0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : run_Leo-III %s %d THM 0.11/0.34 % Computer : n012.cluster.edu 0.11/0.34 % Model : x86_64 x86_64 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.34 % Memory : 8042.1875MB 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.34 % CPULimit : 1440 0.11/0.34 % WCLimit : 180 0.11/0.34 % DateTime : Thu Jul 4 07:29:40 EDT 2024 0.11/0.34 % CPUTime : 1.10/1.11 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 2.39/1.83 % [INFO] Parsing done (710ms). 2.39/1.85 % [INFO] Running in sequential loop mode. 3.68/2.35 % [INFO] eprover registered as external prover. 3.68/2.36 % [INFO] Scanning for conjecture ... 3.96/2.58 % [INFO] Found a conjecture (or negated_conjecture) and 283 axioms. Running axiom selection ... 4.23/2.82 % [INFO] Axiom selection finished. Selected 283 axioms (removed 0 axioms). 5.24/3.34 % [INFO] Problem is higher-order (TPTP THF). 5.35/3.41 % [INFO] Type checking passed. 5.35/3.42 % [CONFIG] Using configuration: timeout(180) with strategy. Searching for refutation ... 139.25/42.37 % External prover 'e' found a proof! 139.25/42.37 % [INFO] Killing All external provers ... 139.25/42.38 % Time passed: 41841ms (effective reasoning time: 40518ms) 139.25/42.38 % Solved by strategy 139.25/42.38 % Axioms used in derivation (283): fact_106_order__subst2, fact_192_dual__order_Ostrict__trans1, fact_80_order__class_Oorder_Oeq__iff, fact_232_le__Suc__ex, fact_281_add__mono__thms__linordered__field_I4_J, fact_27_le__neq__implies__less, fact_66_dual__order_Oeq__iff, fact_280_add__mono__thms__linordered__field_I3_J, fact_26_less__mono__imp__le__mono, fact_48_Until_OIH_I1_J, fact_3_nat__neq__iff, fact_229_le__add2, fact_278_add__less__le__mono, fact_279_add__le__less__mono, fact_81_order__class_Oorder_Oeq__iff, fact_246_add__right__cancel, fact_263_add__mono, fact_144_leD, fact_137_less__imp__not__less, fact_276_add__less__imp__less__left, fact_59_order_Ostrict__implies__order, fact_225_add__less__mono, fact_5_less__not__refl2, fact_8_nat__less__induct, fact_21_progress__mono, fact_239_progress__time__conv, fact_145_leD, fact_271_add__mono__thms__linordered__field_I2_J, fact_37_pinf_I5_J, fact_30_less__imp__le__nat, fact_194_dual__order_Ostrict__trans2, fact_142_order_Ostrict__implies__not__eq, fact_126_ord__less__eq__trans, fact_228_le__add1, fact_160_order__less__le__subst1, fact_174_le__less__trans, fact_244_add__less__cancel__right, fact_147_le__less, fact_197_verit__comp__simplify1_I3_J, fact_249_add__less__cancel__left, fact_97_ord__le__eq__subst, fact_102_ord__eq__le__subst, fact_107_order__subst1, fact_65_dual__order_Oeq__iff, fact_154_order__le__less__subst2, fact_219_less__add__eq__less, fact_215__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062, fact_39_minf_I1_J, fact_34_pinf_I2_J, fact_12_assms_I2_J, fact_140_dual__order_Ostrict__trans, fact_114_order__less__subst2, fact_15_le__trans, fact_270_add__mono__thms__linordered__field_I5_J, fact_259_add__right__imp__eq, fact_128_less__imp__not__eq, fact_236_trans__le__add2, fact_255_add_Oassoc, fact_267_le__iff__add, fact_200_verit__la__disequality, fact_157_order__less__le__subst1, fact_223_not__add__less2, fact_119_less__imp__neq, fact_211__C3_C, fact_141_not__less__iff__gr__or__eq, fact_28_less__or__eq__imp__le, fact_29_le__eq__less__or__eq, fact_156_order__le__less__subst2, fact_274_add__strict__left__mono, fact_265_less__eqE, fact_172_less__imp__le, fact_162_order__less__le__subst2, fact_190_order_Ostrict__iff__order, fact_129_less__not__sym, fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_68_dual__order_Otrans, fact_251_ab__semigroup__add__class_Oadd__ac_I1_J, fact_74_order__class_Oorder_Oantisym, fact_109_order__subst1, fact_245_add__left__cancel, fact_70_dual__order_Orefl, fact_50_complete__interval, fact_136_order_Ostrict__trans, fact_138_exists__least__iff, fact_63_dual__order_Oantisym, fact_159_order__less__le__subst1, fact_151_order__le__less__subst1, fact_155_order__le__less__subst2, fact_139_linorder__less__wlog, fact_84_le__cases3, fact_199_less__prefix__def, fact_205_formula_Oinject_I9_J, fact_36_pinf_I4_J, fact_240_le___092_060tau_062__less, fact_158_order__less__le__subst1, fact_231_add__leD2, fact_111_ord__eq__less__subst, fact_146_leI, fact_216_less___092_060tau_062D, fact_93_eq__iff, fact_72_order__trans, fact_53_dual__order_Ostrict__implies__order, fact_121_less__asym_H, fact_177_le__less__linear, fact_104_order__subst2, fact_18_nat__le__linear, fact_52_order_Onot__eq__order__implies__strict, fact_168_antisym__conv1, fact_167_antisym__conv1, fact_153_order__le__less__subst2, fact_178_le__imp__less__or__eq, fact_95_ord__le__eq__subst, fact_181_less__le__not__le, fact_266_add__right__mono, fact_152_order__le__less__subst1, fact_195_Until_Oprems, fact_47_order__refl, fact_260_add__mono__thms__linordered__semiring_I3_J, fact_187_order_Oorder__iff__strict, fact_234_add__le__mono1, fact_122_less__trans, fact_277_add__less__imp__less__right, fact_165_le__neq__trans, fact_149_less__le, fact_85_order_Otrans, fact_143_dual__order_Ostrict__implies__not__eq, fact_176_less__le__trans, fact_44_minf_I7_J, fact_113_order__less__subst1, fact_227_add__leE, fact_241__092_060tau_062__prefix__conv, fact_100_ord__eq__le__subst, fact_40_minf_I2_J, fact_127_dual__order_Oasym, fact_183_order_Ostrict__trans1, fact_91_antisym, fact_250_one__reorient, fact_170_antisym__conv2, fact_209_nat__add__left__cancel__less, fact_105_order__subst2, fact_220_trans__less__add2, fact_182_not__le__imp__less, fact_208_that, fact_179_le__imp__less__or__eq, fact_115_gt__ex, fact_248_add__le__cancel__right, fact_32_progress__prefix__conv, fact_92_antisym, fact_185_order_Ostrict__trans2, fact_22_pinf_I6_J, fact_124_less__irrefl, fact_191_dual__order_Ostrict__trans1, fact_87_le__cases, fact_161_order__less__le__subst2, fact_261_add__mono__thms__linordered__semiring_I2_J, fact_256_add_Ocommute, fact_150_less__le, fact_25_minf_I8_J, fact_171_less__imp__le, fact_130_less__induct, fact_123_less__linear, fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_213__C2_C, fact_269_add__le__imp__le__right, fact_273_add__strict__mono, fact_254_group__cancel_Oadd2, fact_11__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_282_discrete, fact_60_order_Ostrict__implies__order, fact_78_ord__eq__le__trans, fact_230_add__leD1, fact_49_nat__descend__induct, fact_62_Until_OIH_I2_J, fact_9_infinite__descent, fact_212__C1_C, fact_24_minf_I6_J, fact_242__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_243__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_166_le__neq__trans, fact_7_less__irrefl__nat, fact_35_pinf_I3_J, fact_46_order__refl, fact_210_nat__add__left__cancel__le, fact_217_ex__le___092_060tau_062, fact_77_ord__le__eq__trans, fact_207__C11_C, fact_103_order__subst2, fact_118_order_Oasym, fact_98_ord__le__eq__subst, fact_20_progress__le, fact_13__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_43_minf_I5_J, fact_83_antisym__conv, fact_86_order_Otrans, fact_1_assms_I3_J, fact_112_ord__less__eq__subst, fact_38_pinf_I7_J, fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_16_eq__imp__le, fact_134_linorder__cases, fact_224_not__add__less1, fact_233_add__le__mono, fact_253_group__cancel_Oadd1, fact_189_order_Ostrict__iff__order, fact_71_dual__order_Orefl, fact_67_dual__order_Otrans, fact_79_ord__eq__le__trans, fact_75_order__class_Oorder_Oantisym, fact_19_Nat_Oex__has__greatest__nat, fact_135_dual__order_Oirrefl, fact_222_add__less__mono1, fact_206__C21_C, fact_90_linear, fact_201_verit__comp__simplify1_I1_J, fact_221_trans__less__add1, fact_235_trans__le__add1, fact_33_pinf_I1_J, fact_184_order_Ostrict__trans1, fact_69_linorder__wlog, fact_51_order_Onot__eq__order__implies__strict, fact_101_ord__eq__le__subst, fact_203_prefix__of__antimono, fact_193_dual__order_Ostrict__trans2, fact_196_plen__mono, fact_14_le__refl, fact_117_neq__iff, fact_99_ord__eq__le__subst, fact_247_add__le__cancel__left, fact_164_not__less, fact_108_order__subst1, fact_54_dual__order_Ostrict__implies__order, fact_169_antisym__conv2, fact_96_ord__le__eq__subst, fact_89_eq__refl, fact_94_eq__iff, fact_56_dual__order_Ostrict__iff__order, fact_88_eq__refl, fact_264_add__left__mono, fact_57_dual__order_Oorder__iff__strict, fact_6_less__not__refl3, fact_268_add__le__imp__le__left, fact_180_less__le__not__le, fact_198__092_060open_062i_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062, fact_82_antisym__conv, fact_31_nat__less__le, fact_133_less__imp__triv, fact_132_less__imp__not__eq2, fact_58_dual__order_Oorder__iff__strict, fact_41_minf_I3_J, fact_258_add__left__imp__eq, fact_257_add_Oleft__commute, fact_275_add__strict__right__mono, fact_226_add__lessD1, fact_2_assms_I1_J, fact_76_ord__le__eq__trans, fact_272_add__mono__thms__linordered__field_I1_J, fact_4_less__not__refl, fact_252_add__mono__thms__linordered__semiring_I4_J, fact_148_le__less, fact_188_order_Oorder__iff__strict, fact_131_antisym__conv3, fact_218__092_060tau_062__mono, fact_204_prefix__of__imp__linear, fact_120_less__asym, fact_175_less__le__trans, fact_262_add__mono__thms__linordered__semiring_I1_J, fact_64_dual__order_Oantisym, fact_186_order_Ostrict__trans2, fact_55_dual__order_Ostrict__iff__order, fact_238_mono__nat__linear__lb, fact_214__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062, fact_73_order__trans, fact_17_le__antisym, fact_23_pinf_I8_J, fact_110_order__subst1, fact_237_nat__le__iff__add, fact_125_ord__eq__less__trans, fact_10_linorder__neqE__nat, fact_163_not__le, fact_116_neqE, fact_173_le__less__trans, fact_42_minf_I4_J, fact_202_ex__prefix__of 139.25/42.38 % No. of inferences in proof: 846 139.25/42.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 41841 ms resp. 40518 ms w/o parsing 140.59/43.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 140.59/43.01 thf(prefix1027212443list_a_type, type, prefix1027212443list_a: $tType). 140.59/43.01 thf(trace_1367752404list_a_type, type, trace_1367752404list_a: $tType). 140.59/43.01 thf(i_type, type, i: $tType). 140.59/43.01 thf(formula_a_type, type, formula_a: $tType). 140.59/43.01 thf(list_a_type, type, list_a: $tType). 140.59/43.01 thf(nat_type, type, nat: $tType). 140.59/43.01 thf(one_one_nat_type, type, one_one_nat: nat). 140.59/43.01 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 140.59/43.01 thf(until_a_type, type, until_a: (formula_a > (i > (formula_a > formula_a)))). 140.59/43.01 thf(sat_a_type, type, sat_a: (trace_1367752404list_a > (list_a > (nat > (formula_a > $o))))). 140.59/43.01 thf(monito1457594016ress_a_type, type, monito1457594016ress_a: (trace_1367752404list_a > (formula_a > (nat > nat)))). 140.59/43.01 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 140.59/43.01 thf(ord_le887097159list_a_type, type, ord_le887097159list_a: (prefix1027212443list_a > (prefix1027212443list_a > $o))). 140.59/43.01 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 140.59/43.01 thf(ord_le699472955list_a_type, type, ord_le699472955list_a: (prefix1027212443list_a > (prefix1027212443list_a > $o))). 140.59/43.01 thf(tau_Pr257024512list_a_type, type, tau_Pr257024512list_a: (trace_1367752404list_a > (nat > nat))). 140.59/43.01 thf(plen_P694648887list_a_type, type, plen_P694648887list_a: (prefix1027212443list_a > nat)). 140.59/43.01 thf(prefix1041802747list_a_type, type, prefix1041802747list_a: (prefix1027212443list_a > (trace_1367752404list_a > $o))). 140.59/43.01 thf(i2_type, type, i2: i). 140.59/43.01 thf(phi_type, type, phi: formula_a). 140.59/43.01 thf(phi_1_type, type, phi_1: formula_a). 140.59/43.01 thf(phi_2_type, type, phi_2: formula_a). 140.59/43.01 thf(pi_type, type, pi: prefix1027212443list_a). 140.59/43.01 thf(sigma_type, type, sigma: trace_1367752404list_a). 140.59/43.01 thf(sigma2_type, type, sigma2: trace_1367752404list_a). 140.59/43.01 thf(b_type, type, b: nat). 140.59/43.01 thf(i3_type, type, i3: nat). 140.59/43.01 thf(ia_type, type, ia: nat). 140.59/43.01 thf(j_type, type, j: nat). 140.59/43.01 thf(ja_type, type, ja: nat). 140.59/43.01 thf(k_type, type, k: nat). 140.59/43.01 thf(sk1_type, type, sk1: (prefix1027212443list_a > trace_1367752404list_a)). 140.59/43.01 thf(sk2_type, type, sk2: (nat > ((nat > $o) > nat))). 140.59/43.01 thf(sk3_type, type, sk3: ((nat > $o) > nat)). 140.59/43.01 thf(sk4_type, type, sk4: (prefix1027212443list_a > ((prefix1027212443list_a > prefix1027212443list_a) > (prefix1027212443list_a > (prefix1027212443list_a > prefix1027212443list_a))))). 140.59/43.01 thf(sk5_type, type, sk5: (prefix1027212443list_a > ((prefix1027212443list_a > prefix1027212443list_a) > (prefix1027212443list_a > (prefix1027212443list_a > prefix1027212443list_a))))). 140.59/43.01 thf(sk6_type, type, sk6: (nat > (nat > ((nat > prefix1027212443list_a) > (prefix1027212443list_a > nat))))). 140.59/43.01 thf(sk7_type, type, sk7: (nat > (nat > ((nat > prefix1027212443list_a) > (prefix1027212443list_a > nat))))). 140.59/43.01 thf(sk75_type, type, sk75: (nat > nat)). 140.59/43.01 thf(sk85_type, type, sk85: nat). 140.59/43.01 thf(sk99_type, type, sk99: (nat > nat)). 140.59/43.01 thf(sk108_type, type, sk108: nat). 140.59/43.01 thf(sk110_type, type, sk110: (nat > nat)). 140.59/43.01 thf(sk111_type, type, sk111: (nat > nat)). 140.59/43.01 thf(sk120_type, type, sk120: (nat > nat)). 140.59/43.01 thf(239,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_le__less__trans)). 140.59/43.01 thf(1105,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 140.59/43.01 thf(23,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) = (B = A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_antisym__conv)). 140.59/43.01 thf(347,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) = (B = A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 140.59/43.01 thf(282,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_not__add__less1)). 140.59/43.01 thf(1237,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 140.59/43.01 thf(186,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_le__less)). 140.59/43.01 thf(893,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 140.59/43.01 thf(202,axiom,((ord_less_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_181_less__le__not__le)). 140.59/43.01 thf(941,plain,(((ord_less_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)],[202])). 140.59/43.01 thf(117,axiom,((! [A:nat,B:nat,C:trace_1367752404list_a]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ C @ A) @ (tau_Pr257024512list_a @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218__092_060tau_062__mono)). 140.59/43.01 thf(666,plain,((! [A:nat,B:nat,C:trace_1367752404list_a]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ C @ A) @ (tau_Pr257024512list_a @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 140.59/43.01 thf(219,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_less__irrefl__nat)). 140.59/43.01 thf(1031,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 140.59/43.01 thf(18,axiom,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_le699472955list_a @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))))) <= (ord_le699472955list_a @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_order__subst1)). 140.59/43.01 thf(333,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_le699472955list_a @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))))) | ~ (ord_le699472955list_a @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 140.59/43.01 thf(105,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_18_nat__le__linear)). 140.59/43.01 thf(628,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)],[105])). 140.59/43.01 thf(273,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__imp__le__nat)). 140.59/43.01 thf(1211,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 140.59/43.01 thf(172,axiom,((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198__092_060open_062i_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062)). 140.59/43.01 thf(837,plain,((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 140.59/43.01 thf(1,conjecture,((ord_less_nat @ k @ (plen_P694648887list_a @ pi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 140.59/43.01 thf(2,negated_conjecture,((~ (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(neg_conjecture,[status(cth)],[1])). 140.59/43.01 thf(286,plain,((~ (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 140.59/43.01 thf(4212,plain,(((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(paramod_ordered,[status(thm)],[837,286])). 140.59/43.01 thf(4226,plain,((k != ia) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[4212])). 140.59/43.01 thf(226,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_add__less__imp__less__left)). 140.59/43.01 thf(1068,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 140.59/43.01 thf(152,axiom,((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062)). 