%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP102^1 : 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 : n007.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 08:06:46 AM UTC 2026
% Result : Theorem 157.67s 35.93s
% Output : Refutation 159.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP102^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.12/0.20 % Computer : n007.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.21 % CPULimit : 300
% 0.12/0.21 % WCLimit : 300
% 0.12/0.21 % DateTime : Tue Sep 29 19:51:41 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 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
% 1.20/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.45/1.34 % [INFO] Parsing done (401ms).
% 2.45/1.35 % [INFO] Running in sequential loop mode.
% 3.54/1.75 % [INFO] eprover registered as external prover.
% 3.54/1.76 % [INFO] Scanning for conjecture ...
% 3.77/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 254 axioms. Running axiom selection ...
% 3.96/2.01 % [INFO] Axiom selection finished. Selected 254 axioms (removed 0 axioms).
% 4.81/2.25 % [INFO] Problem is higher-order (TPTP THF).
% 4.81/2.28 % [INFO] Type checking passed.
% 4.81/2.29 % [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 ...
% 157.67/35.92 % External prover 'e' found a proof!
% 157.67/35.92 % [INFO] Killing All external provers ...
% 157.67/35.92 % Time passed: 35582ms (effective reasoning time: 34561ms)
% 157.67/35.92 % 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)>
% 157.67/35.93 % Axioms used in derivation (254): fact_28_ord__eq__le__trans, fact_73_ord__less__eq__subst, fact_186_nat__induct__at__least, fact_32_order_Otrans, fact_151_minf_I3_J, fact_217_Suc__le__lessD, fact_207_Suc__lessD, fact_5_nth__equalityI, fact_228_Suc__diff__diff, fact_120_order__less__le__subst1, fact_208_Nat_OlessE, fact_27_ord__le__eq__trans, fact_135_greater__le__neq__conv, fact_127_list__strict__asc__trans__le, fact_31_le__cases3, fact_46_linorder__less__wlog, fact_216_le__less__Suc__eq, fact_30_antisym__conv, fact_105_order_Ostrict__trans2, fact_18_le__neq__implies__less, fact_232_list__ex__rev, fact_34_eq__refl, fact_79_less__not__refl3, fact_177_length__rev, fact_249_diff__le__mono, fact_90_size__neq__size__imp__neq, fact_175_Suc__le__mono, fact_133_complete__interval, fact_35_linear, fact_128_list__asc__trans__le, fact_194_less__Suc__induct, fact_235_zero__induct__lemma, fact_20_dual__order_Oantisym, fact_39_ord__eq__le__subst, fact_124_le__less, fact_54_antisym__conv3, fact_17_less__or__eq__imp__le, fact_38_ord__le__eq__subst, fact_223_nat__induct_H, fact_146_pinf_I4_J, fact_82_nat__neq__iff, fact_59_ord__less__eq__trans, fact_121_order__le__less__subst2, fact_92_neq__if__length__neq, fact_190_rev__swap, fact_191_rev__swap, fact_55_less__induct, fact_247_le__diff__iff_H, fact_140_minf_I8_J, fact_21_dual__order_Oeq__iff, fact_167_nat_Oinject, fact_68_neq__iff, fact_174_lessI, fact_203_less__SucI, fact_215_less__Suc__eq__le, fact_132_nat__descend__induct, fact_188_n__not__Suc__n, fact_204_less__SucE, fact_138_list__strict__desc__imp__list__desc, fact_180_le__SucI, fact_226_list__ex__length, fact_141_minf_I6_J, fact_99_dual__order_Oorder__iff__strict, fact_83_Nat_Oex__has__greatest__nat, fact_16_le__eq__less__or__eq, fact_63_less__trans, fact_111_less__le__trans, fact_101_dual__order_Ostrict__trans2, fact