0.00/0.00 % Leo-III: Strategy 1 (for '60') 137.10/30.45 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 137.10/30.45 % [INFO] Parsing done (230ms). 137.10/30.45 % [INFO] Running in sequential loop mode. 137.10/30.45 % [CONFIG] Using configuration: timeout(60) with strategy 137.10/30.45 % [INFO] eprover registered as external prover. 137.10/30.45 % [INFO] cvc4 registered as external prover. 137.10/30.45 % [INFO] Parsing finished. Scanning for conjecture ... 137.10/30.45 % [INFO] Found a conjecture and 254 axioms. Running axiom selection ... 137.10/30.45 % [INFO] Axiom selection finished. Selected 254 axioms (removed 0 axioms). 137.10/30.45 % [INFO] Problem is higher-order (TPTP THF). 137.10/30.45 % [INFO] Type checking passed. Searching for refutation ... 137.10/30.45 % External prover 'cvc4' found a proof! 137.10/30.45 % [INFO] Killing All external provers ... 137.10/30.45 % Time passed: 25967ms (effective reasoning time: 25367ms) 137.10/30.45 % Solved by strategy 137.10/30.45 % Axioms used in derivation (254): fact_28_ord__eq__le__trans, fact_73_ord__less__eq__subst, fact_186_nat__induct__at__least, fact_32_order_Otrans, fact_151_minf_I3_J, fact_217_Suc__le__lessD, fact_207_Suc__lessD, fact_5_nth__equalityI, fact_228_Suc__diff__diff, fact_120_order__less__le__subst1, fact_208_Nat_OlessE, fact_27_ord__le__eq__trans, fact_135_greater__le__neq__conv, fact_127_list__strict__asc__trans__le, fact_31_le__cases3, fact_46_linorder__less__wlog, fact_216_le__less__Suc__eq, fact_30_antisym__conv, fact_105_order_Ostrict__trans2, fact_18_le__neq__implies__less, fact_232_list__ex__rev, fact_34_eq__refl, fact_79_less__not__refl3, fact_177_length__rev, fact_249_diff__le__mono, fact_90_size__neq__size__imp__neq, fact_175_Suc__le__mono, fact_133_complete__interval, fact_35_linear, fact_128_list__asc__trans__le, fact_194_less__Suc__induct, fact_235_zero__induct__lemma, fact_20_dual__order_Oantisym, fact_39_ord__eq__le__subst, fact_124_le__less, fact_54_antisym__conv3, fact_17_less__or__eq__imp__le, fact_38_ord__le__eq__subst, fact_223_nat__induct_H, fact_146_pinf_I4_J, fact_82_nat__neq__iff, fact_59_ord__less__eq__trans, fact_121_order__le__less__subst2, fact_92_neq__if__length__neq, fact_190_rev__swap, fact_191_rev__swap, fact_55_less__induct, fact_247_le__diff__iff_H, fact_140_minf_I8_J, fact_21_dual__order_Oeq__iff, fact_167_nat_Oinject, fact_68_neq__iff, fact_174_lessI, fact_203_less__SucI, fact_215_less__Suc__eq__le, fact_132_nat__descend__induct, fact_188_n__not__Suc__n, fact_204_less__SucE, fact_138_list__strict__desc__imp__list__desc, fact_180_le__SucI, fact_226_list__ex__length, fact_141_minf_I6_J, fact_99_dual__order_Oorder__iff__strict, fact_83_Nat_Oex__has__greatest__nat, fact_16_le__eq__less__or__eq, fact_63_less__trans, fact_111_less__le__trans, fact_101_dual__order_Ostrict__trans2, fact_91_neq__if__length__neq, fact_48_less__imp__not__less, fact_69_neqE, fact_210_lift__Suc__mono__less, fact_72_order__less__subst1, fact_130_list__strict__asc__trans, fact_87_le__trans, fact_187_transitive__stepwise__le, fact_66_less__imp__neq, fact_71_order__less__subst2, fact_206_Suc__lessE, fact_161_verit__comp__simplify1_I1_J, fact_150_minf_I2_J, fact_95_list__desc__trans, fact_182_le__Suc__eq, fact_77_nat__less__induct, fact_200_not__less__eq, fact_227_list__ex__length, fact_40_order__subst2, fact_196_Suc__less__SucD, fact_144_pinf_I2_J, fact_164_sorted__rev__iff__nth__mono, fact_205_Suc__lessI, fact_139_ge__less__neq__conv, fact_195_less__trans__Suc, fact_213_le__imp__less__Suc, fact_184_not__less__eq__eq, fact_102_dual__order_Ostrict__trans1, fact_96_order_Onot__eq__order__implies__strict, fact_43_order_Ostrict__implies__not__eq, fact_94_Ex__list__of__length, fact_110_le__less__linear, fact_173_Suc__mono, fact_230_diff__diff__cancel, fact_23_linorder__wlog, fact_153_minf_I5_J, fact_58_dual__order_Oasym, fact_221_Suc__leI, fact_159_list__ord__le__sorted__eq, fact_171_rev__rev__ident, fact_4_nth__equalityI, fact_149_minf_I1_J, fact_13_length__induct, fact_41_order__subst1, fact_219_dec__induct, fact_88_le__refl, fact_50_dual__order_Oirrefl, fact_115_antisym__conv1, fact_109_le__imp__less__or__eq, fact_45_dual__order_Ostrict__trans, fact_75_linorder__neqE__nat, fact_214_less__eq__Suc__le, fact_224_rev__nth, fact_14_nat__less__le, fact_168_rev__is__rev__conv, fact_143_pinf_I1_J, fact_24_dual__order_Orefl, fact_9_list__eq__iff__nth__eq, fact_42_dual__order_Ostrict__implies__not__eq, fact_129_list__strict__desc__trans, fact_198_Suc__less__eq2, fact_165_sorted__iff__nth__Suc, fact_233_i__append__nth2, fact_236_less__diff__imp__less, fact_160_verit__la__disequality, fact_170_rev__rev__ident, fact_242_nat__diff__right__cancel__less, fact_116_le__neq__trans, fact_246_diff__le__mono2, fact_225_rev__nth, fact_162_sorted__iff__nth__mono__less, fact_53_less__imp__not__eq2, fact_229_diff__Suc__Suc, fact_163_sorted__rev__nth__mono, fact_179_le__SucE, fact_202_Ex__less__Suc, fact_52_less__imp__triv, fact_19_less__mono__imp__le__mono, fact_62_less__linear, fact_234_i__append__nth2, fact_222_sorted__rev__iff__nth__Suc, fact_47_exists__least__iff, fact_178_Suc__leD, fact_237_nat__diff__left__cancel__eq1, fact_239_nat__diff__left__cancel__less, fact_107_not__le__imp__less, fact_251_le__diff__iff, fact_189_Suc__inject, fact_152_minf_I4_J, fact_11_list__desc__trans__le, fact_12_length__induct, fact_114_antisym__conv2, fact_193_strict__inc__induct, fact_10_order__refl, fact_74_ord__eq__less__subst, fact_37_eq__iff, fact_56_less__not__sym, fact_218_inc__induct, fact_113_less__imp__le, fact_245_diff__commute, fact_211_lift__Suc__antimono__le, fact_93_Ex__list__of__length, fact_97_dual__order_Ostrict__implies__order, fact_185_full__nat__induct, fact_1_i__append__eq__i__append__conv, fact_250_Nat_Odiff__diff__eq, fact_166_old_Onat_Oinject, fact_123_less__le, fact_201_less__Suc__eq, fact_26_order__class_Oorder_Oantisym, fact_78_less__irrefl__nat, fact_119_order__less__le__subst2, fact_60_ord__eq__less__trans, fact_241_nat__diff__right__cancel__eq2, fact_231_list__ex__rev, fact_89_size__neq__size__imp__neq, fact_243_diff__less__mono2, fact_137_list__strict__asc__imp__list__asc, fact_80_less__not__refl2, fact_64_less__asym_H, fact_240_nat__diff__right__cancel__eq1, fact_22_dual__order_Otrans, conj_1, fact_2_i__append__nth1, fact_209_lift__Suc__mono__less__iff, fact_145_pinf_I3_J, fact_126_leD, fact_6_Skolem__list__nth, fact_3_i__append__nth1, fact_125_leI, fact_181_Suc__le__D, fact_70_gt__ex, fact_112_le__less__trans, fact_248_diff__le__self, fact_156_verit__comp__simplify1_I3_J, fact_108_less__le__not__le, fact_106_order_Ostrict__trans1, fact_100_order_Ostrict__implies__order, fact_147_pinf_I5_J, fact_85_le__antisym, fact_25_order__trans, fact_134_le__greater__neq__conv, fact_49_order_Ostrict__trans, fact_67_order_Oasym, fact_122_order__le__less__subst1, fact_169_rev__is__rev__conv, fact_197_less__antisym, fact_142_pinf_I8_J, fact_148_pinf_I7_J, fact_8_list__eq__iff__nth__eq, fact_15_less__imp__le__nat, fact_172_Suc__less__eq, fact_44_not__less__iff__gr__or__eq, fact_36_antisym, fact_86_eq__imp__le, fact_7_Skolem__list__nth, fact_51_linorder__cases, fact_104_order_Oorder__iff__strict, fact_65_less__asym, fact_212_lift__Suc__mono__le, fact_117_not__less, fact_192_not__less__less__Suc__eq, fact_155_pinf_I6_J, fact_103_order_Ostrict__iff__order, fact_81_less__not__refl, fact_136_less__ge__neq__conv, conj_0, fact_131_list__asc__trans, fact_0_i__append__eq__i__append__conv, fact_76_infinite__descent, fact_57_less__imp__not__eq, fact_61_less__irrefl, fact_199_All__less__Suc, fact_238_nat__diff__left__cancel__eq2, fact_154_minf_I7_J, fact_84_nat__le__linear, fact_118_not__le, fact_157_sorted__iff__nth__mono, fact_183_Suc__n__not__le__n, fact_220_Suc__le__eq, fact_98_dual__order_Ostrict__iff__order, fact_176_length__rev, fact_33_le__cases, fact_244_less__imp__diff__less, fact_29_order__class_Oorder_Oeq__iff, fact_158_sorted__nth__mono 137.10/30.45 % No. of inferences in proof: 566 137.10/30.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 25967 ms resp. 25367 ms w/o parsing 137.10/30.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 137.10/30.45 thf(list_nat_type, type, list_nat: $tType). 137.10/30.45 thf(list_a_type, type, list_a: $tType). 137.10/30.45 thf(nat_type, type, nat: $tType). 137.10/30.45 thf(a_type, type, a: $tType). 137.10/30.45 thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))). 137.10/30.45 thf(list_asc_nat_type, type, list_asc_nat: (list_nat > $o)). 137.10/30.45 thf(list_desc_nat_type, type, list_desc_nat: (list_nat > $o)). 137.10/30.45 thf(list_strict_asc_nat_type, type, list_strict_asc_nat: (list_nat > $o)). 137.10/30.45 thf(list_strict_desc_nat_type, type, list_strict_desc_nat: (list_nat > $o)). 137.10/30.45 thf(listIn923761578nd_nat_type, type, listIn923761578nd_nat: (list_nat > ((nat > nat) > (nat > nat)))). 137.10/30.45 thf(listIn1312259492pend_a_type, type, listIn1312259492pend_a: (list_a > ((nat > a) > (nat > a)))). 137.10/30.45 thf(linorder_sorted_nat_type, type, linorder_sorted_nat: (list_nat > $o)). 137.10/30.45 thf(list_ex_nat_type, type, list_ex_nat: ((nat > $o) > (list_nat > $o))). 137.10/30.45 thf(list_ex_a_type, type, list_ex_a: ((a > $o) > (list_a > $o))). 137.10/30.45 thf(nth_nat_type, type, nth_nat: (list_nat > (nat > nat))). 137.10/30.45 thf(nth_a_type, type, nth_a: (list_a > (nat > a))). 137.10/30.45 thf(rev_nat_type, type, rev_nat: (list_nat > list_nat)). 137.10/30.45 thf(rev_a_type, type, rev_a: (list_a > list_a)). 137.10/30.45 thf(suc_type, type, suc: (nat > nat)). 137.10/30.45 thf(size_size_list_nat_type, type, size_size_list_nat: (list_nat > nat)). 137.10/30.45 thf(size_size_list_a_type, type, size_size_list_a: (list_a > nat)). 137.10/30.45 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 137.10/30.45 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 137.10/30.45 thf(f_type, type, f: (nat > a)). 137.10/30.45 thf(g_type, type, g: (nat > a)). 137.10/30.45 thf(xs_type, type, xs: list_a). 137.10/30.45 thf(ys_type, type, ys: list_a). 137.10/30.45 thf(sk1_type, type, sk1: nat). 137.10/30.45 thf(sk2_type, type, sk2: (nat > ((nat > nat) > (nat > (nat > nat))))). 137.10/30.45 thf(sk3_type, type, sk3: (nat > ((nat > nat) > (nat > (nat > nat))))). 137.10/30.45 thf(159,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_dual__order_Oasym)). 137.10/30.45 thf(809,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 137.10/30.45 thf(228,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_le__imp__less__Suc)). 137.10/30.45 thf(1105,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 137.10/30.45 thf(27,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((A = (suc @ B)) <= (~ (ord_less_eq_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_le__SucE)). 137.10/30.45 thf(347,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((A = (suc @ B)) | (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 137.10/30.45 thf(222,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_le__less)). 