140.59/43.01 thf(782,plain,((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 140.59/43.01 thf(274,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_pinf_I4_J)). 140.59/43.01 thf(1213,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 140.59/43.01 thf(1214,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ (sk120 @ A) @ B)) | (~ (B = A)))),inference(cnf,[status(esa)],[1213])). 140.59/43.01 thf(1215,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ (sk120 @ A) @ B)))),inference(lifteq,[status(thm)],[1214])). 140.59/43.01 thf(1216,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk120 @ A) @ A)))),inference(simp,[status(thm)],[1215])). 140.59/43.01 thf(2798,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk120 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[782,1216])). 140.59/43.01 thf(2802,plain,(! [A:nat] : (((sk120 @ A) != k) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2798])). 140.59/43.01 thf(2808,plain,(((sk120 @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != k)),inference(simp,[status(thm)],[2802])). 140.59/43.01 thf(257,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_gt__ex)). 140.59/43.01 thf(1162,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 140.59/43.01 thf(1163,plain,(! [A:nat] : ((ord_less_nat @ A @ (sk110 @ A)))),inference(cnf,[status(esa)],[1162])). 140.59/43.01 thf(199,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_not__add__less2)). 140.59/43.01 thf(933,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 140.59/43.01 thf(934,plain,((~ (? [A:nat,B:nat]: (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(miniscope,[status(thm)],[933])). 140.59/43.01 thf(935,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(cnf,[status(esa)],[934])). 140.59/43.01 thf(3514,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_nat @ A @ (sk110 @ A)) != (ord_less_nat @ (plus_plus_nat @ B @ C) @ C)))),inference(paramod_ordered,[status(thm)],[1163,935])). 140.59/43.01 thf(3523,plain,(! [C:nat,B:nat,A:nat] : ((A != (plus_plus_nat @ B @ C)) | ((sk110 @ A) != C))),inference(simp,[status(thm)],[3514])). 140.59/43.01 thf(3549,plain,(! [B:nat,A:nat] : (((sk110 @ (plus_plus_nat @ A @ B)) != B))),inference(simp,[status(thm)],[3523])). 140.59/43.01 thf(181,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (B != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_dual__order_Ostrict__iff__order)). 140.59/43.01 thf(877,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 140.59/43.01 thf(878,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(lifteq,[status(thm)],[877])). 140.59/43.01 thf(120,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A != B) => ((ord_le887097159list_a @ A @ B) <= (ord_le699472955list_a @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_order_Onot__eq__order__implies__strict)). 140.59/43.01 thf(677,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((~ (A = B)) => ((ord_le887097159list_a @ A @ B) | ~ (ord_le699472955list_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 140.59/43.01 thf(261,axiom,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_exists__least__iff)). 140.59/43.01 thf(1172,plain,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 140.59/43.01 thf(1173,plain,(((^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))) = (('?') @ nat))),inference(lifteq,[status(thm)],[1172])). 140.59/43.01 thf(256,axiom,((! [A:nat,B:list_a]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) => ((sat_a @ sigma @ B @ A @ phi_2) = (sat_a @ sigma2 @ B @ A @ phi_2))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Until_OIH_I2_J)). 140.59/43.01 thf(1158,plain,((! [A:nat,B:list_a]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) => ((sat_a @ sigma @ B @ A @ phi_2) = (sat_a @ sigma2 @ B @ A @ phi_2))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 140.59/43.01 thf(94,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_add__right__mono)). 140.59/43.01 thf(582,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 140.59/43.01 thf(251,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_27_le__neq__implies__less)). 140.59/43.01 thf(1142,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)],[251])). 140.59/43.01 thf(34,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 @ D @ E) <= (A @ E @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_linorder__wlog)). 140.59/43.01 thf(379,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 @ D @ E) | ~ (A @ E @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 140.59/43.01 thf(35,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__right__cancel)). 140.59/43.01 thf(385,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 140.59/43.01 thf(81,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => (((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_le699472955list_a @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_ord__le__eq__subst)). 140.59/43.01 thf(533,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => (((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_le699472955list_a @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 140.59/43.01 thf(91,axiom,((ord_le699472955list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_le__less)). 140.59/43.01 thf(575,plain,(((ord_le699472955list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 140.59/43.01 thf(576,plain,(((ord_le699472955list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (A = B))))),inference(lifteq,[status(thm)],[575])). 140.59/43.01 thf(61,axiom,((ord_le699472955list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_dual__order_Oorder__iff__strict)). 140.59/43.01 thf(482,plain,(((ord_le699472955list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 140.59/43.01 thf(483,plain,(((ord_le699472955list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A))))),inference(lifteq,[status(thm)],[482])). 140.59/43.01 thf(1275,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (A = B))))),inference(rewrite,[status(thm)],[576,483])). 140.59/43.01 thf(280,axiom,((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I3_J)). 140.59/43.01 thf(1233,plain,((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 140.59/43.01 thf(204,axiom,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_le887097159list_a @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F))) => (ord_le887097159list_a @ A @ (B @ D)))) <= (ord_le699472955list_a @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_order__le__less__subst1)). 140.59/43.01 thf(945,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_le887097159list_a @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))) => (ord_le887097159list_a @ A @ (B @ D)))) | ~ (ord_le699472955list_a @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 140.59/43.01 thf(197,axiom,((! [A:nat]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) <= (ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212__C1_C)). 140.59/43.01 thf(930,plain,((! [A:nat]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) | ~ (ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 140.59/43.01 thf(258,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_not__le__imp__less)). 140.59/43.01 thf(1164,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 140.59/43.01 thf(156,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ B) <= (ord_less_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_dual__order_Ostrict__trans1)). 140.59/43.01 thf(797,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ C @ B) | ~ (ord_less_nat @ C @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 140.59/43.01 thf(221,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_pinf_I3_J)). 140.59/43.01 thf(1044,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 140.59/43.01 thf(1045,plain,(! [B:nat,A:nat] : ((~ (B = A)) | (~ (ord_less_nat @ (sk99 @ A) @ B)))),inference(cnf,[status(esa)],[1044])). 140.59/43.01 thf(1046,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ (sk99 @ A) @ B)))),inference(lifteq,[status(thm)],[1045])). 140.59/43.01 thf(1047,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk99 @ A) @ A)))),inference(simp,[status(thm)],[1046])). 140.59/43.01 thf(4211,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk99 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[837,1047])). 140.59/43.01 thf(4223,plain,(! [A:nat] : (((sk99 @ A) != ia) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[4211])). 140.59/43.01 thf(4247,plain,(((sk99 @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia)),inference(simp,[status(thm)],[4223])). 140.59/43.01 thf(179,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_minf_I4_J)). 140.59/43.01 thf(868,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 140.59/43.01 thf(869,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ B @ (sk75 @ A))) | (~ (B = A)))),inference(cnf,[status(esa)],[868])). 140.59/43.01 thf(870,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ B @ (sk75 @ A))))),inference(lifteq,[status(thm)],[869])). 140.59/43.01 thf(871,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ (sk75 @ A))))),inference(simp,[status(thm)],[870])). 140.59/43.01 thf(3513,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk110 @ A)) != (ord_less_nat @ B @ (sk75 @ B))))),inference(paramod_ordered,[status(thm)],[1163,871])). 140.59/43.01 thf(3544,plain,(! [B:nat,A:nat] : ((A != B) | ((sk110 @ A) != (sk75 @ B)))),inference(simp,[status(thm)],[3513])). 140.59/43.01 thf(3562,plain,(! [A:nat] : (((sk110 @ A) != (sk75 @ A)))),inference(simp,[status(thm)],[3544])). 140.59/43.01 thf(236,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_less__imp__not__less)). 140.59/43.01 thf(1095,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 140.59/43.01 thf(188,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_dual__order_Ostrict__trans)). 140.59/43.01 thf(898,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 140.59/43.01 thf(25,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_add_Ocommute)). 140.59/43.01 thf(354,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 140.59/43.01 thf(355,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(lifteq,[status(thm)],[354])). 140.59/43.01 thf(164,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_discrete)). 140.59/43.01 thf(818,plain,(((ord_less_nat) = (^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 140.59/43.01 thf(819,plain,(((^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))) = (ord_less_nat))),inference(lifteq,[status(thm)],[818])). 140.59/43.01 thf(19,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_le__iff__add)). 140.59/43.01 thf(337,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 140.59/43.01 thf(338,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(lifteq,[status(thm)],[337])). 140.59/43.01 thf(1296,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C)))) | ((^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))) != (ord_less_eq_nat))),inference(paramod_ordered,[status(thm)],[819,338])). 140.59/43.01 thf(1298,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C)))) | ((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: (B)) != (^ [A:nat,B:nat]: (B)))),inference(simp,[status(thm)],[1296])). 140.59/43.01 thf(1300,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C)))) | ((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A)))),inference(simp,[status(thm)],[1298])). 140.59/43.01 thf(3626,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C)))) | ((^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)) != (^ [A:nat,B:nat]: (A))) | ((plus_plus_nat) != (^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[355,1300])). 140.59/43.01 thf(3633,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C)))) | ((^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: (A)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: (B)) != (^ [A:nat,B:nat]: (one_one_nat)))),inference(simp,[status(thm)],[3626])). 140.59/43.01 thf(3634,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C)))) | ((^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: (B)) != (^ [A:nat,B:nat]: (one_one_nat)))),inference(simp,[status(thm)],[3633])). 140.59/43.01 thf(246,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_add__less__imp__less__right)). 140.59/43.01 thf(1127,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 140.59/43.01 thf(128,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_ord__le__eq__trans)). 140.59/43.01 thf(709,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 140.59/43.01 thf(3,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_order__refl)). 140.59/43.01 thf(287,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 140.59/43.01 thf(288,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ A))),inference(cnf,[status(esa)],[287])). 140.59/43.01 thf(9,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_94_eq__iff)). 140.59/43.01 thf(301,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)],[9])). 140.59/43.01 thf(14,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add_Oassoc)). 140.59/43.01 thf(320,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 140.59/43.01 thf(113,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_one__reorient)). 140.59/43.01 thf(651,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 140.59/43.01 thf(131,axiom,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_ord__le__eq__trans)). 140.59/43.01 thf(719,plain,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 140.59/43.01 thf(154,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_ord__eq__less__subst)). 140.59/43.01 thf(785,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 140.59/43.01 thf(31,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (B != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_dual__order_Ostrict__iff__order)). 140.59/43.01 thf(371,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 140.59/43.01 thf(372,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))))),inference(lifteq,[status(thm)],[371])). 140.59/43.01 thf(68,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_dual__order_Orefl)). 140.59/43.01 thf(504,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 140.59/43.01 thf(173,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ D @ D)) => ((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))) <= (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_linorder__less__wlog)). 140.59/43.01 thf(838,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ D @ D)) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 140.59/43.01 thf(78,axiom,((ord_le699472955list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) | (ord_le887097159list_a @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_order_Oorder__iff__strict)). 140.59/43.01 thf(526,plain,(((ord_le699472955list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) | (ord_le887097159list_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 140.59/43.01 thf(527,plain,(((ord_le699472955list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) | (ord_le887097159list_a @ A @ B))))),inference(lifteq,[status(thm)],[526])). 140.59/43.01 thf(1266,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) | (ord_le887097159list_a @ A @ B))))),inference(rewrite,[status(thm)],[527,483])). 140.59/43.01 thf(1278,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (A = B))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) | (ord_le887097159list_a @ A @ B)))) | ((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A))) != (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A))))),inference(paramod_ordered,[status(thm)],[1275,1266])). 140.59/43.01 thf(1279,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (A = B))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) | (ord_le887097159list_a @ A @ B))))),inference(pattern_uni,[status(thm)],[1278:[]])). 140.59/43.01 thf(205,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_order_Ostrict__iff__order)). 140.59/43.01 thf(949,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 140.59/43.01 thf(57,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le887097159list_a @ C @ B) <= (ord_le699472955list_a @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_dual__order_Ostrict__trans2)). 140.59/43.01 thf(460,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le887097159list_a @ C @ B) | ~ (ord_le699472955list_a @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 140.59/43.01 thf(132,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:trace_1367752404list_a]: (((prefix1041802747list_a @ B @ C) => (prefix1041802747list_a @ A @ C)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_prefix__of__antimono)). 140.59/43.01 thf(724,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:trace_1367752404list_a]: (((prefix1041802747list_a @ B @ C) => (prefix1041802747list_a @ A @ C)) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 140.59/43.01 thf(1238,plain,((~ (? [A:nat,B:nat]: (ord_less_nat @ (plus_plus_nat @ A @ B) @ A)))),inference(miniscope,[status(thm)],[1237])). 