_91_neq__if__length__neq, fact_48_less__imp__not__less, fact_69_neqE, fact_210_lift__Suc__mono__less, fact_72_order__less__subst1, fact_130_list__strict__asc__trans, fact_87_le__trans, fact_187_transitive__stepwise__le, fact_66_less__imp__neq, fact_71_order__less__subst2, fact_206_Suc__lessE, fact_161_verit__comp__simplify1_I1_J, fact_150_minf_I2_J, fact_95_list__desc__trans, fact_182_le__Suc__eq, fact_77_nat__less__induct, fact_200_not__less__eq, fact_227_list__ex__length, fact_40_order__subst2, fact_196_Suc__less__SucD, fact_144_pinf_I2_J, fact_164_sorted__rev__iff__nth__mono, fact_205_Suc__lessI, fact_139_ge__less__neq__conv, fact_195_less__trans__Suc, fact_213_le__imp__less__Suc, fact_184_not__less__eq__eq, fact_102_dual__order_Ostrict__trans1, fact_96_order_Onot__eq__order__implies__strict, fact_43_order_Ostrict__implies__not__eq, fact_94_Ex__list__of__length, fact_110_le__less__linear, fact_173_Suc__mono, fact_230_diff__diff__cancel, fact_23_linorder__wlog, fact_153_minf_I5_J, fact_58_dual__order_Oasym, fact_221_Suc__leI, fact_159_list__ord__le__sorted__eq, fact_171_rev__rev__ident, fact_4_nth__equalityI, fact_149_minf_I1_J, fact_13_length__induct, fact_41_order__subst1, fact_219_dec__induct, fact_88_le__refl, fact_50_dual__order_Oirrefl, fact_115_antisym__conv1, fact_109_le__imp__less__or__eq, fact_45_dual__order_Ostrict__trans, fact_75_linorder__neqE__nat, fact_214_less__eq__Suc__le, fact_224_rev__nth, fact_14_nat__less__le, fact_168_rev__is__rev__conv, fact_143_pinf_I1_J, fact_24_dual__order_Orefl, fact_9_list__eq__iff__nth__eq, fact_42_dual__order_Ostrict__implies__not__eq, fact_129_list__strict__desc__trans, fact_198_Suc__less__eq2, fact_165_sorted__iff__nth__Suc, fact_233_i__append__nth2, fact_236_less__diff__imp__less, fact_160_verit__la__disequality, fact_170_rev__rev__ident, fact_242_nat__diff__right__cancel__less, fact_116_le__neq__trans, fact_246_diff__le__mono2, fact_225_rev__nth, fact_162_sorted__iff__nth__mono__less, fact_53_less__imp__not__eq2, fact_229_diff__Suc__Suc, fact_163_sorted__rev__nth__mono, fact_179_le__SucE, fact_202_Ex__less__Suc, fact_52_less__imp__triv, fact_19_less__mono__imp__le__mono, fact_62_less__linear, fact_234_i__append__nth2, fact_222_sorted__rev__iff__nth__Suc, fact_47_exists__least__iff, fact_178_Suc__leD, fact_237_nat__diff__left__cancel__eq1, fact_239_nat__diff__left__cancel__less, fact_107_not__le__imp__less, fact_251_le__diff__iff, fact_189_Suc__inject, fact_152_minf_I4_J, fact_11_list__desc__trans__le, fact_12_length__induct, fact_114_antisym__conv2, fact_193_strict__inc__induct, fact_10_order__refl, fact_74_ord__eq__less__subst, fact_37_eq__iff, fact_56_less__not__sym, fact_218_inc__induct, fact_113_less__imp__le, fact_245_diff__commute, fact_211_lift__Suc__antimono__le, fact_93_Ex__list__of__length, fact_97_dual__order_Ostrict__implies__order, fact_185_full__nat__induct, fact_1_i__append__eq__i__append__conv, fact_250_Nat_Odiff__diff__eq, fact_166_old_Onat_Oinject, fact_123_less__le, fact_201_less__Suc__eq, fact_26_order__class_Oorder_Oantisym, fact_78_less__irrefl__nat, fact_119_order__less__le__subst2, fact_60_ord__eq__less__trans, fact_241_nat__diff__right__cancel__eq2, fact_231_list__ex__rev, fact_89_size__neq__size__imp__neq, fact_243_diff__less__mono2, fact_137_list__strict__asc__imp__list__asc, fact_80_less__not__refl2, fact_64_less__asym_H, fact_240_nat__diff__right