Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP125^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:06:51 AM UTC 2026

% Result   : Theorem 192.43s 40.73s
% Output   : Refutation 194.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ITP125^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20  % Computer : n006.cluster.edu
% 0.10/0.20  % Model    : x86_64 x86_64
% 0.10/0.20  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20  % Memory   : 8046.5625MB
% 0.10/0.20  % OS       : Linux 6.8.0-71-generic
% 0.10/0.20  % CPULimit : 300
% 0.10/0.20  % WCLimit  : 300
% 0.10/0.20  % DateTime : Tue Sep 29 19:56:54 UTC 2026
% 0.10/0.21  % CPUTime  : 
% 0.10/0.21  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.93/0.79  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.90/1.33  % [INFO] 	 Parsing done (531ms). 
% 2.90/1.34  % [INFO] 	 Running in sequential loop mode. 
% 3.98/1.67  % [INFO] 	 eprover registered as external prover. 
% 3.98/1.68  % [INFO] 	 Scanning for conjecture ... 
% 4.35/1.79  % [INFO] 	 Found a conjecture (or negated_conjecture) and 283 axioms. Running axiom selection ... 
% 4.97/1.99  % [INFO] 	 Axiom selection finished. Selected 283 axioms (removed 0 axioms). 
% 6.16/2.37  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 6.58/2.42  % [INFO] 	 Type checking passed. 
% 6.58/2.43  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 192.43/40.72  % External prover 'e' found a proof!
% 192.43/40.72  % [INFO] 	 Killing All external provers ... 
% 192.43/40.72  % Time passed: 40380ms (effective reasoning time: 39381ms)
% 192.43/40.72  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 192.43/40.73  % 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
% 192.43/40.73  % No. of inferences in proof: 1306
% 192.43/40.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 40380 ms resp. 39381 ms w/o parsing
% 194.15/41.11  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 194.15/41.11  thf(prefix1027212443list_a_type, type, prefix1027212443list_a: $tType).
% 194.15/41.11  thf(trace_1367752404list_a_type, type, trace_1367752404list_a: $tType).
% 194.15/41.11  thf(i_type, type, i: $tType).
% 194.15/41.11  thf(formula_a_type, type, formula_a: $tType).
% 194.15/41.11  thf(list_a_type, type, list_a: $tType).
% 194.15/41.11  thf(nat_type, type, nat: $tType).
% 194.15/41.11  thf(one_one_nat_decl, type, one_one_nat: nat).
% 194.15/41.11  thf(plus_plus_nat_decl, type, plus_plus_nat: (nat > (nat > nat))).
% 194.15/41.11  thf(until_a_decl, type, until_a: (formula_a > (i > (formula_a > formula_a)))).
% 194.15/41.11  thf(sat_a_decl, type, sat_a: (trace_1367752404list_a > (list_a > (nat > (formula_a > $o))))).
% 194.15/41.11  thf(monito1457594016ress_a_decl, type, monito1457594016ress_a: (trace_1367752404list_a > (formula_a > (nat > nat)))).
% 194.15/41.11  thf(ord_less_nat_decl, type, ord_less_nat: (nat > (nat > $o))).
% 194.15/41.11  thf(ord_le887097159list_a_decl, type, ord_le887097159list_a: (prefix1027212443list_a > (prefix1027212443list_a > $o))).
% 194.15/41.11  thf(ord_less_eq_nat_decl, type, ord_less_eq_nat: (nat > (nat > $o))).
% 194.15/41.11  thf(ord_le699472955list_a_decl, type, ord_le699472955list_a: (prefix1027212443list_a > (prefix1027212443list_a > $o))).
% 194.15/41.11  thf(tau_Pr257024512list_a_decl, type, tau_Pr257024512list_a: (trace_1367752404list_a > (nat > nat))).
% 194.15/41.11  thf(plen_P694648887list_a_decl, type, plen_P694648887list_a: (prefix1027212443list_a > nat)).
% 194.15/41.11  thf(prefix1041802747list_a_decl, type, prefix1041802747list_a: (prefix1027212443list_a > (trace_1367752404list_a > $o))).
% 194.15/41.11  thf(i2_decl, type, i2: i).
% 194.15/41.11  thf(phi_decl, type, phi: formula_a).
% 194.15/41.11  thf(phi_1_decl, type, phi_1: formula_a).
% 194.15/41.11  thf(phi_2_decl, type, phi_2: formula_a).
% 194.15/41.11  thf(pi_decl, type, pi: prefix1027212443list_a).
% 194.15/41.11  thf(sigma_decl, type, sigma: trace_1367752404list_a).
% 194.15/41.11  thf(sigma2_decl, type, sigma2: trace_1367752404list_a).
% 194.15/41.11  thf(b_decl, type, b: nat).
% 194.15/41.11  thf(i3_decl, type, i3: nat).
% 194.15/41.11  thf(ia_decl, type, ia: nat).
% 194.15/41.11  thf(j_decl, type, j: nat).
% 194.15/41.11  thf(ja_decl, type, ja: nat).
% 194.15/41.11  thf(k_decl, type, k: nat).
% 194.15/41.11  thf(sk1_decl, type, sk1: (nat > (nat > ((nat > prefix1027212443list_a) > (prefix1027212443list_a > nat))))).
% 194.15/41.11  thf(sk2_decl, type, sk2: (nat > (nat > ((nat > prefix1027212443list_a) > (prefix1027212443list_a > nat))))).
% 194.15/41.11  thf(sk3_decl, type, sk3: (prefix1027212443list_a > trace_1367752404list_a)).
% 194.15/41.11  thf(sk4_decl, type, sk4: (prefix1027212443list_a > (prefix1027212443list_a > ((prefix1027212443list_a > nat) > (nat > prefix1027212443list_a))))).
% 194.15/41.11  thf(sk5_decl, type, sk5: (prefix1027212443list_a > (prefix1027212443list_a > ((prefix1027212443list_a > nat) > (nat > prefix1027212443list_a))))).
% 194.15/41.11  thf(sk6_decl, type, sk6: (nat > ((nat > nat) > (nat > (nat > nat))))).
% 194.15/41.11  thf(sk7_decl, type, sk7: (nat > ((nat > nat) > (nat > (nat > nat))))).
% 194.15/41.11  thf(sk8_decl, type, sk8: (prefix1027212443list_a > (prefix1027212443list_a > ((prefix1027212443list_a > nat) > (nat > prefix1027212443list_a))))).
% 194.15/41.11  thf(sk9_decl, type, sk9: (prefix1027212443list_a > (prefix1027212443list_a > ((prefix1027212443list_a > nat) > (nat > prefix1027212443list_a))))).
% 194.15/41.11  thf(sk10_decl, type, sk10: (nat > (nat > nat))).
% 194.15/41.11  thf(sk11_decl, type, sk11: (nat > (nat > (nat > $o)))).
% 194.15/41.11  thf(sk12_decl, type, sk12: (nat > (nat > (nat > $o)))).
% 194.15/41.11  thf(sk13_decl, type, sk13: (nat > (nat > (nat > $o)))).
% 194.15/41.11  thf(sk14_decl, type, sk14: (nat > (nat > (nat > $o)))).
% 194.15/41.11  thf(sk32_decl, type, sk32: (trace_1367752404list_a > (nat > (nat > nat)))).
% 194.15/41.11  thf(sk60_decl, type, sk60: (nat > nat)).
% 194.15/41.11  thf(sk80_decl, type, sk80: (nat > nat)).
% 194.15/41.11  thf(sk95_decl, type, sk95: nat).
% 194.15/41.11  thf(sk108_decl, type, sk108: nat).
% 194.15/41.11  thf(sk112_decl, type, sk112: (nat > nat)).
% 194.15/41.11  thf(sk113_decl, type, sk113: (nat > nat)).
% 194.15/41.11  thf(sk116_decl, type, sk116: (nat > nat)).
% 194.15/41.11  thf(sk121_decl, type, sk121: ((nat > (nat > $o)) > nat)).
% 194.15/41.11  thf(sk122_decl, type, sk122: ((nat > (nat > $o)) > nat)).
% 194.15/41.11  thf(sk123_decl, type, sk123: ((nat > (nat > $o)) > nat)).
% 194.15/41.11  thf(sk124_decl, type, sk124: ((nat > (nat > $o)) > nat)).
% 194.15/41.11  thf(sk125_decl, type, sk125: ((nat > (nat > $o)) > nat)).
% 194.15/41.11  thf(sk1_def, definition, sk1 = (^ [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)))))) ).
% 194.15/41.11  thf(sk2_def, definition, sk2 = (^ [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: (@+ [E:nat]: ~ ((ord_less_eq_nat @ (sk1 @ A @ B @ C @ D) @ E) => (ord_le699472955list_a @ (C @ (sk1 @ A @ B @ C @ D)) @ (C @ E))))) ).
% 194.15/41.11  thf(sk3_def, definition, sk3 = (^ [A:prefix1027212443list_a]: (@+ [B:trace_1367752404list_a]: (prefix1041802747list_a @ A @ B))) ).
% 194.15/41.11  thf(sk4_def, definition, sk4 = (^ [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)))))) ).
% 194.15/41.11  thf(sk5_def, definition, sk5 = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: (@+ [E:prefix1027212443list_a]: ~ ((ord_le699472955list_a @ (sk4 @ A @ B @ C @ D) @ E) => (ord_less_eq_nat @ (C @ (sk4 @ A @ B @ C @ D)) @ (C @ E))))) ).
% 194.15/41.11  thf(sk6_def, definition, sk6 = (^ [A:nat,B:(nat > nat),C:nat,D:nat]: (@+ [E:nat]: ~ (! [F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) ).
% 194.15/41.11  thf(sk7_def, definition, sk7 = (^ [A:nat,B:(nat > nat),C:nat,D:nat]: (@+ [E:nat]: ~ ((ord_less_eq_nat @ (sk6 @ A @ B @ C @ D) @ E) => (ord_less_eq_nat @ (B @ (sk6 @ A @ B @ C @ D)) @ (B @ E))))) ).
% 194.15/41.11  thf(sk8_def, definition, sk8 = (^ [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)))))) ).
% 194.15/41.11  thf(sk9_def, definition, sk9 = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: (@+ [E:prefix1027212443list_a]: ~ ((ord_le699472955list_a @ (sk8 @ A @ B @ C @ D) @ E) => (ord_less_eq_nat @ (C @ (sk8 @ A @ B @ C @ D)) @ (C @ E))))) ).
% 194.15/41.11  thf(sk10_def, definition, sk10 = (@+ [A:(nat > (nat > nat))]: ! [B:nat,C:nat]: ((A @ C @ (plus_plus_nat @ B @ C)) = B)) ).
% 194.15/41.11  thf(sk32_def, definition, sk32 = (^ [A:trace_1367752404list_a,B:nat,C:nat]: (@+ [D:nat]: ((ord_less_eq_nat @ C @ D) & (ord_less_eq_nat @ B @ (tau_Pr257024512list_a @ A @ D))))) ).
% 194.15/41.11  thf(sk60_def, definition, sk60 = (^ [A:nat]: (@+ [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))) ).
% 194.15/41.11  thf(sk80_def, definition, sk80 = (^ [A:nat]: (@+ [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))) ).
% 194.15/41.11  thf(sk95_def, definition, sk95 = (@+ [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))))))) ).
% 194.15/41.11  thf(sk108_def, definition, sk108 = (@+ [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))))))) ).
% 194.15/41.11  thf(sk112_def, definition, sk112 = (^ [A:nat]: (@+ [B:nat]: (ord_less_nat @ A @ B))) ).
% 194.15/41.11  thf(sk113_def, definition, sk113 = (^ [A:nat]: (@+ [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))) ).
% 194.15/41.11  thf(sk116_def, definition, sk116 = (^ [A:nat]: (@+ [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))) ).
% 194.15/41.11  thf(sk121_def, definition, sk121 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ (! [C:nat]: ((ord_less_nat @ B @ C) => (A @ B @ C))))) ).
% 194.15/41.11  thf(sk122_def, definition, sk122 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ ((ord_less_nat @ (sk121 @ A) @ B) => (A @ (sk121 @ A) @ B)))) ).
% 194.15/41.11  thf(sk123_def, definition, sk123 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ (A @ B @ B))) ).
% 194.15/41.11  thf(sk124_def, definition, sk124 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ (! [C:nat]: ((A @ C @ B) => (A @ B @ C))))) ).
% 194.15/41.11  thf(sk125_def, definition, sk125 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ ((A @ B @ (sk124 @ A)) => (A @ (sk124 @ A) @ B)))) ).
% 194.15/41.11  thf(171,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_le__less__trans)).
% 194.15/41.11  thf(892,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
% 194.15/41.11  thf(285,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_add__le__less__mono)).
% 194.15/41.11  thf(1322,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])).
% 194.15/41.11  thf(82,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/sandbox/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)).
% 194.15/41.11  thf(574,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)],[82])).
% 194.15/41.11  thf(15,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/sandbox/benchmark/theBenchmark.p',fact_255_add_Oassoc)).
% 194.15/41.11  thf(322,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)],[15])).
% 194.15/41.11  thf(323,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)],[322])).
% 194.15/41.11  thf(324,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)],[323])).
% 194.15/41.11  thf(3814,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)],[574,324])).
% 194.15/41.11  thf(9,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_add__leE)).
% 194.15/41.11  thf(303,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 194.15/41.11  thf(304,plain,(! [C:nat,B:nat,A:nat] : (((~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) | (ord_less_eq_nat @ A @ C)) & (~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) | (ord_less_eq_nat @ B @ C))))),inference(cnf,[status(esa)],[303])).
% 194.15/41.11  thf(306,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)) | (ord_less_eq_nat @ B @ C))),inference(cnfConj,[status(thm)],[304])).
% 194.15/41.11  thf(3871,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[3814,306])).
% 194.15/41.11  thf(3872,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[3871])).
% 194.15/41.11  thf(3873,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[3872:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ j))]])).
% 194.15/41.11  thf(146,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_pinf_I7_J)).
% 194.15/41.11  thf(809,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
% 194.15/41.11  thf(152,axiom,((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062)).
% 194.15/41.11  thf(824,plain,((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
% 194.15/41.11  thf(264,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_minf_I3_J)).
% 194.15/41.11  thf(1244,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])).
% 194.15/41.11  thf(1245,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ B @ (sk113 @ A))) | (~ (B = A)))),inference(cnf,[status(esa)],[1244])).
% 194.15/41.11  thf(1246,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ B @ (sk113 @ A))))),inference(lifteq,[status(thm)],[1245])).
% 194.15/41.11  thf(1247,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ (sk113 @ A))))),inference(simp,[status(thm)],[1246])).
% 194.15/41.11  thf(2088,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk113 @ A))))),inference(paramod_ordered,[status(thm)],[824,1247])).
% 194.15/41.11  thf(2089,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk113 @ A))))),inference(simp,[status(thm)],[2088])).
% 194.15/41.11  thf(2092,plain,(! [A:nat] : ((k != A) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (sk113 @ A)))),inference(simp,[status(thm)],[2089])).
% 194.15/41.11  thf(2094,plain,(((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (sk113 @ k))),inference(simp,[status(thm)],[2092])).
% 194.15/41.11  thf(199,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_less__imp__not__less)).
% 194.15/41.11  thf(1024,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])).
% 194.15/41.11  thf(246,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/sandbox/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)).
% 194.15/41.11  thf(1191,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)],[246])).
% 194.15/41.11  thf(1192,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)],[1191])).
% 194.15/41.11  thf(1193,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)) & (ord_less_eq_nat @ sk108 @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) & (ord_less_eq_nat @ sk108 @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))))),inference(cnf,[status(esa)],[1192])).
% 194.15/41.11  thf(1194,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(cnfConj,[status(thm)],[1193])).
% 194.15/41.11  thf(5012,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)],[1194,324])).
% 194.15/41.11  thf(305,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)) | (ord_less_eq_nat @ A @ C))),inference(cnfConj,[status(thm)],[304])).
% 194.15/41.11  thf(5086,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[5012,305])).
% 194.15/41.11  thf(5087,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[5086])).
% 194.15/41.11  thf(5088,plain,((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[5087:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ sk108))]])).
% 194.15/41.11  thf(238,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_minf_I5_J)).
% 194.15/41.11  thf(1168,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
% 194.15/41.11  thf(281,axiom,((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I3_J)).
% 194.15/41.11  thf(1314,plain,((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])).
% 194.15/41.11  thf(138,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_verit__comp__simplify1_I1_J)).
% 194.15/41.11  thf(778,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
% 194.15/41.11  thf(779,plain,((~ (? [A:nat]: (ord_less_nat @ A @ A)))),inference(miniscope,[status(thm)],[778])).
% 194.15/41.11  thf(780,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ A)))),inference(cnf,[status(esa)],[779])).
% 194.15/41.11  thf(1761,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ A)))),inference(paramod_ordered,[status(thm)],[1314,780])).
% 194.15/41.11  thf(1762,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ A)))),inference(simp,[status(thm)],[1761])).
% 194.15/41.11  thf(1765,plain,(! [A:nat] : ((i3 != A) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[1762])).
% 194.15/41.11  thf(1767,plain,(((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != i3)),inference(simp,[status(thm)],[1765])).
% 194.15/41.11  thf(23,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (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/sandbox/benchmark/theBenchmark.p',fact_106_order__subst2)).
% 194.15/41.11  thf(343,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (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)],[23])).
% 194.15/41.11  thf(344,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:(nat > nat),D:nat]: ((ord_less_eq_nat @ (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(miniscope,[status(thm)],[343])).
% 194.15/41.11  thf(345,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : (((~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ (C @ B) @ D) | (ord_less_eq_nat @ (sk6 @ D @ (C) @ B @ A) @ (sk7 @ D @ (C) @ B @ A)) | (ord_less_eq_nat @ (C @ A) @ D)) & (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ (C @ B) @ D) | ~ (ord_less_eq_nat @ (C @ (sk6 @ D @ (C) @ B @ A)) @ (C @ (sk7 @ D @ (C) @ B @ A))) | (ord_less_eq_nat @ (C @ A) @ D))))),inference(cnf,[status(esa)],[344])).
% 194.15/41.11  thf(347,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ (C @ B) @ D)) | (~ (ord_less_eq_nat @ (C @ (sk6 @ D @ (C) @ B @ A)) @ (C @ (sk7 @ D @ (C) @ B @ A)))) | (ord_less_eq_nat @ (C @ A) @ D))),inference(cnfConj,[status(thm)],[345])).
% 194.15/41.12  thf(206,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_not__add__less2)).
% 194.15/41.12  thf(1042,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])).
% 194.15/41.12  thf(1043,plain,((~ (? [A:nat,B:nat]: (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(miniscope,[status(thm)],[1042])).
% 194.15/41.12  thf(1044,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(cnf,[status(esa)],[1043])).
% 194.15/41.12  thf(6844,plain,(! [B:nat,A:nat] : (~ (($true)) | ((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)],[824,1044])).
% 194.15/41.12  thf(6845,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(simp,[status(thm)],[6844])).
% 194.15/41.12  thf(6850,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)],[6845])).
% 194.15/41.12  thf(6855,plain,(! [A:nat] : (((plus_plus_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != k))),inference(simp,[status(thm)],[6850])).
% 194.15/41.12  thf(241,axiom,((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_Until_Oprems)).
% 194.15/41.12  thf(1177,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)],[241])).
% 194.15/41.12  thf(185,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_minf_I4_J)).
% 194.15/41.12  thf(941,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
% 194.15/41.12  thf(942,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ B @ (sk80 @ A))) | (~ (B = A)))),inference(cnf,[status(esa)],[941])).
% 194.15/41.12  thf(943,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ B @ (sk80 @ A))))),inference(lifteq,[status(thm)],[942])).
% 194.15/41.12  thf(944,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ (sk80 @ A))))),inference(simp,[status(thm)],[943])).
% 194.15/41.12  thf(2462,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk80 @ A))))),inference(paramod_ordered,[status(thm)],[1177,944])).
% 194.15/41.12  thf(2463,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 @ (sk80 @ A))))),inference(simp,[status(thm)],[2462])).
% 194.15/41.12  thf(2474,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk80 @ A)))),inference(simp,[status(thm)],[2463])).
% 194.15/41.12  thf(2480,plain,(((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk80 @ ia))),inference(simp,[status(thm)],[2474])).
% 194.15/41.12  thf(137,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_pinf_I3_J)).
% 194.15/41.12  thf(774,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
% 194.15/41.12  thf(775,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ (sk60 @ A) @ B)) | (~ (B = A)))),inference(cnf,[status(esa)],[774])).
% 194.15/41.12  thf(776,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ (sk60 @ A) @ B)))),inference(lifteq,[status(thm)],[775])).
% 194.15/41.12  thf(777,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk60 @ A) @ A)))),inference(simp,[status(thm)],[776])).
% 194.15/41.12  thf(223,axiom,((! [A:nat,B:(nat > $o),C:nat]: ((! [D:nat]: ((ord_less_nat @ A @ D) => (B @ D))) => ((! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((! [E:nat]: ((ord_less_nat @ D @ E) => (B @ E))) => (B @ D)))) => (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_nat__descend__induct)).
% 194.15/41.12  thf(1110,plain,((! [A:nat,B:(nat > $o),C:nat]: ((! [D:nat]: ((ord_less_nat @ A @ D) => (B @ D))) => ((! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((! [E:nat]: ((ord_less_nat @ D @ E) => (B @ E))) => (B @ D)))) => (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
% 194.15/41.12  thf(19,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/sandbox/benchmark/theBenchmark.p',fact_247_add__le__cancel__left)).
% 194.15/41.12  thf(333,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)],[19])).
% 194.15/41.12  thf(99,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/sandbox/benchmark/theBenchmark.p',fact_236_trans__le__add2)).
% 194.15/41.12  thf(628,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)],[99])).