140.59/43.01 thf(1239,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A)))),inference(cnf,[status(esa)],[1238])). 140.59/43.01 thf(4213,plain,(! [B:nat,A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ A)))),inference(paramod_ordered,[status(thm)],[837,1239])). 140.59/43.01 thf(4228,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != ia) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[4213])). 140.59/43.01 thf(4238,plain,(! [A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) @ A) != ia))),inference(simp,[status(thm)],[4228])). 140.59/43.01 thf(193,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 @ (plus_plus_nat @ (A @ B) @ C) @ (A @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_mono__nat__linear__lb)). 140.59/43.01 thf(917,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 @ (plus_plus_nat @ (A @ B) @ C) @ (A @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 140.59/43.01 thf(126,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: (((ord_le699472955list_a @ B @ A) = (B = A)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_antisym__conv)). 140.59/43.01 thf(702,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: (((ord_le699472955list_a @ B @ A) = (B = A)) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 140.59/43.01 thf(163,axiom,((prefix1041802747list_a @ pi @ sigma2)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_assms_I2_J)). 140.59/43.01 thf(817,plain,((prefix1041802747list_a @ pi @ sigma2)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 140.59/43.01 thf(88,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ord__eq__le__subst)). 140.59/43.01 thf(559,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 140.59/43.01 thf(109,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ A @ B) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_le__neq__trans)). 140.59/43.01 thf(638,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 140.59/43.01 thf(233,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((A = B) & (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_add__mono__thms__linordered__field_I2_J)). 140.59/43.01 thf(1087,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((A = B) & (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 140.59/43.01 thf(253,axiom,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:trace_1367752404list_a,D:nat]: ((prefix1041802747list_a @ A @ B) => ((prefix1041802747list_a @ A @ C) => ((ord_less_nat @ D @ (plen_P694648887list_a @ A)) => ((tau_Pr257024512list_a @ B @ D) = (tau_Pr257024512list_a @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241__092_060tau_062__prefix__conv)). 140.59/43.01 thf(1147,plain,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:trace_1367752404list_a,D:nat]: ((prefix1041802747list_a @ A @ B) => ((prefix1041802747list_a @ A @ C) => ((ord_less_nat @ D @ (plen_P694648887list_a @ A)) => ((tau_Pr257024512list_a @ B @ D) = (tau_Pr257024512list_a @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 140.59/43.01 thf(47,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((! [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 @ (C @ B) @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_order__subst2)). 140.59/43.01 thf(421,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: (((! [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 @ (C @ B) @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 140.59/43.01 thf(211,axiom,((~ (! [A:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ A)) => ((ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi))) => (~ (ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 140.59/43.01 thf(966,plain,((~ (! [A:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ A)) => ((ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi))) => (~ (ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 140.59/43.01 thf(967,plain,((~ (! [A:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ A)) => ((ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi))) => (~ (ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi))))))))),inference(polarity_switch,[status(thm)],[966])). 140.59/43.01 thf(969,plain,((ord_less_eq_nat @ sk85 @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(cnf,[status(esa)],[967])). 140.59/43.01 thf(15,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_add__le__mono)). 140.59/43.01 thf(323,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 140.59/43.01 thf(324,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D)))))),inference(miniscope,[status(thm)],[323])). 140.59/43.01 thf(325,plain,(! [D:nat,C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | (~ (ord_less_eq_nat @ C @ D)))),inference(cnf,[status(esa)],[324])). 140.59/43.01 thf(4,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A != B) & (ord_le699472955list_a @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_less__le)). 140.59/43.01 thf(289,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (A = B) & (ord_le699472955list_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 140.59/43.01 thf(12,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((ord_less_eq_nat @ D @ C) <= (A @ D))) => (? [D:nat]: (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)) & (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Nat_Oex__has__greatest__nat)). 140.59/43.01 thf(309,plain,((! [A:(nat > $o),B:nat,C:nat]: (((! [D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (A @ D))) => (? [D:nat]: (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)) & (A @ D)))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 140.59/43.01 thf(310,plain,((! [A:(nat > $o)]: (((? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ B) | ~ (A @ C))) => (? [B:nat]: (! [C:nat]: ((A @ C) => (ord_less_eq_nat @ C @ B)) & (A @ B)))) | ~ (? [B:nat]: (A @ B))))),inference(miniscope,[status(thm)],[309])). 140.59/43.01 thf(313,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (ord_less_eq_nat @ (sk2 @ B @ (A)) @ B)) | (A @ (sk3 @ (A))) | (~ (A @ C)))),inference(cnf,[status(esa)],[310])). 140.59/43.01 thf(316,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (ord_less_eq_nat @ (sk2 @ B @ (A)) @ B)) | (A @ (sk3 @ (A))) | (~ (A @ C)))),inference(simp,[status(thm)],[313])). 140.59/43.01 thf(302,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = ((=) @ nat))),inference(lifteq,[status(thm)],[301])). 140.59/43.01 thf(1406,plain,(((ord_less_nat) = ((=) @ nat)) | ((^ [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) & ~ (B = A))))),inference(paramod_ordered,[status(thm)],[302,878])). 140.59/43.01 thf(1413,plain,(((ord_less_nat) = ((=) @ nat)) | ((ord_less_eq_nat) != (ord_less_eq_nat)) | ((^ [A:nat,B:nat]: (ord_less_eq_nat @ B @ A)) != (^ [A:nat,B:nat]: ~ (B = A)))),inference(simp,[status(thm)],[1406])). 140.59/43.01 thf(1415,plain,(((ord_less_nat) = ((=) @ nat)) | ((^ [A:nat,B:nat]: (ord_less_eq_nat @ B @ A)) != (^ [A:nat,B:nat]: ~ (B = A)))),inference(simp,[status(thm)],[1413])). 140.59/43.01 thf(63,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_add__le__imp__le__right)). 140.59/43.01 thf(492,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 140.59/43.01 thf(50,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_le__add1)). 140.59/43.01 thf(442,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 140.59/43.01 thf(443,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(cnf,[status(esa)],[442])). 140.59/43.01 thf(3457,plain,(! [B:nat,A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ A)))),inference(paramod_ordered,[status(thm)],[782,1239])). 140.59/43.01 thf(3468,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != k) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[3457])). 140.59/43.01 thf(3473,plain,(! [A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) @ A) != k))),inference(simp,[status(thm)],[3468])). 140.59/43.01 thf(72,axiom,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ja))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062)). 140.59/43.01 thf(514,plain,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 140.59/43.01 thf(254,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_less__not__refl2)). 140.59/43.01 thf(1151,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 140.59/43.01 thf(80,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_order_Ostrict__iff__order)). 140.59/43.01 thf(531,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 140.59/43.01 thf(532,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))))),inference(lifteq,[status(thm)],[531])). 140.59/43.01 thf(290,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (A = B) & (ord_le699472955list_a @ A @ B))))),inference(lifteq,[status(thm)],[289])). 140.59/43.01 thf(1382,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (A = B) & (ord_le699472955list_a @ A @ B)))) | ((ord_le887097159list_a) != (ord_le887097159list_a))),inference(paramod_ordered,[status(thm)],[532,290])). 140.59/43.01 thf(1383,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (A = B) & (ord_le699472955list_a @ A @ B))))),inference(pattern_uni,[status(thm)],[1382:[]])). 140.59/43.01 thf(894,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(lifteq,[status(thm)],[893])). 140.59/43.01 thf(1302,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(rewrite,[status(thm)],[338,894])). 140.59/43.01 thf(145,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ E @ F))) => (? [E:nat]: ! [F:nat]: ((((C @ F) | (A @ F)) = ((D @ F) | (B @ F))) <= (ord_less_nat @ E @ F)))) <= (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_pinf_I2_J)). 140.59/43.01 thf(756,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ E @ F))) => (? [E:nat]: ! [F:nat]: ((((C @ F) | (A @ F)) = ((D @ F) | (B @ F))) | ~ (ord_less_nat @ E @ F)))) | ~ (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 140.59/43.01 thf(249,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_not__le)). 140.59/43.01 thf(1136,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 140.59/43.01 thf(171,axiom,((! [A:trace_1367752404list_a,B:nat,C:nat]: (((ord_less_nat @ C @ B) => ((tau_Pr257024512list_a @ A @ B) = (tau_Pr257024512list_a @ A @ C))) <= (ord_less_eq_nat @ (tau_Pr257024512list_a @ A @ B) @ (tau_Pr257024512list_a @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_le___092_060tau_062__less)). 140.59/43.01 thf(834,plain,((! [A:trace_1367752404list_a,B:nat,C:nat]: (((ord_less_nat @ C @ B) => ((tau_Pr257024512list_a @ A @ B) = (tau_Pr257024512list_a @ A @ C))) | ~ (ord_less_eq_nat @ (tau_Pr257024512list_a @ A @ B) @ (tau_Pr257024512list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 140.59/43.01 thf(146,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_add__less__le__mono)). 140.59/43.01 thf(766,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 140.59/43.01 thf(259,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_minf_I3_J)). 140.59/43.01 thf(1166,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 140.59/43.01 thf(1167,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ B @ (sk111 @ A))) | (~ (B = A)))),inference(cnf,[status(esa)],[1166])). 140.59/43.01 thf(1168,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ B @ (sk111 @ A))))),inference(lifteq,[status(thm)],[1167])). 140.59/43.01 thf(1169,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ (sk111 @ A))))),inference(simp,[status(thm)],[1168])). 140.59/43.01 thf(3175,plain,(! [B:nat,A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(paramod_ordered,[status(thm)],[782,935])). 140.59/43.01 thf(3179,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != k) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != B))),inference(simp,[status(thm)],[3175])). 140.59/43.01 thf(3189,plain,(! [A:nat] : (((plus_plus_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != k))),inference(simp,[status(thm)],[3179])). 140.59/43.01 thf(136,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_trans__less__add1)). 140.59/43.01 thf(734,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 140.59/43.01 thf(6,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_linear)). 140.59/43.01 thf(293,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 140.59/43.01 thf(178,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_less__asym_H)). 140.59/43.01 thf(866,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 140.59/43.01 thf(39,axiom,((! [A:prefix1027212443list_a]: (ord_le699472955list_a @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_dual__order_Orefl)). 140.59/43.01 thf(396,plain,((! [A:prefix1027212443list_a]: (ord_le699472955list_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 140.59/43.01 thf(215,axiom,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => ((? [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_nat @ E @ D) & (ord_less_eq_nat @ A @ E))) & (ord_less_eq_nat @ A @ D))) <= (~ (C @ B)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_complete__interval)). 140.59/43.01 thf(988,plain,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => (? [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_nat @ E @ D) & (ord_less_eq_nat @ A @ E))) & (ord_less_eq_nat @ A @ D)) | (C @ B))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 140.59/43.01 thf(270,axiom,((! [A:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b)) => (ord_less_nat @ A @ (plen_P694648887list_a @ pi))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211__C3_C)). 140.59/43.01 thf(1201,plain,((! [A:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b)) => (ord_less_nat @ A @ (plen_P694648887list_a @ pi))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 140.59/43.01 thf(312,plain,(! [D:nat,C:nat,B:nat,A:(nat > $o)] : ((A @ (sk2 @ B @ (A))) | (~ (A @ C)) | (ord_less_eq_nat @ C @ (sk3 @ (A))) | (~ (A @ D)))),inference(cnf,[status(esa)],[310])). 140.59/43.01 thf(228,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_add__le__less__mono)). 140.59/43.01 thf(1072,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 140.59/43.01 thf(54,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add__le__mono1)). 140.59/43.01 thf(453,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 140.59/43.01 thf(1692,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk75 @ A))))),inference(paramod_ordered,[status(thm)],[782,871])). 140.59/43.01 thf(1696,plain,(! [A:nat] : ((k != A) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (sk75 @ A)))),inference(simp,[status(thm)],[1692])). 140.59/43.01 thf(1697,plain,(((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (sk75 @ k))),inference(simp,[status(thm)],[1696])). 140.59/43.01 thf(141,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_verit__comp__simplify1_I1_J)). 140.59/43.01 thf(746,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 140.59/43.01 thf(747,plain,((~ (? [A:nat]: (ord_less_nat @ A @ A)))),inference(miniscope,[status(thm)],[746])). 140.59/43.01 thf(748,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ A)))),inference(cnf,[status(esa)],[747])). 140.59/43.01 thf(3511,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk110 @ A)) != (ord_less_nat @ B @ B)))),inference(paramod_ordered,[status(thm)],[1163,748])). 140.59/43.01 thf(3541,plain,(! [B:nat,A:nat] : ((A != B) | ((sk110 @ A) != B))),inference(simp,[status(thm)],[3511])). 140.59/43.01 thf(3559,plain,(! [A:nat] : (((sk110 @ A) != A))),inference(simp,[status(thm)],[3541])). 140.59/43.01 thf(235,axiom,((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Until_Oprems)). 140.59/43.01 thf(1094,plain,((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 140.59/43.01 thf(4257,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk120 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[1094,1216])). 140.59/43.01 thf(4272,plain,(! [A:nat] : (((sk120 @ A) != ia) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[4257])). 140.59/43.01 thf(4285,plain,(((sk120 @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia)),inference(simp,[status(thm)],[4272])). 140.59/43.01 thf(5,axiom,((! [A:prefix1027212443list_a]: ? [B:trace_1367752404list_a]: (prefix1041802747list_a @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ex__prefix__of)). 140.59/43.01 thf(291,plain,((! [A:prefix1027212443list_a]: ? [B:trace_1367752404list_a]: (prefix1041802747list_a @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 140.59/43.01 thf(292,plain,(! [A:prefix1027212443list_a] : ((prefix1041802747list_a @ A @ (sk1 @ A)))),inference(cnf,[status(esa)],[291])). 140.59/43.01 thf(950,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(lifteq,[status(thm)],[949])). 140.59/43.01 thf(1437,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[950,878])). 140.59/43.01 thf(1438,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(pattern_uni,[status(thm)],[1437:[]])). 140.59/43.01 thf(195,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_136_order_Ostrict__trans)). 140.59/43.01 thf(925,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)],[195])). 