__cancel__eq1, fact_22_dual__order_Otrans, conj_1, fact_2_i__append__nth1, fact_209_lift__Suc__mono__less__iff, fact_145_pinf_I3_J, fact_126_leD, fact_6_Skolem__list__nth, fact_3_i__append__nth1, fact_125_leI, fact_181_Suc__le__D, fact_70_gt__ex, fact_112_le__less__trans, fact_248_diff__le__self, fact_156_verit__comp__simplify1_I3_J, fact_108_less__le__not__le, fact_106_order_Ostrict__trans1, fact_100_order_Ostrict__implies__order, fact_147_pinf_I5_J, fact_85_le__antisym, fact_25_order__trans, fact_134_le__greater__neq__conv, fact_49_order_Ostrict__trans, fact_67_order_Oasym, fact_122_order__le__less__subst1, fact_169_rev__is__rev__conv, fact_197_less__antisym, fact_142_pinf_I8_J, fact_148_pinf_I7_J, fact_8_list__eq__iff__nth__eq, fact_15_less__imp__le__nat, fact_172_Suc__less__eq, fact_44_not__less__iff__gr__or__eq, fact_36_antisym, fact_86_eq__imp__le, fact_7_Skolem__list__nth, fact_51_linorder__cases, fact_104_order_Oorder__iff__strict, fact_65_less__asym, fact_212_lift__Suc__mono__le, fact_117_not__less, fact_192_not__less__less__Suc__eq, fact_155_pinf_I6_J, fact_103_order_Ostrict__iff__order, fact_81_less__not__refl, fact_136_less__ge__neq__conv, conj_0, fact_131_list__asc__trans, fact_0_i__append__eq__i__append__conv, fact_76_infinite__descent, fact_57_less__imp__not__eq, fact_61_less__irrefl, fact_199_All__less__Suc, fact_238_nat__diff__left__cancel__eq2, fact_154_minf_I7_J, fact_84_nat__le__linear, fact_118_not__le, fact_157_sorted__iff__nth__mono, fact_183_Suc__n__not__le__n, fact_220_Suc__le__eq, fact_98_dual__order_Ostrict__iff__order, fact_176_length__rev, fact_33_le__cases, fact_244_less__imp__diff__less, fact_29_order__class_Oorder_Oeq__iff, fact_158_sorted__nth__mono
% 157.67/35.93 % No. of inferences in proof: 990
% 157.67/35.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 35582 ms resp. 34561 ms w/o parsing
% 159.48/36.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 159.48/36.23 thf(list_nat_type, type, list_nat: $tType).
% 159.48/36.23 thf(list_a_type, type, list_a: $tType).
% 159.48/36.23 thf(nat_type, type, nat: $tType).
% 159.48/36.23 thf(a_type, type, a: $tType).
% 159.48/36.23 thf(minus_minus_nat_decl, type, minus_minus_nat: (nat > (nat > nat))).
% 159.48/36.23 thf(list_asc_nat_decl, type, list_asc_nat: (list_nat > $o)).
% 159.48/36.23 thf(list_desc_nat_decl, type, list_desc_nat: (list_nat > $o)).
% 159.48/36.23 thf(list_strict_asc_nat_decl, type, list_strict_asc_nat: (list_nat > $o)).
% 159.48/36.23 thf(list_strict_desc_nat_decl, type, list_strict_desc_nat: (list_nat > $o)).
% 159.48/36.23 thf(listIn923761578nd_nat_decl, type, listIn923761578nd_nat: (list_nat > ((nat > nat) > (nat > nat)))).
% 159.48/36.23 thf(listIn1312259492pend_a_decl, type, listIn1312259492pend_a: (list_a > ((nat > a) > (nat > a)))).
% 159.48/36.23 thf(linorder_sorted_nat_decl, type, linorder_sorted_nat: (list_nat > $o)).
% 159.48/36.23 thf(list_ex_nat_decl, type, list_ex_nat: ((nat > $o) > (list_nat > $o))).
% 159.48/36.23 thf(list_ex_a_decl, type, list_ex_a: ((a > $o) > (list_a > $o))).
% 159.48/36.23 thf(nth_nat_decl, type, nth_nat: (list_nat > (nat > nat))).
% 159.48/36.23 thf(nth_a_decl, type, nth_a: (list_a > (nat > a))).
% 159.48/36.23 thf(rev_nat_decl, type, rev_nat: (list_nat > list_nat)).
% 159.48/36.23 thf(rev_a_decl, type, rev_a: (list_a > list_a)).
% 159.48/36.23 thf(suc_decl, type, suc: (nat > nat)).