137.10/30.45 thf(1063,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 137.10/30.45 thf(1064,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(lifteq,[status(thm)],[1063])). 137.10/30.45 thf(83,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_order_Oorder__iff__strict)). 137.10/30.45 thf(575,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 137.10/30.45 thf(576,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(lifteq,[status(thm)],[575])). 137.10/30.45 thf(1233,plain,(((^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(rewrite,[status(thm)],[1064,576])). 137.10/30.45 thf(212,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_dual__order_Oorder__iff__strict)). 137.10/30.45 thf(1021,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 137.10/30.45 thf(1022,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B))))),inference(lifteq,[status(thm)],[1021])). 137.10/30.45 thf(1230,plain,(((^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))) = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B))))),inference(rewrite,[status(thm)],[1022,576])). 137.10/30.45 thf(1236,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B)))) | ((^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))) != (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(paramod_ordered,[status(thm)],[1233,1230])). 137.10/30.45 thf(1237,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (^ [A:nat,B:nat]: ((B = A) | (ord_less_nat @ A @ B))))),inference(pattern_uni,[status(thm)],[1236:[]])). 137.10/30.45 thf(147,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_order__le__less__subst2)). 137.10/30.45 thf(777,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 137.10/30.45 thf(113,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_dual__order_Ostrict__trans2)). 137.10/30.45 thf(666,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 137.10/30.45 thf(58,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => (((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_order__subst1)). 137.10/30.45 thf(481,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 137.10/30.45 thf(216,axiom,((list_asc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)) <= (ord_less_eq_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_list__asc__trans__le)). 137.10/30.45 thf(1031,plain,(((list_asc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)) | ~ (ord_less_eq_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 137.10/30.45 thf(23,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_le__diff__iff_H)). 137.10/30.45 thf(333,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 137.10/30.45 thf(101,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_not__less__eq)). 137.10/30.45 thf(628,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 137.10/30.45 thf(224,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_Suc__less__eq2)). 137.10/30.45 thf(1068,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 137.10/30.45 thf(15,axiom,((! [A:list_a,B:list_a]: (((rev_a @ A) = (rev_a @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_rev__is__rev__conv)). 137.10/30.45 thf(308,plain,((! [A:list_a,B:list_a]: (((rev_a @ A) = (rev_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 137.10/30.45 thf(226,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => (((~ (C @ B)) => (? [D:nat]: ((ord_less_eq_nat @ D @ B) & ! [E:nat]: ((! [F:nat]: (((ord_less_nat @ F @ E) & (ord_less_eq_nat @ A @ F)) => (C @ F))) => (ord_less_eq_nat @ E @ D)) & ! [E:nat]: ((C @ E) <= ((ord_less_eq_nat @ A @ E) & (ord_less_nat @ E @ D))) & (ord_less_eq_nat @ A @ D)))) <= (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_complete__interval)). 137.10/30.45 thf(1073,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => (((~ (C @ B)) => (? [D:nat]: ((ord_less_eq_nat @ D @ B) & ! [E:nat]: ((! [F:nat]: (((ord_less_nat @ F @ E) & (ord_less_eq_nat @ A @ F)) => (C @ F))) => (ord_less_eq_nat @ E @ D)) & ! [E:nat]: ((C @ E) | ~ ((ord_less_eq_nat @ A @ E) & (ord_less_nat @ E @ D))) & (ord_less_eq_nat @ A @ D)))) | ~ (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 137.10/30.45 thf(175,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_106_order_Ostrict__trans1)). 137.10/30.45 thf(873,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)],[175])). 137.10/30.45 thf(6,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq_nat @ A @ B) => (((! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))) <= (! [D:nat]: (C @ D @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_transitive__stepwise__le)). 137.10/30.45 thf(269,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq_nat @ A @ B) => (((! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))) | ~ (! [D:nat]: (C @ D @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 137.10/30.45 thf(219,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ B) => ((! [D:nat]: ((((C @ (suc @ D)) => (C @ D)) <= (ord_less_nat @ D @ B)) <= (ord_less_eq_nat @ A @ D))) => (C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_inc__induct)). 137.10/30.45 thf(1041,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ B) => ((! [D:nat]: (((C @ (suc @ D)) => (C @ D)) | ~ (ord_less_nat @ D @ B) | ~ (ord_less_eq_nat @ A @ D))) => (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 137.10/30.45 thf(67,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_nat_Oinject)). 137.10/30.45 thf(523,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 137.10/30.45 thf(243,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_less__SucI)). 137.10/30.45 thf(1158,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 137.10/30.45 thf(85,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__imp__not__eq)). 137.10/30.45 thf(582,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 137.10/30.45 thf(34,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_eq__imp__le)). 137.10/30.45 thf(384,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 137.10/30.45 thf(246,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ A) @ B) <= ((suc @ A) != B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_Suc__lessI)). 137.10/30.45 thf(1164,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) | ((suc @ A) = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 137.10/30.45 thf(137,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_dual__order_Ostrict__implies__not__eq)). 137.10/30.45 thf(747,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 137.10/30.45 thf(25,axiom,((! [A:list_nat,B:list_nat]: (((rev_nat @ A) = B) = (A = (rev_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_rev__swap)). 137.10/30.45 thf(340,plain,((! [A:list_nat,B:list_nat]: (((rev_nat @ A) = B) = (A = (rev_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 137.10/30.45 thf(161,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_less__trans__Suc)). 137.10/30.45 thf(829,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 137.10/30.45 thf(165,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_less__eq__Suc__le)). 137.10/30.45 thf(840,plain,(((ord_less_nat) = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 137.10/30.45 thf(841,plain,(((^ [A:nat]: (ord_less_eq_nat @ (suc @ A))) = (ord_less_nat))),inference(lifteq,[status(thm)],[840])). 137.10/30.45 thf(20,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_85_le__antisym)). 137.10/30.45 thf(320,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)],[20])). 137.10/30.45 thf(47,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_diff__le__mono)). 137.10/30.45 thf(436,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 137.10/30.45 thf(1,conjecture,((! [A:nat]: (~ (ord_less_nat @ A @ (size_size_list_a @ xs)) | ((nth_a @ xs @ A) = (nth_a @ ys @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)). 137.10/30.45 thf(2,negated_conjecture,((~ (! [A:nat]: (~ (ord_less_nat @ A @ (size_size_list_a @ xs)) | ((nth_a @ xs @ A) = (nth_a @ ys @ A)))))),inference(neg_conjecture,[status(cth)],[1])). 137.10/30.45 thf(257,plain,((~ (! [A:nat]: (~ (ord_less_nat @ A @ (size_size_list_a @ xs)) | ((nth_a @ xs @ A) = (nth_a @ ys @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 137.10/30.45 thf(132,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => (((ord_less_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F))))) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_order__less__subst1)). 137.10/30.45 thf(724,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 137.10/30.45 thf(149,axiom,((! [A:nat]: ((listIn1312259492pend_a @ xs @ f @ A) = (listIn1312259492pend_a @ ys @ g @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 137.10/30.45 thf(785,plain,((! [A:nat]: ((listIn1312259492pend_a @ xs @ (f) @ A) = (listIn1312259492pend_a @ ys @ (g) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 137.10/30.45 thf(259,plain,((ord_less_nat @ sk1 @ (size_size_list_a @ xs))),inference(cnf,[status(esa)],[257])). 137.10/30.45 thf(583,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (~ (A = B)))),inference(cnf,[status(esa)],[582])). 137.10/30.45 thf(584,plain,(! [B:nat,A:nat] : ((A != B) | (~ (ord_less_nat @ A @ B)))),inference(lifteq,[status(thm)],[583])). 137.10/30.45 thf(585,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ A)))),inference(simp,[status(thm)],[584])). 137.10/30.45 thf(1262,plain,(! [A:nat] : (((ord_less_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_nat @ A @ A)))),inference(paramod_ordered,[status(thm)],[259,585])). 137.10/30.45 thf(1263,plain,(! [A:nat] : ((sk1 != A) | ((size_size_list_a @ xs) != A))),inference(simp,[status(thm)],[1262])). 137.10/30.45 thf(1264,plain,(((size_size_list_a @ xs) != sk1)),inference(simp,[status(thm)],[1263])). 137.10/30.45 thf(156,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ A @ C)) => ((ord_less_nat @ B @ A) => (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_nat__diff__left__cancel__eq1)). 137.10/30.45 thf(802,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ A @ C)) => ((ord_less_nat @ B @ A) => (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 137.10/30.45 thf(220,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_dual__order_Ostrict__implies__order)). 137.10/30.45 thf(1059,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 137.10/30.45 thf(55,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_le__diff__iff)). 137.10/30.45 thf(460,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 137.10/30.45 thf(86,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((A != C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_less__ge__neq__conv)). 137.10/30.45 thf(586,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: (~ (A = C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 137.10/30.45 thf(587,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: (~ (A = C) | ~ (ord_less_eq_nat @ B @ C))))),inference(lifteq,[status(thm)],[586])). 137.10/30.45 thf(164,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_less__not__sym)). 