140.59/43.01 thf(269,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_le__eq__less__or__eq)). 140.59/43.01 thf(1199,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 140.59/43.01 thf(160,axiom,((prefix1041802747list_a @ pi @ sigma)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I1_J)). 140.59/43.01 thf(810,plain,((prefix1041802747list_a @ pi @ sigma)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 140.59/43.01 thf(29,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_ab__semigroup__add__class_Oadd__ac_I1_J)). 140.59/43.01 thf(366,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 140.59/43.01 thf(244,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_dual__order_Oorder__iff__strict)). 140.59/43.01 thf(1123,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 140.59/43.01 thf(1124,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(lifteq,[status(thm)],[1123])). 140.59/43.01 thf(1311,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(rewrite,[status(thm)],[1124,894])). 140.59/43.01 thf(129,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: (((ord_le887097159list_a @ B @ C) => (ord_le887097159list_a @ A @ C)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_order_Ostrict__trans1)). 140.59/43.01 thf(714,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: (((ord_le887097159list_a @ B @ C) => (ord_le887097159list_a @ A @ C)) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 140.59/43.01 thf(71,axiom,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_dual__order_Oeq__iff)). 140.59/43.01 thf(512,plain,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 140.59/43.01 thf(49,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: (((ord_le887097159list_a @ C @ B) <= (ord_le887097159list_a @ C @ A)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_dual__order_Ostrict__trans1)). 140.59/43.01 thf(439,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ C @ B) | ~ (ord_le887097159list_a @ C @ A) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 140.59/43.01 thf(83,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_nat__le__iff__add)). 140.59/43.01 thf(546,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 140.59/43.01 thf(155,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_less__not__refl3)). 140.59/43.01 thf(793,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 140.59/43.01 thf(2407,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk99 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[1233,1047])). 140.59/43.01 thf(2420,plain,(! [A:nat] : (((sk99 @ A) != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2407])). 140.59/43.01 thf(2441,plain,(((sk99 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != i3)),inference(simp,[status(thm)],[2420])). 140.59/43.01 thf(262,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_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_160_order__less__le__subst1)). 140.59/43.01 thf(1174,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_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)],[262])). 140.59/43.01 thf(275,axiom,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))) <= (ord_le699472955list_a @ C @ D)) <= (ord_less_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_order__less__le__subst1)). 140.59/43.02 thf(1217,plain,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: (((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))) | ~ (ord_le699472955list_a @ C @ D) | ~ (ord_less_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 140.59/43.02 thf(165,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_less__asym)). 140.59/43.02 thf(820,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 140.59/43.02 thf(134,axiom,((! [A:trace_1367752404list_a,B:nat,C:nat]: ((ord_less_nat @ B @ C) <= (ord_less_nat @ (tau_Pr257024512list_a @ A @ B) @ (tau_Pr257024512list_a @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_less___092_060tau_062D)). 140.59/43.02 thf(729,plain,((! [A:trace_1367752404list_a,B:nat,C:nat]: ((ord_less_nat @ B @ C) | ~ (ord_less_nat @ (tau_Pr257024512list_a @ A @ B) @ (tau_Pr257024512list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 140.59/43.02 thf(208,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_add__strict__right__mono)). 140.59/43.02 thf(957,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 140.59/43.02 thf(234,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_antisym__conv3)). 140.59/43.02 thf(1091,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 140.59/43.02 thf(43,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ C @ B) <= (ord_le699472955list_a @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_dual__order_Otrans)). 140.59/43.02 thf(407,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ C @ B) | ~ (ord_le699472955list_a @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 140.59/43.02 thf(123,axiom,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ (B @ C)) => (((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) <= (ord_le699472955list_a @ E @ F))) => (ord_le887097159list_a @ A @ (B @ D))) <= (ord_le699472955list_a @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_order__less__le__subst1)). 140.59/43.02 thf(693,plain,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ (B @ C)) => (((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) | ~ (ord_le699472955list_a @ E @ F))) => (ord_le887097159list_a @ A @ (B @ D))) | ~ (ord_le699472955list_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 140.59/43.02 thf(106,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ C @ D) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_add__mono__thms__linordered__semiring_I1_J)). 140.59/43.02 thf(630,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ C @ D) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 140.59/43.02 thf(62,axiom,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le699472955list_a @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_ord__eq__le__subst)). 140.59/43.02 thf(484,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le699472955list_a @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 140.59/43.02 thf(182,axiom,((! [A:nat,B:list_a]: (((sat_a @ sigma @ B @ A @ phi_1) = (sat_a @ sigma2 @ B @ A @ phi_1)) <= (ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Until_OIH_I1_J)). 140.59/43.02 thf(879,plain,((! [A:nat,B:list_a]: (((sat_a @ sigma @ B @ A @ phi_1) = (sat_a @ sigma2 @ B @ A @ phi_1)) | ~ (ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 140.59/43.02 thf(3507,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_nat @ A @ (sk110 @ A)) != (ord_less_nat @ (plus_plus_nat @ B @ C) @ B)))),inference(paramod_ordered,[status(thm)],[1163,1239])). 140.59/43.02 thf(3536,plain,(! [C:nat,B:nat,A:nat] : ((A != (plus_plus_nat @ B @ C)) | ((sk110 @ A) != B))),inference(simp,[status(thm)],[3507])). 140.59/43.02 thf(3556,plain,(! [B:nat,A:nat] : (((sk110 @ (plus_plus_nat @ A @ B)) != A))),inference(simp,[status(thm)],[3536])). 140.59/43.02 thf(185,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_order_Ostrict__implies__not__eq)). 140.59/43.02 thf(889,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 140.59/43.02 thf(230,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_add__strict__left__mono)). 140.59/43.02 thf(1079,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 140.59/43.02 thf(267,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_order_Oorder__iff__strict)). 140.59/43.02 thf(1195,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 140.59/43.02 thf(85,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_15_le__trans)). 140.59/43.02 thf(551,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)],[85])). 140.59/43.02 thf(22,axiom,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_eq__iff)). 140.59/43.02 thf(345,plain,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 140.59/43.02 thf(346,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))) = ((=) @ prefix1027212443list_a))),inference(lifteq,[status(thm)],[345])). 140.59/43.02 thf(1389,plain,(((ord_le887097159list_a) = ((=) @ prefix1027212443list_a)) | ((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))) != (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))))),inference(paramod_ordered,[status(thm)],[346,532])). 140.59/43.02 thf(1390,plain,(((ord_le887097159list_a) = ((=) @ prefix1027212443list_a)) | ((ord_le699472955list_a) != (ord_le699472955list_a)) | ((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (ord_le699472955list_a @ B @ A)) != (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ~ (A = B)))),inference(simp,[status(thm)],[1389])). 140.59/43.02 thf(1392,plain,(((ord_le887097159list_a) = ((=) @ prefix1027212443list_a)) | ((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (ord_le699472955list_a @ B @ A)) != (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ~ (A = B)))),inference(simp,[status(thm)],[1390])). 140.59/43.02 thf(55,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_less__imp__le)). 140.59/43.02 thf(456,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 140.59/43.02 thf(16,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: ((((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (C @ E) @ (C @ F)) <= (ord_le699472955list_a @ E @ F))) => (ord_le887097159list_a @ (C @ A) @ D)) <= (ord_le887097159list_a @ (C @ B) @ D)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_order__le__less__subst2)). 140.59/43.02 thf(326,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: (((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (C @ E) @ (C @ F)) | ~ (ord_le699472955list_a @ E @ F))) => (ord_le887097159list_a @ (C @ A) @ D)) | ~ (ord_le887097159list_a @ (C @ B) @ D) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 140.59/43.02 thf(327,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: (! [C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: (((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (C @ E) @ (C @ F)) | ~ (ord_le699472955list_a @ E @ F))) => (ord_le887097159list_a @ (C @ A) @ D)) | ~ (ord_le887097159list_a @ (C @ B) @ D)) | ~ (ord_le699472955list_a @ A @ B)))),inference(miniscope,[status(thm)],[326])). 140.59/43.02 thf(329,plain,(! [D:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),B:prefix1027212443list_a,A:prefix1027212443list_a] : ((ord_le699472955list_a @ (sk4 @ D @ (C) @ B @ A) @ (sk5 @ D @ (C) @ B @ A)) | (ord_le887097159list_a @ (C @ A) @ D) | (~ (ord_le887097159list_a @ (C @ B) @ D)) | (~ (ord_le699472955list_a @ A @ B)))),inference(cnf,[status(esa)],[327])). 140.59/43.02 thf(263,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_ord__less__eq__subst)). 140.59/43.02 thf(1178,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: (((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 140.59/43.02 thf(76,axiom,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_order__class_Oorder_Oeq__iff)). 140.59/43.02 thf(522,plain,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 140.59/43.02 thf(170,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_less__imp__not__eq)). 140.59/43.02 thf(830,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 140.59/43.02 thf(139,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_nat__less__le)). 140.59/43.02 thf(742,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 140.59/43.02 thf(13,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_add__left__cancel)). 140.59/43.02 thf(317,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 140.59/43.02 thf(243,axiom,((~ (! [A:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ A)) => ((ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) => (~ (ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 140.59/43.02 thf(1118,plain,((~ (! [A:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ A)) => ((ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) => (~ (ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 140.59/43.02 thf(1119,plain,((~ (! [A:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ A)) => ((ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) => (~ (ord_less_eq_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))))))))),inference(polarity_switch,[status(thm)],[1118])). 140.59/43.02 thf(1121,plain,((ord_less_eq_nat @ sk108 @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(cnf,[status(esa)],[1119])). 140.59/43.02 thf(278,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_dual__order_Ostrict__implies__not__eq)). 140.59/43.02 thf(1227,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 140.59/43.02 thf(42,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (A = B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_add__mono__thms__linordered__semiring_I2_J)). 140.59/43.02 thf(403,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (A = B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 140.59/43.02 thf(36,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((~ (ord_le887097159list_a @ A @ B)) => ((ord_le699472955list_a @ A @ B) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_antisym__conv1)). 140.59/43.02 thf(388,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((~ (ord_le887097159list_a @ A @ B)) => ((ord_le699472955list_a @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 140.59/43.02 thf(26,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: (((ord_le887097159list_a @ A @ C) <= (ord_le887097159list_a @ B @ C)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_le__less__trans)). 140.59/43.02 thf(356,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ C) | ~ (ord_le887097159list_a @ B @ C) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 140.59/43.02 thf(97,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: ((((ord_le699472955list_a @ (C @ A) @ D) <= (! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (C @ E) @ (C @ F)) <= (ord_le699472955list_a @ E @ F)))) <= ((C @ B) = D)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_ord__le__eq__subst)). 140.59/43.02 thf(593,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_le699472955list_a @ (C @ A) @ D) | ~ (! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (C @ E) @ (C @ F)) | ~ (ord_le699472955list_a @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 140.59/43.02 thf(101,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: (((A = B) <= (ord_le699472955list_a @ B @ A)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_antisym)). 140.59/43.02 thf(610,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) | ~ (ord_le699472955list_a @ B @ A) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 140.59/43.02 thf(66,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) <= (ord_le887097159list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_dual__order_Ostrict__implies__order)). 140.59/43.02 thf(499,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) | ~ (ord_le887097159list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 140.59/43.02 thf(124,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ ((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add__leE)). 140.59/43.02 thf(697,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ (~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 140.59/43.02 thf(1196,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(lifteq,[status(thm)],[1195])). 140.59/43.02 thf(1314,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(rewrite,[status(thm)],[1196,894])). 140.59/43.02 thf(1514,plain,(((^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B)))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) != (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(paramod_ordered,[status(thm)],[1302,1314])). 140.59/43.02 thf(1515,plain,(((^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(pattern_uni,[status(thm)],[1514:[]])). 140.59/43.02 thf(3614,plain,(((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))) = (ord_less_nat)) | ((^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))) != (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(paramod_ordered,[status(thm)],[1300,1515])). 140.59/43.02 thf(3615,plain,(((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))) = (ord_less_nat))),inference(pattern_uni,[status(thm)],[3614:[]])). 140.59/43.02 thf(281,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_122_less__trans)). 140.59/43.02 thf(1234,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)],[281])). 140.59/43.02 thf(153,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) & (ord_less_nat @ A @ B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_add__mono__thms__linordered__field_I5_J)). 140.59/43.02 thf(783,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) & (ord_less_nat @ A @ B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 140.59/43.02 thf(175,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_less__not__sym)). 