% 159.48/36.23 thf(size_size_list_nat_decl, type, size_size_list_nat: (list_nat > nat)).
% 159.48/36.23 thf(size_size_list_a_decl, type, size_size_list_a: (list_a > nat)).
% 159.48/36.23 thf(ord_less_nat_decl, type, ord_less_nat: (nat > (nat > $o))).
% 159.48/36.23 thf(ord_less_eq_nat_decl, type, ord_less_eq_nat: (nat > (nat > $o))).
% 159.48/36.23 thf(f_decl, type, f: (nat > a)).
% 159.48/36.23 thf(g_decl, type, g: (nat > a)).
% 159.48/36.23 thf(xs_decl, type, xs: list_a).
% 159.48/36.23 thf(ys_decl, type, ys: list_a).
% 159.48/36.23 thf(sk1_decl, type, sk1: nat).
% 159.48/36.23 thf(sk7_decl, type, sk7: (nat > ((nat > $o) > nat))).
% 159.48/36.23 thf(sk8_decl, type, sk8: ((nat > (nat > $o)) > nat)).
% 159.48/36.23 thf(sk9_decl, type, sk9: ((nat > (nat > $o)) > nat)).
% 159.48/36.23 thf(sk10_decl, type, sk10: ((nat > (nat > $o)) > nat)).
% 159.48/36.23 thf(sk11_decl, type, sk11: ((nat > (nat > $o)) > nat)).
% 159.48/36.23 thf(sk12_decl, type, sk12: (nat > ((nat > nat) > (nat > (nat > nat))))).
% 159.48/36.23 thf(sk13_decl, type, sk13: (nat > ((nat > nat) > (nat > (nat > nat))))).
% 159.48/36.23 thf(sk22_decl, type, sk22: (nat > list_nat)).
% 159.48/36.23 thf(sk23_decl, type, sk23: (nat > nat)).
% 159.48/36.23 thf(sk35_decl, type, sk35: (nat > list_a)).
% 159.48/36.23 thf(sk51_decl, type, sk51: (nat > nat)).
% 159.48/36.23 thf(sk53_decl, type, sk53: (nat > nat)).
% 159.48/36.23 thf(sk63_decl, type, sk63: (nat > nat)).
% 159.48/36.23 thf(sk72_decl, type, sk72: (nat > nat)).
% 159.48/36.23 thf(sk96_decl, type, sk96: (nat > nat)).
% 159.48/36.23 thf(sk1_def, definition, sk1 = (@+ [A:nat]: ~ (~ (ord_less_nat @ A @ (size_size_list_a @ xs)) | ((nth_a @ xs @ A) = (nth_a @ ys @ A)))) ).
% 159.48/36.23 thf(sk7_def, definition, sk7 = (^ [A:nat,B:(nat > $o)]: (@+ [C:nat]: ~ ((ord_less_eq_nat @ A @ C) => ((B @ C) => (B @ (suc @ C)))))) ).
% 159.48/36.23 thf(sk8_def, definition, sk8 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ (! [C:nat]: ((ord_less_eq_nat @ B @ C) => (A @ B @ C))))) ).
% 159.48/36.23 thf(sk9_def, definition, sk9 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ ((ord_less_eq_nat @ (sk8 @ A) @ B) => (A @ (sk8 @ A) @ B)))) ).
% 159.48/36.23 thf(sk10_def, definition, sk10 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ (! [C:nat]: ((A @ C @ B) => (A @ B @ C))))) ).
% 159.48/36.23 thf(sk11_def, definition, sk11 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ ((A @ B @ (sk10 @ A)) => (A @ (sk10 @ A) @ B)))) ).
% 159.48/36.23 thf(sk12_def, definition, sk12 = (^ [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)))))) ).
% 159.48/36.23 thf(sk13_def, definition, sk13 = (^ [A:nat,B:(nat > nat),C:nat,D:nat]: (@+ [E:nat]: ~ ((ord_less_eq_nat @ (sk12 @ A @ B @ C @ D) @ E) => (ord_less_eq_nat @ (B @ (sk12 @ A @ B @ C @ D)) @ (B @ E))))) ).
% 159.48/36.23 thf(sk22_def, definition, sk22 = (^ [A:nat]: (@+ [B:list_nat]: ((size_size_list_nat @ B) = A))) ).