137.10/30.45 thf(838,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 137.10/30.45 thf(186,axiom,(((= @ list_a) = (^ [A:list_a,B:list_a]: (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ A)) => ((nth_a @ A @ C) = (nth_a @ B @ C))) & ((size_size_list_a @ A) = (size_size_list_a @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_list__eq__iff__nth__eq)). 137.10/30.45 thf(917,plain,(((= @ list_a) = (^ [A:list_a,B:list_a]: (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ A)) => ((nth_a @ A @ C) = (nth_a @ B @ C))) & ((size_size_list_a @ A) = (size_size_list_a @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 137.10/30.45 thf(125,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_minf_I5_J)). 137.10/30.45 thf(702,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 137.10/30.45 thf(138,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_order_Ostrict__implies__not__eq)). 137.10/30.45 thf(751,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 137.10/30.45 thf(78,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_not__less__eq__eq)). 137.10/30.45 thf(559,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 137.10/30.45 thf(105,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_less__le)). 137.10/30.45 thf(638,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 137.10/30.45 thf(144,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_order_Ostrict__implies__order)). 137.10/30.45 thf(770,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 137.10/30.45 thf(9,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_ord__eq__le__trans)). 137.10/30.45 thf(289,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 137.10/30.45 thf(18,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_84_nat__le__linear)). 137.10/30.45 thf(316,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)],[18])). 137.10/30.45 thf(227,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((~ (! [C:nat]: ((B != (suc @ C)) <= (ord_less_nat @ A @ C)))) <= (B != (suc @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_Nat_OlessE)). 137.10/30.45 thf(1100,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: (~ (B = (suc @ C)) | ~ (ord_less_nat @ A @ C))) | (B = (suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 137.10/30.45 thf(3,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_order__subst2)). 137.10/30.45 thf(261,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 137.10/30.45 thf(88,axiom,((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)). 137.10/30.45 thf(591,plain,((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 137.10/30.45 thf(230,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_62_less__linear)). 137.10/30.45 thf(1109,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)],[230])). 137.10/30.45 thf(108,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ord__less__eq__subst)). 137.10/30.45 thf(646,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 137.10/30.45 thf(59,axiom,((! [A:(nat > $o),B:list_nat]: ((list_ex_nat @ A @ (rev_nat @ B)) = (list_ex_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_list__ex__rev)). 137.10/30.45 thf(485,plain,((! [A:(nat > $o),B:list_nat]: ((list_ex_nat @ (A) @ (rev_nat @ B)) = (list_ex_nat @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 137.10/30.45 thf(198,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_47_exists__least__iff)). 137.10/30.45 thf(965,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)],[198])). 137.10/30.45 thf(966,plain,(((^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: (~ (A @ C) | ~ (ord_less_nat @ C @ B)) & (A @ B))) = ('?' @ nat))),inference(lifteq,[status(thm)],[965])). 137.10/30.45 thf(253,axiom,((list_ex_nat = (^ [A:(nat > $o),B:list_nat]: ? [C:nat]: ((A @ (nth_nat @ B @ C)) & (ord_less_nat @ C @ (size_size_list_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_list__ex__length)). 137.10/30.45 thf(1182,plain,(((list_ex_nat) = (^ [A:(nat > $o),B:list_nat]: ? [C:nat]: ((A @ (nth_nat @ B @ C)) & (ord_less_nat @ C @ (size_size_list_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 137.10/30.45 thf(1183,plain,(((list_ex_nat) = (^ [A:(nat > $o),B:list_nat]: ? [C:nat]: ((A @ (nth_nat @ B @ C)) & (ord_less_nat @ C @ (size_size_list_nat @ B)))))),inference(lifteq,[status(thm)],[1182])). 137.10/30.45 thf(181,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_less__irrefl__nat)). 137.10/30.45 thf(905,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 137.10/30.45 thf(241,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_Suc__lessD)). 137.10/30.45 thf(1151,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 137.10/30.45 thf(193,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) <= (ord_less_nat @ F @ E))) => ((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ F @ E))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_minf_I2_J)). 137.10/30.45 thf(937,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) | ~ (ord_less_nat @ F @ E))) => ((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ F @ E))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 137.10/30.45 thf(120,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_pinf_I5_J)). 137.10/30.45 thf(687,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 137.10/30.45 thf(122,axiom,((! [A:nat,B:list_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((nth_nat @ (rev_nat @ B) @ A) = (nth_nat @ B @ (minus_minus_nat @ (size_size_list_nat @ B) @ (suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_rev__nth)). 137.10/30.45 thf(692,plain,((! [A:nat,B:list_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((nth_nat @ (rev_nat @ B) @ A) = (nth_nat @ B @ (minus_minus_nat @ (size_size_list_nat @ B) @ (suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 137.10/30.45 thf(135,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_le__neq__trans)). 137.10/30.45 thf(734,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 137.10/30.45 thf(173,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) <= (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_diff__less__mono2)). 137.10/30.45 thf(866,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) | ~ (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 137.10/30.45 thf(38,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_old_Onat_Oinject)). 137.10/30.45 thf(396,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 137.10/30.45 thf(183,axiom,((ord_less_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_108_less__le__not__le)). 137.10/30.45 thf(910,plain,(((ord_less_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)],[183])). 137.10/30.45 thf(911,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))))),inference(lifteq,[status(thm)],[910])). 137.10/30.45 thf(639,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(lifteq,[status(thm)],[638])). 137.10/30.45 thf(1344,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[911,639])). 137.10/30.45 thf(1345,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(pattern_uni,[status(thm)],[1344:[]])). 137.10/30.45 thf(4,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_29_order__class_Oorder_Oeq__iff)). 137.10/30.45 thf(265,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)],[4])). 137.10/30.45 thf(92,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_le__less__trans)). 137.10/30.45 thf(602,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 137.10/30.45 thf(202,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_gt__ex)). 137.10/30.45 thf(981,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 137.10/30.45 thf(143,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_less__not__refl3)). 137.10/30.45 thf(766,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 137.10/30.45 thf(33,axiom,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Suc__n__not__le__n)). 137.10/30.45 thf(381,plain,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 137.10/30.45 thf(382,plain,((~ (? [A:nat]: (ord_less_eq_nat @ (suc @ A) @ A)))),inference(miniscope,[status(thm)],[381])). 137.10/30.45 thf(383,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ (suc @ A) @ A)))),inference(cnf,[status(esa)],[382])). 137.10/30.45 thf(2002,plain,(! [A:nat] : (((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ (suc @ A) @ A)))),inference(paramod_ordered,[status(thm)],[591,383])). 137.10/30.45 thf(2006,plain,(! [A:nat] : (((size_size_list_a @ xs) != (suc @ A)) | ((size_size_list_a @ ys) != A))),inference(simp,[status(thm)],[2002])). 137.10/30.45 thf(2011,plain,(((size_size_list_a @ xs) != (suc @ (size_size_list_a @ ys)))),inference(simp,[status(thm)],[2006])). 137.10/30.45 thf(48,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_order__trans)). 137.10/30.45 thf(439,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 137.10/30.45 thf(69,axiom,((list_asc_nat = linorder_sorted_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_list__ord__le__sorted__eq)). 137.10/30.45 thf(529,plain,(((list_asc_nat) = (linorder_sorted_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 137.10/30.45 thf(71,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_le__SucI)). 137.10/30.45 thf(534,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 137.10/30.45 thf(154,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_nat__less__le)). 137.10/30.45 thf(798,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 137.10/30.45 thf(242,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_17_less__or__eq__imp__le)). 137.10/30.45 thf(1153,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)],[242])). 137.10/30.45 thf(141,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_44_not__less__iff__gr__or__eq)). 137.10/30.45 thf(761,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)],[141])). 137.10/30.45 thf(177,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_order_Ostrict__iff__order)). 137.10/30.45 thf(894,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 137.10/30.45 thf(118,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (B != C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_ge__less__neq__conv)). 137.10/30.45 thf(682,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 137.10/30.45 thf(683,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))))),inference(lifteq,[status(thm)],[682])). 137.10/30.45 thf(1519,plain,(((^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))))),inference(rewrite,[status(thm)],[683,576])). 137.10/30.45 thf(91,axiom,((! [A:list_a,B:nat,C:(nat > a)]: ((ord_less_eq_nat @ (size_size_list_a @ A) @ B) => ((listIn1312259492pend_a @ A @ C @ B) = (C @ (minus_minus_nat @ B @ (size_size_list_a @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_i__append__nth2)). 137.10/30.45 thf(598,plain,((! [A:list_a,B:nat,C:(nat > a)]: ((ord_less_eq_nat @ (size_size_list_a @ A) @ B) => ((listIn1312259492pend_a @ A @ (C) @ B) = (C @ (minus_minus_nat @ B @ (size_size_list_a @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 137.10/30.45 thf(11,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_le__refl)). 137.10/30.45 thf(297,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 137.10/30.45 thf(41,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_diff__le__self)). 