140.59/43.02 thf(857,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 140.59/43.02 thf(4253,plain,(((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(paramod_ordered,[status(thm)],[1094,286])). 140.59/43.02 thf(4263,plain,((k != ia) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[4253])). 140.59/43.02 thf(328,plain,(! [D:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),B:prefix1027212443list_a,A:prefix1027212443list_a] : ((~ (ord_le699472955list_a @ (C @ (sk4 @ D @ (C) @ B @ A)) @ (C @ (sk5 @ D @ (C) @ B @ A)))) | (ord_le887097159list_a @ (C @ A) @ D) | (~ (ord_le887097159list_a @ (C @ B) @ D)) | (~ (ord_le699472955list_a @ A @ B)))),inference(cnf,[status(esa)],[327])). 140.59/43.02 thf(1294,plain,(! [A:nat] : (((ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat)) = (ord_less_nat @ A)))),inference(func_ext,[status(esa)],[819])). 140.59/43.02 thf(1252,plain,(! [A:nat] : (((ord_less_eq_nat @ A) = (^ [B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),inference(func_ext,[status(esa)],[338])). 140.59/43.02 thf(4967,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A) = (^ [C:nat]: ? [D:nat]: (C = (plus_plus_nat @ B @ D)))) | ((ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat)) != (ord_less_eq_nat @ B)))),inference(paramod_ordered,[status(thm)],[1294,1252])). 140.59/43.02 thf(4968,plain,(! [A:nat] : (((ord_less_nat @ A) = (^ [B:nat]: ? [C:nat]: (B = (plus_plus_nat @ (plus_plus_nat @ A @ one_one_nat) @ C)))))),inference(pattern_uni,[status(thm)],[4967:[bind(A, $thf(C)),bind(B, $thf(plus_plus_nat @ C @ one_one_nat))]])). 140.59/43.02 thf(4973,plain,(! [A:nat] : (((ord_less_nat @ A) = (^ [B:nat]: ? [C:nat]: (B = (plus_plus_nat @ (plus_plus_nat @ A @ one_one_nat) @ C)))))),inference(simp,[status(thm)],[4968])). 140.59/43.02 thf(321,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(cnf,[status(esa)],[320])). 140.59/43.02 thf(322,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(lifteq,[status(thm)],[321])). 140.59/43.02 thf(6862,plain,(! [A:nat] : (((ord_less_nat @ A) = (^ [B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ (plus_plus_nat @ one_one_nat @ C))))))),inference(rewrite,[status(thm)],[4973,322])). 140.59/43.02 thf(4249,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk111 @ A))))),inference(paramod_ordered,[status(thm)],[1094,1169])). 140.59/43.02 thf(4262,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk111 @ A)))),inference(simp,[status(thm)],[4249])). 140.59/43.02 thf(4276,plain,(((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk111 @ ia))),inference(simp,[status(thm)],[4262])). 140.59/43.02 thf(20,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_64_dual__order_Oantisym)). 140.59/43.02 thf(339,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)],[20])). 140.59/43.02 thf(86,axiom,((! [A:nat,B:nat,C:trace_1367752404list_a]: ? [D:nat]: ((ord_less_eq_nat @ B @ (tau_Pr257024512list_a @ C @ D)) & (ord_less_eq_nat @ A @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_ex__le___092_060tau_062)). 140.59/43.02 thf(554,plain,((! [A:nat,B:nat,C:trace_1367752404list_a]: ? [D:nat]: ((ord_less_eq_nat @ B @ (tau_Pr257024512list_a @ C @ D)) & (ord_less_eq_nat @ A @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 140.59/43.02 thf(118,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (! [C:nat]: (B != (plus_plus_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_less__eqE)). 140.59/43.02 thf(669,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (! [C:nat]: ~ (B = (plus_plus_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 140.59/43.02 thf(1691,plain,(((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(paramod_ordered,[status(thm)],[782,286])). 140.59/43.02 thf(1695,plain,((k != k) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[1691])). 140.59/43.02 thf(1700,plain,(((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[1695])). 140.59/43.02 thf(255,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_134_linorder__cases)). 140.59/43.02 thf(1155,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)],[255])). 140.59/43.02 thf(218,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_10_linorder__neqE__nat)). 140.59/43.02 thf(1028,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)],[218])). 140.59/43.02 thf(231,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_minf_I5_J)). 140.59/43.02 thf(1082,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 140.59/43.02 thf(189,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((A @ D) <= (ord_less_nat @ D @ C))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__induct)). 140.59/43.02 thf(901,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((A @ D) | ~ (ord_less_nat @ D @ C))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 140.59/43.02 thf(229,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => (((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) => (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_less__add__eq__less)). 140.59/43.02 thf(1075,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => (((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) => (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 140.59/43.02 thf(272,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C))) <= (! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) <= (ord_less_nat @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_less__mono__imp__le__mono)). 140.59/43.02 thf(1207,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C))) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) | ~ (ord_less_nat @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 140.59/43.02 thf(96,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ A @ C) <= (ord_le699472955list_a @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_order__trans)). 140.59/43.02 thf(590,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ A @ C) | ~ (ord_le699472955list_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 140.59/43.02 thf(652,plain,(! [A:nat] : (((one_one_nat = A) = (A = one_one_nat)))),inference(cnf,[status(esa)],[651])). 140.59/43.02 thf(653,plain,(! [A:nat] : (((one_one_nat = A) = (A = one_one_nat)))),inference(lifteq,[status(thm)],[652])). 140.59/43.02 thf(311,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((A @ (sk2 @ B @ (A))) | (A @ (sk3 @ (A))) | (~ (A @ C)))),inference(cnf,[status(esa)],[310])). 140.59/43.02 thf(315,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((A @ (sk2 @ B @ (A))) | (A @ (sk3 @ (A))) | (~ (A @ C)))),inference(simp,[status(thm)],[311])). 140.59/43.02 thf(4746,plain,(! [D:nat,C:nat,B:(nat > $o),A:nat] : ((B @ (sk2 @ C @ (B))) | (B @ (sk3 @ (B))) | (~ (A = one_one_nat)) | ((one_one_nat = A) != (B @ D)))),inference(paramod_ordered,[status(thm)],[653,315])). 140.59/43.02 thf(4762,plain,(! [D:nat,C:nat,B:(nat > $o),A:nat] : ((A != one_one_nat) | (B @ (sk2 @ C @ (B))) | (B @ (sk3 @ (B))) | ((one_one_nat = A) != (B @ D)))),inference(lifteq,[status(thm)],[4746])). 140.59/43.02 thf(4779,plain,(! [A:nat] : ((one_one_nat = (sk3 @ ((=) @ nat @ one_one_nat))) | (one_one_nat = (sk2 @ A @ ((=) @ nat @ one_one_nat))))),inference(pre_uni,[status(thm)],[4762:[bind(A, $thf(one_one_nat)),bind(B, $thf((=) @ nat @ one_one_nat)),bind(C, $thf(C)),bind(D, $thf(one_one_nat))]])). 140.59/43.02 thf(4845,plain,(! [A:nat] : (((sk3 @ ((=) @ nat @ one_one_nat)) = one_one_nat) | ((sk2 @ A @ ((=) @ nat @ one_one_nat)) = one_one_nat))),inference(lifteq,[status(thm)],[4779])). 140.59/43.02 thf(4846,plain,(! [A:nat] : (((sk3 @ ((=) @ nat @ one_one_nat)) = one_one_nat) | ((sk2 @ A @ ((=) @ nat @ one_one_nat)) = one_one_nat))),inference(simp,[status(thm)],[4845])). 140.59/43.02 thf(73,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_le__cases)). 140.59/43.02 thf(515,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 140.59/43.02 thf(114,axiom,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((ord_le887097159list_a @ A @ (B @ C)) => (((ord_le887097159list_a @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_order__less__le__subst1)). 140.59/43.02 thf(654,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((ord_le887097159list_a @ A @ (B @ C)) => ((ord_le887097159list_a @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 140.59/43.02 thf(285,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_23_pinf_I8_J)). 140.59/43.02 thf(1246,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)],[285])). 140.59/43.02 thf(151,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_order_Ostrict__trans1)). 140.59/43.02 thf(779,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 140.59/43.02 thf(279,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ C @ D) & (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_add__mono__thms__linordered__field_I3_J)). 140.59/43.02 thf(1231,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ C @ D) & (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 140.59/43.02 thf(75,axiom,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ j))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062)). 140.59/43.02 thf(521,plain,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ j))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 140.59/43.02 thf(4535,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ j))),inference(rewrite,[status(thm)],[521,322])). 140.59/43.02 thf(1317,plain,(((^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A)))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) != (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(paramod_ordered,[status(thm)],[1314,1311])). 140.59/43.02 thf(1318,plain,(((^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(pattern_uni,[status(thm)],[1317:[]])). 140.59/43.02 thf(201,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_trans__less__add2)). 140.59/43.02 thf(938,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 140.59/43.02 thf(194,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 @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_order__le__less__subst1)). 140.59/43.02 thf(921,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 @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 140.59/43.02 thf(82,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_group__cancel_Oadd1)). 140.59/43.02 thf(541,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 140.59/43.02 thf(260,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_nat @ C @ D) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_add__mono__thms__linordered__field_I4_J)). 140.59/43.02 thf(1170,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_nat @ C @ D) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 140.59/43.02 thf(40,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ A @ C) <= (ord_le699472955list_a @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_order_Otrans)). 140.59/43.02 thf(398,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ A @ C) | ~ (ord_le699472955list_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 140.59/43.02 thf(87,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_le__add2)). 140.59/43.02 thf(557,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 140.59/43.02 thf(558,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(cnf,[status(esa)],[557])). 140.59/43.02 thf(149,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_less__irrefl)). 140.59/43.02 thf(773,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 140.59/43.02 thf(116,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_eq__refl)). 140.59/43.02 thf(662,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 140.59/43.02 thf(4261,plain,(! [B:nat,A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(paramod_ordered,[status(thm)],[1094,935])). 140.59/43.02 thf(4275,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != ia) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != B))),inference(simp,[status(thm)],[4261])). 140.59/43.02 thf(4288,plain,(! [A:nat] : (((plus_plus_nat @ A @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia))),inference(simp,[status(thm)],[4275])). 140.59/43.02 thf(284,axiom,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_ord__less__eq__trans)). 140.59/43.02 thf(1241,plain,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 140.59/43.02 thf(3505,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk110 @ A)) != (ord_less_nat @ (sk99 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[1163,1047])). 140.59/43.02 thf(3545,plain,(! [B:nat,A:nat] : ((A != (sk99 @ B)) | ((sk110 @ A) != B))),inference(simp,[status(thm)],[3505])). 140.59/43.02 thf(3563,plain,(! [A:nat] : (((sk110 @ (sk99 @ A)) != A))),inference(simp,[status(thm)],[3545])). 140.59/43.02 thf(190,axiom,((! [A:nat,B:trace_1367752404list_a,C:trace_1367752404list_a,D:formula_a]: (((monito1457594016ress_a @ B @ D @ A) = (monito1457594016ress_a @ C @ D @ A)) <= (! [E:nat]: (((tau_Pr257024512list_a @ B @ E) = (tau_Pr257024512list_a @ C @ E)) <= (ord_less_nat @ E @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_progress__time__conv)). 140.59/43.02 thf(906,plain,((! [A:nat,B:trace_1367752404list_a,C:trace_1367752404list_a,D:formula_a]: (((monito1457594016ress_a @ B @ D @ A) = (monito1457594016ress_a @ C @ D @ A)) | ~ (! [E:nat]: (((tau_Pr257024512list_a @ B @ E) = (tau_Pr257024512list_a @ C @ E)) | ~ (ord_less_nat @ E @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 140.59/43.02 thf(7,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_eq__refl)). 140.59/43.02 thf(295,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 140.59/43.02 thf(296,plain,(! [B:prefix1027212443list_a,A:prefix1027212443list_a] : ((ord_le699472955list_a @ A @ B) | (~ (A = B)))),inference(cnf,[status(esa)],[295])). 140.59/43.02 thf(297,plain,(! [B:prefix1027212443list_a,A:prefix1027212443list_a] : ((A != B) | (ord_le699472955list_a @ A @ B))),inference(lifteq,[status(thm)],[296])). 140.59/43.02 thf(298,plain,(! [A:prefix1027212443list_a] : ((ord_le699472955list_a @ A @ A))),inference(simp,[status(thm)],[297])). 140.59/43.02 thf(48,axiom,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)) => (((~ (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ B @ A)) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((~ ((~ (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ C @ A))) <= ((~ (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C))) <= ((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_le__cases3)). 140.59/43.02 thf(425,plain,((! [A:nat,B:nat,C:nat]: ((~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)) => ((~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ A)) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (~ (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ A)) | ~ (~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ C)) | ~ ((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 140.59/43.02 thf(1689,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ A)))),inference(paramod_ordered,[status(thm)],[782,748])). 140.59/43.02 thf(1693,plain,(! [A:nat] : ((k != A) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[1689])). 140.59/43.02 thf(1698,plain,(((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != k)),inference(simp,[status(thm)],[1693])). 140.59/43.02 thf(167,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_minf_I6_J)). 140.59/43.02 thf(824,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 140.59/43.02 thf(174,axiom,((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062)). 140.59/43.02 thf(856,plain,((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 140.59/43.02 thf(51,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_add__leD2)). 140.59/43.02 thf(444,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 140.59/43.02 thf(98,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_antisym)). 140.59/43.02 thf(601,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 140.59/43.02 thf(2043,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk111 @ A))))),inference(paramod_ordered,[status(thm)],[782,1169])). 140.59/43.02 thf(2045,plain,(! [A:nat] : ((k != A) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (sk111 @ A)))),inference(simp,[status(thm)],[2043])). 140.59/43.02 thf(2048,plain,(((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (sk111 @ k))),inference(simp,[status(thm)],[2045])). 140.59/43.02 thf(4260,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk75 @ A))))),inference(paramod_ordered,[status(thm)],[1094,871])). 140.59/43.02 thf(4270,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk75 @ A)))),inference(simp,[status(thm)],[4260])). 140.59/43.02 thf(4283,plain,(((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk75 @ ia))),inference(simp,[status(thm)],[4270])). 140.59/43.02 thf(245,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_44_minf_I7_J)). 140.59/43.02 thf(1125,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)],[245])). 