% 159.48/36.23 thf(sk23_def, definition, sk23 = (@+ [A:(nat > nat)]: ! [B:nat]: ((A @ (suc @ B)) = B)) ).
% 159.48/36.23 thf(sk35_def, definition, sk35 = (^ [A:nat]: (@+ [B:list_a]: ((size_size_list_a @ B) = A))) ).
% 159.48/36.23 thf(sk51_def, definition, sk51 = (^ [A:nat]: (@+ [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))) ).
% 159.48/36.23 thf(sk53_def, definition, sk53 = (^ [A:nat]: (@+ [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))) ).
% 159.48/36.23 thf(sk63_def, definition, sk63 = (^ [A:nat]: (@+ [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))) ).
% 159.48/36.23 thf(sk72_def, definition, sk72 = (^ [A:nat]: (@+ [B:nat]: (ord_less_nat @ A @ B))) ).
% 159.48/36.23 thf(sk96_def, definition, sk96 = (^ [A:nat]: (@+ [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))) ).
% 159.48/36.23 thf(139,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_verit__comp__simplify1_I1_J)).
% 159.48/36.23 thf(809,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
% 159.48/36.23 thf(124,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_verit__comp__simplify1_I3_J)).
% 159.48/36.23 thf(759,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])).
% 159.48/36.23 thf(760,plain,(! [B:nat,A:nat] : (((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(cnf,[status(esa)],[759])).
% 159.48/36.23 thf(761,plain,(! [B:nat,A:nat] : (((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(lifteq,[status(thm)],[760])).
% 159.48/36.23 thf(171,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_pinf_I4_J)).
% 159.48/36.23 thf(907,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
% 159.48/36.23 thf(908,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ (sk63 @ A) @ B)) | (~ (B = A)))),inference(cnf,[status(esa)],[907])).
% 159.48/36.23 thf(909,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ (sk63 @ A) @ B)))),inference(lifteq,[status(thm)],[908])).
% 159.48/36.23 thf(910,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk63 @ A) @ A)))),inference(simp,[status(thm)],[909])).
% 159.48/36.23 thf(8329,plain,(! [C:nat,B:nat,A:nat] : ((~ (~ (ord_less_eq_nat @ A @ B))) | ((ord_less_nat @ B @ A) != (ord_less_nat @ (sk63 @ C) @ C)))),inference(paramod_ordered,[status(thm)],[761,910])).
% 159.48/36.23 thf(8330,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | ((ord_less_nat @ B @ A) != (ord_less_nat @ (sk63 @ C) @ C)))),inference(simp,[status(thm)],[8329])).
% 159.48/36.23 thf(8331,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ (sk63 @ A)))),inference(pattern_uni,[status(thm)],[8330:[bind(A, $thf(A)),bind(B, $thf(sk63 @ A)),bind(C, $thf(A))]])).
% 159.48/36.23 thf(35,axiom,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_Suc__n__not__le__n)).
% 159.48/36.23 thf(388,plain,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 159.48/36.23 thf(389,plain,((~ (? [A:nat]: (ord_less_eq_nat @ (suc @ A) @ A)))),inference(miniscope,[status(thm)],[388])).
% 159.48/36.23 thf(390,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ (suc @ A) @ A)))),inference(cnf,[status(esa)],[389])).
% 159.48/36.23 thf(10354,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ A @ (sk63 @ A)) != (ord_less_eq_nat @ (suc @ B) @ B)))),inference(paramod_ordered,[status(thm)],[8331,390])).
% 159.48/36.23 thf(10355,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ A @ (sk63 @ A)) != (ord_less_eq_nat @ (suc @ B) @ B)))),inference(simp,[status(thm)],[10354])).
% 159.48/36.23 thf(10390,plain,(! [B:nat,A:nat] : ((A != (suc @ B)) | ((sk63 @ A) != B))),inference(simp,[status(thm)],[10355])).
% 159.48/36.23 thf(10410,plain,(! [A:nat] : (((sk63 @ (suc @ A)) != A))),inference(simp,[status(thm)],[10390])).
% 159.48/36.23 thf(19,axiom,((! [A:list_a,B:list_a]: (((rev_a @ A) = (rev_a @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_rev__is__rev__conv)).