% 194.15/41.12  thf(282,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A != B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_le__neq__implies__less)).
% 194.15/41.12  thf(1315,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)],[282])).
% 194.15/41.12  thf(65,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A != B) => ((ord_le699472955list_a @ A @ B) => (ord_le887097159list_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_order_Onot__eq__order__implies__strict)).
% 194.15/41.12  thf(518,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((~ (A = B)) => ((ord_le699472955list_a @ A @ B) => (ord_le887097159list_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
% 194.15/41.12  thf(40,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (~ (ord_less_eq_nat @ B @ C))) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => (((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_le__cases3)).
% 194.15/41.12  thf(402,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (~ (ord_less_eq_nat @ B @ C))) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ C @ B))) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => (((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
% 194.15/41.12  thf(403,plain,(! [C:nat,B:nat,A:nat] : ((((ord_less_eq_nat @ A @ B) | (sk11 @ B @ A @ C)) & ((ord_less_eq_nat @ B @ C) | (sk11 @ B @ A @ C)) & (~ (sk11 @ B @ A @ C) | (ord_less_eq_nat @ B @ A) | (sk12 @ A @ C @ B)) & (~ (sk11 @ B @ A @ C) | (ord_less_eq_nat @ A @ C) | (sk12 @ A @ C @ B)) & (~ (sk11 @ B @ A @ C) | ~ (sk12 @ A @ C @ B) | (ord_less_eq_nat @ A @ C) | (sk13 @ C @ B @ A)) & (~ (sk11 @ B @ A @ C) | ~ (sk12 @ A @ C @ B) | (ord_less_eq_nat @ C @ B) | (sk13 @ C @ B @ A)) & (~ (sk11 @ B @ A @ C) | ~ (sk12 @ A @ C @ B) | ~ (sk13 @ C @ B @ A) | (ord_less_eq_nat @ C @ B) | (sk14 @ B @ C @ A)) & (~ (sk11 @ B @ A @ C) | ~ (sk12 @ A @ C @ B) | ~ (sk13 @ C @ B @ A) | (ord_less_eq_nat @ B @ A) | (sk14 @ B @ C @ A)) & (~ (sk11 @ B @ A @ C) | ~ (sk12 @ A @ C @ B) | ~ (sk13 @ C @ B @ A) | ~ (sk14 @ B @ C @ A) | (ord_less_eq_nat @ B @ C) | (ord_less_eq_nat @ C @ A)) & (~ (sk11 @ B @ A @ C) | ~ (sk12 @ A @ C @ B) | ~ (sk13 @ C @ B @ A) | ~ (sk14 @ B @ C @ A) | (ord_less_eq_nat @ B @ C) | (ord_less_eq_nat @ A @ B)) & (~ (sk11 @ B @ A @ C) | ~ (sk12 @ A @ C @ B) | ~ (sk13 @ C @ B @ A) | ~ (sk14 @ B @ C @ A) | (ord_less_eq_nat @ C @ A) | (ord_less_eq_nat @ C @ A)) & (~ (sk11 @ B @ A @ C) | ~ (sk12 @ A @ C @ B) | ~ (sk13 @ C @ B @ A) | ~ (sk14 @ B @ C @ A) | (ord_less_eq_nat @ C @ A) | (ord_less_eq_nat @ A @ B))))),inference(cnf,[status(esa)],[402])).
% 194.15/41.12  thf(408,plain,(! [C:nat,B:nat,A:nat] : ((~ (sk11 @ B @ A @ C)) | (~ (sk12 @ A @ C @ B)) | (~ (sk13 @ C @ B @ A)) | (~ (sk14 @ B @ C @ A)) | (ord_less_eq_nat @ C @ A) | (ord_less_eq_nat @ A @ B))),inference(cnfConj,[status(thm)],[403])).
% 194.15/41.12  thf(253,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_not__le)).
% 194.15/41.12  thf(1211,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])).
% 194.15/41.12  thf(194,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_le__less)).
% 194.15/41.12  thf(1005,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
% 194.15/41.12  thf(3,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_order__refl)).
% 194.15/41.12  thf(287,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 194.15/41.12  thf(288,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ A))),inference(cnf,[status(esa)],[287])).
% 194.15/41.12  thf(143,axiom,((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox/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)).
% 194.15/41.12  thf(796,plain,((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
% 194.15/41.12  thf(14,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_antisym)).
% 194.15/41.12  thf(319,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 194.15/41.12  thf(320,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ A)) | (A = B))),inference(cnf,[status(esa)],[319])).
% 194.15/41.12  thf(321,plain,(! [B:nat,A:nat] : ((A = B) | (~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ A)))),inference(lifteq,[status(thm)],[320])).
% 194.15/41.12  thf(1,conjecture,((ord_less_nat @ k @ (plen_P694648887list_a @ pi))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 194.15/41.12  thf(2,negated_conjecture,((~ (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(neg_conjecture,[status(cth)],[1])).
% 194.15/41.12  thf(286,plain,((~ (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 194.15/41.12  thf(2751,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (B != k))),inference(paramod_ordered,[status(thm)],[321,286])).
% 194.15/41.12  thf(2752,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ A @ k)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))))),inference(pattern_uni,[status(thm)],[2751:[bind(A, $thf(A)),bind(B, $thf(k))]])).
% 194.15/41.12  thf(4004,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[796,2752])).
% 194.15/41.12  thf(4005,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[4004])).
% 194.15/41.12  thf(4025,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (j != A) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k))),inference(simp,[status(thm)],[4005])).
% 194.15/41.12  thf(4064,plain,((~ (ord_less_eq_nat @ k @ j)) | (~ (ord_less_nat @ j @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k)),inference(simp,[status(thm)],[4025])).
% 194.15/41.12  thf(20887,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ j @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ j)))),inference(paramod_ordered,[status(thm)],[288,4064])).
% 194.15/41.12  thf(20888,plain,(! [A:nat] : ((~ (ord_less_nat @ j @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ j)))),inference(simp,[status(thm)],[20887])).
% 194.15/41.12  thf(21086,plain,(! [A:nat] : ((~ (ord_less_nat @ j @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (A != k) | (A != j))),inference(simp,[status(thm)],[20888])).
% 194.15/41.12  thf(21114,plain,((~ (ord_less_nat @ j @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (k != j)),inference(simp,[status(thm)],[21086])).
% 194.15/41.12  thf(278,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_1 @ (plen_P694648887list_a @ pi)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212__C1_C)).
% 194.15/41.12  thf(1290,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_1 @ (plen_P694648887list_a @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])).
% 194.15/41.12  thf(190,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_dual__order_Ostrict__iff__order)).
% 194.15/41.12  thf(993,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])).
% 194.15/41.12  thf(994,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(lifteq,[status(thm)],[993])).
% 194.15/41.12  thf(129,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => (((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/sandbox/benchmark/theBenchmark.p',fact_97_ord__le__eq__subst)).
% 194.15/41.12  thf(741,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => (((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)],[129])).
% 194.15/41.12  thf(215,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/sandbox/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)).
% 194.15/41.12  thf(1085,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)],[215])).
% 194.15/41.12  thf(1086,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)],[1085])).
% 194.15/41.12  thf(1087,plain,(((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) & (ord_less_eq_nat @ sk95 @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi))) & (ord_less_eq_nat @ sk95 @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi))))),inference(cnf,[status(esa)],[1086])).
% 194.15/41.12  thf(1088,plain,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(cnfConj,[status(thm)],[1087])).
% 194.15/41.12  thf(4422,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(rewrite,[status(thm)],[1088,324])).
% 194.15/41.12  thf(4479,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[4422,306])).
% 194.15/41.12  thf(4480,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[4479])).
% 194.15/41.12  thf(4481,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[4480:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ sk95))]])).
% 194.15/41.12  thf(4709,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[4481,305])).
% 194.15/41.12  thf(4710,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[4709])).
% 194.15/41.12  thf(4711,plain,((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[4710:[bind(A, $thf(b)),bind(B, $thf(one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ sk95))]])).
% 194.15/41.12  thf(272,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_pinf_I4_J)).
% 194.15/41.12  thf(1269,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])).
% 194.15/41.12  thf(96,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_dual__order_Otrans)).
% 194.15/41.12  thf(614,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
% 194.15/41.12  thf(28,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_add_Ocommute)).
% 194.15/41.12  thf(359,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 194.15/41.12  thf(360,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(lifteq,[status(thm)],[359])).
% 194.15/41.12  thf(1326,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) = (plus_plus_nat @ B @ A)))),inference(func_ext,[status(esa)],[360])).
% 194.15/41.12  thf(30,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/sandbox/benchmark/theBenchmark.p',fact_257_add_Oleft__commute)).
% 194.15/41.12  thf(364,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)],[30])).
% 194.15/41.12  thf(365,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(cnf,[status(esa)],[364])).
% 194.15/41.12  thf(366,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(lifteq,[status(thm)],[365])).
% 194.15/41.12  thf(78,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/sandbox/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)).
% 194.15/41.12  thf(559,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)],[78])).
% 194.15/41.12  thf(3499,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)],[559,324])).
% 194.15/41.12  thf(14068,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) @ (tau_Pr257024512list_a @ sigma2 @ ja)) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[366,3499])).
% 194.15/41.12  thf(14069,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[14068:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(b)),bind(C, $thf(one_one_nat))]])).
% 194.15/41.12  thf(16069,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[14069,306])).
% 194.15/41.12  thf(16070,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[16069])).
% 194.15/41.12  thf(16071,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[16070:[bind(A, $thf(b)),bind(B, $thf(plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ ja))]])).
% 194.15/41.12  thf(18283,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma2 @ ja)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,16071])).
% 194.15/41.12  thf(18284,plain,((ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ia)) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[18283:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(284,axiom,((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062)).
% 194.15/41.12  thf(1321,plain,((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])).
% 194.15/41.12  thf(3988,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[1321,2752])).
% 194.15/41.12  thf(3989,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[3988])).
% 194.15/41.12  thf(4035,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (ja != A) | ((monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)) != k))),inference(simp,[status(thm)],[3989])).
% 194.15/41.12  thf(4073,plain,((~ (ord_less_eq_nat @ k @ ja)) | (~ (ord_less_nat @ ja @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)) != k)),inference(simp,[status(thm)],[4035])).
% 194.15/41.12  thf(24059,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ ja @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ ja)))),inference(paramod_ordered,[status(thm)],[288,4073])).
% 194.15/41.12  thf(24060,plain,(! [A:nat] : ((~ (ord_less_nat @ ja @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ ja)))),inference(simp,[status(thm)],[24059])).
% 194.15/41.12  thf(24237,plain,(! [A:nat] : ((~ (ord_less_nat @ ja @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)) != k) | (A != k) | (A != ja))),inference(simp,[status(thm)],[24060])).
% 194.15/41.12  thf(24305,plain,((~ (ord_less_nat @ ja @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)) != k) | (k != ja)),inference(simp,[status(thm)],[24237])).
% 194.15/41.12  thf(67,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_ord__le__eq__trans)).
% 194.15/41.12  thf(523,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
% 194.15/41.12  thf(234,axiom,((! [A:nat,B:nat]: ((A != B) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_linorder__neqE__nat)).
% 194.15/41.12  thf(1158,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])).
% 194.15/41.12  thf(6875,plain,(! [D:nat,C:nat,B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != k) | ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) != (plus_plus_nat @ D @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))))),inference(paramod_ordered,[status(thm)],[324,6855])).
% 194.15/41.12  thf(6876,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ B @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))) != k))),inference(pattern_uni,[status(thm)],[6875:[bind(A, $thf(E)),bind(B, $thf(F)),bind(C, $thf(monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))),bind(D, $thf(plus_plus_nat @ E @ F))]])).
% 194.15/41.12  thf(6883,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ B @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))) != k))),inference(simp,[status(thm)],[6876])).
% 194.15/41.12  thf(6848,plain,(! [B:nat,A:nat] : (~ (($true)) | ((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)],[1314,1044])).
% 194.15/41.12  thf(6849,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(simp,[status(thm)],[6848])).
% 194.15/41.12  thf(6853,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != B))),inference(simp,[status(thm)],[6849])).
% 194.15/41.12  thf(6859,plain,(! [A:nat] : (((plus_plus_nat @ A @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != i3))),inference(simp,[status(thm)],[6853])).
% 194.15/41.12  thf(7634,plain,(! [D:nat,C:nat,B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != i3) | ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) != (plus_plus_nat @ D @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)))))),inference(paramod_ordered,[status(thm)],[324,6859])).
% 194.15/41.12  thf(7635,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ B @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)))) != i3))),inference(pattern_uni,[status(thm)],[7634:[bind(A, $thf(E)),bind(B, $thf(F)),bind(C, $thf(monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))),bind(D, $thf(plus_plus_nat @ E @ F))]])).
% 194.15/41.12  thf(7641,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ B @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)))) != i3))),inference(simp,[status(thm)],[7635])).
% 194.15/41.12  thf(260,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_gt__ex)).
% 194.15/41.12  thf(1234,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])).
% 194.15/41.12  thf(1235,plain,(! [A:nat] : ((ord_less_nat @ A @ (sk112 @ A)))),inference(cnf,[status(esa)],[1234])).
% 194.15/41.12  thf(4692,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[4481,306])).
% 194.15/41.12  thf(4693,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[4692])).
% 194.15/41.12  thf(4694,plain,((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[4693:[bind(A, $thf(b)),bind(B, $thf(one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ sk95))]])).
% 194.15/41.12  thf(4769,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[4694,2752])).
% 194.15/41.12  thf(4770,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[4769])).
% 194.15/41.12  thf(4794,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (one_one_nat != A) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k))),inference(simp,[status(thm)],[4770])).
% 194.15/41.12  thf(4804,plain,((~ (ord_less_eq_nat @ k @ one_one_nat)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k)),inference(simp,[status(thm)],[4794])).
% 194.15/41.12  thf(7039,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,4804])).
% 194.15/41.12  thf(7040,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[7039])).
% 194.15/41.12  thf(7151,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (A != one_one_nat) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[7040])).
% 194.15/41.12  thf(7203,plain,((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[7151])).
% 194.15/41.12  thf(70,axiom,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le699472955list_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_order__subst1)).
% 194.15/41.12  thf(533,plain,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le699472955list_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
% 194.15/41.12  thf(5753,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[3499,306])).
% 194.15/41.12  thf(5754,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[5753])).
% 194.15/41.12  thf(5755,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[5754:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ ja))]])).
% 194.15/41.12  thf(144,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_neq__iff)).
% 194.15/41.12  thf(797,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
% 194.15/41.12  thf(12,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_eq__iff)).
% 194.15/41.12  thf(314,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)],[12])).
% 194.15/41.12  thf(315,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = ((=) @ nat))),inference(lifteq,[status(thm)],[314])).
% 194.15/41.12  thf(1327,plain,(! [A:nat] : (((^ [B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))) = ((=) @ nat @ A)))),inference(func_ext,[status(esa)],[315])).
% 194.15/41.12  thf(115,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ C) => (ord_le699472955list_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_order__trans)).
% 194.15/41.12  thf(698,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ C) => (ord_le699472955list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
% 194.15/41.12  thf(186,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_ord__less__eq__subst)).
% 194.15/41.12  thf(945,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])).
% 194.15/41.12  thf(71,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/sandbox/benchmark/theBenchmark.p',fact_210_nat__add__left__cancel__le)).
% 194.15/41.12  thf(538,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)],[71])).
% 194.15/41.12  thf(257,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_order_Ostrict__trans1)).
% 194.15/41.12  thf(1222,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])).
% 194.15/41.12  thf(274,axiom,((! [A:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b)) => (ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207__C11_C)).
% 194.15/41.12  thf(1275,plain,((! [A:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b)) => (ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])).
% 194.15/41.12  thf(1090,plain,((ord_less_eq_nat @ sk95 @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)))),inference(cnfConj,[status(thm)],[1087])).
% 194.15/41.12  thf(3978,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ sk95 @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi))) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[1090,2752])).
% 194.15/41.12  thf(3979,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ sk95 @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi))) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[3978])).
% 194.15/41.12  thf(4026,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (sk95 != A) | ((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k))),inference(simp,[status(thm)],[3979])).
% 194.15/41.12  thf(4065,plain,((~ (ord_less_eq_nat @ k @ sk95)) | (~ (ord_less_nat @ sk95 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k)),inference(simp,[status(thm)],[4026])).
% 194.15/41.12  thf(22235,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ sk95 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ sk95)))),inference(paramod_ordered,[status(thm)],[288,4065])).
% 194.15/41.12  thf(22236,plain,(! [A:nat] : ((~ (ord_less_nat @ sk95 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ sk95)))),inference(simp,[status(thm)],[22235])).
% 194.15/41.12  thf(22406,plain,(! [A:nat] : ((~ (ord_less_nat @ sk95 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (A != k) | (A != sk95))),inference(simp,[status(thm)],[22236])).
% 194.15/41.12  thf(22460,plain,((~ (ord_less_nat @ sk95 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk95 != k)),inference(simp,[status(thm)],[22406])).
% 194.15/41.12  thf(22513,plain,(! [A:nat] : (~ (($true)) | ((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk95 != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ sk95 @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,22460])).
% 194.15/41.12  thf(22514,plain,(! [A:nat] : (((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk95 != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ sk95 @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[22513])).
% 194.15/41.12  thf(22522,plain,(! [A:nat] : (((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk95 != k) | (A != sk95) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[22514])).
% 194.15/41.12  thf(22532,plain,(((monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk95 != k) | ((sk112 @ sk95) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[22522])).
% 194.15/41.12  thf(175,axiom,((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox/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)).
% 194.15/41.12  thf(910,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)],[175])).
% 194.15/41.12  thf(1270,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ (sk116 @ A) @ B)) | (~ (B = A)))),inference(cnf,[status(esa)],[1269])).
% 194.15/41.12  thf(1271,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ (sk116 @ A) @ B)))),inference(lifteq,[status(thm)],[1270])).
% 194.15/41.12  thf(1272,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk116 @ A) @ A)))),inference(simp,[status(thm)],[1271])).
% 194.15/41.12  thf(2449,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[910,1272])).
% 194.15/41.12  thf(2450,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(simp,[status(thm)],[2449])).
% 194.15/41.12  thf(2453,plain,(! [A:nat] : (((sk116 @ A) != ia) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2450])).
% 194.15/41.12  thf(2459,plain,(((sk116 @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia)),inference(simp,[status(thm)],[2453])).
% 194.15/41.12  thf(213,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) & (C @ F)) = ((B @ F) & (D @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_pinf_I1_J)).
% 194.15/41.12  thf(1063,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) & (C @ F)) = ((B @ F) & (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
% 194.15/41.12  thf(22,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ A) => (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_dual__order_Oantisym)).
% 194.15/41.12  thf(340,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 194.15/41.12  thf(1196,plain,((ord_less_eq_nat @ sk108 @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))),inference(cnfConj,[status(thm)],[1193])).
% 194.15/41.12  thf(6,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_linear)).
% 194.15/41.12  thf(296,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 194.15/41.12  thf(297,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A))),inference(cnf,[status(esa)],[296])).
% 194.15/41.12  thf(5069,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[5012,306])).
% 194.15/41.12  thf(5070,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[5069])).
% 194.15/41.12  thf(5071,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[5070:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ sk108))]])).
% 194.15/41.12  thf(5348,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[5071,306])).
% 194.15/41.12  thf(5349,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[5348])).
% 194.15/41.12  thf(5350,plain,((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[5349:[bind(A, $thf(b)),bind(B, $thf(one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ sk108))]])).
% 194.15/41.12  thf(5428,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[5350,2752])).
% 194.15/41.12  thf(5429,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[5428])).
% 194.15/41.12  thf(5444,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (one_one_nat != A) | ((tau_Pr257024512list_a @ sigma @ sk108) != k))),inference(simp,[status(thm)],[5429])).
% 194.15/41.12  thf(5456,plain,((~ (ord_less_eq_nat @ k @ one_one_nat)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k)),inference(simp,[status(thm)],[5444])).
% 194.15/41.12  thf(8849,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[297,5456])).
% 194.15/41.12  thf(8850,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[8849])).
% 194.15/41.12  thf(8851,plain,((ord_less_eq_nat @ one_one_nat @ k) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k)),inference(pattern_uni,[status(thm)],[8850:[bind(A, $thf(k)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(193,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_order_Ostrict__implies__not__eq)).
% 194.15/41.12  thf(1001,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
% 194.15/41.12  thf(4494,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[4422,305])).
% 194.15/41.12  thf(4495,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[4494])).
% 194.15/41.12  thf(4496,plain,((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[4495:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ sk95))]])).
% 194.15/41.12  thf(119,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (! [C:nat]: (B != (plus_plus_nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_less__eqE)).
% 194.15/41.12  thf(709,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (! [C:nat]: ~ (B = (plus_plus_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
% 194.15/41.12  thf(5365,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[5071,305])).
% 194.15/41.12  thf(5366,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[5365])).
% 194.15/41.12  thf(5367,plain,((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[5366:[bind(A, $thf(b)),bind(B, $thf(one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ sk108))]])).
% 194.15/41.12  thf(5504,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[5367,2752])).
% 194.15/41.12  thf(5505,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[5504])).
% 194.15/41.12  thf(5527,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (b != A) | ((tau_Pr257024512list_a @ sigma @ sk108) != k))),inference(simp,[status(thm)],[5505])).
% 194.15/41.12  thf(5536,plain,((~ (ord_less_eq_nat @ k @ b)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k)),inference(simp,[status(thm)],[5527])).
% 194.15/41.12  thf(12135,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ b)))),inference(paramod_ordered,[status(thm)],[288,5536])).
% 194.15/41.12  thf(12136,plain,(! [A:nat] : ((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ b)))),inference(simp,[status(thm)],[12135])).
% 194.15/41.12  thf(12277,plain,(! [A:nat] : ((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | (A != k) | (A != b))),inference(simp,[status(thm)],[12136])).