140.59/43.02 thf(3456,plain,(! [B:nat,A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ A)))),inference(paramod_ordered,[status(thm)],[1233,1239])). 140.59/43.02 thf(3467,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[3456])). 140.59/43.02 thf(3472,plain,(! [A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) @ A) != i3))),inference(simp,[status(thm)],[3467])). 140.59/43.02 thf(743,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(lifteq,[status(thm)],[742])). 140.59/43.02 thf(213,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_141_not__less__iff__gr__or__eq)). 140.59/43.02 thf(975,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)],[213])). 140.59/43.02 thf(3174,plain,(! [B:nat,A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(paramod_ordered,[status(thm)],[1233,935])). 140.59/43.02 thf(3184,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != B))),inference(simp,[status(thm)],[3174])). 140.59/43.02 thf(3187,plain,(! [A:nat] : (((plus_plus_nat @ A @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != i3))),inference(simp,[status(thm)],[3184])). 140.59/43.02 thf(168,axiom,((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062)). 140.59/43.02 thf(826,plain,((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 140.59/43.02 thf(92,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_trans__le__add2)). 140.59/43.02 thf(577,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 140.59/43.02 thf(110,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) <= (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_dual__order_Otrans)). 140.59/43.02 thf(641,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 140.59/43.02 thf(200,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_less_eq_nat @ (plen_P694648887list_a @ A) @ (plen_P694648887list_a @ B)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_plen__mono)). 140.59/43.02 thf(936,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_less_eq_nat @ (plen_P694648887list_a @ A) @ (plen_P694648887list_a @ B)) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 140.59/43.02 thf(1370,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A)))) | ((ord_le887097159list_a) != (ord_le887097159list_a))),inference(paramod_ordered,[status(thm)],[532,372])). 140.59/43.02 thf(1371,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))))),inference(pattern_uni,[status(thm)],[1370:[]])). 140.59/43.02 thf(4219,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk75 @ A))))),inference(paramod_ordered,[status(thm)],[837,871])). 140.59/43.02 thf(4225,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk75 @ A)))),inference(simp,[status(thm)],[4219])). 140.59/43.02 thf(4236,plain,(((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk75 @ ia))),inference(simp,[status(thm)],[4225])). 140.59/43.02 thf(59,axiom,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((((C @ B) = D) => ((ord_le699472955list_a @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_ord__le__eq__subst)). 140.59/43.02 thf(466,plain,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((((C @ B) = D) => ((ord_le699472955list_a @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 140.59/43.02 thf(334,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat]: (! [D:nat]: ((ord_less_eq_nat @ C @ D) => ((ord_le699472955list_a @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))))) | ~ (ord_le699472955list_a @ A @ (B @ C))))),inference(miniscope,[status(thm)],[333])). 140.59/43.02 thf(335,plain,(! [D:nat,C:nat,B:(nat > prefix1027212443list_a),A:prefix1027212443list_a] : ((~ (ord_less_eq_nat @ C @ D)) | (ord_le699472955list_a @ A @ (B @ D)) | (~ (ord_le699472955list_a @ (B @ (sk6 @ D @ C @ (B) @ A)) @ (B @ (sk7 @ D @ C @ (B) @ A)))) | (~ (ord_le699472955list_a @ A @ (B @ C))))),inference(cnf,[status(esa)],[334])). 140.59/43.02 thf(24,axiom,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((((ord_le699472955list_a @ A @ (B @ D)) <= (! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) <= (ord_le699472955list_a @ E @ F)))) <= (ord_le699472955list_a @ C @ D)) <= (ord_le699472955list_a @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_order__subst1)). 140.59/43.02 thf(350,plain,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ (B @ D)) | ~ (! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) | ~ (ord_le699472955list_a @ E @ F))) | ~ (ord_le699472955list_a @ C @ D) | ~ (ord_le699472955list_a @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 140.59/43.02 thf(37,axiom,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:prefix1027212443list_a]: (((prefix1041802747list_a @ C @ B) => ((ord_le699472955list_a @ C @ A) | (ord_le699472955list_a @ A @ C))) <= (prefix1041802747list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_prefix__of__imp__linear)). 140.59/43.02 thf(391,plain,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:prefix1027212443list_a]: (((prefix1041802747list_a @ C @ B) => ((ord_le699472955list_a @ C @ A) | (ord_le699472955list_a @ A @ C))) | ~ (prefix1041802747list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 140.59/43.02 thf(250,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_order_Ostrict__trans2)). 140.59/43.02 thf(1139,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 140.59/43.02 thf(1407,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[878,743])). 140.59/43.02 thf(1408,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(pattern_uni,[status(thm)],[1407:[]])). 140.59/43.02 thf(222,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_nat @ (C @ E) @ (C @ F)) <= (ord_less_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_order__less__le__subst2)). 140.59/43.02 thf(1048,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 140.59/43.02 thf(33,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_add__leD1)). 140.59/43.02 thf(377,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 140.59/43.02 thf(137,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_25_minf_I8_J)). 140.59/43.02 thf(737,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)],[137])). 140.59/43.02 thf(70,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_le__Suc__ex)). 140.59/43.02 thf(509,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 140.59/43.02 thf(177,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_verit__comp__simplify1_I3_J)). 140.59/43.02 thf(863,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 140.59/43.02 thf(340,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ A)) | (B = A))),inference(cnf,[status(esa)],[339])). 140.59/43.02 thf(341,plain,(! [B:nat,A:nat] : ((B = A) | (~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ A)))),inference(lifteq,[status(thm)],[340])). 140.59/43.02 thf(3506,plain,(! [A:nat] : (((ord_less_nat @ A @ (sk110 @ A)) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1163,286])). 140.59/43.02 thf(3542,plain,(! [A:nat] : ((A != k) | ((sk110 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[3506])). 140.59/43.02 thf(3560,plain,(((sk110 @ k) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[3542])). 140.59/43.02 thf(6372,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ A)) | (A != (plen_P694648887list_a @ pi)) | (B != (sk110 @ k)))),inference(paramod_ordered,[status(thm)],[341,3560])). 140.59/43.02 thf(6373,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ A @ (sk110 @ k))) | (~ (ord_less_eq_nat @ (sk110 @ k) @ A)) | (A != (plen_P694648887list_a @ pi)))),inference(pattern_uni,[status(thm)],[6372:[bind(A, $thf(A)),bind(B, $thf(sk110 @ k))]])). 140.59/43.02 thf(6585,plain,((~ (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk110 @ k))) | (~ (ord_less_eq_nat @ (sk110 @ k) @ (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[6373])). 140.59/43.02 thf(99,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: (((A = B) | (ord_le887097159list_a @ A @ B)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_le__imp__less__or__eq)). 140.59/43.02 thf(604,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) | (ord_le887097159list_a @ A @ B) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 140.59/43.02 thf(28,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_eq__imp__le)). 140.59/43.02 thf(362,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 140.59/43.02 thf(89,axiom,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))) <= (ord_le699472955list_a @ C @ D)) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_order__subst1)). 140.59/43.02 thf(567,plain,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: (((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))) | ~ (ord_le699472955list_a @ C @ D) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 140.59/43.02 thf(103,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_add__left__imp__eq)). 140.59/43.02 thf(616,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 140.59/43.02 thf(10,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_86_order_Otrans)). 140.59/43.02 thf(303,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)],[10])). 140.59/43.02 thf(161,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_leD)). 140.59/43.02 thf(811,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 140.59/43.02 thf(64,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => (~ (ord_le887097159list_a @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_leD)). 140.59/43.02 thf(494,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => (~ (ord_le887097159list_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 140.59/43.02 thf(1338,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (A = B) & (ord_le699472955list_a @ A @ B)))) | ((ord_le887097159list_a) != (ord_le887097159list_a))),inference(paramod_ordered,[status(thm)],[372,290])). 140.59/43.02 thf(1339,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (A = B) & (ord_le699472955list_a @ A @ B))))),inference(pattern_uni,[status(thm)],[1338:[]])). 140.59/43.02 thf(125,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_le__refl)). 140.59/43.02 thf(700,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 140.59/43.02 thf(187,axiom,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((C) <= (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_less__imp__triv)). 140.59/43.02 thf(895,plain,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((C) | ~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 140.59/43.02 thf(147,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_38_pinf_I7_J)). 140.59/43.02 thf(769,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)],[147])). 140.59/43.02 thf(203,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_order_Oasym)). 140.59/43.02 thf(943,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 140.59/43.02 thf(17,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_add__le__cancel__left)). 140.59/43.02 thf(330,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 140.59/43.02 thf(2404,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk111 @ A))))),inference(paramod_ordered,[status(thm)],[1233,1169])). 140.59/43.02 thf(2425,plain,(! [A:nat] : ((i3 != A) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (sk111 @ A)))),inference(simp,[status(thm)],[2404])). 140.59/43.02 thf(2446,plain,(((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (sk111 @ i3))),inference(simp,[status(thm)],[2425])). 140.59/43.02 thf(4258,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ A)))),inference(paramod_ordered,[status(thm)],[1094,748])). 140.59/43.02 thf(4264,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[4258])). 140.59/43.02 thf(4277,plain,(((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != ia)),inference(simp,[status(thm)],[4264])). 140.59/43.02 thf(198,axiom,((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ k) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_that)). 140.59/43.02 thf(932,plain,((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ k) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 140.59/43.02 thf(224,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) <= (! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_order__le__less__subst2)). 140.59/43.02 thf(1061,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 140.59/43.02 thf(4778,plain,(! [A:nat] : (((sk3 @ (^ [B:nat]: (B = one_one_nat))) = one_one_nat) | ((sk2 @ A @ (^ [B:nat]: (B = one_one_nat))) = one_one_nat))),inference(pre_uni,[status(thm)],[4762:[bind(A, $thf(one_one_nat)),bind(B, $thf(^ [E:nat]: (E = one_one_nat))),bind(C, $thf(C)),bind(D, $thf(one_one_nat))]])). 140.59/43.02 thf(4843,plain,(! [A:nat] : (((sk3 @ (^ [B:nat]: (B = one_one_nat))) = one_one_nat) | ((sk2 @ A @ (^ [B:nat]: (B = one_one_nat))) = one_one_nat))),inference(lifteq,[status(thm)],[4778])). 140.59/43.02 thf(4844,plain,(! [A:nat] : (((sk3 @ (^ [B:nat]: (B = one_one_nat))) = one_one_nat) | ((sk2 @ A @ (^ [B:nat]: (B = one_one_nat))) = one_one_nat))),inference(simp,[status(thm)],[4843])). 140.59/43.02 thf(1690,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk99 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[782,1047])). 140.59/43.02 thf(1694,plain,(! [A:nat] : (((sk99 @ A) != k) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[1690])). 140.59/43.02 thf(1699,plain,(((sk99 @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != k)),inference(simp,[status(thm)],[1694])). 140.59/43.02 thf(183,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_dual__order_Ostrict__trans2)). 140.59/43.02 thf(883,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 140.59/43.02 thf(216,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_less__linear)). 140.59/43.02 thf(1015,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 140.59/43.02 thf(241,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_170_antisym__conv2)). 140.59/43.02 thf(1113,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)],[241])). 140.59/43.02 thf(8,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_add__le__imp__le__left)). 140.59/43.02 thf(299,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 140.59/43.02 thf(1250,plain,(! [A:nat] : (((^ [B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = ((=) @ nat @ A)))),inference(func_ext,[status(esa)],[302])). 140.59/43.02 thf(115,axiom,((! [A:nat,B:nat,C:nat]: ((A = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_add__right__imp__eq)). 140.59/43.02 thf(658,plain,((! [A:nat,B:nat,C:nat]: ((A = C) | ~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 140.59/43.02 thf(191,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((~ (ord_less_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_pinf_I5_J)). 140.59/43.02 thf(912,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (ord_less_nat @ C @ A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 140.59/43.02 thf(169,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_3_nat__neq__iff)). 140.59/43.02 thf(827,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)],[169])). 140.59/43.02 thf(38,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_81_order__class_Oorder_Oeq__iff)). 140.59/43.02 thf(394,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)],[38])). 140.59/43.03 thf(11,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_73_order__trans)). 140.59/43.03 thf(306,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)],[11])). 140.59/43.03 thf(220,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ E @ F))) => (? [E:nat]: ! [F:nat]: ((((C @ F) & (A @ F)) = ((B @ F) & (D @ F))) <= (ord_less_nat @ E @ F)))) <= (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) <= (ord_less_nat @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_pinf_I1_J)). 140.59/43.03 thf(1034,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ E @ F))) => (? [E:nat]: ! [F:nat]: ((((C @ F) & (A @ F)) = ((B @ F) & (D @ F))) | ~ (ord_less_nat @ E @ F)))) | ~ (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) | ~ (ord_less_nat @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 140.59/43.03 thf(271,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((! [D:nat]: ((A @ D) <= (ord_less_nat @ D @ C))) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_nat__less__induct)). 140.59/43.03 thf(1203,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((! [D:nat]: ((A @ D) | ~ (ord_less_nat @ D @ C))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 140.59/43.03 thf(121,axiom,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: (((ord_le699472955list_a @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_ord__eq__le__subst)). 140.59/43.03 thf(680,plain,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: (((ord_le699472955list_a @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 140.59/43.03 thf(84,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_order__class_Oorder_Oantisym)). 140.59/43.03 thf(548,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 140.59/43.03 thf(942,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),inference(lifteq,[status(thm)],[941])). 