% 159.48/36.23 thf(331,plain,((! [A:list_a,B:list_a]: (((rev_a @ A) = (rev_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 159.48/36.23 thf(332,plain,(! [B:list_a,A:list_a] : ((((rev_a @ A) = (rev_a @ B)) = (A = B)))),inference(cnf,[status(esa)],[331])).
% 159.48/36.23 thf(333,plain,(! [B:list_a,A:list_a] : ((((rev_a @ A) = (rev_a @ B)) = (A = B)))),inference(lifteq,[status(thm)],[332])).
% 159.48/36.23 thf(187,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_111_less__le__trans)).
% 159.48/36.23 thf(962,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)],[187])).
% 159.48/36.23 thf(169,axiom,((! [A:list_a]: ((size_size_list_a @ (rev_a @ A)) = (size_size_list_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_length__rev)).
% 159.48/36.23 thf(902,plain,((! [A:list_a]: ((size_size_list_a @ (rev_a @ A)) = (size_size_list_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
% 159.48/36.23 thf(903,plain,(! [A:list_a] : (((size_size_list_a @ (rev_a @ A)) = (size_size_list_a @ A)))),inference(cnf,[status(esa)],[902])).
% 159.48/36.23 thf(904,plain,(! [A:list_a] : (((size_size_list_a @ (rev_a @ A)) = (size_size_list_a @ A)))),inference(lifteq,[status(thm)],[903])).
% 159.48/36.23 thf(80,axiom,((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 159.48/36.23 thf(589,plain,((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
% 159.48/36.23 thf(1,conjecture,((! [A:nat]: (~ (ord_less_nat @ A @ (size_size_list_a @ xs)) | ((nth_a @ xs @ A) = (nth_a @ ys @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)).
% 159.48/36.23 thf(2,negated_conjecture,((~ (! [A:nat]: (~ (ord_less_nat @ A @ (size_size_list_a @ xs)) | ((nth_a @ xs @ A) = (nth_a @ ys @ A)))))),inference(neg_conjecture,[status(cth)],[1])).
% 159.48/36.23 thf(257,plain,((~ (! [A:nat]: (~ (ord_less_nat @ A @ (size_size_list_a @ xs)) | ((nth_a @ xs @ A) = (nth_a @ ys @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 159.48/36.23 thf(258,plain,(((ord_less_nat @ sk1 @ (size_size_list_a @ xs)) & ~ ((nth_a @ xs @ sk1) = (nth_a @ ys @ sk1)))),inference(cnf,[status(esa)],[257])).
% 159.48/36.23 thf(259,plain,((ord_less_nat @ sk1 @ (size_size_list_a @ xs))),inference(cnfConj,[status(thm)],[258])).
% 159.48/36.23 thf(8350,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | ((ord_less_nat @ B @ A) != (ord_less_nat @ sk1 @ (size_size_list_a @ xs))))),inference(paramod_ordered,[status(thm)],[761,259])).
% 159.48/36.23 thf(8351,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | ((ord_less_nat @ B @ A) != (ord_less_nat @ sk1 @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[8350])).
% 159.48/36.23 thf(8352,plain,((~ (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1))),inference(pattern_uni,[status(thm)],[8351:[bind(A, $thf(size_size_list_a @ xs)),bind(B, $thf(sk1))]])).
% 159.48/36.23 thf(8563,plain,(~ (($true)) | ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1))),inference(paramod_ordered,[status(thm)],[589,8352])).
% 159.48/36.23 thf(8564,plain,(((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1))),inference(simp,[status(thm)],[8563])).
% 159.48/36.23 thf(8604,plain,(((size_size_list_a @ xs) != (size_size_list_a @ xs)) | ((size_size_list_a @ ys) != sk1)),inference(simp,[status(thm)],[8564])).
% 159.48/36.23 thf(8626,plain,(((size_size_list_a @ ys) != sk1)),inference(simp,[status(thm)],[8604])).
% 159.48/36.23 thf(8629,plain,(! [A:list_a] : (((size_size_list_a @ A) != sk1) | ((size_size_list_a @ (rev_a @ A)) != (size_size_list_a @ ys)))),inference(paramod_ordered,[status(thm)],[904,8626])).