137.10/30.45 thf(407,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 137.10/30.45 thf(45,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C))) <= (! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_lift__Suc__mono__le)). 137.10/30.45 thf(429,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C))) | ~ (! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 137.10/30.45 thf(150,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_pinf_I8_J)). 137.10/30.45 thf(788,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 137.10/30.45 thf(258,plain,((~ ((nth_a @ xs @ sk1) = (nth_a @ ys @ sk1)))),inference(cnf,[status(esa)],[257])). 137.10/30.45 thf(260,plain,(((nth_a @ ys @ sk1) != (nth_a @ xs @ sk1))),inference(lifteq,[status(thm)],[258])). 137.10/30.45 thf(235,axiom,((! [A:nat,B:nat]: (((B = A) <= (ord_less_nat @ A @ (suc @ B))) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_less__antisym)). 137.10/30.45 thf(1123,plain,((! [A:nat,B:nat]: ((B = A) | ~ (ord_less_nat @ A @ (suc @ B)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 137.10/30.45 thf(172,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_pinf_I4_J)). 137.10/30.45 thf(862,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 137.10/30.45 thf(57,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => (((A @ C) <= (ord_less_eq_nat @ B @ C)) <= (! [D:nat]: ((ord_less_eq_nat @ B @ D) => ((A @ D) => (A @ (suc @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_nat__induct_H)). 137.10/30.45 thf(467,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (! [D:nat]: ((ord_less_eq_nat @ B @ D) => ((A @ D) => (A @ (suc @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 137.10/30.45 thf(168,axiom,((! [A:nat,B:list_nat,C:(nat > nat)]: (((listIn923761578nd_nat @ B @ C @ A) = (nth_nat @ B @ A)) <= (ord_less_nat @ A @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_i__append__nth1)). 137.10/30.45 thf(847,plain,((! [A:nat,B:list_nat,C:(nat > nat)]: (((listIn923761578nd_nat @ B @ (C) @ A) = (nth_nat @ B @ A)) | ~ (ord_less_nat @ A @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 137.10/30.45 thf(251,axiom,((list_desc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)) <= (ord_less_eq_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_list__desc__trans__le)). 137.10/30.45 thf(1178,plain,(((list_desc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)) | ~ (ord_less_eq_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 137.10/30.45 thf(75,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_Suc__diff__diff)). 137.10/30.45 thf(551,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 137.10/30.45 thf(128,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_69_neqE)). 137.10/30.45 thf(710,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)],[128])). 137.10/30.45 thf(166,axiom,((! [A:list_a]: ((size_size_list_a @ (rev_a @ A)) = (size_size_list_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_length__rev)). 137.10/30.45 thf(842,plain,((! [A:list_a]: ((size_size_list_a @ (rev_a @ A)) = (size_size_list_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 137.10/30.45 thf(255,axiom,((! [A:list_nat,B:nat,C:nat]: ((linorder_sorted_nat @ (rev_nat @ A)) => (((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B))) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_sorted__rev__nth__mono)). 137.10/30.45 thf(1195,plain,((! [A:list_nat,B:nat,C:nat]: ((linorder_sorted_nat @ (rev_nat @ A)) => (((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B))) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 137.10/30.45 thf(97,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__asym_H)). 137.10/30.45 thf(615,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 137.10/30.45 thf(35,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_dual__order_Oantisym)). 137.10/30.45 thf(388,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((B = A) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 137.10/30.45 thf(174,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_minf_I4_J)). 137.10/30.45 thf(869,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 137.10/30.45 thf(63,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((A @ (suc @ D)) => (A @ D))) => (A @ (minus_minus_nat @ B @ C))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_zero__induct__lemma)). 137.10/30.45 thf(499,plain,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((A @ (suc @ D)) => (A @ D))) => (A @ (minus_minus_nat @ B @ C))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 137.10/30.45 thf(205,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_less__imp__le)). 137.10/30.45 thf(989,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 137.10/30.45 thf(244,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (B != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_dual__order_Ostrict__iff__order)). 137.10/30.45 thf(1160,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 137.10/30.45 thf(60,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_diff__le__mono2)). 137.10/30.45 thf(488,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 137.10/30.45 thf(76,axiom,((! [A:list_nat]: ((list_strict_desc_nat @ A) => (list_desc_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_list__strict__desc__imp__list__desc)). 137.10/30.45 thf(554,plain,((! [A:list_nat]: ((list_strict_desc_nat @ A) => (list_desc_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 137.10/30.45 thf(114,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_less__not__refl2)). 137.10/30.45 thf(669,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 137.10/30.45 thf(68,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((ord_less_eq_nat @ A @ B) | (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_le__Suc__eq)). 137.10/30.45 thf(526,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((ord_less_eq_nat @ A @ B) | (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 137.10/30.45 thf(1206,plain,((ys != xs) | (sk1 != sk1)),inference(simp,[status(thm)],[260])). 137.10/30.45 thf(1207,plain,((ys != xs)),inference(simp,[status(thm)],[1206])). 137.10/30.45 thf(232,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ (A @ B) @ (A @ C)) <= (ord_less_nat @ B @ C)) <= (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_lift__Suc__mono__less)). 137.10/30.45 thf(1114,plain,((! [A:(nat > nat),B:nat,C:nat]: ((ord_less_nat @ (A @ B) @ (A @ C)) | ~ (ord_less_nat @ B @ C) | ~ (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 137.10/30.45 thf(109,axiom,((list_desc_nat = (^ [A:list_nat]: ! [B:nat]: ((! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)))) <= (ord_less_nat @ B @ (size_size_list_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_list__desc__trans)). 137.10/30.45 thf(654,plain,(((list_desc_nat) = (^ [A:list_nat]: ! [B:nat]: (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))) | ~ (ord_less_nat @ B @ (size_size_list_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 137.10/30.45 thf(208,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ C @ B)) => (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_nat__diff__right__cancel__less)). 137.10/30.45 thf(1002,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ C @ B)) => (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 137.10/30.45 thf(93,axiom,((! [A:nat]: ? [B:list_a]: ((size_size_list_a @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Ex__list__of__length)). 137.10/30.45 thf(605,plain,((! [A:nat]: ? [B:list_a]: ((size_size_list_a @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 137.10/30.45 thf(99,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) <= (ord_less_nat @ D @ E))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_less__mono__imp__le__mono)). 137.10/30.45 thf(622,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) | ~ (ord_less_nat @ D @ E))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 137.10/30.45 thf(163,axiom,((list_ex_a = (^ [A:(a > $o),B:list_a]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ B)) & (A @ (nth_a @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_list__ex__length)). 137.10/30.46 thf(836,plain,(((list_ex_a) = (^ [A:(a > $o),B:list_a]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ B)) & (A @ (nth_a @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 137.10/30.46 thf(837,plain,(((list_ex_a) = (^ [A:(a > $o),B:list_a]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ B)) & (A @ (nth_a @ B @ C)))))),inference(lifteq,[status(thm)],[836])). 137.10/30.46 thf(26,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_n__not__Suc__n)). 137.10/30.46 thf(343,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 137.10/30.46 thf(152,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 @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_order__less__subst2)). 137.10/30.46 thf(792,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 @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 137.10/30.46 thf(266,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = (= @ nat))),inference(lifteq,[status(thm)],[265])). 137.10/30.46 thf(103,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_75_linorder__neqE__nat)). 137.10/30.46 thf(633,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)],[103])). 137.10/30.46 thf(157,axiom,((linorder_sorted_nat = (^ [A:list_nat]: ! [B:nat,C:nat]: (((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_sorted__iff__nth__mono)). 137.10/30.46 thf(805,plain,(((linorder_sorted_nat) = (^ [A:list_nat]: ! [B:nat,C:nat]: (((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 137.10/30.46 thf(16,axiom,((! [A:(a > $o),B:list_a]: ((list_ex_a @ A @ (rev_a @ B)) = (list_ex_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_list__ex__rev)). 137.10/30.46 thf(311,plain,((! [A:(a > $o),B:list_a]: ((list_ex_a @ (A) @ (rev_a @ B)) = (list_ex_a @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 137.10/30.46 thf(248,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_pinf_I6_J)). 137.10/30.46 thf(1170,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 137.10/30.46 thf(225,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_less__imp__not__less)). 137.10/30.46 thf(1071,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 137.10/30.46 thf(530,plain,(((linorder_sorted_nat) = (list_asc_nat))),inference(lifteq,[status(thm)],[529])). 137.10/30.46 thf(189,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ (suc @ A)) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_le__less__Suc__eq)). 137.10/30.46 thf(926,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ (suc @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 137.10/30.46 thf(214,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_Suc__le__eq)). 137.10/30.46 thf(1026,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 137.10/30.46 thf(247,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_not__less)). 137.10/30.46 thf(1167,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 137.10/30.46 thf(298,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ A))),inference(cnf,[status(esa)],[297])). 