% 194.15/41.12  thf(12303,plain,((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != b)),inference(simp,[status(thm)],[12277])).
% 194.15/41.12  thf(8,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_less__le)).
% 194.15/41.12  thf(301,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)],[8])).
% 194.15/41.12  thf(81,axiom,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((A = (B @ C)) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_ord__eq__le__subst)).
% 194.15/41.12  thf(565,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((A = (B @ C)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
% 194.15/41.12  thf(3334,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[559,306])).
% 194.15/41.12  thf(3335,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[3334])).
% 194.15/41.12  thf(3336,plain,((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[3335:[bind(A, $thf(plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b)),bind(B, $thf(one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ ja))]])).
% 194.15/41.12  thf(2359,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,286])).
% 194.15/41.12  thf(2360,plain,(! [A:nat] : (((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[2359])).
% 194.15/41.12  thf(2365,plain,(! [A:nat] : ((A != k) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[2360])).
% 194.15/41.12  thf(2374,plain,(((sk112 @ k) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[2365])).
% 194.15/41.12  thf(2895,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ A)) | (B != (plen_P694648887list_a @ pi)) | (A != (sk112 @ k)))),inference(paramod_ordered,[status(thm)],[321,2374])).
% 194.15/41.12  thf(2896,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ (sk112 @ k) @ A)) | (~ (ord_less_eq_nat @ A @ (sk112 @ k))) | (A != (plen_P694648887list_a @ pi)))),inference(pattern_uni,[status(thm)],[2895:[bind(A, $thf(sk112 @ k)),bind(B, $thf(B))]])).
% 194.15/41.12  thf(3138,plain,((~ (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi))) | (~ (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k)))),inference(simp,[status(thm)],[2896])).
% 194.15/41.12  thf(3577,plain,((~ (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi))) | ~ (($true)) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k)))),inference(paramod_ordered,[status(thm)],[3336,3138])).
% 194.15/41.12  thf(3578,plain,((~ (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k)))),inference(simp,[status(thm)],[3577])).
% 194.15/41.12  thf(3597,plain,((~ (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi))) | ((plen_P694648887list_a @ pi) != one_one_nat) | ((tau_Pr257024512list_a @ sigma2 @ ja) != (sk112 @ k))),inference(simp,[status(thm)],[3578])).
% 194.15/41.12  thf(154,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/sandbox/benchmark/theBenchmark.p',fact_249_add__less__cancel__left)).
% 194.15/41.12  thf(829,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)],[154])).
% 194.15/41.12  thf(404,plain,(! [C:nat,B:nat,A:nat] : ((~ (sk11 @ B @ A @ C)) | (~ (sk12 @ A @ C @ B)) | (~ (sk13 @ C @ B @ A)) | (ord_less_eq_nat @ B @ A) | (sk14 @ B @ C @ A))),inference(cnfConj,[status(thm)],[403])).
% 194.15/41.12  thf(41,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/sandbox/benchmark/theBenchmark.p',fact_254_group__cancel_Oadd2)).
% 194.15/41.12  thf(417,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)],[41])).
% 194.15/41.12  thf(3345,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[559,305])).
% 194.15/41.12  thf(3346,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[3345])).
% 194.15/41.12  thf(3347,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[3346:[bind(A, $thf(plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b)),bind(B, $thf(one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ ja))]])).
% 194.15/41.12  thf(3654,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[3347,306])).
% 194.15/41.12  thf(3655,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[3654])).
% 194.15/41.12  thf(3656,plain,((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[3655:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(b)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ ja))]])).
% 194.15/41.12  thf(3972,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[3656,2752])).
% 194.15/41.12  thf(3973,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[3972])).
% 194.15/41.12  thf(4033,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (b != A) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k))),inference(simp,[status(thm)],[3973])).
% 194.15/41.12  thf(4072,plain,((~ (ord_less_eq_nat @ k @ b)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k)),inference(simp,[status(thm)],[4033])).
% 194.15/41.12  thf(5193,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(paramod_ordered,[status(thm)],[297,4072])).
% 194.15/41.12  thf(5194,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(simp,[status(thm)],[5193])).
% 194.15/41.12  thf(5195,plain,((ord_less_eq_nat @ b @ k) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k)),inference(pattern_uni,[status(thm)],[5194:[bind(A, $thf(k)),bind(B, $thf(b))]])).
% 194.15/41.12  thf(36,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__right__cancel)).
% 194.15/41.12  thf(389,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
% 194.15/41.12  thf(7053,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[288,4804])).
% 194.15/41.12  thf(7054,plain,(! [A:nat] : ((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[7053])).
% 194.15/41.12  thf(7168,plain,(! [A:nat] : ((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (A != k) | (A != one_one_nat))),inference(simp,[status(thm)],[7054])).
% 194.15/41.12  thf(7192,plain,((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != one_one_nat)),inference(simp,[status(thm)],[7168])).
% 194.15/41.12  thf(7206,plain,(! [A:nat] : (~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != one_one_nat) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,7192])).
% 194.15/41.12  thf(7207,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != one_one_nat) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[7206])).
% 194.15/41.12  thf(7238,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != one_one_nat) | (A != one_one_nat) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[7207])).
% 194.15/41.12  thf(7241,plain,(((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != one_one_nat) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[7238])).
% 194.15/41.12  thf(1787,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[1314,777])).
% 194.15/41.12  thf(1788,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(simp,[status(thm)],[1787])).
% 194.15/41.12  thf(1790,plain,(! [A:nat] : (((sk60 @ A) != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[1788])).
% 194.15/41.12  thf(1792,plain,(((sk60 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != i3)),inference(simp,[status(thm)],[1790])).
% 194.15/41.12  thf(122,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_add__leD2)).
% 194.15/41.12  thf(719,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
% 194.15/41.12  thf(279,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat]: (A @ D @ D)) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_linorder__less__wlog)).
% 194.15/41.12  thf(1292,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat]: (A @ D @ D)) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])).
% 194.15/41.12  thf(1293,plain,((! [A:(nat > (nat > $o))]: ((! [B:nat,C:nat]: ((ord_less_nat @ B @ C) => (A @ B @ C))) => ((! [B:nat]: (A @ B @ B)) => ((! [B:nat,C:nat]: ((A @ C @ B) => (A @ B @ C))) => (! [B:nat,C:nat]: (A @ B @ C))))))),inference(miniscope,[status(thm)],[1292])).
% 194.15/41.12  thf(1294,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((((ord_less_nat @ (sk121 @ (A)) @ (sk122 @ (A))) | ~ (A @ (sk123 @ (A)) @ (sk123 @ (A))) | (A @ (sk125 @ (A)) @ (sk124 @ (A))) | (A @ B @ C)) & ((ord_less_nat @ (sk121 @ (A)) @ (sk122 @ (A))) | ~ (A @ (sk123 @ (A)) @ (sk123 @ (A))) | ~ (A @ (sk124 @ (A)) @ (sk125 @ (A))) | (A @ B @ C)) & (~ (A @ (sk121 @ (A)) @ (sk122 @ (A))) | ~ (A @ (sk123 @ (A)) @ (sk123 @ (A))) | (A @ (sk125 @ (A)) @ (sk124 @ (A))) | (A @ B @ C)) & (~ (A @ (sk121 @ (A)) @ (sk122 @ (A))) | ~ (A @ (sk123 @ (A)) @ (sk123 @ (A))) | ~ (A @ (sk124 @ (A)) @ (sk125 @ (A))) | (A @ B @ C))))),inference(cnf,[status(esa)],[1293])).
% 194.15/41.12  thf(1295,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((ord_less_nat @ (sk121 @ (A)) @ (sk122 @ (A))) | (~ (A @ (sk123 @ (A)) @ (sk123 @ (A)))) | (A @ (sk125 @ (A)) @ (sk124 @ (A))) | (A @ B @ C))),inference(cnfConj,[status(thm)],[1294])).
% 194.15/41.12  thf(1299,plain,(! [B:nat,A:nat] : ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) | (~ ((sk123 @ ((=) @ nat)) = (sk123 @ ((=) @ nat)))) | ((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | (A = B))),inference(replace_andrewseq,[status(thm)],[1295:[bind(A, $thf((=) @ nat))]])).
% 194.15/41.12  thf(1309,plain,(! [B:nat,A:nat] : (((sk123 @ ((=) @ nat)) != (sk123 @ ((=) @ nat))) | ((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | (A = B) | (ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))))),inference(lifteq,[status(thm)],[1299])).
% 194.15/41.12  thf(1310,plain,(! [B:nat,A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | (A = B) | (ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))))),inference(simp,[status(thm)],[1309])).
% 194.15/41.12  thf(10379,plain,(! [B:nat,A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | (ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) | (B != (plen_P694648887list_a @ pi)) | (A != (sk112 @ k)))),inference(paramod_ordered,[status(thm)],[1310,2374])).
% 194.15/41.12  thf(10380,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | (ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) | (A != (plen_P694648887list_a @ pi)))),inference(pattern_uni,[status(thm)],[10379:[bind(A, $thf(sk112 @ k)),bind(B, $thf(B))]])).
% 194.15/41.12  thf(10688,plain,(((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | (ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat)))),inference(simp,[status(thm)],[10380])).
% 194.15/41.12  thf(11233,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ~ (($true)) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ A @ (sk80 @ A))))),inference(paramod_ordered,[status(thm)],[10688,944])).
% 194.15/41.12  thf(11234,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ A @ (sk80 @ A))))),inference(simp,[status(thm)],[11233])).
% 194.15/41.12  thf(11257,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk121 @ ((=) @ nat)) != A) | ((sk122 @ ((=) @ nat)) != (sk80 @ A)))),inference(simp,[status(thm)],[11234])).
% 194.15/41.12  thf(11299,plain,(((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk122 @ ((=) @ nat)) != (sk80 @ (sk121 @ ((=) @ nat))))),inference(simp,[status(thm)],[11257])).
% 194.15/41.12  thf(4842,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[4711,2752])).
% 194.15/41.12  thf(4843,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[4842])).
% 194.15/41.12  thf(4867,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (b != A) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k))),inference(simp,[status(thm)],[4843])).
% 194.15/41.12  thf(4872,plain,((~ (ord_less_eq_nat @ k @ b)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k)),inference(simp,[status(thm)],[4867])).
% 194.15/41.12  thf(7748,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ b)))),inference(paramod_ordered,[status(thm)],[288,4872])).
% 194.15/41.12  thf(7749,plain,(! [A:nat] : ((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ b)))),inference(simp,[status(thm)],[7748])).
% 194.15/41.12  thf(7876,plain,(! [A:nat] : ((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (A != k) | (A != b))),inference(simp,[status(thm)],[7749])).
% 194.15/41.12  thf(7896,plain,((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != b)),inference(simp,[status(thm)],[7876])).
% 194.15/41.12  thf(7905,plain,(! [A:nat] : (~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != b) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,7896])).
% 194.15/41.12  thf(7906,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != b) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[7905])).
% 194.15/41.12  thf(7939,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != b) | (A != b) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[7906])).
% 194.15/41.12  thf(7945,plain,(((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (k != b) | ((sk112 @ b) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[7939])).
% 194.15/41.12  thf(276,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_pinf_I5_J)).
% 194.15/41.12  thf(1279,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])).
% 194.15/41.12  thf(210,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_order_Ostrict__iff__order)).
% 194.15/41.12  thf(1055,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])).
% 194.15/41.12  thf(33,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_dual__order_Ostrict__iff__order)).
% 194.15/41.12  thf(374,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)],[33])).
% 194.15/41.12  thf(375,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))))),inference(lifteq,[status(thm)],[374])).
% 194.15/41.12  thf(1409,plain,(! [A:prefix1027212443list_a] : (((ord_le887097159list_a @ A) = (^ [B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A)))))),inference(func_ext,[status(esa)],[375])).
% 194.15/41.12  thf(27,axiom,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_eq__iff)).
% 194.15/41.12  thf(357,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)],[27])).
% 194.15/41.12  thf(16,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__left__cancel)).
% 194.15/41.12  thf(325,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)],[16])).
% 194.15/41.12  thf(3717,plain,((~ (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi))) | ~ (($true)) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k)))),inference(paramod_ordered,[status(thm)],[3656,3138])).
% 194.15/41.12  thf(3718,plain,((~ (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k)))),inference(simp,[status(thm)],[3717])).
% 194.15/41.12  thf(3734,plain,((~ (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi))) | ((plen_P694648887list_a @ pi) != b) | ((tau_Pr257024512list_a @ sigma2 @ ja) != (sk112 @ k))),inference(simp,[status(thm)],[3718])).
% 194.15/41.12  thf(14018,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[366,4422])).
% 194.15/41.12  thf(14019,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[14018:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(b)),bind(C, $thf(one_one_nat))]])).
% 194.15/41.12  thf(4,axiom,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((ord_le887097159list_a @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le887097159list_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_order__less__le__subst1)).
% 194.15/41.12  thf(289,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((ord_le887097159list_a @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le887097159list_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 194.15/41.12  thf(1056,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(lifteq,[status(thm)],[1055])).
% 194.15/41.12  thf(1494,plain,(! [A:nat] : (((ord_less_nat @ A) = (^ [B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B)))))),inference(func_ext,[status(esa)],[1056])).
% 194.15/41.12  thf(13,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_order_Otrans)).
% 194.15/41.12  thf(316,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 194.15/41.12  thf(2361,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ B @ B)))),inference(paramod_ordered,[status(thm)],[1235,780])).
% 194.15/41.12  thf(2362,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ B @ B)))),inference(simp,[status(thm)],[2361])).
% 194.15/41.12  thf(2370,plain,(! [B:nat,A:nat] : ((A != B) | ((sk112 @ A) != B))),inference(simp,[status(thm)],[2362])).
% 194.15/41.12  thf(2373,plain,(! [A:nat] : (((sk112 @ A) != A))),inference(simp,[status(thm)],[2370])).
% 194.15/41.12  thf(93,axiom,((! [A:nat,B:nat,C:trace_1367752404list_a]: ? [D:nat]: ((ord_less_eq_nat @ A @ D) & (ord_less_eq_nat @ B @ (tau_Pr257024512list_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_ex__le___092_060tau_062)).
% 194.15/41.12  thf(606,plain,((! [A:nat,B:nat,C:trace_1367752404list_a]: ? [D:nat]: ((ord_less_eq_nat @ A @ D) & (ord_less_eq_nat @ B @ (tau_Pr257024512list_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
% 194.15/41.12  thf(2445,plain,(~ (($true)) | ((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)],[910,286])).
% 194.15/41.12  thf(2446,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(simp,[status(thm)],[2445])).
% 194.15/41.12  thf(2456,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)],[2446])).
% 194.15/41.12  thf(163,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_less__le__not__le)).
% 194.15/41.12  thf(862,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
% 194.15/41.12  thf(863,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))))),inference(lifteq,[status(thm)],[862])).
% 194.15/41.12  thf(1496,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[1056,863])).
% 194.15/41.12  thf(1497,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(pattern_uni,[status(thm)],[1496:[]])).
% 194.15/41.12  thf(1476,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A)))) | ((ord_less_nat) != (ord_less_nat))),inference(paramod_ordered,[status(thm)],[994,863])).
% 194.15/41.12  thf(1477,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(pattern_uni,[status(thm)],[1476:[]])).
% 194.15/41.12  thf(2237,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(rewrite,[status(thm)],[1497,1477])).
% 194.15/41.12  thf(1941,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk80 @ A))))),inference(paramod_ordered,[status(thm)],[1314,944])).
% 194.15/41.12  thf(1942,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk80 @ A))))),inference(simp,[status(thm)],[1941])).
% 194.15/41.12  thf(1944,plain,(! [A:nat] : ((i3 != A) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (sk80 @ A)))),inference(simp,[status(thm)],[1942])).
% 194.15/41.12  thf(1946,plain,(((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (sk80 @ i3))),inference(simp,[status(thm)],[1944])).
% 194.15/41.12  thf(7784,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(paramod_ordered,[status(thm)],[297,4872])).
% 194.15/41.12  thf(7785,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(simp,[status(thm)],[7784])).
% 194.15/41.12  thf(7786,plain,((ord_less_eq_nat @ b @ k) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k)),inference(pattern_uni,[status(thm)],[7785:[bind(A, $thf(k)),bind(B, $thf(b))]])).
% 194.15/41.12  thf(5157,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ b)))),inference(paramod_ordered,[status(thm)],[288,4072])).
% 194.15/41.12  thf(5158,plain,(! [A:nat] : ((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ b)))),inference(simp,[status(thm)],[5157])).
% 194.15/41.12  thf(5258,plain,(! [A:nat] : ((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (A != k) | (A != b))),inference(simp,[status(thm)],[5158])).
% 194.15/41.12  thf(5272,plain,((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != b)),inference(simp,[status(thm)],[5258])).
% 194.15/41.12  thf(5623,plain,(! [A:nat] : (~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != b) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,5272])).
% 194.15/41.12  thf(5624,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != b) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[5623])).
% 194.15/41.12  thf(5657,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != b) | (A != b) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[5624])).
% 194.15/41.12  thf(5663,plain,(((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != b) | ((sk112 @ b) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[5657])).
% 194.15/41.12  thf(89,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_nat__le__iff__add)).
% 194.15/41.12  thf(591,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
% 194.15/41.12  thf(8813,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[288,5456])).
% 194.15/41.12  thf(8814,plain,(! [A:nat] : ((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[8813])).
% 194.15/41.12  thf(8945,plain,(! [A:nat] : ((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | (A != k) | (A != one_one_nat))),inference(simp,[status(thm)],[8814])).
% 194.15/41.12  thf(8971,plain,((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != one_one_nat)),inference(simp,[status(thm)],[8945])).
% 194.15/41.12  thf(12036,plain,(! [A:nat] : (~ (($true)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != one_one_nat) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,8971])).
% 194.15/41.12  thf(12037,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != one_one_nat) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[12036])).
% 194.15/41.12  thf(12041,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != one_one_nat) | (A != one_one_nat) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[12037])).
% 194.15/41.12  thf(12051,plain,(((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != one_one_nat) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[12041])).
% 194.15/41.12  thf(11190,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ~ (($true)) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[10688,777])).
% 194.15/41.12  thf(11191,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(simp,[status(thm)],[11190])).
% 194.15/41.12  thf(11276,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk121 @ ((=) @ nat)) != (sk60 @ A)) | ((sk122 @ ((=) @ nat)) != A))),inference(simp,[status(thm)],[11191])).
% 194.15/41.12  thf(11293,plain,(((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk121 @ ((=) @ nat)) != (sk60 @ (sk122 @ ((=) @ nat))))),inference(simp,[status(thm)],[11276])).
% 194.15/41.12  thf(34,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_eq_nat @ C @ D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_add__mono__thms__linordered__semiring_I2_J)).
% 194.15/41.12  thf(376,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_eq_nat @ C @ D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
% 194.15/41.12  thf(231,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/sandbox/benchmark/theBenchmark.p',fact_213__C2_C)).
% 194.15/41.12  thf(1151,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)],[231])).
% 194.15/41.12  thf(151,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_dual__order_Oirrefl)).
% 194.15/41.12  thf(821,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
% 194.15/41.12  thf(54,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((~ (ord_le887097159list_a @ A @ B)) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_antisym__conv2)).
% 194.15/41.12  thf(480,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)],[54])).
% 194.15/41.12  thf(52,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_le__add1)).
% 194.15/41.12  thf(475,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
% 194.15/41.12  thf(180,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_less__not__sym)).
% 194.15/41.12  thf(924,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])).
% 194.15/41.12  thf(24,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_dual__order_Oantisym)).
% 194.15/41.12  thf(348,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)],[24])).
% 194.15/41.12  thf(1575,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ A)))),inference(paramod_ordered,[status(thm)],[824,780])).
% 194.15/41.12  thf(1576,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ A)))),inference(simp,[status(thm)],[1575])).
% 194.15/41.12  thf(1579,plain,(! [A:nat] : ((k != A) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[1576])).
% 194.15/41.12  thf(1581,plain,(((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != k)),inference(simp,[status(thm)],[1579])).
% 194.15/41.12  thf(25,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ C) => (ord_le699472955list_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_order_Otrans)).
% 194.15/41.12  thf(351,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ C) => (ord_le699472955list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 194.15/41.12  thf(352,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => (! [C:prefix1027212443list_a]: ((ord_le699472955list_a @ B @ C) => (ord_le699472955list_a @ A @ C)))))),inference(miniscope,[status(thm)],[351])).
% 194.15/41.12  thf(353,plain,(! [C:prefix1027212443list_a,B:prefix1027212443list_a,A:prefix1027212443list_a] : ((~ (ord_le699472955list_a @ A @ B)) | (~ (ord_le699472955list_a @ B @ C)) | (ord_le699472955list_a @ A @ C))),inference(cnf,[status(esa)],[352])).
% 194.15/41.12  thf(134,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_trans__less__add1)).
% 194.15/41.12  thf(766,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)],[134])).
% 194.15/41.12  thf(38,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_add__right__imp__eq)).
% 194.15/41.12  thf(395,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)],[38])).
% 194.15/41.12  thf(396,plain,(! [C:nat,B:nat,A:nat] : ((~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))) | (A = C))),inference(cnf,[status(esa)],[395])).
% 194.15/41.12  thf(397,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ A @ B) != (plus_plus_nat @ C @ B)) | (A = C))),inference(lifteq,[status(thm)],[396])).
% 194.15/41.12  thf(101,axiom,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le887097159list_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_order__less__le__subst1)).
% 194.15/41.12  thf(634,plain,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le887097159list_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
% 194.15/41.12  thf(169,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_pinf_I2_J)).
% 194.15/41.12  thf(877,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
% 194.15/41.12  thf(5145,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,4072])).
% 194.15/41.12  thf(5146,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[5145])).