140.59/43.03 thf(1419,plain,(((^ [A:nat,B:nat]: (~ (ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[942,878])). 140.59/43.03 thf(1420,plain,(((^ [A:nat,B:nat]: (~ (ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(pattern_uni,[status(thm)],[1419:[]])). 140.59/43.03 thf(112,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_add__left__mono)). 140.59/43.03 thf(648,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 140.59/43.03 thf(1508,plain,(((^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A)))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) != (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(paramod_ordered,[status(thm)],[1302,1311])). 140.59/43.03 thf(1509,plain,(((^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(pattern_uni,[status(thm)],[1508:[]])). 140.59/43.03 thf(142,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_less__not__refl)). 140.59/43.03 thf(749,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 140.59/43.03 thf(21,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_add__mono)). 140.59/43.03 thf(342,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 140.59/43.03 thf(252,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_le__less__linear)). 140.59/43.03 thf(1145,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 140.59/43.03 thf(217,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]: ((((A @ F) | (C @ F)) = ((D @ F) | (B @ F))) <= (ord_less_nat @ F @ E))) <= (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ F @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_minf_I2_J)). 140.59/43.03 thf(1018,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]: ((((A @ F) | (C @ F)) = ((D @ F) | (B @ F))) | ~ (ord_less_nat @ F @ E)) | ~ (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 140.59/43.03 thf(968,plain,((ord_less_eq_nat @ sk85 @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)))),inference(cnf,[status(esa)],[967])). 140.59/43.03 thf(56,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_less__prefix__def)). 140.59/43.03 thf(458,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 140.59/43.03 thf(150,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_dual__order_Oirrefl)). 140.59/43.03 thf(776,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 140.59/43.03 thf(93,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_less__le__not__le)). 140.59/43.03 thf(580,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 140.59/43.03 thf(127,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ (C @ B) @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le699472955list_a @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_order__subst2)). 140.59/43.03 thf(705,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ (C @ B) @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le699472955list_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 140.59/43.03 thf(277,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_less__le)). 140.59/43.03 thf(1225,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 140.59/43.03 thf(212,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: (((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_nat @ (C @ A) @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_order__le__less__subst2)). 140.59/43.03 thf(971,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: (((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_nat @ (C @ A) @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 140.59/43.03 thf(138,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_117_neq__iff)). 140.59/43.03 thf(739,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)],[138])). 140.59/43.03 thf(227,axiom,((! [A:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b)) => (ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213__C2_C)). 140.59/43.03 thf(1070,plain,((! [A:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b)) => (ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 140.59/43.03 thf(180,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_28_less__or__eq__imp__le)). 140.59/43.03 thf(872,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)],[180])). 140.59/43.03 thf(207,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_nat__add__left__cancel__less)). 140.59/43.03 thf(954,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 140.59/43.03 thf(119,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) & (C = D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_add__mono__thms__linordered__semiring_I3_J)). 140.59/43.03 thf(673,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) & (C = D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 140.59/43.03 thf(95,axiom,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_ord__eq__le__trans)). 140.59/43.03 thf(585,plain,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 140.59/43.03 thf(130,axiom,((! [A:trace_1367752404list_a,B:formula_a,C:nat]: (ord_less_eq_nat @ (monito1457594016ress_a @ A @ B @ C) @ C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_progress__le)). 140.59/43.03 thf(717,plain,((! [A:trace_1367752404list_a,B:formula_a,C:nat]: (ord_less_eq_nat @ (monito1457594016ress_a @ A @ B @ C) @ C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 140.59/43.03 thf(58,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_add__le__cancel__right)). 140.59/43.03 thf(463,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 140.59/43.03 thf(206,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_nat @ C @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_add__less__mono)). 140.59/43.03 thf(951,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_nat @ C @ D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 140.59/43.03 thf(27,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_add_Oleft__commute)). 140.59/43.03 thf(359,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 140.59/43.03 thf(1451,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[950,743])). 140.59/43.03 thf(1452,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(pattern_uni,[status(thm)],[1451:[]])). 140.59/43.03 thf(265,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_infinite__descent)). 140.59/43.03 thf(1188,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 140.59/43.03 thf(264,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_dual__order_Ostrict__implies__order)). 140.59/43.03 thf(1186,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 140.59/43.03 thf(970,plain,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ sk85))),inference(cnf,[status(esa)],[967])). 140.59/43.03 thf(4982,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ sk85))),inference(rewrite,[status(thm)],[970,322])). 140.59/43.03 thf(3622,plain,(((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) = (ord_less_nat)) | ((^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))) != (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(paramod_ordered,[status(thm)],[1300,1509])). 140.59/43.03 thf(3623,plain,(((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) = (ord_less_nat))),inference(pattern_uni,[status(thm)],[3622:[]])). 140.59/43.03 thf(3510,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk110 @ A)) != (ord_less_nat @ (sk120 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[1163,1216])). 140.59/43.03 thf(3546,plain,(! [B:nat,A:nat] : ((A != (sk120 @ B)) | ((sk110 @ A) != B))),inference(simp,[status(thm)],[3510])). 140.59/43.03 thf(3564,plain,(! [A:nat] : (((sk110 @ (sk120 @ A)) != A))),inference(simp,[status(thm)],[3546])). 140.59/43.03 thf(140,axiom,((! [A:nat]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) <= (ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206__C21_C)). 140.59/43.03 thf(744,plain,((! [A:nat]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) | ~ (ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 140.59/43.03 thf(336,plain,(! [D:nat,C:nat,B:(nat > prefix1027212443list_a),A:prefix1027212443list_a] : ((~ (ord_less_eq_nat @ C @ D)) | (ord_le699472955list_a @ A @ (B @ D)) | (ord_less_eq_nat @ (sk6 @ D @ C @ (B) @ A) @ (sk7 @ D @ C @ (B) @ A)) | (~ (ord_le699472955list_a @ A @ (B @ C))))),inference(cnf,[status(esa)],[334])). 140.59/43.03 thf(102,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: (((ord_le699472955list_a @ B @ C) => (ord_le887097159list_a @ A @ C)) <= (ord_le887097159list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_order_Ostrict__trans2)). 140.59/43.03 thf(613,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: (((ord_le699472955list_a @ B @ C) => (ord_le887097159list_a @ A @ C)) | ~ (ord_le887097159list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 140.59/43.03 thf(4220,plain,(! [B:nat,A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(paramod_ordered,[status(thm)],[837,935])). 140.59/43.03 thf(4222,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != ia) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != B))),inference(simp,[status(thm)],[4220])). 140.59/43.03 thf(4246,plain,(! [A:nat] : (((plus_plus_nat @ A @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia))),inference(simp,[status(thm)],[4222])). 140.59/43.03 thf(276,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_order__less__subst1)). 140.59/43.03 thf(1221,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 140.59/43.03 thf(459,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))))),inference(lifteq,[status(thm)],[458])). 140.59/43.03 thf(1352,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A)))) | ((ord_le887097159list_a) != (ord_le887097159list_a))),inference(paramod_ordered,[status(thm)],[459,372])). 140.59/43.03 thf(1353,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (~ (ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))))),inference(pattern_uni,[status(thm)],[1352:[]])). 140.59/43.03 thf(223,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_49_nat__descend__induct)). 140.59/43.03 thf(1052,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)],[223])). 140.59/43.03 thf(133,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_dual__order_Oasym)). 140.59/43.03 thf(727,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 140.59/43.03 thf(314,plain,(! [D:nat,C:nat,B:nat,A:(nat > $o)] : ((~ (ord_less_eq_nat @ (sk2 @ B @ (A)) @ B)) | (~ (A @ C)) | (ord_less_eq_nat @ C @ (sk3 @ (A))) | (~ (A @ D)))),inference(cnf,[status(esa)],[310])). 140.59/43.03 thf(2797,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk120 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[1233,1216])). 140.59/43.03 thf(2801,plain,(! [A:nat] : (((sk120 @ A) != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2797])). 140.59/43.03 thf(2807,plain,(((sk120 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != i3)),inference(simp,[status(thm)],[2801])). 140.59/43.03 thf(176,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((ord_less_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_nat @ (C @ E) @ (C @ F)) <= (ord_less_nat @ E @ F)))) <= (ord_less_nat @ (C @ B) @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_order__less__subst2)). 140.59/43.03 thf(859,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_nat @ E @ F))) | ~ (ord_less_nat @ (C @ B) @ D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 140.59/43.03 thf(283,axiom,((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062)). 140.59/43.03 thf(1240,plain,((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 140.59/43.03 thf(4216,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk120 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[837,1216])). 140.59/43.03 thf(4224,plain,(! [A:nat] : (((sk120 @ A) != ia) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[4216])). 140.59/43.03 thf(4235,plain,(((sk120 @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia)),inference(simp,[status(thm)],[4224])). 140.59/43.03 thf(214,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)) = ((D @ F) & (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_minf_I1_J)). 140.59/43.03 thf(978,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)) = ((D @ F) & (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 140.59/43.03 thf(52,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((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_eq_nat @ A @ (B @ D)))) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_order__subst1)). 140.59/43.03 thf(446,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: (((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_eq_nat @ A @ (B @ D)))) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 140.59/43.03 thf(90,axiom,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le887097159list_a @ (C @ A) @ D)) <= (ord_le887097159list_a @ (C @ B) @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_order__le__less__subst2)). 140.59/43.03 thf(571,plain,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le887097159list_a @ (C @ A) @ D)) | ~ (ord_le887097159list_a @ (C @ B) @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 140.59/43.03 thf(2403,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ A)))),inference(paramod_ordered,[status(thm)],[1233,748])). 140.59/43.03 thf(2414,plain,(! [A:nat] : ((i3 != A) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2403])). 140.59/43.03 thf(2435,plain,(((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != i3)),inference(simp,[status(thm)],[2414])). 140.59/43.03 thf(1450,plain,(((ord_less_nat) = ((=) @ nat)) | ((^ [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(paramod_ordered,[status(thm)],[302,950])). 140.59/43.03 thf(1457,plain,(((ord_less_nat) = ((=) @ nat)) | ((ord_less_eq_nat) != (ord_less_eq_nat)) | ((^ [A:nat,B:nat]: (ord_less_eq_nat @ B @ A)) != (^ [A:nat,B:nat]: ~ (A = B)))),inference(simp,[status(thm)],[1450])). 140.59/43.03 thf(1459,plain,(((ord_less_nat) = ((=) @ nat)) | ((^ [A:nat,B:nat]: (ord_less_eq_nat @ B @ A)) != (^ [A:nat,B:nat]: ~ (A = B)))),inference(simp,[status(thm)],[1457])). 140.59/43.03 thf(122,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: (((ord_le699472955list_a @ B @ C) => (ord_le699472955list_a @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ord__eq__le__trans)). 140.59/43.03 thf(688,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: (((ord_le699472955list_a @ B @ C) => (ord_le699472955list_a @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 140.59/43.03 thf(77,axiom,((! [A:prefix1027212443list_a]: (ord_le699472955list_a @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_order__refl)). 140.59/43.03 thf(524,plain,((! [A:prefix1027212443list_a]: (ord_le699472955list_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 140.59/43.03 thf(148,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_22_pinf_I6_J)). 140.59/43.03 thf(771,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)],[148])). 140.59/43.03 thf(240,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_ord__eq__less__trans)). 140.59/43.03 thf(1108,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 140.59/43.03 thf(4289,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(rewrite,[status(thm)],[514,322])). 140.59/43.03 thf(4252,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk99 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[1094,1047])). 140.59/43.03 thf(4265,plain,(! [A:nat] : (((sk99 @ A) != ia) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[4252])). 140.59/43.03 thf(4278,plain,(((sk99 @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia)),inference(simp,[status(thm)],[4265])). 140.59/43.03 thf(53,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((~ (ord_le887097159list_a @ A @ B)) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_antisym__conv2)). 140.59/43.03 thf(450,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((~ (ord_le887097159list_a @ A @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 140.59/43.03 thf(232,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_less__le__trans)). 140.59/43.03 thf(1084,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 140.59/43.03 thf(162,axiom,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:trace_1367752404list_a,D:formula_a]: ((((monito1457594016ress_a @ B @ D @ (plen_P694648887list_a @ A)) = (monito1457594016ress_a @ C @ D @ (plen_P694648887list_a @ A))) <= (prefix1041802747list_a @ A @ C)) <= (prefix1041802747list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_progress__prefix__conv)). 140.59/43.03 thf(813,plain,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:trace_1367752404list_a,D:formula_a]: (((monito1457594016ress_a @ B @ D @ (plen_P694648887list_a @ A)) = (monito1457594016ress_a @ C @ D @ (plen_P694648887list_a @ A))) | ~ (prefix1041802747list_a @ A @ C) | ~ (prefix1041802747list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 140.59/43.03 thf(318,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(cnf,[status(esa)],[317])). 