137.10/30.46 thf(43,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_87_le__trans)). 137.10/30.46 thf(412,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)],[43])). 137.10/30.46 thf(262,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:(nat > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_less_eq_nat @ (C @ B) @ D)))))),inference(miniscope,[status(thm)],[261])). 137.10/30.46 thf(264,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ (C @ A) @ D) | (ord_less_eq_nat @ (sk2 @ D @ (C) @ B @ A) @ (sk3 @ D @ (C) @ B @ A)) | (~ (ord_less_eq_nat @ (C @ B) @ D)))),inference(cnf,[status(esa)],[262])). 137.10/30.46 thf(121,axiom,((! [A:nat,B:(nat > (a > $o))]: ((! [C:nat]: ((? [D:a]: (B @ C @ D)) <= (ord_less_nat @ C @ A))) = (? [C:list_a]: (((size_size_list_a @ C) = A) & ! [D:nat]: ((B @ D @ (nth_a @ C @ D)) <= (ord_less_nat @ D @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Skolem__list__nth)). 137.10/30.46 thf(689,plain,((! [A:nat,B:(nat > (a > $o))]: ((! [C:nat]: (? [D:a]: (B @ C @ D) | ~ (ord_less_nat @ C @ A))) = (? [C:list_a]: (((size_size_list_a @ C) = A) & ! [D:nat]: ((B @ D @ (nth_a @ C @ D)) | ~ (ord_less_nat @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 137.10/30.46 thf(65,axiom,((! [A:list_nat,B:list_nat]: ((A != B) <= ((size_size_list_nat @ A) != (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_size__neq__size__imp__neq)). 137.10/30.46 thf(513,plain,((! [A:list_nat,B:list_nat]: (~ (A = B) | ((size_size_list_nat @ A) = (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 137.10/30.46 thf(240,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_ord__eq__less__trans)). 137.10/30.46 thf(1146,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 137.10/30.46 thf(210,axiom,((! [A:list_a,B:list_a,C:(nat > a),D:(nat > a)]: ((((listIn1312259492pend_a @ A @ C) = (listIn1312259492pend_a @ B @ D)) = ((A = B) & (C = D))) <= ((size_size_list_a @ A) = (size_size_list_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_i__append__eq__i__append__conv)). 137.10/30.46 thf(1007,plain,((! [A:list_a,B:list_a,C:(nat > a),D:(nat > a)]: ((((listIn1312259492pend_a @ A @ C) = (listIn1312259492pend_a @ B @ D)) = ((A = B) & ((C) = (D)))) | ~ ((size_size_list_a @ A) = (size_size_list_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 137.10/30.46 thf(40,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_full__nat__induct)). 137.10/30.46 thf(402,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 137.10/30.46 thf(145,axiom,((! [A:nat,B:nat,C:nat]: (((A = C) <= (ord_less_nat @ B @ A)) <= ((minus_minus_nat @ A @ B) = (minus_minus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_nat__diff__right__cancel__eq1)). 137.10/30.46 thf(772,plain,((! [A:nat,B:nat,C:nat]: ((A = C) | ~ (ord_less_nat @ B @ A) | ~ ((minus_minus_nat @ A @ B) = (minus_minus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 137.10/30.46 thf(8,axiom,((! [A:list_nat,B:list_nat]: (((rev_nat @ A) = (rev_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_rev__is__rev__conv)). 137.10/30.46 thf(286,plain,((! [A:list_nat,B:list_nat]: (((rev_nat @ A) = (rev_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 137.10/30.46 thf(84,axiom,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => ((A = B) <= (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nth__equalityI)). 137.10/30.46 thf(577,plain,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => ((A = B) | ~ (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 137.10/30.46 thf(197,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_nat @ A @ B) => ((! [D:nat]: (C @ D @ (suc @ D))) => ((! [D:nat,E:nat,F:nat]: ((ord_less_nat @ D @ E) => ((((C @ E @ F) => (C @ D @ F)) <= (C @ D @ E)) <= (ord_less_nat @ E @ F)))) => (C @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_less__Suc__induct)). 137.10/30.46 thf(958,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_nat @ A @ B) => ((! [D:nat]: (C @ D @ (suc @ D))) => ((! [D:nat,E:nat,F:nat]: ((ord_less_nat @ D @ E) => (((C @ E @ F) => (C @ D @ F)) | ~ (C @ D @ E) | ~ (ord_less_nat @ E @ F)))) => (C @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 137.10/30.46 thf(79,axiom,((linorder_sorted_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ (suc @ B) @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_sorted__iff__nth__Suc)). 137.10/30.46 thf(562,plain,(((linorder_sorted_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ (suc @ B) @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 137.10/30.46 thf(200,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_less__irrefl)). 137.10/30.46 thf(975,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 137.10/30.46 thf(50,axiom,((! [A:list_nat]: ((list_asc_nat @ A) <= (list_strict_asc_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_list__strict__asc__imp__list__asc)). 137.10/30.46 thf(445,plain,((! [A:list_nat]: ((list_asc_nat @ A) | ~ (list_strict_asc_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 137.10/30.46 thf(95,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Suc__mono)). 137.10/30.46 thf(611,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 137.10/30.46 thf(129,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_not__le)). 137.10/30.46 thf(713,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 137.10/30.46 thf(229,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_minf_I6_J)). 137.10/30.46 thf(1107,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 137.10/30.46 thf(187,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))) <= (~ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_infinite__descent)). 137.10/30.46 thf(919,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)) | (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 137.10/30.46 thf(126,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_order_Ostrict__trans2)). 137.10/30.46 thf(704,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 137.10/30.46 thf(194,axiom,((! [A:list_a,B:list_a]: (((size_size_list_a @ A) != (size_size_list_a @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_neq__if__length__neq)). 137.10/30.46 thf(947,plain,((! [A:list_a,B:list_a]: ((~ ((size_size_list_a @ A) = (size_size_list_a @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 137.10/30.46 thf(28,axiom,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => ((C @ B) <= (! [D:nat]: (((C @ D) => (C @ (suc @ D))) <= (ord_less_eq_nat @ A @ D))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_nat__induct__at__least)). 137.10/30.46 thf(350,plain,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => ((C @ B) | ~ (! [D:nat]: (((C @ D) => (C @ (suc @ D))) | ~ (ord_less_eq_nat @ A @ D))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 137.10/30.46 thf(73,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C)) <= (! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_lift__Suc__antimono__le)). 137.10/30.46 thf(540,plain,((! [A:(nat > nat),B:nat,C:nat]: ((ord_less_eq_nat @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C) | ~ (! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 137.10/30.46 thf(36,axiom,((! [A:nat,B:nat]: (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A) | (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_verit__la__disequality)). 137.10/30.46 thf(391,plain,((! [A:nat,B:nat]: (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 137.10/30.46 thf(238,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) => (B != C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_greater__le__neq__conv)). 137.10/30.46 thf(1139,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) => (~ (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 137.10/30.46 thf(142,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_Suc__less__SucD)). 137.10/30.46 thf(764,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 137.10/30.46 thf(179,axiom,((! [A:list_nat,B:nat,C:nat]: ((linorder_sorted_nat @ A) => (((ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)) <= (ord_less_nat @ C @ (size_size_list_nat @ A))) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_sorted__nth__mono)). 137.10/30.46 thf(900,plain,((! [A:list_nat,B:nat,C:nat]: ((linorder_sorted_nat @ A) => ((ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)) | ~ (ord_less_nat @ C @ (size_size_list_nat @ A)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 137.10/30.46 thf(233,axiom,((! [A:list_nat]: ((linorder_sorted_nat @ (rev_nat @ A)) = (! [B:nat]: ((ord_less_eq_nat @ (nth_nat @ A @ (suc @ B)) @ (nth_nat @ A @ B)) <= (ord_less_nat @ (suc @ B) @ (size_size_list_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_sorted__rev__iff__nth__Suc)). 137.10/30.46 thf(1117,plain,((! [A:list_nat]: ((linorder_sorted_nat @ (rev_nat @ A)) = (! [B:nat]: ((ord_less_eq_nat @ (nth_nat @ A @ (suc @ B)) @ (nth_nat @ A @ B)) | ~ (ord_less_nat @ (suc @ B) @ (size_size_list_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 137.10/30.46 thf(211,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_pinf_I1_J)). 137.10/30.46 thf(1011,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 137.10/30.46 thf(151,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (A != C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_le__greater__neq__conv)). 137.10/30.46 thf(790,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 137.10/30.46 thf(791,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))))),inference(lifteq,[status(thm)],[790])). 137.10/30.46 thf(1542,plain,(((^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))))),inference(rewrite,[status(thm)],[791,576])). 137.10/30.46 thf(52,axiom,((! [A:list_nat]: ((size_size_list_nat @ (rev_nat @ A)) = (size_size_list_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_length__rev)). 137.10/30.46 thf(451,plain,((! [A:list_nat]: ((size_size_list_nat @ (rev_nat @ A)) = (size_size_list_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 137.10/30.46 thf(64,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Nat_Odiff__diff__eq)). 137.10/30.46 thf(509,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 137.10/30.46 thf(13,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_dual__order_Orefl)). 137.10/30.46 thf(303,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 137.10/30.46 thf(270,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:(nat > (nat > $o))]: (((! [D:nat,E:nat]: ((C @ D @ E) => (! [F:nat]: ((C @ E @ F) => (C @ D @ F))))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))) | ~ (! [D:nat]: (C @ D @ D))))))),inference(miniscope,[status(thm)],[269])). 137.10/30.46 thf(271,plain,(! [C:(nat > (nat > $o)),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (C @ (sk4 @ (C) @ B @ A) @ (sk5 @ (C) @ B @ A)) | (~ (C @ (sk7 @ (C) @ B @ A) @ (suc @ (sk7 @ (C) @ B @ A)))) | (C @ A @ B) | (~ (C @ (sk8 @ (C) @ B @ A) @ (sk8 @ (C) @ B @ A))))),inference(cnf,[status(esa)],[270])). 137.10/30.46 thf(250,axiom,((! [A:list_nat]: ((linorder_sorted_nat @ (rev_nat @ A)) = (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)) <= (ord_less_nat @ C @ (size_size_list_nat @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_sorted__rev__iff__nth__mono)). 