% 194.15/41.12  thf(5247,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (A != b) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[5146])).
% 194.15/41.12  thf(5282,plain,((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((sk112 @ b) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[5247])).
% 194.15/41.12  thf(8684,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((sk112 @ b) != (plen_P694648887list_a @ pi)) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(paramod_ordered,[status(thm)],[297,5282])).
% 194.15/41.12  thf(8685,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((sk112 @ b) != (plen_P694648887list_a @ pi)) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(simp,[status(thm)],[8684])).
% 194.15/41.12  thf(8686,plain,((ord_less_eq_nat @ b @ k) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((sk112 @ b) != (plen_P694648887list_a @ pi))),inference(pattern_uni,[status(thm)],[8685:[bind(A, $thf(k)),bind(B, $thf(b))]])).
% 194.15/41.12  thf(192,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_less__trans)).
% 194.15/41.12  thf(998,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
% 194.15/41.12  thf(249,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_add__less__le__mono)).
% 194.15/41.12  thf(1201,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])).
% 194.15/41.12  thf(6846,plain,(! [B:nat,A:nat] : (~ (($true)) | ((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)],[1177,1044])).
% 194.15/41.12  thf(6847,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(simp,[status(thm)],[6846])).
% 194.15/41.12  thf(6854,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)],[6847])).
% 194.15/41.12  thf(6860,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)],[6854])).
% 194.15/41.12  thf(14063,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) @ (tau_Pr257024512list_a @ sigma @ j)) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[366,3814])).
% 194.15/41.12  thf(14064,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[14063:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(b)),bind(C, $thf(one_one_nat))]])).
% 194.15/41.12  thf(15667,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[14064,306])).
% 194.15/41.12  thf(15668,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[15667])).
% 194.15/41.12  thf(15669,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[15668:[bind(A, $thf(b)),bind(B, $thf(plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ j))]])).
% 194.15/41.12  thf(18411,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma @ j)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,15669])).
% 194.15/41.12  thf(18412,plain,((ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ ia)) @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[18411:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(2470,plain,(! [A:nat] : (~ (($true)) | ((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)],[1177,780])).
% 194.15/41.12  thf(2471,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(simp,[status(thm)],[2470])).
% 194.15/41.12  thf(2478,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2471])).
% 194.15/41.12  thf(2483,plain,(((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != ia)),inference(simp,[status(thm)],[2478])).
% 194.15/41.12  thf(290,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat]: ((ord_le887097159list_a @ A @ (B @ C)) => (! [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_le887097159list_a @ A @ (B @ D)))))))),inference(miniscope,[status(thm)],[289])).
% 194.15/41.12  thf(291,plain,(! [D:nat,C:nat,B:(nat > prefix1027212443list_a),A:prefix1027212443list_a] : (((~ (ord_le887097159list_a @ A @ (B @ C)) | ~ (ord_less_eq_nat @ C @ D) | (ord_less_eq_nat @ (sk1 @ D @ C @ (B) @ A) @ (sk2 @ D @ C @ (B) @ A)) | (ord_le887097159list_a @ A @ (B @ D))) & (~ (ord_le887097159list_a @ A @ (B @ C)) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_le699472955list_a @ (B @ (sk1 @ D @ C @ (B) @ A)) @ (B @ (sk2 @ D @ C @ (B) @ A))) | (ord_le887097159list_a @ A @ (B @ D)))))),inference(cnf,[status(esa)],[290])).
% 194.15/41.12  thf(293,plain,(! [D:nat,C:nat,B:(nat > prefix1027212443list_a),A:prefix1027212443list_a] : ((~ (ord_le887097159list_a @ A @ (B @ C))) | (~ (ord_less_eq_nat @ C @ D)) | (~ (ord_le699472955list_a @ (B @ (sk1 @ D @ C @ (B) @ A)) @ (B @ (sk2 @ D @ C @ (B) @ A)))) | (ord_le887097159list_a @ A @ (B @ D)))),inference(cnfConj,[status(thm)],[291])).
% 194.15/41.12  thf(188,axiom,((! [A:nat,B:trace_1367752404list_a,C:trace_1367752404list_a,D:formula_a]: ((! [E:nat]: ((ord_less_nat @ E @ A) => ((tau_Pr257024512list_a @ B @ E) = (tau_Pr257024512list_a @ C @ E)))) => ((monito1457594016ress_a @ B @ D @ A) = (monito1457594016ress_a @ C @ D @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_progress__time__conv)).
% 194.15/41.12  thf(956,plain,((! [A:nat,B:trace_1367752404list_a,C:trace_1367752404list_a,D:formula_a]: ((! [E:nat]: ((ord_less_nat @ E @ A) => ((tau_Pr257024512list_a @ B @ E) = (tau_Pr257024512list_a @ C @ E)))) => ((monito1457594016ress_a @ B @ D @ A) = (monito1457594016ress_a @ C @ D @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
% 194.15/41.12  thf(2357,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (sk60 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[1235,777])).
% 194.15/41.12  thf(2358,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (sk60 @ B) @ B)))),inference(simp,[status(thm)],[2357])).
% 194.15/41.12  thf(2368,plain,(! [B:nat,A:nat] : ((A != (sk60 @ B)) | ((sk112 @ A) != B))),inference(simp,[status(thm)],[2358])).
% 194.15/41.12  thf(2371,plain,(! [A:nat] : (((sk112 @ (sk60 @ A)) != A))),inference(simp,[status(thm)],[2368])).
% 194.15/41.12  thf(221,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_less__le)).
% 194.15/41.12  thf(1104,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
% 194.15/41.12  thf(263,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_not__le__imp__less)).
% 194.15/41.12  thf(1242,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])).
% 194.15/41.12  thf(11,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/sandbox/benchmark/theBenchmark.p',fact_268_add__le__imp__le__left)).
% 194.15/41.12  thf(312,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)],[11])).
% 194.15/41.12  thf(283,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_not__add__less1)).
% 194.15/41.12  thf(1318,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])).
% 194.15/41.12  thf(1319,plain,((~ (? [A:nat,B:nat]: (ord_less_nat @ (plus_plus_nat @ A @ B) @ A)))),inference(miniscope,[status(thm)],[1318])).
% 194.15/41.12  thf(1320,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A)))),inference(cnf,[status(esa)],[1319])).
% 194.15/41.12  thf(7663,plain,(! [B:nat,A:nat] : (~ (($true)) | ((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)],[1314,1320])).
% 194.15/41.12  thf(7664,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(simp,[status(thm)],[7663])).
% 194.15/41.12  thf(7669,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[7664])).
% 194.15/41.12  thf(7675,plain,(! [A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) @ A) != i3))),inference(simp,[status(thm)],[7669])).
% 194.15/41.12  thf(14120,plain,(! [D:nat,C:nat,B:nat,A:nat] : (((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) != i3) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) @ D)))),inference(paramod_ordered,[status(thm)],[366,7675])).
% 194.15/41.12  thf(14121,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) @ B)) != i3))),inference(pattern_uni,[status(thm)],[14120:[bind(A, $thf(monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))),bind(B, $thf(I)),bind(C, $thf(J)),bind(D, $thf(plus_plus_nat @ I @ J))]])).
% 194.15/41.12  thf(14253,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) @ B)) != i3))),inference(simp,[status(thm)],[14121])).
% 194.15/41.12  thf(214,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) & (C @ F)) = ((B @ F) & (D @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_minf_I1_J)).
% 194.15/41.12  thf(1074,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) & (C @ F)) = ((B @ F) & (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
% 194.15/41.12  thf(251,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_not__less)).
% 194.15/41.12  thf(1206,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])).
% 194.15/41.12  thf(248,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_minf_I7_J)).
% 194.15/41.12  thf(1199,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)],[248])).
% 194.15/41.12  thf(280,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_trans__less__add2)).
% 194.15/41.12  thf(1311,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])).
% 194.15/41.12  thf(10,axiom,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_order__subst1)).
% 194.15/41.12  thf(307,plain,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 194.15/41.12  thf(7661,plain,(! [B:nat,A:nat] : (~ (($true)) | ((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)],[1177,1320])).
% 194.15/41.12  thf(7662,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(simp,[status(thm)],[7661])).
% 194.15/41.12  thf(7668,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)],[7662])).
% 194.15/41.12  thf(7674,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)],[7668])).
% 194.15/41.12  thf(292,plain,(! [D:nat,C:nat,B:(nat > prefix1027212443list_a),A:prefix1027212443list_a] : ((~ (ord_le887097159list_a @ A @ (B @ C))) | (~ (ord_less_eq_nat @ C @ D)) | (ord_less_eq_nat @ (sk1 @ D @ C @ (B) @ A) @ (sk2 @ D @ C @ (B) @ A)) | (ord_le887097159list_a @ A @ (B @ D)))),inference(cnfConj,[status(thm)],[291])).
% 194.15/41.12  thf(6840,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(paramod_ordered,[status(thm)],[910,1044])).
% 194.15/41.12  thf(6841,plain,(! [B:nat,A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (plus_plus_nat @ A @ B) @ B)))),inference(simp,[status(thm)],[6840])).
% 194.15/41.12  thf(6851,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ B) != ia) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != B))),inference(simp,[status(thm)],[6841])).
% 194.15/41.12  thf(6856,plain,(! [A:nat] : (((plus_plus_nat @ A @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia))),inference(simp,[status(thm)],[6851])).
% 194.15/41.12  thf(178,axiom,((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062)).
% 194.15/41.12  thf(920,plain,((ord_less_eq_nat @ ja @ (monito1457594016ress_a @ sigma2 @ phi_2 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
% 194.15/41.12  thf(14443,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[14019,306])).
% 194.15/41.12  thf(14444,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[14443])).
% 194.15/41.12  thf(14445,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[14444:[bind(A, $thf(b)),bind(B, $thf(plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ sk95))]])).
% 194.15/41.12  thf(35,axiom,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((A = (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_ord__eq__le__subst)).
% 194.15/41.12  thf(380,plain,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((A = (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 194.15/41.12  thf(63,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_order__class_Oorder_Oantisym)).
% 194.15/41.12  thf(512,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
% 194.15/41.12  thf(46,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_antisym__conv)).
% 194.15/41.12  thf(439,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)],[46])).
% 194.15/41.12  thf(232,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_add__strict__mono)).
% 194.15/41.12  thf(1153,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
% 194.15/41.12  thf(133,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_order__less__le__subst2)).
% 194.15/41.12  thf(761,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
% 194.15/41.12  thf(211,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/sandbox/benchmark/theBenchmark.p',fact_209_nat__add__left__cancel__less)).
% 194.15/41.12  thf(1057,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)],[211])).
% 194.15/41.12  thf(236,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_le__eq__less__or__eq)).
% 194.15/41.12  thf(1163,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
% 194.15/41.12  thf(216,axiom,((! [A:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b)) => (ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206__C21_C)).
% 194.15/41.12  thf(1091,plain,((! [A:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ A) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b)) => (ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
% 194.15/41.12  thf(302,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))))),inference(lifteq,[status(thm)],[301])).
% 194.15/41.12  thf(240,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_antisym__conv3)).
% 194.15/41.12  thf(1174,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)],[240])).
% 194.15/41.12  thf(37,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((~ (ord_le887097159list_a @ A @ B)) => ((ord_le699472955list_a @ A @ B) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_antisym__conv1)).
% 194.15/41.12  thf(392,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)],[37])).
% 194.15/41.12  thf(43,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_antisym)).
% 194.15/41.12  thf(424,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
% 194.15/41.12  thf(262,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_less__imp__neq)).
% 194.15/41.12  thf(1238,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])).
% 194.15/41.12  thf(153,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_less__not__refl3)).
% 194.15/41.12  thf(825,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
% 194.15/41.12  thf(74,axiom,((ord_le699472955list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_order_Oorder__iff__strict)).
% 194.15/41.12  thf(547,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)],[74])).
% 194.15/41.12  thf(548,plain,(((ord_le699472955list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (A = B))))),inference(lifteq,[status(thm)],[547])).
% 194.15/41.12  thf(62,axiom,((ord_le699472955list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_dual__order_Oorder__iff__strict)).
% 194.15/41.12  thf(510,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)],[62])).
% 194.15/41.12  thf(511,plain,(((ord_le699472955list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A))))),inference(lifteq,[status(thm)],[510])).
% 194.15/41.12  thf(1343,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)],[548,511])).
% 194.15/41.12  thf(167,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_discrete)).
% 194.15/41.12  thf(872,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)],[167])).
% 194.15/41.12  thf(873,plain,(((^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))) = (ord_less_nat))),inference(lifteq,[status(thm)],[872])).
% 194.15/41.12  thf(1370,plain,(! [A:nat] : (((ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat)) = (ord_less_nat @ A)))),inference(func_ext,[status(esa)],[873])).
% 194.15/41.12  thf(20,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_le__iff__add)).
% 194.15/41.12  thf(336,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)],[20])).
% 194.15/41.12  thf(337,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(lifteq,[status(thm)],[336])).
% 194.15/41.12  thf(1329,plain,(! [A:nat] : (((ord_less_eq_nat @ A) = (^ [B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),inference(func_ext,[status(esa)],[337])).
% 194.15/41.12  thf(6351,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)],[1370,1329])).
% 194.15/41.12  thf(6352,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)],[6351:[bind(A, $thf(C)),bind(B, $thf(plus_plus_nat @ C @ one_one_nat))]])).
% 194.15/41.12  thf(6355,plain,(! [A:nat] : (((ord_less_nat @ A) = (^ [B:nat]: ? [C:nat]: (B = (plus_plus_nat @ (plus_plus_nat @ A @ one_one_nat) @ C)))))),inference(simp,[status(thm)],[6352])).
% 194.15/41.12  thf(6550,plain,(! [A:nat] : (((ord_less_nat @ A) = (^ [B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ (plus_plus_nat @ one_one_nat @ C))))))),inference(rewrite,[status(thm)],[6355,324])).
% 194.15/41.12  thf(198,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_order_Ostrict__trans2)).
% 194.15/41.12  thf(1021,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
% 194.15/41.12  thf(224,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_less__imp__le__nat)).
% 194.15/41.12  thf(1123,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
% 194.15/41.12  thf(407,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | (sk11 @ B @ A @ C))),inference(cnfConj,[status(thm)],[403])).
% 194.15/41.12  thf(113,axiom,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_dual__order_Oeq__iff)).
% 194.15/41.12  thf(693,plain,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
% 194.15/41.12  thf(3882,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[3814,305])).
% 194.15/41.12  thf(3883,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[3882])).
% 194.15/41.12  thf(3884,plain,((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[3883:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ j))]])).
% 194.15/41.12  thf(149,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (ord_less_nat @ A @ B)) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_antisym__conv2)).
% 194.15/41.12  thf(815,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)],[149])).
% 194.15/41.12  thf(158,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_order__le__less__subst1)).
% 194.15/41.12  thf(847,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
% 194.15/41.12  thf(29,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_order__class_Oorder_Oantisym)).
% 194.15/41.12  thf(361,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 194.15/41.12  thf(159,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_dual__order_Ostrict__implies__not__eq)).
% 194.15/41.12  thf(852,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
% 194.15/41.12  thf(1457,plain,(! [A:nat] : (((ord_less_nat @ A) = (^ [B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A)))))),inference(func_ext,[status(esa)],[863])).
% 194.15/41.12  thf(1195,plain,((ord_less_eq_nat @ sk108 @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(cnfConj,[status(thm)],[1193])).
% 194.15/41.12  thf(226,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_order__less__subst1)).
% 194.15/41.12  thf(1128,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
% 194.15/41.12  thf(277,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ord__eq__less__subst)).
% 194.15/41.12  thf(1281,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])).
% 194.15/41.12  thf(3665,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[3347,305])).
% 194.15/41.12  thf(3666,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b) @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[3665])).
% 194.15/41.12  thf(3667,plain,((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[3666:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(b)),bind(C, $thf(tau_Pr257024512list_a @ sigma2 @ ja))]])).
% 194.15/41.12  thf(197,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_nat__less__induct)).
% 194.15/41.12  thf(1012,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
% 194.15/41.12  thf(222,axiom,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:trace_1367752404list_a,D:formula_a]: ((prefix1041802747list_a @ A @ B) => ((prefix1041802747list_a @ A @ C) => ((monito1457594016ress_a @ B @ D @ (plen_P694648887list_a @ A)) = (monito1457594016ress_a @ C @ D @ (plen_P694648887list_a @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_progress__prefix__conv)).
% 194.15/41.12  thf(1106,plain,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:trace_1367752404list_a,D:formula_a]: ((prefix1041802747list_a @ A @ B) => ((prefix1041802747list_a @ A @ C) => ((monito1457594016ress_a @ B @ D @ (plen_P694648887list_a @ A)) = (monito1457594016ress_a @ C @ D @ (plen_P694648887list_a @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
% 194.15/41.12  thf(3914,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ A @ k)) | ~ (($true)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ k @ A)))),inference(paramod_ordered,[status(thm)],[3336,2752])).
% 194.15/41.12  thf(3915,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ A @ k)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ k @ A)))),inference(simp,[status(thm)],[3914])).
% 194.15/41.12  thf(4029,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ A @ k)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (k != one_one_nat) | ((tau_Pr257024512list_a @ sigma2 @ ja) != A))),inference(simp,[status(thm)],[3915])).
% 194.15/41.12  thf(4068,plain,((~ (ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ k)) | (~ (ord_less_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ (plen_P694648887list_a @ pi))) | (k != one_one_nat)),inference(simp,[status(thm)],[4029])).
% 194.15/41.12  thf(22704,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ (plen_P694648887list_a @ pi))) | (k != one_one_nat) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ k)))),inference(paramod_ordered,[status(thm)],[288,4068])).
% 194.15/41.12  thf(22705,plain,(! [A:nat] : ((~ (ord_less_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ (plen_P694648887list_a @ pi))) | (k != one_one_nat) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ k)))),inference(simp,[status(thm)],[22704])).
% 194.15/41.12  thf(22887,plain,(! [A:nat] : ((~ (ord_less_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ (plen_P694648887list_a @ pi))) | (k != one_one_nat) | (A != (tau_Pr257024512list_a @ sigma2 @ ja)) | (A != k))),inference(simp,[status(thm)],[22705])).
% 194.15/41.12  thf(22948,plain,((~ (ord_less_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ (plen_P694648887list_a @ pi))) | (k != one_one_nat) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k)),inference(simp,[status(thm)],[22887])).
% 194.15/41.12  thf(242,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => (ord_less_eq_nat @ (plen_P694648887list_a @ A) @ (plen_P694648887list_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_plen__mono)).
% 194.15/41.12  thf(1178,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => (ord_less_eq_nat @ (plen_P694648887list_a @ A) @ (plen_P694648887list_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
% 194.15/41.12  thf(18327,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma @ sk108)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[1326,5012])).
% 194.15/41.12  thf(18328,plain,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ ia)) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[18327:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat))]])).
% 194.15/41.12  thf(23231,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ ia))) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(rewrite,[status(thm)],[18328,324])).
% 194.15/41.12  thf(168,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_add__less__mono)).
% 194.15/41.12  thf(874,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])).
% 194.15/41.12  thf(18367,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma @ j)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[1326,3814])).
% 194.15/41.12  thf(18368,plain,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ ia)) @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[18367:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat))]])).
% 194.15/41.12  thf(23822,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ ia))) @ (tau_Pr257024512list_a @ sigma @ j))),inference(rewrite,[status(thm)],[18368,324])).
% 194.15/41.12  thf(18479,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ b @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,4481])).
% 194.15/41.12  thf(18480,plain,((ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ b) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[18479:[bind(A, $thf(b)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(218,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_less__linear)).
% 194.15/41.12  thf(1096,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
% 194.15/41.12  thf(90,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ B @ C) => (ord_le887097159list_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_le__less__trans)).
% 194.15/41.12  thf(593,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ B @ C) => (ord_le887097159list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
% 194.15/41.12  thf(165,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_minf_I6_J)).
% 194.15/41.12  thf(869,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
% 194.15/41.12  thf(94,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_le__add2)).
% 194.15/41.12  thf(610,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
% 194.15/41.12  thf(11239,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ~ (($true)) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[10688,1272])).
% 194.15/41.12  thf(11240,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(simp,[status(thm)],[11239])).
% 194.15/41.12  thf(11262,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk121 @ ((=) @ nat)) != (sk116 @ A)) | ((sk122 @ ((=) @ nat)) != A))),inference(simp,[status(thm)],[11240])).
% 194.15/41.12  thf(11304,plain,(((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk121 @ ((=) @ nat)) != (sk116 @ (sk122 @ ((=) @ nat))))),inference(simp,[status(thm)],[11262])).
% 194.15/41.12  thf(161,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_less__le__trans)).
% 194.15/41.12  thf(857,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
% 194.15/41.12  thf(1089,plain,((ord_less_eq_nat @ sk95 @ (monito1457594016ress_a @ sigma2 @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(cnfConj,[status(thm)],[1087])).
% 194.15/41.12  thf(381,plain,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a]: ((A = (B @ C)) => (! [D:prefix1027212443list_a]: ((ord_le699472955list_a @ C @ D) => ((! [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)))))))),inference(miniscope,[status(thm)],[380])).
% 194.15/41.12  thf(382,plain,(! [D:prefix1027212443list_a,C:prefix1027212443list_a,B:(prefix1027212443list_a > nat),A:nat] : (((~ (A = (B @ C)) | ~ (ord_le699472955list_a @ C @ D) | (ord_le699472955list_a @ (sk8 @ D @ C @ (B) @ A) @ (sk9 @ D @ C @ (B) @ A)) | (ord_less_eq_nat @ A @ (B @ D))) & (~ (A = (B @ C)) | ~ (ord_le699472955list_a @ C @ D) | ~ (ord_less_eq_nat @ (B @ (sk8 @ D @ C @ (B) @ A)) @ (B @ (sk9 @ D @ C @ (B) @ A))) | (ord_less_eq_nat @ A @ (B @ D)))))),inference(cnf,[status(esa)],[381])).