140.59/43.03 thf(319,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(lifteq,[status(thm)],[318])). 140.59/43.03 thf(238,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_less__imp__neq)). 140.59/43.03 thf(1101,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 140.59/43.03 thf(107,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((B = A) <= (ord_le699472955list_a @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_dual__order_Oantisym)). 140.59/43.03 thf(632,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((B = A) | ~ (ord_le699472955list_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 140.59/43.03 thf(41,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_66_dual__order_Oeq__iff)). 140.59/43.03 thf(401,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)],[41])). 140.59/43.03 thf(3502,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk110 @ A)) != (ord_less_nat @ B @ (sk111 @ B))))),inference(paramod_ordered,[status(thm)],[1163,1169])). 140.59/43.03 thf(3543,plain,(! [B:nat,A:nat] : ((A != B) | ((sk110 @ A) != (sk111 @ B)))),inference(simp,[status(thm)],[3502])). 140.59/43.03 thf(3561,plain,(! [A:nat] : (((sk111 @ A) != (sk110 @ A)))),inference(simp,[status(thm)],[3543])). 140.59/43.03 thf(210,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_52_order_Onot__eq__order__implies__strict)). 140.59/43.03 thf(963,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)],[210])). 140.59/43.03 thf(74,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D)) <= ((A = B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__mono__thms__linordered__semiring_I4_J)). 140.59/43.03 thf(517,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D)) | ~ ((A = B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 140.59/43.03 thf(135,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_168_antisym__conv1)). 140.59/43.03 thf(731,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)],[135])). 140.59/43.03 thf(46,axiom,((! [A:nat,B:nat,C:trace_1367752404list_a,D:formula_a]: ((ord_less_eq_nat @ (monito1457594016ress_a @ C @ D @ A) @ (monito1457594016ress_a @ C @ D @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_progress__mono)). 140.59/43.03 thf(418,plain,((! [A:nat,B:nat,C:trace_1367752404list_a,D:formula_a]: ((ord_less_eq_nat @ (monito1457594016ress_a @ C @ D @ A) @ (monito1457594016ress_a @ C @ D @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 140.59/43.03 thf(266,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_order_Ostrict__implies__order)). 140.59/43.03 thf(1193,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 140.59/43.03 thf(192,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_179_le__imp__less__or__eq)). 140.59/43.03 thf(914,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)],[192])). 140.59/43.03 thf(1305,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (ord_less_nat)) | ((^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))) != (ord_less_eq_nat))),inference(paramod_ordered,[status(thm)],[894,819])). 140.59/43.03 thf(1307,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (ord_less_nat)) | ((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: (B)) != (^ [A:nat,B:nat]: (B)))),inference(simp,[status(thm)],[1305])). 140.59/43.03 thf(1309,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (ord_less_nat)) | ((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A)))),inference(simp,[status(thm)],[1307])). 140.59/43.03 thf(1122,plain,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(cnf,[status(esa)],[1119])). 140.59/43.03 thf(5287,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(rewrite,[status(thm)],[1122,322])). 140.59/43.03 thf(157,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_add__less__cancel__left)). 140.59/43.03 thf(800,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 140.59/43.03 thf(242,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_leI)). 140.59/43.03 thf(1116,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 140.59/43.03 thf(248,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_not__less)). 140.59/43.03 thf(1133,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 140.59/43.03 thf(1345,plain,(((ord_le887097159list_a) = ((=) @ prefix1027212443list_a)) | ((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))) != (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))))),inference(paramod_ordered,[status(thm)],[346,372])). 140.59/43.03 thf(1346,plain,(((ord_le887097159list_a) = ((=) @ prefix1027212443list_a)) | ((ord_le699472955list_a) != (ord_le699472955list_a)) | ((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (ord_le699472955list_a @ B @ A)) != (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ~ (B = A)))),inference(simp,[status(thm)],[1345])). 140.59/43.03 thf(1348,plain,(((ord_le887097159list_a) = ((=) @ prefix1027212443list_a)) | ((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: (ord_le699472955list_a @ B @ A)) != (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ~ (B = A)))),inference(simp,[status(thm)],[1346])). 140.59/43.03 thf(104,axiom,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: (((ord_le699472955list_a @ C @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) <= (ord_le699472955list_a @ E @ F))) => (ord_le699472955list_a @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_ord__eq__le__subst)). 140.59/43.03 thf(620,plain,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: (((ord_le699472955list_a @ C @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ (B @ E) @ (B @ F)) | ~ (ord_le699472955list_a @ E @ F))) => (ord_le699472955list_a @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 140.59/43.03 thf(143,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_116_neqE)). 140.59/43.03 thf(752,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)],[143])). 140.59/43.03 thf(44,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_group__cancel_Oadd2)). 140.59/43.03 thf(410,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 140.59/43.03 thf(1248,plain,(! [A:nat] : (((plus_plus_nat @ A) = (^ [B:nat]: (plus_plus_nat @ B @ A))))),inference(func_ext,[status(esa)],[355])). 140.59/43.03 thf(32,axiom,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ B) => ((ord_le699472955list_a @ (C @ B) @ D) => ((ord_le699472955list_a @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_le699472955list_a @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_order__subst2)). 140.59/43.03 thf(373,plain,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ B) => ((ord_le699472955list_a @ (C @ B) @ D) => ((ord_le699472955list_a @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_le699472955list_a @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 140.59/43.03 thf(237,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((C = D) & (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_add__mono__thms__linordered__field_I1_J)). 140.59/43.03 thf(1097,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((C = D) & (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 140.59/43.03 thf(304,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))),inference(miniscope,[status(thm)],[303])). 140.59/43.03 thf(305,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ C)) | (ord_less_eq_nat @ A @ C))),inference(cnf,[status(esa)],[304])). 140.59/43.03 thf(294,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A))),inference(cnf,[status(esa)],[293])). 140.59/43.03 thf(4254,plain,(! [B:nat,A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ A)))),inference(paramod_ordered,[status(thm)],[1094,1239])). 140.59/43.03 thf(4273,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != ia) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[4254])). 140.59/43.03 thf(4286,plain,(! [A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) @ A) != ia))),inference(simp,[status(thm)],[4273])). 140.59/43.03 thf(69,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_nat__add__left__cancel__le)). 140.59/43.03 thf(506,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 140.59/43.03 thf(159,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_add__less__cancel__right)). 140.59/43.03 thf(807,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 140.59/43.03 thf(268,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_add__lessD1)). 140.59/43.03 thf(1197,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 140.59/43.03 thf(60,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_ord__le__eq__subst)). 140.59/43.03 thf(474,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 140.59/43.03 thf(209,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_add__less__mono1)). 140.59/43.03 thf(960,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 140.59/43.03 thf(108,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_200_verit__la__disequality)). 140.59/43.03 thf(635,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)],[108])). 140.59/43.03 thf(225,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_166_le__neq__trans)). 140.59/43.03 thf(1065,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)],[225])). 140.59/43.03 thf(184,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_nat @ C @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_add__strict__mono)). 140.59/43.03 thf(886,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_nat @ C @ D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 140.59/43.03 thf(196,axiom,((! [A:nat]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) <= (ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207__C11_C)). 140.59/43.03 thf(928,plain,((! [A:nat]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) | ~ (ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 140.59/43.03 thf(45,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le887097159list_a @ A @ C) <= (ord_le699472955list_a @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_less__le__trans)). 140.59/43.03 thf(415,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le887097159list_a @ A @ C) | ~ (ord_le699472955list_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 140.59/43.03 thf(4217,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ A)))),inference(paramod_ordered,[status(thm)],[837,748])). 140.59/43.03 thf(4232,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[4217])). 140.59/43.03 thf(4242,plain,(((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != ia)),inference(simp,[status(thm)],[4232])). 140.59/43.03 thf(79,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_trans__le__add1)). 140.59/43.03 thf(528,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 140.59/43.03 thf(111,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) <= (ord_less_eq_nat @ (C @ B) @ D)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_order__subst2)). 140.59/43.03 thf(644,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: (((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ (ord_less_eq_nat @ (C @ B) @ D) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 140.59/43.03 thf(1120,plain,((ord_less_eq_nat @ sk108 @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))),inference(cnf,[status(esa)],[1119])). 140.59/43.03 thf(67,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_le__antisym)). 140.59/43.03 thf(501,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 140.59/43.03 thf(331,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(cnf,[status(esa)],[330])). 140.59/43.03 thf(332,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(lifteq,[status(thm)],[331])). 140.59/43.03 thf(247,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_less__imp__not__eq2)). 140.59/43.03 thf(1129,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 140.59/43.03 thf(2408,plain,(((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(paramod_ordered,[status(thm)],[1233,286])). 140.59/43.03 thf(2430,plain,((k != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[2408])). 140.59/43.03 thf(4208,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk111 @ A))))),inference(paramod_ordered,[status(thm)],[837,1169])). 140.59/43.03 thf(4229,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk111 @ A)))),inference(simp,[status(thm)],[4208])). 140.59/43.03 thf(4239,plain,(((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk111 @ ia))),inference(simp,[status(thm)],[4229])). 140.59/43.03 thf(166,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_less__imp__le)). 140.59/43.03 thf(822,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 140.59/43.03 thf(30,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) <= (ord_le887097159list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_order_Ostrict__implies__order)). 140.59/43.03 thf(369,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) | ~ (ord_le887097159list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 140.59/43.03 thf(100,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: (((ord_le699472955list_a @ B @ A) => (A = B)) <= (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_order__class_Oorder_Oantisym)). 140.59/43.03 thf(607,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: (((ord_le699472955list_a @ B @ A) => (A = B)) | ~ (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 140.59/43.03 thf(158,axiom,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: (((ord_le699472955list_a @ (C @ B) @ D) => ((ord_le887097159list_a @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_le887097159list_a @ (C @ E) @ (C @ F)))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_order__less__le__subst2)). 140.59/43.03 thf(803,plain,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: (((ord_le699472955list_a @ (C @ B) @ D) => ((ord_le887097159list_a @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_le887097159list_a @ (C @ E) @ (C @ F)))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 140.59/43.03 thf(2409,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk75 @ A))))),inference(paramod_ordered,[status(thm)],[1233,871])). 140.59/43.03 thf(2415,plain,(! [A:nat] : ((i3 != A) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (sk75 @ A)))),inference(simp,[status(thm)],[2409])). 140.59/43.03 thf(2436,plain,(((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (sk75 @ i3))),inference(simp,[status(thm)],[2415])). 140.59/43.03 thf(144,axiom,((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062)). 140.59/43.03 thf(755,plain,((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 140.59/43.03 thf(65,axiom,((! [A:formula_a,B:i,C:formula_a,D:formula_a,E:i,F:formula_a]: (((until_a @ A @ B @ C) = (until_a @ D @ E @ F)) = ((B = E) & (C = F) & (A = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_formula_Oinject_I9_J)). 140.59/43.03 thf(496,plain,((! [A:formula_a,B:i,C:formula_a,D:formula_a,E:i,F:formula_a]: (((until_a @ A @ B @ C) = (until_a @ D @ E @ F)) = ((B = E) & (C = F) & (A = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 140.59/43.03 thf(24982,plain,(($false)),inference(e,[status(thm)],[1105,347,1237,893,941,666,1031,333,628,1211,4226,1068,2808,3549,878,677,1173,1158,582,1142,379,385,533,1275,1233,945,930,1164,797,4247,3562,1095,898,3634,1127,782,709,288,301,320,651,719,785,372,504,838,1279,949,460,724,4238,917,702,817,559,638,1087,1147,421,969,325,289,316,1415,492,443,3473,514,1151,1383,966,1302,756,1136,834,766,1169,3189,877,734,293,866,396,988,1201,312,1072,453,1697,3559,4285,292,1438,925,1199,810,366,1311,714,512,439,546,793,1047,1163,2441,1123,1174,1217,820,729,957,894,746,1091,407,693,630,484,879,3556,889,1079,1195,551,1392,456,329,1178,522,830,742,317,1121,1227,403,388,356,593,610,499,697,3615,1234,783,1118,857,4263,328,6862,4276,339,933,554,669,526,1700,1155,1028,1082,901,1075,1207,590,837,4846,515,654,1246,779,371,1266,1231,4535,1318,938,921,541,1170,398,558,1515,773,662,4288,1241,3563,906,298,425,1698,824,856,444,601,2048,4283,1125,3472,286,743,291,975,3187,826,577,641,936,1371,4236,1239,466,335,350,391,1139,1408,1048,377,737,509,863,6585,604,362,567,616,303,811,494,1339,345,323,1162,483,700,895,769,943,330,2446,4277,932,1061,4844,1699,1044,868,883,1015,1113,299,1250,653,658,912,521,1213,827,394,306,1034,1166,1203,531,680,548,1420,648,1509,749,342,355,1145,1018,968,458,776,557,580,295,705,1225,971,739,1070,872,954,1252,673,585,717,463,951,359,1300,1452,1188,1186,4982,3623,3564,744,336,613,4246,1221,1353,1052,727,314,2807,859,1240,4235,1094,978,446,571,2435,1459,482,688,524,1216,771,1108,4289,4278,450,1084,813,319,748,1101,632,401,3561,963,517,731,418,1294,1193,290,914,346,1309,5287,800,287,1116,1133,1348,620,752,315,410,818,1248,373,950,1097,305,326,294,1314,341,3560,4286,506,807,1197,1172,474,960,635,532,1065,886,928,415,4242,528,644,442,871,1120,501,332,1129,2430,575,4239,822,369,607,322,803,337,354,935,309,2436,755,496])). 140.59/43.03 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 140.59/43.03 % [INFO] Killing All external provers ... 140.92/43.23 EOF