137.10/30.46 thf(1175,plain,((! [A:list_nat]: ((linorder_sorted_nat @ (rev_nat @ A)) = (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)) | ~ (ord_less_nat @ C @ (size_size_list_nat @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 137.10/30.46 thf(136,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) <= (ord_less_nat @ E @ F))) <= (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ E @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_pinf_I2_J)). 137.10/30.46 thf(737,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => (? [E:nat]: ! [F:nat]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) | ~ (ord_less_nat @ E @ F)) | ~ (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 137.10/30.46 thf(19,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_order__refl)). 137.10/30.46 thf(318,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 137.10/30.46 thf(160,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => (((! [D:nat]: ((((C @ (suc @ D)) <= (C @ D)) <= (ord_less_nat @ D @ B)) <= (ord_less_eq_nat @ A @ D))) => (C @ B)) <= (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_dec__induct)). 137.10/30.46 thf(811,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => (((! [D:nat]: ((C @ (suc @ D)) | ~ (C @ D) | ~ (ord_less_nat @ D @ B) | ~ (ord_less_eq_nat @ A @ D))) => (C @ B)) | ~ (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 137.10/30.46 thf(62,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_27_ord__le__eq__trans)). 137.10/30.46 thf(494,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)],[62])). 137.10/30.46 thf(102,axiom,(((= @ list_nat) = (^ [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) & ! [C:nat]: (((nth_nat @ A @ C) = (nth_nat @ B @ C)) <= (ord_less_nat @ C @ (size_size_list_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_list__eq__iff__nth__eq)). 137.10/30.46 thf(631,plain,(((= @ list_nat) = (^ [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) & ! [C:nat]: (((nth_nat @ A @ C) = (nth_nat @ B @ C)) | ~ (ord_less_nat @ C @ (size_size_list_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 137.10/30.46 thf(140,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_verit__comp__simplify1_I1_J)). 137.10/30.46 thf(758,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 137.10/30.46 thf(21,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_ord__le__eq__subst)). 137.10/30.46 thf(323,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 137.10/30.46 thf(90,axiom,((! [A:(list_a > $o),B:list_a]: ((A @ B) <= (! [C:list_a]: ((! [D:list_a]: ((ord_less_nat @ (size_size_list_a @ D) @ (size_size_list_a @ C)) => (A @ D))) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_length__induct)). 137.10/30.46 thf(594,plain,((! [A:(list_a > $o),B:list_a]: ((A @ B) | ~ (! [C:list_a]: ((! [D:list_a]: ((ord_less_nat @ (size_size_list_a @ D) @ (size_size_list_a @ C)) => (A @ D))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 137.10/30.46 thf(245,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_leD)). 137.10/30.46 thf(1162,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 137.10/30.46 thf(215,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) <= (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_not__le__imp__less)). 137.10/30.46 thf(1029,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 137.10/30.46 thf(100,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_le__eq__less__or__eq)). 137.10/30.46 thf(626,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 137.10/30.46 thf(231,axiom,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_lessI)). 137.10/30.46 thf(1112,plain,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 137.10/30.46 thf(171,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ (C @ E) @ (C @ F)) <= (ord_less_nat @ E @ F))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_order__less__le__subst2)). 137.10/30.46 thf(858,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_nat @ E @ F))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 137.10/30.46 thf(30,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Suc__le__mono)). 137.10/30.46 thf(367,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 137.10/30.46 thf(191,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A != B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_le__neq__implies__less)). 137.10/30.46 thf(932,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (A = B)) => (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 137.10/30.46 thf(221,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_Suc__le__lessD)). 137.10/30.46 thf(1061,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_eq_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 137.10/30.46 thf(184,axiom,((linorder_sorted_nat = (^ [A:list_nat]: ! [B:nat,C:nat]: (((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_sorted__iff__nth__mono__less)). 137.10/30.46 thf(912,plain,(((linorder_sorted_nat) = (^ [A:list_nat]: ! [B:nat,C:nat]: (((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 137.10/30.46 thf(203,axiom,((! [A:nat,B:nat,C:nat]: (((B = C) <= (ord_less_nat @ C @ A)) <= ((minus_minus_nat @ A @ B) = (minus_minus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_nat__diff__left__cancel__eq2)). 137.10/30.46 thf(983,plain,((! [A:nat,B:nat,C:nat]: ((B = C) | ~ (ord_less_nat @ C @ A) | ~ ((minus_minus_nat @ A @ B) = (minus_minus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 137.10/30.46 thf(256,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_114_antisym__conv2)). 137.10/30.46 thf(1198,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)],[256])). 137.10/30.46 thf(39,axiom,((! [A:list_a]: ((rev_a @ (rev_a @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rev__rev__ident)). 137.10/30.46 thf(399,plain,((! [A:list_a]: ((rev_a @ (rev_a @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 137.10/30.46 thf(94,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) <= (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_dual__order_Ostrict__trans)). 137.10/30.46 thf(608,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ B) | ~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 137.10/30.46 thf(207,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_order_Oasym)). 137.10/30.46 thf(1000,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 137.10/30.46 thf(12,axiom,((! [A:list_nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ B) => ((listIn923761578nd_nat @ A @ C @ B) = (C @ (minus_minus_nat @ B @ (size_size_list_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_i__append__nth2)). 137.10/30.46 thf(299,plain,((! [A:list_nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ B) => ((listIn923761578nd_nat @ A @ (C) @ B) = (C @ (minus_minus_nat @ B @ (size_size_list_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 137.10/30.46 thf(104,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_minf_I8_J)). 137.10/30.46 thf(636,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 137.10/30.46 thf(123,axiom,((! [A:list_a,B:list_a]: ((A != B) <= ((size_size_list_a @ A) != (size_size_list_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_size__neq__size__imp__neq)). 137.10/30.46 thf(695,plain,((! [A:list_a,B:list_a]: (~ (A = B) | ((size_size_list_a @ A) = (size_size_list_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 137.10/30.46 thf(37,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_21_dual__order_Oeq__iff)). 137.10/30.46 thf(394,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)],[37])). 137.10/30.46 thf(204,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_54_antisym__conv3)). 137.10/30.46 thf(986,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)],[204])). 137.10/30.46 thf(5,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_37_eq__iff)). 137.10/30.46 thf(267,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)],[5])). 137.10/30.46 thf(169,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__imp__neq)). 137.10/30.46 thf(851,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 137.10/30.46 thf(70,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) <= (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_dual__order_Otrans)). 137.10/30.46 thf(531,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 137.10/30.46 thf(117,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_pinf_I7_J)). 137.10/30.46 thf(680,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 137.10/30.46 thf(112,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_less__not__refl)). 137.10/30.46 thf(663,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 137.10/30.46 thf(98,axiom,((! [A:list_a,B:list_a]: (((! [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ A)) => ((nth_a @ A @ C) = (nth_a @ B @ C)))) => (A = B)) <= ((size_size_list_a @ A) = (size_size_list_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_nth__equalityI)). 137.10/30.46 thf(617,plain,((! [A:list_a,B:list_a]: (((! [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ A)) => ((nth_a @ A @ C) = (nth_a @ B @ C)))) => (A = B)) | ~ ((size_size_list_a @ A) = (size_size_list_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 137.10/30.46 thf(54,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_33_le__cases)). 137.10/30.46 thf(458,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)],[54])). 137.10/30.46 thf(170,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_63_less__trans)). 137.10/30.46 thf(855,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)],[170])). 137.10/30.46 thf(106,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Suc__less__eq)). 137.10/30.46 thf(640,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 137.10/30.46 thf(127,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_52_less__imp__triv)). 137.10/30.46 thf(707,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)],[127])). 137.10/30.46 thf(263,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ (C @ A) @ D) | (~ (ord_less_eq_nat @ (C @ (sk2 @ D @ (C) @ B @ A)) @ (C @ (sk3 @ D @ (C) @ B @ A)))) | (~ (ord_less_eq_nat @ (C @ B) @ D)))),inference(cnf,[status(esa)],[262])). 137.10/30.46 thf(42,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_32_order_Otrans)). 137.10/30.46 thf(409,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)],[42])). 137.10/30.46 thf(115,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_dual__order_Oirrefl)). 137.10/30.46 thf(673,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 137.10/30.46 thf(22,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_35_linear)). 137.10/30.46 thf(331,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)],[22])). 137.10/30.46 thf(195,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_order__less__le__subst1)). 137.10/30.46 thf(951,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 137.10/30.46 thf(107,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ (suc @ A)) & (B @ C))) = (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ C)) | (B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_Ex__less__Suc)). 