% 194.15/41.12  thf(384,plain,(! [D:prefix1027212443list_a,C:prefix1027212443list_a,B:(prefix1027212443list_a > nat),A:nat] : ((~ (A = (B @ C))) | (~ (ord_le699472955list_a @ C @ D)) | (~ (ord_less_eq_nat @ (B @ (sk8 @ D @ C @ (B) @ A)) @ (B @ (sk9 @ D @ C @ (B) @ A)))) | (ord_less_eq_nat @ A @ (B @ D)))),inference(cnfConj,[status(thm)],[382])).
% 194.15/41.12  thf(387,plain,(! [D:prefix1027212443list_a,C:prefix1027212443list_a,B:(prefix1027212443list_a > nat),A:nat] : ((A != (B @ C)) | (~ (ord_le699472955list_a @ C @ D)) | (~ (ord_less_eq_nat @ (B @ (sk8 @ D @ C @ (B) @ A)) @ (B @ (sk9 @ D @ C @ (B) @ A)))) | (ord_less_eq_nat @ A @ (B @ D)))),inference(lifteq,[status(thm)],[384])).
% 194.15/41.12  thf(388,plain,(! [C:prefix1027212443list_a,B:prefix1027212443list_a,A:(prefix1027212443list_a > nat)] : ((~ (ord_le699472955list_a @ B @ C)) | (~ (ord_less_eq_nat @ (A @ (sk8 @ C @ B @ (A) @ (A @ B))) @ (A @ (sk9 @ C @ B @ (A) @ (A @ B))))) | (ord_less_eq_nat @ (A @ B) @ (A @ C)))),inference(simp,[status(thm)],[387])).
% 194.15/41.12  thf(14047,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) @ (tau_Pr257024512list_a @ sigma @ sk108)) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ b @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[366,5012])).
% 194.15/41.12  thf(14048,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[14047:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(b)),bind(C, $thf(one_one_nat))]])).
% 194.15/41.12  thf(14781,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[14048,306])).
% 194.15/41.12  thf(14782,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)) @ (tau_Pr257024512list_a @ sigma @ sk108)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[14781])).
% 194.15/41.12  thf(14783,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[14782:[bind(A, $thf(b)),bind(B, $thf(plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ sk108))]])).
% 194.15/41.12  thf(228,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_dual__order_Oasym)).
% 194.15/41.12  thf(1138,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
% 194.15/41.12  thf(26,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ A) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_antisym__conv)).
% 194.15/41.12  thf(354,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 194.15/41.12  thf(355,plain,(! [B:prefix1027212443list_a,A:prefix1027212443list_a] : ((~ (ord_le699472955list_a @ A @ B)) | ((ord_le699472955list_a @ B @ A) = (B = A)))),inference(cnf,[status(esa)],[354])).
% 194.15/41.12  thf(356,plain,(! [B:prefix1027212443list_a,A:prefix1027212443list_a] : (((ord_le699472955list_a @ B @ A) = (B = A)) | (~ (ord_le699472955list_a @ A @ B)))),inference(lifteq,[status(thm)],[355])).
% 194.15/41.12  thf(17,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_add__leD1)).
% 194.15/41.12  thf(328,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 194.15/41.12  thf(2439,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk80 @ A))))),inference(paramod_ordered,[status(thm)],[910,944])).
% 194.15/41.12  thf(2440,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 @ (sk80 @ A))))),inference(simp,[status(thm)],[2439])).
% 194.15/41.12  thf(2454,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk80 @ A)))),inference(simp,[status(thm)],[2440])).
% 194.15/41.12  thf(2460,plain,(((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk80 @ ia))),inference(simp,[status(thm)],[2454])).
% 194.15/41.12  thf(7089,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[297,4804])).
% 194.15/41.12  thf(7090,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[7089])).
% 194.15/41.12  thf(7091,plain,((ord_less_eq_nat @ one_one_nat @ k) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k)),inference(pattern_uni,[status(thm)],[7090:[bind(A, $thf(k)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(201,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dual__order_Ostrict__implies__order)).
% 194.15/41.12  thf(1028,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
% 194.15/41.12  thf(694,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))) = ((=) @ prefix1027212443list_a))),inference(lifteq,[status(thm)],[693])).
% 194.15/41.12  thf(1361,plain,(! [A:prefix1027212443list_a] : (((^ [B:prefix1027212443list_a]: ((ord_le699472955list_a @ B @ A) & (ord_le699472955list_a @ A @ B))) = ((=) @ prefix1027212443list_a @ A)))),inference(func_ext,[status(esa)],[694])).
% 194.15/41.12  thf(21,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_dual__order_Ostrict__implies__order)).
% 194.15/41.12  thf(338,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)],[21])).
% 194.15/41.12  thf(339,plain,(! [B:prefix1027212443list_a,A:prefix1027212443list_a] : ((~ (ord_le887097159list_a @ A @ B)) | (ord_le699472955list_a @ A @ B))),inference(cnf,[status(esa)],[338])).
% 194.15/41.12  thf(108,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_add__mono)).
% 194.15/41.12  thf(669,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
% 194.15/41.12  thf(1413,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B)))) | ((ord_le887097159list_a) != (ord_le887097159list_a))),inference(paramod_ordered,[status(thm)],[375,302])).
% 194.15/41.12  thf(1414,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (B = A))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))))),inference(pattern_uni,[status(thm)],[1413:[]])).
% 194.15/41.12  thf(57,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ (C @ B) @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le887097159list_a @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_order__le__less__subst2)).
% 194.15/41.12  thf(489,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ (C @ B) @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le887097159list_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
% 194.15/41.12  thf(1785,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[824,777])).
% 194.15/41.12  thf(1786,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(simp,[status(thm)],[1785])).
% 194.15/41.12  thf(1789,plain,(! [A:nat] : (((sk60 @ A) != k) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[1786])).
% 194.15/41.12  thf(1791,plain,(((sk60 @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != k)),inference(simp,[status(thm)],[1789])).
% 194.15/41.12  thf(7734,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,4872])).
% 194.15/41.12  thf(7735,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[7734])).
% 194.15/41.12  thf(7871,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | (A != b) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[7735])).
% 194.15/41.12  thf(7895,plain,((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma2 @ sk95) != k) | ((sk112 @ b) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[7871])).
% 194.15/41.12  thf(131,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_order__subst2)).
% 194.15/41.12  thf(753,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => ((ord_less_eq_nat @ (C @ B) @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_eq_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])).
% 194.15/41.12  thf(4165,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[3873,306])).
% 194.15/41.12  thf(4166,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ B @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[4165])).
% 194.15/41.12  thf(4167,plain,((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[4166:[bind(A, $thf(b)),bind(B, $thf(one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ j))]])).
% 194.15/41.12  thf(18287,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[1326,4422])).
% 194.15/41.12  thf(18288,plain,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ia)) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[18287:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat))]])).
% 194.15/41.12  thf(21792,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ia))) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(rewrite,[status(thm)],[18288,324])).
% 194.15/41.12  thf(174,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_infinite__descent)).
% 194.15/41.12  thf(901,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
% 194.15/41.12  thf(476,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(cnf,[status(esa)],[475])).
% 194.15/41.12  thf(254,axiom,((! [A:nat,B:list_a]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) => ((sat_a @ sigma @ B @ A @ phi_2) = (sat_a @ sigma2 @ B @ A @ phi_2))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Until_OIH_I2_J)).
% 194.15/41.12  thf(1214,plain,((! [A:nat,B:list_a]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) => ((sat_a @ sigma @ B @ A @ phi_2) = (sat_a @ sigma2 @ B @ A @ phi_2))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])).
% 194.15/41.12  thf(4180,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | (ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(paramod_ordered,[status(thm)],[3873,305])).
% 194.15/41.12  thf(4181,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ C) | ((ord_less_eq_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(simp,[status(thm)],[4180])).
% 194.15/41.12  thf(4182,plain,((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[4181:[bind(A, $thf(b)),bind(B, $thf(one_one_nat)),bind(C, $thf(tau_Pr257024512list_a @ sigma @ j))]])).
% 194.15/41.12  thf(4309,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[4182,2752])).
% 194.15/41.12  thf(4310,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[4309])).
% 194.15/41.12  thf(4331,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (b != A) | ((tau_Pr257024512list_a @ sigma @ j) != k))),inference(simp,[status(thm)],[4310])).
% 194.15/41.12  thf(4338,plain,((~ (ord_less_eq_nat @ k @ b)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k)),inference(simp,[status(thm)],[4331])).
% 194.15/41.12  thf(6392,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,4338])).
% 194.15/41.12  thf(6393,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[6392])).
% 194.15/41.12  thf(6538,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | (A != b) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[6393])).
% 194.15/41.12  thf(6539,plain,((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((sk112 @ b) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[6538])).
% 194.15/41.12  thf(4239,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[4167,2752])).
% 194.15/41.12  thf(4240,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ j)) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[4239])).
% 194.15/41.12  thf(4258,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (one_one_nat != A) | ((tau_Pr257024512list_a @ sigma @ j) != k))),inference(simp,[status(thm)],[4240])).
% 194.15/41.12  thf(4264,plain,((~ (ord_less_eq_nat @ k @ one_one_nat)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k)),inference(simp,[status(thm)],[4258])).
% 194.15/41.12  thf(5802,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,4264])).
% 194.15/41.12  thf(5803,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[5802])).
% 194.15/41.12  thf(5941,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | (A != one_one_nat) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[5803])).
% 194.15/41.12  thf(5947,plain,((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[5941])).
% 194.15/41.12  thf(219,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_nat__neq__iff)).
% 194.15/41.12  thf(1099,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
% 194.15/41.12  thf(116,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_one__reorient)).
% 194.15/41.12  thf(701,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
% 194.15/41.12  thf(64,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le699472955list_a @ B @ C) => (ord_le887097159list_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_order_Ostrict__trans2)).
% 194.15/41.12  thf(515,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le699472955list_a @ B @ C) => (ord_le887097159list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
% 194.15/41.12  thf(247,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_dual__order_Oorder__iff__strict)).
% 194.15/41.12  thf(1197,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
% 194.15/41.12  thf(1198,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(lifteq,[status(thm)],[1197])).
% 194.15/41.12  thf(162,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_order_Oorder__iff__strict)).
% 194.15/41.12  thf(860,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
% 194.15/41.12  thf(861,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(lifteq,[status(thm)],[860])).
% 194.15/41.12  thf(1382,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)],[1198,861])).
% 194.15/41.12  thf(176,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (C = D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_add__mono__thms__linordered__field_I1_J)).
% 194.15/41.12  thf(911,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (C = D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])).
% 194.15/41.12  thf(3916,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ sk108 @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[1196,2752])).
% 194.15/41.12  thf(3917,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ sk108 @ (monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi))) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[3916])).
% 194.15/41.12  thf(4021,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (sk108 != A) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k))),inference(simp,[status(thm)],[3917])).
% 194.15/41.12  thf(4060,plain,((~ (ord_less_eq_nat @ k @ sk108)) | (~ (ord_less_nat @ sk108 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k)),inference(simp,[status(thm)],[4021])).
% 194.15/41.12  thf(20065,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ sk108 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ sk108)))),inference(paramod_ordered,[status(thm)],[288,4060])).
% 194.15/41.12  thf(20066,plain,(! [A:nat] : ((~ (ord_less_nat @ sk108 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ sk108)))),inference(simp,[status(thm)],[20065])).
% 194.15/41.12  thf(20216,plain,(! [A:nat] : ((~ (ord_less_nat @ sk108 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (A != k) | (A != sk108))),inference(simp,[status(thm)],[20066])).
% 194.15/41.12  thf(20283,plain,((~ (ord_less_nat @ sk108 @ (plen_P694648887list_a @ pi))) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk108 != k)),inference(simp,[status(thm)],[20216])).
% 194.15/41.12  thf(20322,plain,(! [A:nat] : (~ (($true)) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk108 != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ sk108 @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,20283])).
% 194.15/41.12  thf(20323,plain,(! [A:nat] : (((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk108 != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ sk108 @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[20322])).
% 194.15/41.12  thf(20329,plain,(! [A:nat] : (((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk108 != k) | (A != sk108) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[20323])).
% 194.15/41.12  thf(20337,plain,(((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (sk108 != k) | ((sk112 @ sk108) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[20329])).
% 194.15/41.12  thf(85,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (ord_le699472955list_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_less__le__not__le)).
% 194.15/41.12  thf(579,plain,(((ord_le887097159list_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)],[85])).
% 194.15/41.12  thf(580,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (ord_le699472955list_a @ B @ A))))),inference(lifteq,[status(thm)],[579])).
% 194.15/41.12  thf(1429,plain,(! [A:prefix1027212443list_a] : (((ord_le887097159list_a @ A) = (^ [B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (ord_le699472955list_a @ B @ A)))))),inference(func_ext,[status(esa)],[580])).
% 194.15/41.12  thf(2464,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[1177,777])).
% 194.15/41.12  thf(2465,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(simp,[status(thm)],[2464])).
% 194.15/41.12  thf(2477,plain,(! [A:nat] : (((sk60 @ A) != ia) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2465])).
% 194.15/41.12  thf(2482,plain,(((sk60 @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia)),inference(simp,[status(thm)],[2477])).
% 194.15/41.12  thf(18407,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma @ sk108)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,14783])).
% 194.15/41.12  thf(18408,plain,((ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma @ ia)) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[18407:[bind(A, $thf(tau_Pr257024512list_a @ sigma @ ia)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(32,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/sandbox/benchmark/theBenchmark.p',fact_251_ab__semigroup__add__class_Oadd__ac_I1_J)).
% 194.15/41.12  thf(371,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)],[32])).
% 194.15/41.12  thf(1367,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)],[337,861])).
% 194.15/41.12  thf(1524,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)],[1367,1382])).
% 194.15/41.12  thf(1525,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)],[1524:[]])).
% 194.15/41.12  thf(270,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_dual__order_Ostrict__trans)).
% 194.15/41.12  thf(1263,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])).
% 194.15/41.12  thf(271,axiom,((! [A:trace_1367752404list_a,B:nat,C:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ A @ B) @ (tau_Pr257024512list_a @ A @ C)) => ((ord_less_nat @ C @ B) => ((tau_Pr257024512list_a @ A @ B) = (tau_Pr257024512list_a @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_le___092_060tau_062__less)).
% 194.15/41.12  thf(1266,plain,((! [A:trace_1367752404list_a,B:nat,C:nat]: ((ord_less_eq_nat @ (tau_Pr257024512list_a @ A @ B) @ (tau_Pr257024512list_a @ A @ C)) => ((ord_less_nat @ C @ B) => ((tau_Pr257024512list_a @ A @ B) = (tau_Pr257024512list_a @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])).
% 194.15/41.12  thf(212,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/sandbox/benchmark/theBenchmark.p',fact_275_add__strict__right__mono)).
% 194.15/41.12  thf(1060,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)],[212])).
% 194.15/41.12  thf(208,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_order_Ostrict__trans)).
% 194.15/41.12  thf(1050,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
% 194.15/41.12  thf(50,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/sandbox/benchmark/theBenchmark.p',fact_269_add__le__imp__le__right)).
% 194.15/41.12  thf(457,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)],[50])).
% 194.15/41.12  thf(18379,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma2 @ ja)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ b @ one_one_nat))))),inference(paramod_ordered,[status(thm)],[1326,3499])).
% 194.15/41.12  thf(18380,plain,((ord_less_eq_nat @ (plus_plus_nat @ (plus_plus_nat @ b @ one_one_nat) @ (tau_Pr257024512list_a @ sigma2 @ ia)) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[18379:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(plus_plus_nat @ b @ one_one_nat))]])).
% 194.15/41.12  thf(24412,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ (plus_plus_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ia))) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(rewrite,[status(thm)],[18380,324])).
% 194.15/41.12  thf(123,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_le__refl)).
% 194.15/41.12  thf(721,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
% 194.15/41.12  thf(1433,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (ord_le699472955list_a @ B @ A))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B)))) | ((ord_le887097159list_a) != (ord_le887097159list_a))),inference(paramod_ordered,[status(thm)],[580,302])).
% 194.15/41.12  thf(1434,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (ord_le699472955list_a @ B @ A))) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B))))),inference(pattern_uni,[status(thm)],[1433:[]])).
% 194.15/41.12  thf(3912,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ A @ k)))),inference(paramod_ordered,[status(thm)],[3336,2752])).
% 194.15/41.12  thf(3913,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ A @ k)))),inference(simp,[status(thm)],[3912])).
% 194.15/41.12  thf(4022,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_nat @ A @ (plen_P694648887list_a @ pi))) | (one_one_nat != A) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k))),inference(simp,[status(thm)],[3913])).
% 194.15/41.12  thf(4061,plain,((~ (ord_less_eq_nat @ k @ one_one_nat)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k)),inference(simp,[status(thm)],[4022])).
% 194.15/41.12  thf(4534,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[288,4061])).
% 194.15/41.12  thf(4535,plain,(! [A:nat] : ((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[4534])).
% 194.15/41.12  thf(4626,plain,(! [A:nat] : ((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (A != k) | (A != one_one_nat))),inference(simp,[status(thm)],[4535])).
% 194.15/41.12  thf(4644,plain,((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != one_one_nat)),inference(simp,[status(thm)],[4626])).
% 194.15/41.12  thf(308,plain,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ (B @ C)) => (! [D:prefix1027212443list_a]: ((ord_le699472955list_a @ C @ D) => ((! [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)))))))),inference(miniscope,[status(thm)],[307])).
% 194.15/41.12  thf(309,plain,(! [D:prefix1027212443list_a,C:prefix1027212443list_a,B:(prefix1027212443list_a > nat),A:nat] : (((~ (ord_less_eq_nat @ A @ (B @ C)) | ~ (ord_le699472955list_a @ C @ D) | (ord_le699472955list_a @ (sk4 @ D @ C @ (B) @ A) @ (sk5 @ D @ C @ (B) @ A)) | (ord_less_eq_nat @ A @ (B @ D))) & (~ (ord_less_eq_nat @ A @ (B @ C)) | ~ (ord_le699472955list_a @ C @ D) | ~ (ord_less_eq_nat @ (B @ (sk4 @ D @ C @ (B) @ A)) @ (B @ (sk5 @ D @ C @ (B) @ A))) | (ord_less_eq_nat @ A @ (B @ D)))))),inference(cnf,[status(esa)],[308])).
% 194.15/41.12  thf(311,plain,(! [D:prefix1027212443list_a,C:prefix1027212443list_a,B:(prefix1027212443list_a > nat),A:nat] : ((~ (ord_less_eq_nat @ A @ (B @ C))) | (~ (ord_le699472955list_a @ C @ D)) | (~ (ord_less_eq_nat @ (B @ (sk4 @ D @ C @ (B) @ A)) @ (B @ (sk5 @ D @ C @ (B) @ A)))) | (ord_less_eq_nat @ A @ (B @ D)))),inference(cnfConj,[status(thm)],[309])).
% 194.15/41.12  thf(72,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ C @ D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_add__mono__thms__linordered__semiring_I1_J)).
% 194.15/41.12  thf(541,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ C @ D)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
% 194.15/41.12  thf(239,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/sandbox/benchmark/theBenchmark.p',fact_219_less__add__eq__less)).
% 194.15/41.12  thf(1170,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)],[239])).
% 194.15/41.12  thf(200,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_less__asym)).
% 194.15/41.12  thf(1026,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
% 194.15/41.12  thf(244,axiom,((! [A:nat,B:nat]: ((A != B) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_order_Onot__eq__order__implies__strict)).
% 194.15/41.12  thf(1185,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
% 194.15/41.12  thf(88,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/sandbox/benchmark/theBenchmark.p',fact_253_group__cancel_Oadd1)).
% 194.15/41.12  thf(586,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)],[88])).
% 194.15/41.12  thf(170,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_less__not__refl2)).
% 194.15/41.12  thf(888,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
% 194.15/41.12  thf(11192,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ~ (($true)) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ A @ (sk113 @ A))))),inference(paramod_ordered,[status(thm)],[10688,1247])).
% 194.15/41.12  thf(11193,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ A @ (sk113 @ A))))),inference(simp,[status(thm)],[11192])).
% 194.15/41.12  thf(11281,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk121 @ ((=) @ nat)) != A) | ((sk122 @ ((=) @ nat)) != (sk113 @ A)))),inference(simp,[status(thm)],[11193])).
% 194.15/41.12  thf(11296,plain,(((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk122 @ ((=) @ nat)) != (sk113 @ (sk121 @ ((=) @ nat))))),inference(simp,[status(thm)],[11281])).
% 194.15/41.12  thf(179,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_verit__comp__simplify1_I3_J)).
% 194.15/41.12  thf(921,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
% 194.15/41.12  thf(181,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A != B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_le__neq__trans)).
% 194.15/41.12  thf(926,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)],[181])).
% 194.15/41.12  thf(12171,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(paramod_ordered,[status(thm)],[297,5536])).
% 194.15/41.12  thf(12172,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(simp,[status(thm)],[12171])).
% 194.15/41.12  thf(12173,plain,((ord_less_eq_nat @ b @ k) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ sk108) != k)),inference(pattern_uni,[status(thm)],[12172:[bind(A, $thf(k)),bind(B, $thf(b))]])).
% 194.15/41.12  thf(7,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/sandbox/benchmark/theBenchmark.p',fact_15_le__trans)).
% 194.15/41.12  thf(298,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)],[7])).
% 194.15/41.12  thf(130,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_trans__le__add1)).
% 194.15/41.12  thf(750,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])).
% 194.15/41.12  thf(160,axiom,((prefix1041802747list_a @ pi @ sigma2)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_assms_I2_J)).
