (^ [E:nat]: ((D @ E) & (member_nat @ E @ B))))) | ~ (! [E:nat]: ((member_nat @ E @ A) => ((C @ E) => (D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
239.52/52.83	thf(361,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((~ (A = (B @ C))) | (~ (ord_less_nat @ C @ D)) | (ord_less_nat @ A @ (B @ D)) | (ord_less_nat @ (sk11 @ D @ C @ (B) @ A) @ (sk12 @ D @ C @ (B) @ A)))),inference(cnf,[status(esa)],[360])).
239.52/52.83	thf(363,plain,(! [D:nat,C:nat,B:(nat > nat),A:nat] : ((A != (B @ C)) | (~ (ord_less_nat @ C @ D)) | (ord_less_nat @ A @ (B @ D)) | (ord_less_nat @ (sk11 @ D @ C @ (B) @ A) @ (sk12 @ D @ C @ (B) @ A)))),inference(lifteq,[status(thm)],[361])).
239.52/52.83	thf(364,plain,(! [C:nat,B:nat,A:(nat > nat)] : ((~ (ord_less_nat @ B @ C)) | (ord_less_nat @ (A @ B) @ (A @ C)) | (ord_less_nat @ (sk11 @ C @ B @ (A) @ (A @ B)) @ (sk12 @ C @ B @ (A) @ (A @ B))))),inference(simp,[status(thm)],[363])).
239.52/52.83	thf(132,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_le0)).
239.52/52.83	thf(708,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
239.52/52.83	thf(179,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_dual__order_Otrans)).
239.52/52.83	thf(882,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
239.52/52.83	thf(33169,plain,($false),inference(e,[status(thm)],[1411,347,518,468,1110,628,249,893,1840,408,582,1005,1596,683,2395,1073,873,247,511,677,1426,385,384,10358,4220,797,472,16804,1988,670,13736,1310,404,5123,288,5903,17053,885,1046,301,2082,504,934,1132,949,460,1055,724,3195,570,917,751,17852,853,14455,969,284,325,5829,289,316,376,623,253,14547,514,937,353,475,3322,1040,6895,485,1136,1020,574,2017,480,280,634,866,396,411,1405,2154,507,602,981,766,1104,265,307,292,920,380,661,793,1306,3318,366,2000,5122,439,2910,529,10742,9041,714,894,14943,1174,16386,392,297,424,630,429,815,729,1387,1900,910,5611,1091,260,349,16072,566,879,435,329,665,583,757,682,710,842,324,1012,916,7308,1032,252,22754,5201,551,1128,519,15156,5615,980,388,356,15930,989,697,1089,1772,2990,610,1755,5233,1118,256,5830,1028,339,526,637,679,706,686,476,1114,997,1451,2153,1002,1429,605,1759,792,1241,2076,558,3508,5126,794,2909,16548,311,398,1035,1754,573,689,444,694,402,732,772,743,2398,281,259,904,14974,2393,286,577,5612,579,291,391,445,382,572,1090,804,350,1058,1107,604,2079,900,274,22786,377,271,863,784,1117,245,5610,1771,737,1043,434,477,387,494,631,758,816,9275,726,20298,483,626,769,943,668,330,462,1112,367,552,848,700,983,2401,636,1015,1113,299,267,431,653,658,1066,278,868,394,986,306,473,722,1304,1758,680,374,255,1081,617,342,1018,754,553,836,1049,490,675,648,487,776,640,1070,1743,954,1267,557,1770,580,855,2397,1025,3507,673,331,717,15556,5203,1830,338,951,359,10739,643,1038,585,5948,1235,1085,470,7009,7319,907,16206,336,1849,703,1141,613,5613,1052,7303,446,876,1094,978,845,1839,11123,9192,1913,18061,524,368,250,465,17553,627,556,7764,931,22728,588,813,517,319,6893,390,418,995,2394,946,1101,2081,11210,433,2066,1077,8793,272,14700,5194,9542,287,1133,300,432,410,1097,5232,818,405,854,422,1757,865,735,999,620,305,294,341,897,400,696,720,3506,10355,283,268,5290,358,807,740,5204,860,992,17680,850,442,501,369,395,839,277,691,5645,871,254,322,486,940,15412,1009,923,543,676,496,364,708,882,639,15764])).
239.52/52.83	% SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
239.52/52.83	% [INFO] 	 Killing All external provers ... 
239.52/52.83	WARNING: TreeLimitedRun lost 16.21s, total lost is 16.21s
239.52/52.83	WARNING: TreeLimitedRun lost 47.88s, total lost is 64.09s
239.52/52.83	FINAL WATCH: 168.0 CPU 47.6 WC
239.52/52.83	Killed 3 orphans
239.52/52.83	Killed 2 orphans
239.52/52.83	EOF