137.10/30.46 thf(643,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ (suc @ A)) & (B @ C))) = (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ C)) | (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 137.10/30.46 thf(218,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_less__Suc__eq)). 137.10/30.46 thf(1038,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 137.10/30.46 thf(31,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((? [D:nat]: (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)) & (A @ D))) <= (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Nat_Oex__has__greatest__nat)). 137.10/30.46 thf(370,plain,((! [A:(nat > $o),B:nat,C:nat]: (? [D:nat]: (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)) & (A @ D)) | ~ (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 137.10/30.46 thf(239,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_ord__less__eq__trans)). 137.10/30.46 thf(1141,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 137.10/30.46 thf(96,axiom,((list_strict_asc_nat = (^ [A:list_nat]: ! [B:nat]: ((! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))) <= (ord_less_nat @ B @ (size_size_list_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_list__strict__asc__trans)). 137.10/30.46 thf(613,plain,(((list_strict_asc_nat) = (^ [A:list_nat]: ! [B:nat]: (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B))) | ~ (ord_less_nat @ B @ (size_size_list_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 137.10/30.46 thf(17,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_Suc__leD)). 137.10/30.46 thf(314,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 137.10/30.46 thf(82,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((A @ C) <= (! [D:nat]: ((A @ D) <= (ord_less_nat @ D @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_nat__less__induct)). 137.10/30.46 thf(571,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((A @ C) | ~ (! [D:nat]: ((A @ D) | ~ (ord_less_nat @ D @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 137.10/30.46 thf(176,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((! [D:nat,E:nat]: ((A @ D @ E) <= (A @ E @ D))) => (A @ B @ C)) <= (! [D:nat]: (A @ D @ D))) <= (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_linorder__less__wlog)). 137.10/30.46 thf(876,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((A @ D @ E) | ~ (A @ E @ D))) => (A @ B @ C)) | ~ (! [D:nat]: (A @ D @ D)) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 137.10/30.46 thf(206,axiom,((! [A:nat,B:(nat > $o),C:nat]: (((! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((! [E:nat]: ((B @ E) <= (ord_less_nat @ D @ E))) => (B @ D)))) => (B @ C)) <= (! [D:nat]: ((B @ D) <= (ord_less_nat @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_nat__descend__induct)). 137.10/30.46 thf(991,plain,((! [A:nat,B:(nat > $o),C:nat]: (((! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((! [E:nat]: ((B @ E) | ~ (ord_less_nat @ D @ E))) => (B @ D)))) => (B @ C)) | ~ (! [D:nat]: ((B @ D) | ~ (ord_less_nat @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 137.10/30.46 thf(110,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ C) @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_less__imp__diff__less)). 137.10/30.46 thf(656,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ C) @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 137.10/30.46 thf(213,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (A = C)) <= ((minus_minus_nat @ A @ B) = (minus_minus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_nat__diff__right__cancel__eq2)). 137.10/30.46 thf(1023,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (A = C)) | ~ ((minus_minus_nat @ A @ B) = (minus_minus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 137.10/30.46 thf(201,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_dual__order_Ostrict__trans1)). 137.10/30.46 thf(978,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 137.10/30.46 thf(1140,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) => (~ (B = C)))))),inference(lifteq,[status(thm)],[1139])). 137.10/30.46 thf(167,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_less__imp__le__nat)). 137.10/30.46 thf(845,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 137.10/30.46 thf(252,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_minf_I7_J)). 137.10/30.46 thf(1180,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 137.10/30.46 thf(77,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_36_antisym)). 137.10/30.46 thf(556,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)],[77])). 137.10/30.46 thf(180,axiom,((list_asc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_list__asc__trans)). 137.10/30.46 thf(903,plain,(((list_asc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 137.10/30.46 thf(236,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ (suc @ B)) = (A = B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_not__less__less__Suc__eq)). 137.10/30.46 thf(1126,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ (suc @ B)) = (A = B)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 137.10/30.46 thf(66,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) <= (ord_less_eq_nat @ D @ E))) => ((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_linorder__wlog)). 137.10/30.46 thf(517,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) | ~ (ord_less_eq_nat @ D @ E))) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 137.10/30.46 thf(178,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: ((ord_less_nat @ A @ C) => (B != (suc @ C))))) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Suc__lessE)). 137.10/30.46 thf(896,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (~ (B = (suc @ C))))) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 137.10/30.46 thf(134,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_neq__iff)). 137.10/30.46 thf(731,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 137.10/30.46 thf(148,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_minf_I3_J)). 137.10/30.46 thf(781,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 137.10/30.46 thf(87,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_order_Ostrict__trans)). 137.10/30.46 thf(588,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 137.10/30.46 thf(124,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_verit__comp__simplify1_I3_J)). 137.10/30.46 thf(699,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 137.10/30.46 thf(81,axiom,((! [A:nat,B:(nat > (nat > $o))]: ((! [C:nat]: ((? [D:nat]: (B @ C @ D)) <= (ord_less_nat @ C @ A))) = (? [C:list_nat]: (! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_nat @ C @ D))) & ((size_size_list_nat @ C) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_Skolem__list__nth)). 137.10/30.46 thf(568,plain,((! [A:nat,B:(nat > (nat > $o))]: ((! [C:nat]: (? [D:nat]: (B @ C @ D) | ~ (ord_less_nat @ C @ A))) = (? [C:list_nat]: (! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_nat @ C @ D))) & ((size_size_list_nat @ C) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 137.10/30.46 thf(190,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ C)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_less__diff__imp__less)). 137.10/30.46 thf(929,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ C)) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 137.10/30.46 thf(272,plain,(! [C:(nat > (nat > $o)),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (C @ (sk5 @ (C) @ B @ A) @ (sk6 @ (C) @ B @ A)) | (~ (C @ (sk7 @ (C) @ B @ A) @ (suc @ (sk7 @ (C) @ B @ A)))) | (C @ A @ B) | (~ (C @ (sk8 @ (C) @ B @ A) @ (sk8 @ (C) @ B @ A))))),inference(cnf,[status(esa)],[270])). 137.10/30.46 thf(344,plain,((~ (? [A:nat]: (A = (suc @ A))))),inference(miniscope,[status(thm)],[343])). 137.10/30.46 thf(345,plain,(! [A:nat] : ((~ (A = (suc @ A))))),inference(cnf,[status(esa)],[344])). 137.10/30.46 thf(346,plain,(! [A:nat] : (((suc @ A) != A))),inference(lifteq,[status(thm)],[345])). 137.10/30.46 thf(72,axiom,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) != (size_size_list_nat @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_neq__if__length__neq)). 137.10/30.46 thf(536,plain,((! [A:list_nat,B:list_nat]: ((~ ((size_size_list_nat @ A) = (size_size_list_nat @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 137.10/30.46 thf(185,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_le__imp__less__or__eq)). 137.10/30.46 thf(914,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 137.10/30.46 thf(32,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_antisym__conv)). 137.10/30.46 thf(378,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 137.10/30.46 thf(162,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_less__imp__not__eq2)). 137.10/30.46 thf(832,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 137.10/30.46 thf(119,axiom,((! [A:nat,B:nat]: (((A = B) <= (~ (ord_less_nat @ A @ B))) <= (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_less__SucE)). 137.10/30.46 thf(684,plain,((! [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B) | ~ (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 137.10/30.46 thf(130,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_pinf_I3_J)). 137.10/30.46 thf(716,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 137.10/30.46 thf(1161,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(lifteq,[status(thm)],[1160])). 137.10/30.46 thf(155,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Suc__leI)). 137.10/30.46 thf(800,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 137.10/30.46 thf(51,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Suc__inject)). 137.10/30.46 thf(447,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 137.10/30.46 thf(46,axiom,((! [A:list_nat,B:list_nat,C:(nat > nat),D:(nat > nat)]: ((((listIn923761578nd_nat @ A @ C) = (listIn923761578nd_nat @ B @ D)) = ((C = D) & (A = B))) <= ((size_size_list_nat @ A) = (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_i__append__eq__i__append__conv)). 137.10/30.46 thf(432,plain,((! [A:list_nat,B:list_nat,C:(nat > nat),D:(nat > nat)]: ((((listIn923761578nd_nat @ A @ C) = (listIn923761578nd_nat @ B @ D)) = (((C) = (D)) & (A = B))) | ~ ((size_size_list_nat @ A) = (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 137.10/30.46 thf(199,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ord__eq__less__subst)). 137.10/30.46 thf(967,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 137.10/30.46 thf(273,plain,(! [C:(nat > (nat > $o)),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (C @ (sk4 @ (C) @ B @ A) @ (sk6 @ (C) @ B @ A))) | (~ (C @ (sk7 @ (C) @ B @ A) @ (suc @ (sk7 @ (C) @ B @ A)))) | (C @ A @ B) | (~ (C @ (sk8 @ (C) @ B @ A) @ (sk8 @ (C) @ B @ A))))),inference(cnf,[status(esa)],[270])). 137.10/30.46 thf(80,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) <= (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_lift__Suc__mono__less__iff)). 