% 194.15/41.12  thf(856,plain,((prefix1041802747list_a @ pi @ sigma2)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
% 194.15/41.12  thf(18561,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma2 @ ja)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b)))),inference(paramod_ordered,[status(thm)],[1326,3347])).
% 194.15/41.12  thf(18562,plain,((ord_less_eq_nat @ (plus_plus_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ ia)) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[18561:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(b))]])).
% 194.15/41.12  thf(2363,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (sk116 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[1235,1272])).
% 194.15/41.12  thf(2364,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (sk116 @ B) @ B)))),inference(simp,[status(thm)],[2363])).
% 194.15/41.12  thf(2367,plain,(! [B:nat,A:nat] : ((A != (sk116 @ B)) | ((sk112 @ A) != B))),inference(simp,[status(thm)],[2364])).
% 194.15/41.12  thf(2376,plain,(! [A:nat] : (((sk112 @ (sk116 @ A)) != A))),inference(simp,[status(thm)],[2367])).
% 194.15/41.12  thf(92,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((A = B) => ((ord_le699472955list_a @ B @ C) => (ord_le699472955list_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_ord__eq__le__trans)).
% 194.15/41.12  thf(601,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((A = B) => ((ord_le699472955list_a @ B @ C) => (ord_le699472955list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
% 194.15/41.12  thf(230,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_order__le__less__subst2)).
% 194.15/41.12  thf(1146,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
% 194.15/41.12  thf(45,axiom,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le699472955list_a @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_ord__le__eq__subst)).
% 194.15/41.12  thf(430,plain,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ B) => (((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le699472955list_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
% 194.15/41.12  thf(18279,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma2 @ ja)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ b @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,5755])).
% 194.15/41.12  thf(18280,plain,((ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ b) @ (tau_Pr257024512list_a @ sigma2 @ ja))),inference(pattern_uni,[status(thm)],[18279:[bind(A, $thf(b)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(273,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_nat__less__le)).
% 194.15/41.12  thf(1273,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])).
% 194.15/41.12  thf(6406,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ b)))),inference(paramod_ordered,[status(thm)],[288,4338])).
% 194.15/41.12  thf(6407,plain,(! [A:nat] : ((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ b)))),inference(simp,[status(thm)],[6406])).
% 194.15/41.12  thf(6526,plain,(! [A:nat] : ((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | (A != k) | (A != b))),inference(simp,[status(thm)],[6407])).
% 194.15/41.12  thf(6549,plain,((~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | (k != b)),inference(simp,[status(thm)],[6526])).
% 194.15/41.12  thf(6562,plain,(! [A:nat] : (~ (($true)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | (k != b) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,6549])).
% 194.15/41.12  thf(6563,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma @ j) != k) | (k != b) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[6562])).
% 194.15/41.12  thf(6596,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma @ j) != k) | (k != b) | (A != b) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[6563])).
% 194.15/41.12  thf(6598,plain,(((tau_Pr257024512list_a @ sigma @ j) != k) | (k != b) | ((sk112 @ b) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[6596])).
% 194.15/41.12  thf(87,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_order_Ostrict__iff__order)).
% 194.15/41.12  thf(584,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)],[87])).
% 194.15/41.12  thf(80,axiom,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:prefix1027212443list_a]: ((prefix1041802747list_a @ A @ B) => ((prefix1041802747list_a @ C @ B) => ((ord_le699472955list_a @ A @ C) | (ord_le699472955list_a @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_prefix__of__imp__linear)).
% 194.15/41.12  thf(562,plain,((! [A:prefix1027212443list_a,B:trace_1367752404list_a,C:prefix1027212443list_a]: ((prefix1041802747list_a @ A @ B) => ((prefix1041802747list_a @ C @ B) => ((ord_le699472955list_a @ A @ C) | (ord_le699472955list_a @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
% 194.15/41.12  thf(42,axiom,((! [A:prefix1027212443list_a]: (ord_le699472955list_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_dual__order_Orefl)).
% 194.15/41.12  thf(422,plain,((! [A:prefix1027212443list_a]: (ord_le699472955list_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
% 194.15/41.12  thf(423,plain,(! [A:prefix1027212443list_a] : ((ord_le699472955list_a @ A @ A))),inference(cnf,[status(esa)],[422])).
% 194.15/41.12  thf(195,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_add__mono__thms__linordered__field_I4_J)).
% 194.15/41.12  thf(1007,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ A @ B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
% 194.15/41.12  thf(225,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__irrefl__nat)).
% 194.15/41.12  thf(1125,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
% 194.15/41.12  thf(136,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_minf_I8_J)).
% 194.15/41.12  thf(772,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)],[136])).
% 194.15/41.12  thf(84,axiom,((! [A:prefix1027212443list_a]: (ord_le699472955list_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_order__refl)).
% 194.15/41.12  thf(577,plain,((! [A:prefix1027212443list_a]: (ord_le699472955list_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
% 194.15/41.12  thf(1515,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)],[315,1056])).
% 194.15/41.12  thf(1516,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)],[1515])).
% 194.15/41.12  thf(1520,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)],[1516])).
% 194.15/41.12  thf(267,axiom,((((?) @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_exists__least__iff)).
% 194.15/41.12  thf(1256,plain,((((?) @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])).
% 194.15/41.12  thf(390,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(cnf,[status(esa)],[389])).
% 194.15/41.12  thf(391,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(lifteq,[status(thm)],[390])).
% 194.15/41.12  thf(184,axiom,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_ord__eq__less__trans)).
% 194.15/41.12  thf(936,plain,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
% 194.15/41.12  thf(2447,plain,(! [A:nat] : (~ (($true)) | ((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)],[910,780])).
% 194.15/41.12  thf(2448,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(simp,[status(thm)],[2447])).
% 194.15/41.12  thf(2451,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2448])).
% 194.15/41.12  thf(2457,plain,(((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != ia)),inference(simp,[status(thm)],[2451])).
% 194.15/41.12  thf(109,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/sandbox/benchmark/theBenchmark.p',fact_73_order__trans)).
% 194.15/41.12  thf(672,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)],[109])).
% 194.15/41.12  thf(611,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(cnf,[status(esa)],[610])).
% 194.15/41.12  thf(141,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_less__imp__not__eq2)).
% 194.15/41.12  thf(787,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
% 194.15/41.12  thf(21540,plain,(! [A:nat] : (~ (($true)) | ((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (k != j) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ j @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,21114])).
% 194.15/41.12  thf(21541,plain,(! [A:nat] : (((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (k != j) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ j @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[21540])).
% 194.15/41.12  thf(21549,plain,(! [A:nat] : (((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (k != j) | (A != j) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[21541])).
% 194.15/41.12  thf(21558,plain,(((monito1457594016ress_a @ sigma @ phi_2 @ (plen_P694648887list_a @ pi)) != k) | (k != j) | ((sk112 @ j) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[21549])).
% 194.15/41.12  thf(60,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/sandbox/benchmark/theBenchmark.p',fact_248_add__le__cancel__right)).
% 194.15/41.12  thf(498,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)],[60])).
% 194.15/41.12  thf(120,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/sandbox/benchmark/theBenchmark.p',fact_260_add__mono__thms__linordered__semiring_I3_J)).
% 194.15/41.12  thf(713,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)],[120])).
% 194.15/41.12  thf(334,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)],[333])).
% 194.15/41.12  thf(335,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)],[334])).
% 194.15/41.12  thf(7655,plain,(! [B:nat,A:nat] : (~ (($true)) | ((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)],[910,1320])).
% 194.15/41.12  thf(7656,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(simp,[status(thm)],[7655])).
% 194.15/41.12  thf(7666,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)],[7656])).
% 194.15/41.12  thf(7671,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)],[7666])).
% 194.15/41.12  thf(268,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_dual__order_Ostrict__trans1)).
% 194.15/41.12  thf(1258,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])).
% 194.15/41.12  thf(117,axiom,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_verit__la__disequality)).
% 194.15/41.12  thf(704,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
% 194.15/41.12  thf(140,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_less__not__refl)).
% 194.15/41.12  thf(784,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
% 194.15/41.12  thf(8799,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,5456])).
% 194.15/41.12  thf(8800,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[8799])).
% 194.15/41.12  thf(8939,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | (A != one_one_nat) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[8800])).
% 194.15/41.12  thf(8970,plain,((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[8939])).
% 194.15/41.12  thf(127,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((A != B) => (ord_le887097159list_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_le__neq__trans)).
% 194.15/41.12  thf(736,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((~ (A = B)) => (ord_le887097159list_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
% 194.15/41.12  thf(1486,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)],[994,315])).
% 194.15/41.12  thf(1488,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)],[1486])).
% 194.15/41.12  thf(1492,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)],[1488])).
% 194.15/41.12  thf(12337,plain,(! [A:nat] : (~ (($true)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != b) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,12303])).
% 194.15/41.12  thf(12338,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != b) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[12337])).
% 194.15/41.12  thf(12345,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != b) | (A != b) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[12338])).
% 194.15/41.12  thf(12354,plain,(((tau_Pr257024512list_a @ sigma @ sk108) != k) | (k != b) | ((sk112 @ b) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[12345])).
% 194.15/41.12  thf(48,axiom,((! [A:nat,B:nat,C:trace_1367752404list_a,D:formula_a]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (monito1457594016ress_a @ C @ D @ A) @ (monito1457594016ress_a @ C @ D @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_progress__mono)).
% 194.15/41.12  thf(451,plain,((! [A:nat,B:nat,C:trace_1367752404list_a,D:formula_a]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (monito1457594016ress_a @ C @ D @ A) @ (monito1457594016ress_a @ C @ D @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
% 194.15/41.12  thf(18249,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma @ j)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ b @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,3873])).
% 194.15/41.12  thf(18250,plain,((ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ b) @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[18249:[bind(A, $thf(b)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(1372,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (ord_less_nat)) | ((^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))) != (ord_less_eq_nat))),inference(paramod_ordered,[status(thm)],[873,861])).
% 194.15/41.12  thf(1374,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (ord_less_nat)) | ((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: (B)) != (^ [A:nat,B:nat]: (B)))),inference(simp,[status(thm)],[1372])).
% 194.15/41.12  thf(1376,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (ord_less_nat)) | ((^ [A:nat,B:nat]: (plus_plus_nat @ A @ one_one_nat)) != (^ [A:nat,B:nat]: (A)))),inference(simp,[status(thm)],[1374])).
% 194.15/41.12  thf(252,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_leI)).
% 194.15/41.12  thf(1209,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])).
% 194.15/41.12  thf(406,plain,(! [C:nat,B:nat,A:nat] : ((~ (sk11 @ B @ A @ C)) | (ord_less_eq_nat @ A @ C) | (sk12 @ A @ C @ B))),inference(cnfConj,[status(thm)],[403])).
% 194.15/41.12  thf(12602,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi)) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[297,5947])).
% 194.15/41.12  thf(12603,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi)) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[12602])).
% 194.15/41.12  thf(12604,plain,((ord_less_eq_nat @ one_one_nat @ k) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(pattern_uni,[status(thm)],[12603:[bind(A, $thf(k)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(104,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_linorder__wlog)).
% 194.15/41.12  thf(649,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
% 194.15/41.12  thf(7659,plain,(! [B:nat,A:nat] : (~ (($true)) | ((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)],[824,1320])).
% 194.15/41.12  thf(7660,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(simp,[status(thm)],[7659])).
% 194.15/41.12  thf(7665,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)],[7660])).
% 194.15/41.12  thf(7670,plain,(! [A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) @ A) != k))),inference(simp,[status(thm)],[7665])).
% 194.15/41.12  thf(14150,plain,(! [D:nat,C:nat,B:nat,A:nat] : (((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) != k) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) @ D)))),inference(paramod_ordered,[status(thm)],[366,7670])).
% 194.15/41.12  thf(14151,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) @ B)) != k))),inference(pattern_uni,[status(thm)],[14150:[bind(A, $thf(monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))),bind(B, $thf(I)),bind(C, $thf(J)),bind(D, $thf(plus_plus_nat @ I @ J))]])).
% 194.15/41.12  thf(14265,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) @ B)) != k))),inference(simp,[status(thm)],[14151])).
% 194.15/41.12  thf(17633,plain,(! [E:nat,D:nat,C:nat,B:nat,A:nat] : (((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) != k) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ D @ (plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) @ E))))),inference(paramod_ordered,[status(thm)],[366,14265])).
% 194.15/41.12  thf(17634,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) @ (plus_plus_nat @ A @ B)) != k))),inference(pattern_uni,[status(thm)],[17633:[bind(A, $thf(A)),bind(B, $thf(monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))),bind(C, $thf(C)),bind(D, $thf(A)),bind(E, $thf(C))]])).
% 194.15/41.12  thf(17650,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) @ (plus_plus_nat @ A @ B)) != k))),inference(simp,[status(thm)],[17634])).
% 194.15/41.12  thf(58,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_less__imp__le)).
% 194.15/41.12  thf(494,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)],[58])).
% 194.15/41.12  thf(100,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/sandbox/benchmark/theBenchmark.p',fact_266_add__right__mono)).
% 194.15/41.12  thf(631,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)],[100])).
% 194.15/41.12  thf(132,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ C @ A) => (ord_le699472955list_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_dual__order_Otrans)).
% 194.15/41.12  thf(758,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le699472955list_a @ C @ A) => (ord_le699472955list_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
% 194.15/41.12  thf(55,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/sandbox/benchmark/theBenchmark.p',fact_234_add__le__mono1)).
% 194.15/41.12  thf(483,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)],[55])).
% 194.15/41.12  thf(1325,plain,(! [A:nat] : (((plus_plus_nat @ A) = (^ [B:nat]: (plus_plus_nat @ B @ A))))),inference(func_ext,[status(esa)],[360])).
% 194.15/41.12  thf(172,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_less__imp__not__eq)).
% 194.15/41.12  thf(895,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
% 194.15/41.12  thf(135,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/sandbox/benchmark/theBenchmark.p',fact_222_add__less__mono1)).
% 194.15/41.12  thf(769,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)],[135])).
% 194.15/41.12  thf(18325,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ B @ A)) @ (tau_Pr257024512list_a @ sigma @ sk108)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ b @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,5012])).
% 194.15/41.12  thf(18326,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ one_one_nat @ b)) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[18325:[bind(A, $thf(b)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(53,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le699472955list_a @ B @ C) => (ord_le887097159list_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_less__le__trans)).
% 194.15/41.12  thf(477,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le699472955list_a @ B @ C) => (ord_le887097159list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
% 194.15/41.12  thf(147,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_order_Ostrict__implies__order)).
% 194.15/41.12  thf(811,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
% 194.15/41.12  thf(31,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_eq__imp__le)).
% 194.15/41.12  thf(367,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 194.15/41.12  thf(76,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_eq__refl)).
% 194.15/41.12  thf(552,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
% 194.15/41.12  thf(98,axiom,((ord_le699472955list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_le__less)).
% 194.15/41.12  thf(626,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)],[98])).
% 194.15/41.12  thf(177,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_order__less__subst2)).
% 194.15/41.12  thf(915,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])).
% 194.15/41.12  thf(2441,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[910,777])).
% 194.15/41.12  thf(2442,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk60 @ A) @ A)))),inference(simp,[status(thm)],[2441])).
% 194.15/41.12  thf(2455,plain,(! [A:nat] : (((sk60 @ A) != ia) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2442])).
% 194.15/41.12  thf(2461,plain,(((sk60 @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia)),inference(simp,[status(thm)],[2455])).
% 194.15/41.12  thf(18,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:trace_1367752404list_a]: ((ord_le699472955list_a @ A @ B) => ((prefix1041802747list_a @ B @ C) => (prefix1041802747list_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_prefix__of__antimono)).
% 194.15/41.12  thf(330,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:trace_1367752404list_a]: ((ord_le699472955list_a @ A @ B) => ((prefix1041802747list_a @ B @ C) => (prefix1041802747list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 194.15/41.12  thf(66,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => (~ (ord_le887097159list_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_leD)).
% 194.15/41.12  thf(521,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)],[66])).
% 194.15/41.12  thf(1474,plain,(! [A:nat] : (((ord_less_nat @ A) = (^ [B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A)))))),inference(func_ext,[status(esa)],[994])).
% 194.15/41.12  thf(607,plain,(! [C:trace_1367752404list_a,B:nat,A:nat] : (((ord_less_eq_nat @ A @ (sk32 @ C @ B @ A)) & (ord_less_eq_nat @ B @ (tau_Pr257024512list_a @ C @ (sk32 @ C @ B @ A)))))),inference(cnf,[status(esa)],[606])).
% 194.15/41.12  thf(608,plain,(! [C:trace_1367752404list_a,B:nat,A:nat] : ((ord_less_eq_nat @ A @ (sk32 @ C @ B @ A)))),inference(cnfConj,[status(thm)],[607])).
% 194.15/41.12  thf(220,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_leD)).
% 194.15/41.12  thf(1102,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])).
% 194.15/41.12  thf(114,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)) = ((A = D) & (B = E) & (C = F))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_formula_Oinject_I9_J)).
% 194.15/41.12  thf(695,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)) = ((A = D) & (B = E) & (C = F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
% 194.15/41.12  thf(2472,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[1177,1272])).
% 194.15/41.12  thf(2473,plain,(! [A:nat] : (((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(simp,[status(thm)],[2472])).
% 194.15/41.12  thf(2476,plain,(! [A:nat] : (((sk116 @ A) != ia) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2473])).
% 194.15/41.12  thf(2481,plain,(((sk116 @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != ia)),inference(simp,[status(thm)],[2476])).
% 194.15/41.12  thf(393,plain,(! [B:prefix1027212443list_a,A:prefix1027212443list_a] : ((ord_le887097159list_a @ A @ B) | ((ord_le699472955list_a @ A @ B) = (A = B)))),inference(cnf,[status(esa)],[392])).
% 194.15/41.12  thf(394,plain,(! [B:prefix1027212443list_a,A:prefix1027212443list_a] : (((ord_le699472955list_a @ A @ B) = (A = B)) | (ord_le887097159list_a @ A @ B))),inference(lifteq,[status(thm)],[393])).
% 194.15/41.12  thf(203,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_dual__order_Ostrict__trans2)).
% 194.15/41.12  thf(1034,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
% 194.15/41.12  thf(110,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => (((C @ B) = D) => ((! [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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_ord__le__eq__subst)).
% 194.15/41.12  thf(675,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:(prefix1027212443list_a > nat),D:nat]: ((ord_le699472955list_a @ A @ B) => (((C @ B) = D) => ((! [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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
% 194.15/41.12  thf(275,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_pinf_I8_J)).
% 194.15/41.12  thf(1277,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)],[275])).
% 194.15/41.12  thf(97,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/sandbox/benchmark/theBenchmark.p',fact_102_ord__eq__le__subst)).
% 194.15/41.12  thf(617,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)],[97])).
% 194.15/41.12  thf(341,plain,(! [B:prefix1027212443list_a,A:prefix1027212443list_a] : ((~ (ord_le699472955list_a @ A @ B)) | (~ (ord_le699472955list_a @ B @ A)) | (B = A))),inference(cnf,[status(esa)],[340])).
% 194.15/41.12  thf(342,plain,(! [B:prefix1027212443list_a,A:prefix1027212443list_a] : ((B = A) | (~ (ord_le699472955list_a @ A @ B)) | (~ (ord_le699472955list_a @ B @ A)))),inference(lifteq,[status(thm)],[341])).
% 194.15/41.12  thf(69,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_dual__order_Orefl)).
% 194.15/41.12  thf(531,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
% 194.15/41.12  thf(14011,plain,(! [E:nat,D:nat,C:nat,B:nat,A:nat] : (((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) != i3) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ D @ (plus_plus_nat @ E @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))))))),inference(paramod_ordered,[status(thm)],[366,7641])).
% 194.15/41.12  thf(14012,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ B @ (plus_plus_nat @ A @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)))) != i3))),inference(pattern_uni,[status(thm)],[14011:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))),bind(D, $thf(A)),bind(E, $thf(B))]])).
% 194.15/41.12  thf(157,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_minf_I2_J)).
% 194.15/41.12  thf(836,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])).
% 194.15/41.12  thf(4968,plain,(! [A:nat] : (~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != one_one_nat) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,4644])).
% 194.15/41.12  thf(4969,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != one_one_nat) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[4968])).
% 194.15/41.12  thf(5001,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != one_one_nat) | (A != one_one_nat) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[4969])).
% 194.15/41.12  thf(5003,plain,(((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (k != one_one_nat) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[5001])).
% 194.15/41.12  thf(2293,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[1314,1272])).
% 194.15/41.12  thf(2294,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(simp,[status(thm)],[2293])).
% 194.15/41.12  thf(2296,plain,(! [A:nat] : (((sk116 @ A) != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2294])).
% 194.15/41.12  thf(2298,plain,(((sk116 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != i3)),inference(simp,[status(thm)],[2296])).
% 194.15/41.12  thf(3715,plain,(~ (($true)) | (~ (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi)))),inference(paramod_ordered,[status(thm)],[3656,3138])).
% 194.15/41.12  thf(3716,plain,((~ (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k))) | ((ord_less_eq_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[3715])).
% 194.15/41.12  thf(3737,plain,((~ (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k))) | ((sk112 @ k) != b) | ((tau_Pr257024512list_a @ sigma2 @ ja) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[3716])).
% 194.15/41.12  thf(5,axiom,((! [A:prefix1027212443list_a]: ? [B:trace_1367752404list_a]: (prefix1041802747list_a @ A @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_ex__prefix__of)).
% 194.15/41.12  thf(294,plain,((! [A:prefix1027212443list_a]: ? [B:trace_1367752404list_a]: (prefix1041802747list_a @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 194.15/41.12  thf(295,plain,(! [A:prefix1027212443list_a] : ((prefix1041802747list_a @ A @ (sk3 @ A)))),inference(cnf,[status(esa)],[294])).
% 194.15/41.12  thf(326,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(cnf,[status(esa)],[325])).
% 194.15/41.12  thf(327,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(lifteq,[status(thm)],[326])).
% 194.15/41.12  thf(187,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_eq_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_add__mono__thms__linordered__field_I3_J)).
% 194.15/41.12  thf(954,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_eq_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])).
% 194.15/41.12  thf(1368,plain,(! [A:nat] : (((ord_less_eq_nat @ A) = (^ [B:nat]: ((ord_less_nat @ A @ B) | (A = B)))))),inference(func_ext,[status(esa)],[861])).
% 194.15/41.12  thf(409,plain,(! [C:nat,B:nat,A:nat] : ((~ (sk11 @ B @ A @ C)) | (~ (sk12 @ A @ C @ B)) | (~ (sk13 @ C @ B @ A)) | (~ (sk14 @ B @ C @ A)) | (ord_less_eq_nat @ B @ C) | (ord_less_eq_nat @ C @ A))),inference(cnfConj,[status(thm)],[403])).
% 194.15/41.12  thf(310,plain,(! [D:prefix1027212443list_a,C:prefix1027212443list_a,B:(prefix1027212443list_a > nat),A:nat] : ((~ (ord_less_eq_nat @ A @ (B @ C))) | (~ (ord_le699472955list_a @ C @ D)) | (ord_le699472955list_a @ (sk4 @ D @ C @ (B) @ A) @ (sk5 @ D @ C @ (B) @ A)) | (ord_less_eq_nat @ A @ (B @ D)))),inference(cnfConj,[status(thm)],[309])).
% 194.15/41.12  thf(4526,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,4061])).
% 194.15/41.12  thf(4527,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[4526])).
% 194.15/41.12  thf(4615,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (A != one_one_nat) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[4527])).
% 194.15/41.12  thf(4642,plain,((~ (ord_less_eq_nat @ k @ one_one_nat)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[4615])).
% 194.15/41.12  thf(6932,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi)) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[297,4642])).
% 194.15/41.12  thf(6933,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi)) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[6932])).
% 194.15/41.12  thf(6934,plain,((ord_less_eq_nat @ one_one_nat @ k) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(pattern_uni,[status(thm)],[6933:[bind(A, $thf(k)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(2355,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ B @ (sk80 @ B))))),inference(paramod_ordered,[status(thm)],[1235,944])).
% 194.15/41.12  thf(2356,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ B @ (sk80 @ B))))),inference(simp,[status(thm)],[2355])).
% 194.15/41.12  thf(2366,plain,(! [B:nat,A:nat] : ((A != B) | ((sk112 @ A) != (sk80 @ B)))),inference(simp,[status(thm)],[2356])).
% 194.15/41.12  thf(2375,plain,(! [A:nat] : (((sk112 @ A) != (sk80 @ A)))),inference(simp,[status(thm)],[2366])).
% 194.15/41.12  thf(233,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/sandbox/benchmark/theBenchmark.p',fact_277_add__less__imp__less__right)).
% 194.15/41.12  thf(1156,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)],[233])).
% 194.15/41.12  thf(258,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/sandbox/benchmark/theBenchmark.p',fact_241__092_060tau_062__prefix__conv)).
% 194.15/41.12  thf(1225,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)],[258])).
% 194.15/41.12  thf(118,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_nat__le__linear)).
% 194.15/41.12  thf(707,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)],[118])).
% 194.15/41.12  thf(128,axiom,((! [A:trace_1367752404list_a,B:formula_a,C:nat]: (ord_less_eq_nat @ (monito1457594016ress_a @ A @ B @ C) @ C))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_progress__le)).
% 194.15/41.12  thf(739,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)],[128])).
% 194.15/41.12  thf(18289,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ B @ A)) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ b @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,4422])).
% 194.15/41.12  thf(18290,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ (plus_plus_nat @ one_one_nat @ b)) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[18289:[bind(A, $thf(b)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(142,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_ord__less__eq__trans)).
% 194.15/41.12  thf(791,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
% 194.15/41.12  thf(245,axiom,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_less__imp__triv)).
% 194.15/41.12  thf(1188,plain,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
% 194.15/41.12  thf(205,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_add__mono__thms__linordered__field_I2_J)).
% 194.15/41.12  thf(1038,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
% 194.15/41.12  thf(121,axiom,((ord_le887097159list_a = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (ord_le699472955list_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_less__prefix__def)).
% 194.15/41.12  thf(717,plain,(((ord_le887097159list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (ord_le699472955list_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
% 194.15/41.12  thf(11253,plain,(! [B:nat,A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ~ (($true)) | ((ord_less_nat @ (plus_plus_nat @ A @ B) @ A) != (ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat)))))),inference(paramod_ordered,[status(thm)],[10688,1320])).
% 194.15/41.12  thf(11254,plain,(! [B:nat,A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((ord_less_nat @ (plus_plus_nat @ A @ B) @ A) != (ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat)))))),inference(simp,[status(thm)],[11253])).
% 194.15/41.12  thf(11279,plain,(! [B:nat,A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((plus_plus_nat @ A @ B) != (sk121 @ ((=) @ nat))) | (A != (sk122 @ ((=) @ nat))))),inference(simp,[status(thm)],[11254])).
% 194.15/41.12  thf(11295,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((plus_plus_nat @ (sk122 @ ((=) @ nat)) @ A) != (sk121 @ ((=) @ nat))))),inference(simp,[status(thm)],[11279])).
% 194.15/41.12  thf(11229,plain,(! [B:nat,A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ~ (($true)) | ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) != (ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat)))))),inference(paramod_ordered,[status(thm)],[10688,1044])).
% 194.15/41.12  thf(11230,plain,(! [B:nat,A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) != (ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat)))))),inference(simp,[status(thm)],[11229])).
% 194.15/41.12  thf(11282,plain,(! [B:nat,A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((plus_plus_nat @ A @ B) != (sk121 @ ((=) @ nat))) | (B != (sk122 @ ((=) @ nat))))),inference(simp,[status(thm)],[11230])).
% 194.15/41.12  thf(11297,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((plus_plus_nat @ A @ (sk122 @ ((=) @ nat))) != (sk121 @ ((=) @ nat))))),inference(simp,[status(thm)],[11282])).
% 194.15/41.12  thf(255,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_add__mono__thms__linordered__field_I5_J)).
% 194.15/41.12  thf(1218,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])).
% 194.15/41.12  thf(256,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_le__less__linear)).
% 194.15/41.12  thf(1220,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])).
% 194.15/41.12  thf(14004,plain,(! [E:nat,D:nat,C:nat,B:nat,A:nat] : (((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) != k) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ D @ (plus_plus_nat @ E @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))))))),inference(paramod_ordered,[status(thm)],[366,6883])).
% 194.15/41.12  thf(14005,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ B @ (plus_plus_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))) != k))),inference(pattern_uni,[status(thm)],[14004:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))),bind(D, $thf(A)),bind(E, $thf(B))]])).
% 194.15/41.12  thf(7649,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (plus_plus_nat @ B @ C) @ B)))),inference(paramod_ordered,[status(thm)],[1235,1320])).
% 194.15/41.12  thf(7650,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (plus_plus_nat @ B @ C) @ B)))),inference(simp,[status(thm)],[7649])).
% 194.15/41.12  thf(7667,plain,(! [C:nat,B:nat,A:nat] : ((A != (plus_plus_nat @ B @ C)) | ((sk112 @ A) != B))),inference(simp,[status(thm)],[7650])).
% 194.15/41.12  thf(7672,plain,(! [B:nat,A:nat] : (((sk112 @ (plus_plus_nat @ A @ B)) != A))),inference(simp,[status(thm)],[7667])).
% 194.15/41.12  thf(209,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_order_Oasym)).
% 194.15/41.12  thf(1053,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
% 194.15/41.12  thf(1257,plain,(((^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))) = ((?) @ nat))),inference(lifteq,[status(thm)],[1256])).
% 194.15/41.12  thf(702,plain,(! [A:nat] : (((one_one_nat = A) = (A = one_one_nat)))),inference(cnf,[status(esa)],[701])).
% 194.15/41.12  thf(703,plain,(! [A:nat] : (((one_one_nat = A) = (A = one_one_nat)))),inference(lifteq,[status(thm)],[702])).
% 194.15/41.12  thf(164,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_less__mono__imp__le__mono)).
% 194.15/41.12  thf(864,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
% 194.15/41.12  thf(358,plain,(((^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))) = ((=) @ prefix1027212443list_a))),inference(lifteq,[status(thm)],[357])).
% 194.15/41.12  thf(1412,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)],[358,375])).
% 194.15/41.12  thf(1426,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)],[1412])).
% 194.15/41.12  thf(1427,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)],[1426])).
% 194.15/41.12  thf(204,axiom,((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ k) @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_that)).
% 194.15/41.12  thf(1037,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)],[204])).
% 194.15/41.12  thf(18573,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ k) @ (plus_plus_nat @ B @ A)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ b)))),inference(paramod_ordered,[status(thm)],[1326,1037])).
% 194.15/41.12  thf(18574,plain,((ord_less_eq_nat @ (tau_Pr257024512list_a @ sigma2 @ k) @ (plus_plus_nat @ b @ (tau_Pr257024512list_a @ sigma2 @ ia)))),inference(pattern_uni,[status(thm)],[18573:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(b))]])).
% 194.15/41.12  thf(1763,plain,(~ (($true)) | ((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)],[1314,286])).
% 194.15/41.12  thf(1764,plain,(((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[1763])).
% 194.15/41.12  thf(1766,plain,((k != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[1764])).
% 194.15/41.12  thf(2833,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ A)) | (B != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi)) | (A != k))),inference(paramod_ordered,[status(thm)],[321,1766])).
% 194.15/41.12  thf(2834,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ A)) | (~ (ord_less_eq_nat @ A @ k)) | (A != i3) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi)))),inference(pattern_uni,[status(thm)],[2833:[bind(A, $thf(k))]])).
% 194.15/41.12  thf(3117,plain,((~ (ord_less_eq_nat @ k @ i3)) | (~ (ord_less_eq_nat @ i3 @ k)) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[2834])).
% 194.15/41.12  thf(11219,plain,(((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ~ (($true)) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(paramod_ordered,[status(thm)],[10688,286])).
% 194.15/41.12  thf(11220,plain,(((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[11219])).
% 194.15/41.12  thf(11280,plain,(((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk121 @ ((=) @ nat)) != k) | ((sk122 @ ((=) @ nat)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[11220])).
% 194.15/41.12  thf(105,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ C @ A) => (ord_le887097159list_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_dual__order_Ostrict__trans1)).
% 194.15/41.12  thf(656,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ C @ A) => (ord_le887097159list_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
% 194.15/41.12  thf(17003,plain,(! [E:nat,D:nat,C:nat,B:nat,A:nat] : (((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) != i3) | ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) != (plus_plus_nat @ D @ (plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) @ E))))),inference(paramod_ordered,[status(thm)],[366,14253])).
% 194.15/41.12  thf(17004,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) @ (plus_plus_nat @ A @ B)) != i3))),inference(pattern_uni,[status(thm)],[17003:[bind(A, $thf(A)),bind(B, $thf(monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))),bind(C, $thf(C)),bind(D, $thf(A)),bind(E, $thf(C))]])).
% 194.15/41.12  thf(17025,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) @ (plus_plus_nat @ A @ B)) != i3))),inference(simp,[status(thm)],[17004])).
% 194.15/41.12  thf(229,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) | (A = B)) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_less__or__eq__imp__le)).
% 194.15/41.12  thf(1140,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)],[229])).
% 194.15/41.12  thf(383,plain,(! [D:prefix1027212443list_a,C:prefix1027212443list_a,B:(prefix1027212443list_a > nat),A:nat] : ((~ (A = (B @ C))) | (~ (ord_le699472955list_a @ C @ D)) | (ord_le699472955list_a @ (sk8 @ D @ C @ (B) @ A) @ (sk9 @ D @ C @ (B) @ A)) | (ord_less_eq_nat @ A @ (B @ D)))),inference(cnfConj,[status(thm)],[382])).
% 194.15/41.12  thf(385,plain,(! [D:prefix1027212443list_a,C:prefix1027212443list_a,B:(prefix1027212443list_a > nat),A:nat] : ((A != (B @ C)) | (~ (ord_le699472955list_a @ C @ D)) | (ord_le699472955list_a @ (sk8 @ D @ C @ (B) @ A) @ (sk9 @ D @ C @ (B) @ A)) | (ord_less_eq_nat @ A @ (B @ D)))),inference(lifteq,[status(thm)],[383])).
% 194.15/41.12  thf(386,plain,(! [C:prefix1027212443list_a,B:prefix1027212443list_a,A:(prefix1027212443list_a > nat)] : ((~ (ord_le699472955list_a @ B @ C)) | (ord_le699472955list_a @ (sk8 @ C @ B @ (A) @ (A @ B)) @ (sk9 @ C @ B @ (A) @ (A @ B))) | (ord_less_eq_nat @ (A @ B) @ (A @ C)))),inference(simp,[status(thm)],[385])).
% 194.15/41.12  thf(398,plain,((? [A:(nat > (nat > nat))]: ! [B:nat,C:nat]: ((A @ C @ (plus_plus_nat @ B @ C)) = B))),inference(detectInverse,[status(thm)],[397])).
% 194.15/41.12  thf(399,plain,(! [B:nat,A:nat] : (((sk10 @ B @ (plus_plus_nat @ A @ B)) = A))),inference(cnf,[status(esa)],[398])).
% 194.15/41.12  thf(20343,plain,(! [B:nat,A:nat] : (((sk10 @ B @ (plus_plus_nat @ A @ B)) = A))),inference(lifteq,[status(thm)],[399])).
% 194.15/41.12  thf(95,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_order_Ostrict__implies__order)).
% 194.15/41.12  thf(612,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)],[95])).
% 194.15/41.12  thf(2443,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk113 @ A))))),inference(paramod_ordered,[status(thm)],[910,1247])).
% 194.15/41.12  thf(2444,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 @ (sk113 @ A))))),inference(simp,[status(thm)],[2443])).
% 194.15/41.12  thf(2452,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk113 @ A)))),inference(simp,[status(thm)],[2444])).
% 194.15/41.12  thf(2458,plain,(((monito1457594016ress_a @ sigma2 @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk113 @ ia))),inference(simp,[status(thm)],[2452])).
% 194.15/41.12  thf(243,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E)))) => (ord_less_eq_nat @ (plus_plus_nat @ (A @ B) @ C) @ (A @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_mono__nat__linear__lb)).
% 194.15/41.12  thf(1180,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ 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)],[243])).
% 194.15/41.12  thf(77,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_le__Suc__ex)).
% 194.15/41.12  thf(556,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)],[77])).
% 194.15/41.12  thf(183,axiom,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_less_nat @ A @ (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_order__less__le__subst1)).
% 194.15/41.12  thf(931,plain,((! [A:nat,B:(prefix1027212443list_a > nat),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((ord_less_nat @ A @ (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
% 194.15/41.12  thf(112,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((B = C) => (ord_le699472955list_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_ord__le__eq__trans)).
% 194.15/41.12  thf(688,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((B = C) => (ord_le699472955list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
% 194.15/41.12  thf(86,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_le__imp__less__or__eq)).
% 194.15/41.12  thf(581,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)],[86])).
% 194.15/41.12  thf(18365,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ B @ A)) @ (tau_Pr257024512list_a @ sigma @ j)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ b @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,3814])).
% 194.15/41.12  thf(18366,plain,((ord_less_eq_nat @ (plus_plus_nat @ (tau_Pr257024512list_a @ sigma @ ia) @ (plus_plus_nat @ one_one_nat @ b)) @ (tau_Pr257024512list_a @ sigma @ j))),inference(pattern_uni,[status(thm)],[18365:[bind(A, $thf(b)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(3575,plain,(~ (($true)) | (~ (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi)))),inference(paramod_ordered,[status(thm)],[3336,3138])).
% 194.15/41.12  thf(3576,plain,((~ (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k))) | ((ord_less_eq_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (ord_less_eq_nat @ (sk112 @ k) @ (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[3575])).
% 194.15/41.12  thf(3593,plain,((~ (ord_less_eq_nat @ (plen_P694648887list_a @ pi) @ (sk112 @ k))) | ((sk112 @ k) != one_one_nat) | ((tau_Pr257024512list_a @ sigma2 @ ja) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[3576])).
% 194.15/41.12  thf(266,axiom,((! [A:nat,B:nat]: ((A != B) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_neqE)).
% 194.15/41.12  thf(1253,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])).
% 194.15/41.12  thf(189,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => ((C @ A) => ((~ (C @ B)) => (? [D:nat]: ((ord_less_eq_nat @ A @ D) & (ord_less_eq_nat @ D @ B) & ! [E:nat]: (((ord_less_eq_nat @ A @ E) & (ord_less_nat @ E @ D)) => (C @ E)) & ! [E:nat]: ((! [F:nat]: (((ord_less_eq_nat @ A @ F) & (ord_less_nat @ F @ E)) => (C @ F))) => (ord_less_eq_nat @ E @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_complete__interval)).
% 194.15/41.12  thf(963,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => ((C @ A) => ((~ (C @ B)) => (? [D:nat]: ((ord_less_eq_nat @ A @ D) & (ord_less_eq_nat @ D @ B) & ! [E:nat]: (((ord_less_eq_nat @ A @ E) & (ord_less_nat @ E @ D)) => (C @ E)) & ! [E:nat]: ((! [F:nat]: (((ord_less_eq_nat @ A @ F) & (ord_less_nat @ F @ E)) => (C @ F))) => (ord_less_eq_nat @ E @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
% 194.15/41.12  thf(1341,plain,(! [A:prefix1027212443list_a] : (((ord_le699472955list_a @ A) = (^ [B:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) | (B = A)))))),inference(func_ext,[status(esa)],[511])).
% 194.15/41.12  thf(139,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((A != B) => (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_linorder__cases)).
% 194.15/41.12  thf(781,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)],[139])).
% 194.15/41.12  thf(191,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_eq_nat @ A @ B) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_antisym__conv1)).
% 194.15/41.12  thf(995,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)],[191])).
% 194.15/41.12  thf(148,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_pinf_I6_J)).
% 194.15/41.12  thf(813,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])).
% 194.15/41.12  thf(1385,plain,(! [A:prefix1027212443list_a] : (((ord_le887097159list_a @ A) = (^ [B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & ~ (A = B)))))),inference(func_ext,[status(esa)],[302])).
% 194.15/41.12  thf(126,axiom,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ B) => ((ord_le887097159list_a @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le887097159list_a @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_order__le__less__subst2)).
% 194.15/41.12  thf(731,plain,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ B) => ((ord_le887097159list_a @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le887097159list_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
% 194.15/41.12  thf(18453,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma @ sk108)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ b @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,5071])).
% 194.15/41.12  thf(18454,plain,((ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ b) @ (tau_Pr257024512list_a @ sigma @ sk108))),inference(pattern_uni,[status(thm)],[18453:[bind(A, $thf(b)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(202,axiom,((! [A:nat,B:list_a]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) => ((sat_a @ sigma @ B @ A @ phi_1) = (sat_a @ sigma2 @ B @ A @ phi_1))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Until_OIH_I1_J)).
% 194.15/41.12  thf(1030,plain,((! [A:nat,B:list_a]: ((ord_less_nat @ A @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) => ((sat_a @ sigma @ B @ A @ phi_1) = (sat_a @ sigma2 @ B @ A @ phi_1))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
% 194.15/41.12  thf(2468,plain,(~ (($true)) | ((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)],[1177,286])).
% 194.15/41.12  thf(2469,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(simp,[status(thm)],[2468])).
% 194.15/41.12  thf(2475,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)],[2469])).
% 194.15/41.12  thf(182,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_less__asym_H)).
% 194.15/41.12  thf(929,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
% 194.15/41.12  thf(173,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_less__imp__le)).
% 194.15/41.12  thf(899,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])).
% 194.15/41.12  thf(346,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ (C @ B) @ D)) | (ord_less_eq_nat @ (sk6 @ D @ (C) @ B @ A) @ (sk7 @ D @ (C) @ B @ A)) | (ord_less_eq_nat @ (C @ A) @ D))),inference(cnfConj,[status(thm)],[345])).
% 194.15/41.12  thf(207,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_order__less__le__subst1)).
% 194.15/41.12  thf(1045,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
% 194.15/41.12  thf(2090,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk113 @ A))))),inference(paramod_ordered,[status(thm)],[1314,1247])).
% 194.15/41.12  thf(2091,plain,(! [A:nat] : (((ord_less_nat @ i3 @ (monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk113 @ A))))),inference(simp,[status(thm)],[2090])).
% 194.15/41.12  thf(2093,plain,(! [A:nat] : ((i3 != A) | ((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (sk113 @ A)))),inference(simp,[status(thm)],[2091])).
% 194.15/41.12  thf(2095,plain,(((monito1457594016ress_a @ sigma @ phi @ (plen_P694648887list_a @ pi)) != (sk113 @ i3))),inference(simp,[status(thm)],[2093])).
% 194.15/41.12  thf(155,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/sandbox/benchmark/theBenchmark.p',fact_244_add__less__cancel__right)).
% 194.15/41.12  thf(832,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)],[155])).
% 194.15/41.12  thf(111,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_add__mono__thms__linordered__semiring_I4_J)).
% 194.15/41.12  thf(684,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
% 194.15/41.12  thf(75,axiom,((! [A:nat,B:nat,C:trace_1367752404list_a]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (tau_Pr257024512list_a @ C @ A) @ (tau_Pr257024512list_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218__092_060tau_062__mono)).
% 194.15/41.12  thf(549,plain,((! [A:nat,B:nat,C:trace_1367752404list_a]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (tau_Pr257024512list_a @ C @ A) @ (tau_Pr257024512list_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])).