137.10/30.46 thf(564,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) | ~ (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 137.10/30.46 thf(14,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_26_order__class_Oorder_Oantisym)). 137.10/30.46 thf(305,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)],[14])). 137.10/30.46 thf(10,axiom,((! [A:list_nat]: ((rev_nat @ (rev_nat @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_rev__rev__ident)). 137.10/30.46 thf(294,plain,((! [A:list_nat]: ((rev_nat @ (rev_nat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 137.10/30.46 thf(1362,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[1161,639])). 137.10/30.46 thf(1363,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(pattern_uni,[status(thm)],[1362:[]])). 137.10/30.46 thf(158,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_le__less__linear)). 137.10/30.46 thf(807,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 137.10/30.46 thf(249,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_less__Suc__eq__le)). 137.10/30.46 thf(1172,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 137.10/30.46 thf(217,axiom,((! [A:(list_nat > $o),B:list_nat]: ((! [C:list_nat]: ((A @ C) <= (! [D:list_nat]: ((A @ D) <= (ord_less_nat @ (size_size_list_nat @ D) @ (size_size_list_nat @ C)))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_length__induct)). 137.10/30.46 thf(1033,plain,((! [A:(list_nat > $o),B:list_nat]: ((! [C:list_nat]: ((A @ C) | ~ (! [D:list_nat]: ((A @ D) | ~ (ord_less_nat @ (size_size_list_nat @ D) @ (size_size_list_nat @ C)))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 137.10/30.46 thf(223,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_82_nat__neq__iff)). 137.10/30.46 thf(1065,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)],[223])). 137.10/30.46 thf(131,axiom,((! [A:nat,B:list_a,C:(nat > a)]: ((ord_less_nat @ A @ (size_size_list_a @ B)) => ((listIn1312259492pend_a @ B @ C @ A) = (nth_a @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_i__append__nth1)). 137.10/30.46 thf(720,plain,((! [A:nat,B:list_a,C:(nat > a)]: ((ord_less_nat @ A @ (size_size_list_a @ B)) => ((listIn1312259492pend_a @ B @ (C) @ A) = (nth_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 137.10/30.46 thf(196,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) <= (A != B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_linorder__cases)). 137.10/30.46 thf(955,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (A = B) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 137.10/30.46 thf(44,axiom,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)) => ((((~ (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ C)) => (((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 @ B @ C) => (~ (ord_less_eq_nat @ C @ A)))))) <= ((~ (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_le__cases3)). 137.10/30.46 thf(415,plain,((! [A:nat,B:nat,C:nat]: ((~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)) => (((~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ A @ C)) => (((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 @ B @ C) => (~ (ord_less_eq_nat @ C @ A)))))) | ~ (~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 137.10/30.46 thf(153,axiom,((! [A:list_nat]: ((! [B:nat]: ((! [C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))) <= (ord_less_nat @ B @ (size_size_list_nat @ A)))) <= (list_strict_asc_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_list__strict__asc__trans__le)). 137.10/30.46 thf(796,plain,((! [A:list_nat]: (! [B:nat]: (! [C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B))) | ~ (ord_less_nat @ B @ (size_size_list_nat @ A))) | ~ (list_strict_asc_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 137.10/30.46 thf(7,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_diff__diff__cancel)). 137.10/30.46 thf(283,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 137.10/30.46 thf(395,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = (= @ nat))),inference(lifteq,[status(thm)],[394])). 137.10/30.46 thf(133,axiom,((! [A:nat,B:nat]: ((A != B) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_order_Onot__eq__order__implies__strict)). 137.10/30.46 thf(728,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 137.10/30.46 thf(56,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_diff__Suc__Suc)). 137.10/30.46 thf(464,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 137.10/30.46 thf(237,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_minf_I1_J)). 137.10/30.46 thf(1129,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 137.10/30.46 thf(182,axiom,((list_strict_desc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)) <= (ord_less_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_list__strict__desc__trans)). 137.10/30.46 thf(908,plain,(((list_strict_desc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)) | ~ (ord_less_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 137.10/30.46 thf(209,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ (suc @ A)))) = (! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C)) & (B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_All__less__Suc)). 137.10/30.46 thf(1004,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ (suc @ A)))) = (! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C)) & (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 137.10/30.46 thf(49,axiom,((! [A:nat]: ? [B:list_nat]: ((size_size_list_nat @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Ex__list__of__length)). 137.10/30.46 thf(442,plain,((! [A:nat]: ? [B:list_nat]: ((size_size_list_nat @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 137.10/30.46 thf(234,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_115_antisym__conv1)). 137.10/30.46 thf(1120,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)],[234])). 137.10/30.46 thf(24,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (B = (suc @ C))) <= (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Suc__le__D)). 137.10/30.46 thf(337,plain,((! [A:nat,B:nat]: (? [C:nat]: (B = (suc @ C)) | ~ (ord_less_eq_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 137.10/30.46 thf(192,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__asym)). 137.10/30.46 thf(935,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 137.10/30.46 thf(188,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_less__le__trans)). 137.10/30.46 thf(923,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 137.10/30.46 thf(254,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => ((! [D:nat]: ((B = (suc @ D)) => (C @ D))) => ((! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_strict__inc__induct)). 137.10/30.46 thf(1184,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => ((! [D:nat]: ((B = (suc @ D)) => (C @ D))) => ((! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 137.10/30.46 thf(111,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((A @ C) <= (! [D:nat]: ((A @ D) <= (ord_less_nat @ D @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__induct)). 137.10/30.46 thf(659,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((A @ C) | ~ (! [D:nat]: ((A @ D) | ~ (ord_less_nat @ D @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 137.10/30.46 thf(74,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)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_ord__eq__le__subst)). 137.10/30.46 thf(543,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) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 137.10/30.46 thf(146,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_leI)). 137.10/30.46 thf(775,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 137.10/30.46 thf(61,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_diff__commute)). 137.10/30.46 thf(491,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 137.10/30.46 thf(89,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ A @ C)) => (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_nat__diff__left__cancel__less)). 137.10/30.46 thf(592,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ A @ C)) => (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 137.10/30.46 thf(53,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_eq__refl)). 137.10/30.46 thf(454,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 137.10/30.46 thf(29,axiom,((! [A:list_a,B:list_a]: (((rev_a @ A) = B) = (A = (rev_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_rev__swap)). 137.10/30.46 thf(364,plain,((! [A:list_a,B:list_a]: (((rev_a @ A) = B) = (A = (rev_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 137.10/30.46 thf(139,axiom,((! [A:nat,B:list_a]: (((nth_a @ (rev_a @ B) @ A) = (nth_a @ B @ (minus_minus_nat @ (size_size_list_a @ B) @ (suc @ A)))) <= (ord_less_nat @ A @ (size_size_list_a @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_rev__nth)). 137.10/30.46 thf(755,plain,((! [A:nat,B:list_a]: (((nth_a @ (rev_a @ B) @ A) = (nth_a @ B @ (minus_minus_nat @ (size_size_list_a @ B) @ (suc @ A)))) | ~ (ord_less_nat @ A @ (size_size_list_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 137.10/30.46 thf(116,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_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_122_order__le__less__subst1)). 137.10/30.46 thf(676,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_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)],[116])). 137.10/30.46 thf(25140,plain,($false),inference(cvc4,[status(thm)],[809,1105,347,1237,777,666,481,1031,333,628,1068,308,1073,873,269,1041,523,1158,582,384,1164,1233,747,1063,340,829,841,320,436,257,724,785,1264,802,1059,460,587,838,917,702,751,559,638,770,289,316,1100,261,591,1109,646,485,966,1183,905,1151,937,687,692,734,866,396,1345,265,602,981,766,2011,439,529,381,534,798,1153,761,910,894,1021,1519,598,297,407,429,788,260,1123,862,467,847,1178,551,710,842,682,1195,615,388,869,499,989,1160,488,554,1182,669,526,1207,1114,654,1002,605,622,837,343,792,266,633,805,311,1170,1071,530,586,926,1026,1167,298,412,965,264,689,513,1146,1007,402,772,286,577,958,259,562,975,445,611,713,1107,919,704,947,350,540,391,1139,764,900,1117,1011,1542,451,509,303,271,1175,737,318,811,494,631,758,323,594,1162,1029,626,1112,858,367,932,1061,912,983,1198,399,608,1000,299,636,695,394,986,267,851,531,680,663,617,458,836,855,640,707,263,409,1230,673,331,840,576,951,643,1038,585,370,1141,613,314,571,876,991,656,1023,978,1140,845,1180,556,903,1126,517,896,731,781,588,699,568,929,272,383,346,536,914,378,832,684,716,1161,800,447,432,967,790,273,564,305,294,1363,807,1172,1033,1065,720,955,415,796,283,395,728,464,1129,575,908,1004,442,1120,337,935,923,1184,659,543,775,639,491,592,454,364,755,676])). 137.10/30.46 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 137.10/30.46 % [INFO] Killing All external provers ... 137.10/30.46 WARNING: TreeLimitedRun lost 46.26s, total lost is 46.26s 137.10/30.46 FINAL WATCH: 112.2 CPU 26.3 WC 137.10/30.46 Killed 3 orphans 137.10/30.46 Killed 1 orphans 137.10/30.46 EOF