% 194.15/41.12  thf(6442,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(paramod_ordered,[status(thm)],[297,4338])).
% 194.15/41.12  thf(6443,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ b)))),inference(simp,[status(thm)],[6442])).
% 194.15/41.12  thf(6444,plain,((ord_less_eq_nat @ b @ k) | (~ (ord_less_nat @ b @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k)),inference(pattern_uni,[status(thm)],[6443:[bind(A, $thf(k)),bind(B, $thf(b))]])).
% 194.15/41.12  thf(4568,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[297,4061])).
% 194.15/41.12  thf(4569,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[4568])).
% 194.15/41.12  thf(4570,plain,((ord_less_eq_nat @ one_one_nat @ k) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k)),inference(pattern_uni,[status(thm)],[4569:[bind(A, $thf(k)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(235,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/sandbox/benchmark/theBenchmark.p',fact_276_add__less__imp__less__left)).
% 194.15/41.12  thf(1161,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)],[235])).
% 194.15/41.12  thf(145,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_less__induct)).
% 194.15/41.12  thf(800,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
% 194.15/41.12  thf(227,axiom,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_nat @ A @ B) => ((ord_le699472955list_a @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_le887097159list_a @ (C @ E) @ (C @ F)))) => (ord_le887097159list_a @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_order__less__le__subst2)).
% 194.15/41.12  thf(1133,plain,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_nat @ A @ B) => ((ord_le699472955list_a @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_le887097159list_a @ (C @ E) @ (C @ F)))) => (ord_le887097159list_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])).
% 194.15/41.12  thf(12220,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ~ (($true)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,5536])).
% 194.15/41.12  thf(12221,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ b @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[12220])).
% 194.15/41.12  thf(12245,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | (A != b) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[12221])).
% 194.15/41.12  thf(12293,plain,((~ (ord_less_eq_nat @ k @ b)) | ((tau_Pr257024512list_a @ sigma @ sk108) != k) | ((sk112 @ b) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[12245])).
% 194.15/41.12  thf(156,axiom,((prefix1041802747list_a @ pi @ sigma)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I1_J)).
% 194.15/41.12  thf(835,plain,((prefix1041802747list_a @ pi @ sigma)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
% 194.15/41.12  thf(259,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_order__le__less__subst2)).
% 194.15/41.12  thf(1229,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])).
% 194.15/41.12  thf(1388,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)],[358,302])).
% 194.15/41.12  thf(1394,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)],[1388])).
% 194.15/41.12  thf(1395,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)],[1394])).
% 194.15/41.12  thf(150,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_less__irrefl)).
% 194.15/41.12  thf(818,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
% 194.15/41.12  thf(405,plain,(! [C:nat,B:nat,A:nat] : ((~ (sk11 @ B @ A @ C)) | (ord_less_eq_nat @ B @ A) | (sk12 @ A @ C @ B))),inference(cnfConj,[status(thm)],[403])).
% 194.15/41.12  thf(5850,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[297,4264])).
% 194.15/41.12  thf(5851,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[5850])).
% 194.15/41.12  thf(5852,plain,((ord_less_eq_nat @ one_one_nat @ k) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k)),inference(pattern_uni,[status(thm)],[5851:[bind(A, $thf(k)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(299,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (! [C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))),inference(miniscope,[status(thm)],[298])).
% 194.15/41.12  thf(300,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | (~ (ord_less_eq_nat @ B @ C)) | (ord_less_eq_nat @ A @ C))),inference(cnf,[status(esa)],[299])).
% 194.15/41.12  thf(265,axiom,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((ord_le699472955list_a @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_le887097159list_a @ (B @ E) @ (B @ F)))) => (ord_le887097159list_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_order__le__less__subst1)).
% 194.15/41.12  thf(1248,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((ord_le699472955list_a @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_le887097159list_a @ (B @ E) @ (B @ F)))) => (ord_le887097159list_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])).
% 194.15/41.12  thf(23488,plain,(! [A:nat] : (~ (($true)) | (k != one_one_nat) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,22948])).
% 194.15/41.12  thf(23489,plain,(! [A:nat] : ((k != one_one_nat) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (tau_Pr257024512list_a @ sigma2 @ ja) @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[23488])).
% 194.15/41.12  thf(23494,plain,(! [A:nat] : ((k != one_one_nat) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | (A != (tau_Pr257024512list_a @ sigma2 @ ja)) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[23489])).
% 194.15/41.12  thf(23501,plain,((k != one_one_nat) | ((tau_Pr257024512list_a @ sigma2 @ ja) != k) | ((sk112 @ (tau_Pr257024512list_a @ sigma2 @ ja)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[23494])).
% 194.15/41.12  thf(5814,plain,(! [A:nat] : (~ (($true)) | (~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[288,4264])).
% 194.15/41.12  thf(5815,plain,(! [A:nat] : ((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ k @ one_one_nat)))),inference(simp,[status(thm)],[5814])).
% 194.15/41.12  thf(5921,plain,(! [A:nat] : ((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | (A != k) | (A != one_one_nat))),inference(simp,[status(thm)],[5815])).
% 194.15/41.12  thf(5945,plain,((~ (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))) | ((tau_Pr257024512list_a @ sigma @ j) != k) | (k != one_one_nat)),inference(simp,[status(thm)],[5921])).
% 194.15/41.12  thf(5955,plain,(! [A:nat] : (~ (($true)) | ((tau_Pr257024512list_a @ sigma @ j) != k) | (k != one_one_nat) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(paramod_ordered,[status(thm)],[1235,5945])).
% 194.15/41.12  thf(5956,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma @ j) != k) | (k != one_one_nat) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ one_one_nat @ (plen_P694648887list_a @ pi))))),inference(simp,[status(thm)],[5955])).
% 194.15/41.12  thf(5986,plain,(! [A:nat] : (((tau_Pr257024512list_a @ sigma @ j) != k) | (k != one_one_nat) | (A != one_one_nat) | ((sk112 @ A) != (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[5956])).
% 194.15/41.12  thf(5990,plain,(((tau_Pr257024512list_a @ sigma @ j) != k) | (k != one_one_nat) | ((sk112 @ one_one_nat) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[5986])).
% 194.15/41.12  thf(59,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_dual__order_Oeq__iff)).
% 194.15/41.12  thf(496,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
% 194.15/41.12  thf(497,plain,(((^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = ((=) @ nat))),inference(lifteq,[status(thm)],[496])).
% 194.15/41.12  thf(1335,plain,(! [A:nat] : (((^ [B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))) = ((=) @ nat @ A)))),inference(func_ext,[status(esa)],[497])).
% 194.15/41.12  thf(237,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/sandbox/benchmark/theBenchmark.p',fact_274_add__strict__left__mono)).
% 194.15/41.12  thf(1165,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)],[237])).
% 194.15/41.12  thf(107,axiom,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ B) => ((ord_le699472955list_a @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le699472955list_a @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_order__subst2)).
% 194.15/41.12  thf(664,plain,((! [A:nat,B:nat,C:(nat > prefix1027212443list_a),D:prefix1027212443list_a]: ((ord_less_eq_nat @ A @ B) => ((ord_le699472955list_a @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le699472955list_a @ (C @ E) @ (C @ F)))) => (ord_le699472955list_a @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
% 194.15/41.12  thf(39,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_order__class_Oorder_Oeq__iff)).
% 194.15/41.12  thf(400,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)],[39])).
% 194.15/41.12  thf(331,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => (! [C:trace_1367752404list_a]: ((prefix1041802747list_a @ B @ C) => (prefix1041802747list_a @ A @ C)))))),inference(miniscope,[status(thm)],[330])).
% 194.15/41.12  thf(332,plain,(! [C:trace_1367752404list_a,B:prefix1027212443list_a,A:prefix1027212443list_a] : ((~ (ord_le699472955list_a @ A @ B)) | (~ (prefix1041802747list_a @ B @ C)) | (prefix1041802747list_a @ A @ C))),inference(cnf,[status(esa)],[331])).
% 194.15/41.12  thf(269,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/sandbox/benchmark/theBenchmark.p',fact_211__C3_C)).
% 194.15/41.12  thf(1261,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)],[269])).
% 194.15/41.12  thf(83,axiom,((((=) @ prefix1027212443list_a) = (^ [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_order__class_Oorder_Oeq__iff)).
% 194.15/41.12  thf(575,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)],[83])).
% 194.15/41.12  thf(44,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_le__antisym)).
% 194.15/41.12  thf(427,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
% 194.15/41.12  thf(91,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_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/sandbox/benchmark/theBenchmark.p',fact_110_order__subst1)).
% 194.15/41.12  thf(596,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_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)],[91])).
% 194.15/41.12  thf(1577,plain,(~ (($true)) | ((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)],[824,286])).
% 194.15/41.12  thf(1578,plain,(((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ k @ (plen_P694648887list_a @ pi)))),inference(simp,[status(thm)],[1577])).
% 194.15/41.12  thf(1580,plain,((k != k) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[1578])).
% 194.15/41.12  thf(1582,plain,(((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (plen_P694648887list_a @ pi))),inference(simp,[status(thm)],[1580])).
% 194.15/41.12  thf(68,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_add__left__mono)).
% 194.15/41.12  thf(528,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
% 194.15/41.12  thf(103,axiom,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((ord_le699472955list_a @ A @ (B @ C)) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_order__subst1)).
% 194.15/41.12  thf(644,plain,((! [A:prefix1027212443list_a,B:(nat > prefix1027212443list_a),C:nat,D:nat]: ((ord_le699472955list_a @ A @ (B @ C)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
% 194.15/41.12  thf(51,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Nat_Oex__has__greatest__nat)).
% 194.15/41.12  thf(459,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
% 194.15/41.12  thf(124,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/sandbox/benchmark/theBenchmark.p',fact_105_order__subst2)).
% 194.15/41.12  thf(723,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)],[124])).
% 194.15/41.12  thf(166,axiom,((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),file('/export/starexec/sandbox/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)).
% 194.15/41.12  thf(871,plain,((ord_less_eq_nat @ j @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
% 194.15/41.12  thf(217,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_not__less__iff__gr__or__eq)).
% 194.15/41.12  thf(1093,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)],[217])).
% 194.15/41.12  thf(125,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_add__le__mono)).
% 194.15/41.12  thf(728,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
% 194.15/41.12  thf(740,plain,(! [C:nat,B:formula_a,A:trace_1367752404list_a] : ((ord_less_eq_nat @ (monito1457594016ress_a @ A @ B @ C) @ C))),inference(cnf,[status(esa)],[739])).
% 194.15/41.12  thf(261,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_add__lessD1)).
% 194.15/41.12  thf(1236,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])).
% 194.15/41.12  thf(2466,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ ia @ (monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk113 @ A))))),inference(paramod_ordered,[status(thm)],[1177,1247])).
% 194.15/41.12  thf(2467,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 @ (sk113 @ A))))),inference(simp,[status(thm)],[2466])).
% 194.15/41.12  thf(2479,plain,(! [A:nat] : ((ia != A) | ((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk113 @ A)))),inference(simp,[status(thm)],[2467])).
% 194.15/41.12  thf(2484,plain,(((monito1457594016ress_a @ sigma @ (until_a @ phi_1 @ i2 @ phi_2) @ (plen_P694648887list_a @ pi)) != (sk113 @ ia))),inference(simp,[status(thm)],[2479])).
% 194.15/41.12  thf(47,axiom,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((A = (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le699472955list_a @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_ord__eq__le__subst)).
% 194.15/41.12  thf(442,plain,((! [A:prefix1027212443list_a,B:(prefix1027212443list_a > prefix1027212443list_a),C:prefix1027212443list_a,D:prefix1027212443list_a]: ((A = (B @ C)) => ((ord_le699472955list_a @ C @ D) => ((! [E:prefix1027212443list_a,F:prefix1027212443list_a]: ((ord_le699472955list_a @ E @ F) => (ord_le699472955list_a @ (B @ E) @ (B @ F)))) => (ord_le699472955list_a @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
% 194.15/41.12  thf(61,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/sandbox/benchmark/theBenchmark.p',fact_98_ord__le__eq__subst)).
% 194.15/41.12  thf(501,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)],[61])).
% 194.15/41.12  thf(2353,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ B @ (sk113 @ B))))),inference(paramod_ordered,[status(thm)],[1235,1247])).
% 194.15/41.12  thf(2354,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ B @ (sk113 @ B))))),inference(simp,[status(thm)],[2353])).
% 194.15/41.12  thf(2369,plain,(! [B:nat,A:nat] : ((A != B) | ((sk112 @ A) != (sk113 @ B)))),inference(simp,[status(thm)],[2354])).
% 194.15/41.12  thf(2372,plain,(! [A:nat] : (((sk113 @ A) != (sk112 @ A)))),inference(simp,[status(thm)],[2369])).
% 194.15/41.12  thf(1331,plain,(! [A:prefix1027212443list_a] : (((^ [B:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) & (ord_le699472955list_a @ B @ A))) = ((=) @ prefix1027212443list_a @ A)))),inference(func_ext,[status(esa)],[358])).
% 194.15/41.12  thf(56,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le699472955list_a @ C @ A) => (ord_le887097159list_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_dual__order_Ostrict__trans2)).
% 194.15/41.12  thf(486,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le887097159list_a @ A @ B) => ((ord_le699472955list_a @ C @ A) => (ord_le887097159list_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
% 194.15/41.12  thf(106,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_add__left__imp__eq)).
% 194.15/41.12  thf(659,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)],[106])).
% 194.15/41.12  thf(73,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) => (ord_le699472955list_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_eq__refl)).
% 194.15/41.12  thf(543,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a]: ((A = B) => (ord_le699472955list_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
% 194.15/41.12  thf(6834,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (plus_plus_nat @ B @ C) @ C)))),inference(paramod_ordered,[status(thm)],[1235,1044])).
% 194.15/41.12  thf(6835,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_nat @ A @ (sk112 @ A)) != (ord_less_nat @ (plus_plus_nat @ B @ C) @ C)))),inference(simp,[status(thm)],[6834])).
% 194.15/41.12  thf(6852,plain,(! [C:nat,B:nat,A:nat] : ((A != (plus_plus_nat @ B @ C)) | ((sk112 @ A) != C))),inference(simp,[status(thm)],[6835])).
% 194.15/41.12  thf(6857,plain,(! [B:nat,A:nat] : (((sk112 @ (plus_plus_nat @ A @ B)) != B))),inference(simp,[status(thm)],[6852])).
% 194.15/41.12  thf(102,axiom,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ord__eq__le__trans)).
% 194.15/41.12  thf(639,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)],[102])).
% 194.15/41.12  thf(250,axiom,((! [A:trace_1367752404list_a,B:nat,C:nat]: ((ord_less_nat @ (tau_Pr257024512list_a @ A @ B) @ (tau_Pr257024512list_a @ A @ C)) => (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_less___092_060tau_062D)).
% 194.15/41.12  thf(1204,plain,((! [A:trace_1367752404list_a,B:nat,C:nat]: ((ord_less_nat @ (tau_Pr257024512list_a @ A @ B) @ (tau_Pr257024512list_a @ A @ C)) => (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])).
% 194.15/41.12  thf(1939,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk80 @ A))))),inference(paramod_ordered,[status(thm)],[824,944])).
% 194.15/41.12  thf(1940,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ A @ (sk80 @ A))))),inference(simp,[status(thm)],[1939])).
% 194.15/41.12  thf(1943,plain,(! [A:nat] : ((k != A) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (sk80 @ A)))),inference(simp,[status(thm)],[1940])).
% 194.15/41.12  thf(1945,plain,(((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != (sk80 @ k))),inference(simp,[status(thm)],[1943])).
% 194.15/41.12  thf(196,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_le__imp__less__or__eq)).
% 194.15/41.12  thf(1009,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
% 194.15/41.12  thf(2291,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(paramod_ordered,[status(thm)],[824,1272])).
% 194.15/41.12  thf(2292,plain,(! [A:nat] : (((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != (ord_less_nat @ (sk116 @ A) @ A)))),inference(simp,[status(thm)],[2291])).
% 194.15/41.12  thf(2295,plain,(! [A:nat] : (((sk116 @ A) != k) | ((monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)) != A))),inference(simp,[status(thm)],[2292])).
% 194.15/41.12  thf(2297,plain,(((sk116 @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) != k)),inference(simp,[status(thm)],[2295])).
% 194.15/41.12  thf(79,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_le__cases)).
% 194.15/41.12  thf(560,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)],[79])).
% 194.15/41.12  thf(49,axiom,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ B @ C) => (ord_le887097159list_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_order_Ostrict__trans1)).
% 194.15/41.12  thf(454,plain,((! [A:prefix1027212443list_a,B:prefix1027212443list_a,C:prefix1027212443list_a]: ((ord_le699472955list_a @ A @ B) => ((ord_le887097159list_a @ B @ C) => (ord_le887097159list_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
% 194.15/41.12  thf(11225,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ~ (($true)) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ A @ A)))),inference(paramod_ordered,[status(thm)],[10688,780])).
% 194.15/41.12  thf(11226,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((ord_less_nat @ (sk121 @ ((=) @ nat)) @ (sk122 @ ((=) @ nat))) != (ord_less_nat @ A @ A)))),inference(simp,[status(thm)],[11225])).
% 194.15/41.12  thf(11278,plain,(! [A:nat] : (((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk121 @ ((=) @ nat)) != A) | ((sk122 @ ((=) @ nat)) != A))),inference(simp,[status(thm)],[11226])).
% 194.15/41.12  thf(11294,plain,(((sk125 @ ((=) @ nat)) = (sk124 @ ((=) @ nat))) | ((sk122 @ ((=) @ nat)) != (sk121 @ ((=) @ nat)))),inference(simp,[status(thm)],[11278])).
% 194.15/41.12  thf(18361,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ (tau_Pr257024512list_a @ sigma2 @ sk95)) | ((plus_plus_nat @ A @ B) != (plus_plus_nat @ (tau_Pr257024512list_a @ sigma2 @ ia) @ one_one_nat)))),inference(paramod_ordered,[status(thm)],[1326,14445])).
% 194.15/41.12  thf(18362,plain,((ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ (tau_Pr257024512list_a @ sigma2 @ ia)) @ (tau_Pr257024512list_a @ sigma2 @ sk95))),inference(pattern_uni,[status(thm)],[18361:[bind(A, $thf(tau_Pr257024512list_a @ sigma2 @ ia)),bind(B, $thf(one_one_nat))]])).
% 194.15/41.12  thf(35652,plain,(($false)),inference(e,[status(thm)],[892,1322,3873,809,2094,1024,5088,1168,1767,347,6855,2480,941,777,1110,333,628,1315,518,408,1211,1005,21114,1290,994,741,4711,1269,614,18284,24305,523,1158,6883,7641,7203,533,5755,797,1327,698,945,538,1222,1275,16071,22532,2459,1063,340,1196,8851,1001,4496,709,12303,288,301,565,3597,829,404,417,5195,389,7241,1792,4422,719,11299,7945,1279,1055,1409,357,1191,559,1247,325,3734,14019,289,1494,316,2373,606,2456,2237,1946,7786,5663,4072,591,12051,11293,321,376,1151,821,480,475,924,348,574,1581,353,766,397,634,877,8686,998,1201,6860,4065,18412,2483,293,956,774,2371,1104,1242,312,14253,1074,1206,1199,366,1311,307,7674,292,6856,920,14445,5012,380,512,439,1153,761,1057,1163,910,1091,1042,302,1174,392,297,424,1238,825,1343,6550,1021,778,1123,862,407,693,3884,3814,815,14064,847,361,852,3499,1457,1195,1128,1281,3667,324,1012,1106,22948,1178,23231,874,23822,18480,1096,593,869,610,11304,857,1089,1234,388,14783,1138,356,328,2460,7091,1028,1361,339,1292,669,1414,489,1791,7895,547,15669,753,4167,21792,901,476,1214,10688,6539,22460,4804,5947,1099,701,515,1382,911,20337,1429,2482,18408,371,1525,1263,3656,1266,4068,1060,1050,457,24412,721,8971,1434,4644,360,311,541,1170,1026,1185,586,888,11296,343,1318,6859,921,926,12173,298,750,4872,824,856,18562,296,2376,601,1146,430,18280,1273,6598,375,584,562,5456,423,1007,402,1125,772,286,577,579,5350,1520,1256,391,936,1090,2457,6549,672,611,787,21558,20283,498,5282,713,335,4060,7671,1258,704,784,8970,736,1492,12354,451,18250,3138,303,14048,1376,1209,5071,406,12604,649,4073,17650,494,631,758,4064,4264,483,1325,895,769,18326,1177,477,4694,811,5367,367,552,626,915,7675,2461,330,521,1474,780,608,2752,1477,1102,4481,1044,695,2481,394,306,1034,675,7896,374,14265,1277,617,342,531,944,14012,836,5003,2298,3737,295,872,327,954,1368,409,310,993,6934,2375,1156,1225,707,739,18290,791,1188,1038,717,11295,11297,1235,338,1085,359,1218,1220,14005,7672,1053,1257,703,864,1427,18574,3117,11280,1766,336,656,17025,1140,386,7192,314,20343,1272,612,2458,1180,556,931,5536,1321,688,581,4061,18366,3593,7670,1326,1253,963,319,1341,5272,14069,351,3336,4338,1244,781,995,813,1385,731,18454,4182,1030,2475,510,929,899,346,1045,2095,832,684,549,6444,4570,1161,800,287,1133,12293,835,1229,1395,818,405,5852,2374,300,422,1248,23501,305,294,1314,3347,5990,1335,1165,796,1056,664,400,1197,332,1261,575,427,860,596,1582,528,644,459,723,871,1093,395,728,740,1236,5945,2484,442,501,2372,1331,322,486,1320,354,659,543,6857,639,1204,4642,1367,1945,1009,1037,2297,560,496,454,11294,364,18362])).
% 194.15/41.12  % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 194.15/41.12  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------