% 159.48/36.23 thf(8639,plain,(! [A:list_a] : (((size_size_list_a @ A) != sk1) | ((rev_a @ A) != ys))),inference(simp,[status(thm)],[8629])).
% 159.48/36.23 thf(98,axiom,((! [A:nat,B:list_nat,C:(nat > nat)]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((listIn923761578nd_nat @ B @ C @ A) = (nth_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_i__append__nth1)).
% 159.48/36.23 thf(666,plain,((! [A:nat,B:list_nat,C:(nat > nat)]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((listIn923761578nd_nat @ B @ (C) @ A) = (nth_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
% 159.48/36.23 thf(24,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_n__not__Suc__n)).
% 159.48/36.23 thf(349,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 159.48/36.23 thf(350,plain,((~ (? [A:nat]: (A = (suc @ A))))),inference(miniscope,[status(thm)],[349])).
% 159.48/36.23 thf(351,plain,(! [A:nat] : ((~ (A = (suc @ A))))),inference(cnf,[status(esa)],[350])).
% 159.48/36.23 thf(352,plain,(! [A:nat] : (((suc @ A) != A))),inference(lifteq,[status(thm)],[351])).
% 159.48/36.23 thf(28,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Suc__le__mono)).
% 159.48/36.23 thf(363,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 159.48/36.23 thf(364,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(cnf,[status(esa)],[363])).
% 159.48/36.23 thf(365,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(lifteq,[status(thm)],[364])).
% 159.48/36.23 thf(208,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_Suc__le__eq)).
% 159.48/36.23 thf(1066,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
% 159.48/36.23 thf(1067,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),inference(cnf,[status(esa)],[1066])).
% 159.48/36.23 thf(1068,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),inference(lifteq,[status(thm)],[1067])).
% 159.48/36.23 thf(20819,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ A @ B) = (ord_less_nat @ A @ (suc @ B))))),inference(rewrite,[status(thm)],[365,1068])).
% 159.48/36.23 thf(20873,plain,((ord_less_nat @ (size_size_list_a @ xs) @ (suc @ (size_size_list_a @ ys)))),inference(rewrite,[status(thm)],[589,20819])).
% 159.48/36.23 thf(165,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_less__trans__Suc)).
% 159.48/36.23 thf(892,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
% 159.48/36.23 thf(10,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_33_le__cases)).
% 159.48/36.23 thf(295,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)],[10])).
% 159.48/36.23 thf(296,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A))),inference(cnf,[status(esa)],[295])).
% 159.48/36.23 thf(8546,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ~ (($true)) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1)))),inference(paramod_ordered,[status(thm)],[296,8352])).
% 159.48/36.23 thf(8547,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ B @ A) | ((ord_less_eq_nat @ A @ B) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1)))),inference(simp,[status(thm)],[8546])).
% 159.48/36.23 thf(8548,plain,((ord_less_eq_nat @ sk1 @ (size_size_list_a @ xs))),inference(pattern_uni,[status(thm)],[8547:[bind(A, $thf(size_size_list_a @ xs)),bind(B, $thf(sk1))]])).
% 159.48/36.23 thf(20894,plain,((ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs)))),inference(rewrite,[status(thm)],[8548,20819])).
% 159.48/36.23 thf(229,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_minf_I3_J)).
% 159.48/36.23 thf(1145,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])).
% 159.48/36.23 thf(1146,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ B @ (sk96 @ A))) | (~ (B = A)))),inference(cnf,[status(esa)],[1145])).
% 159.48/36.23 thf(1147,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ B @ (sk96 @ A))))),inference(lifteq,[status(thm)],[1146])).
% 159.48/36.23 thf(1148,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ (sk96 @ A))))),inference(simp,[status(thm)],[1147])).
% 159.48/36.23 thf(21017,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs))) != (ord_less_nat @ A @ (sk96 @ A))))),inference(paramod_ordered,[status(thm)],[20894,1148])).
% 159.48/36.23 thf(21018,plain,(! [A:nat] : (((ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs))) != (ord_less_nat @ A @ (sk96 @ A))))),inference(simp,[status(thm)],[21017])).
% 159.48/36.23 thf(21030,plain,(! [A:nat] : ((sk1 != A) | ((sk96 @ A) != (suc @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[21018])).
% 159.48/36.23 thf(21040,plain,(((sk96 @ sk1) != (suc @ (size_size_list_a @ xs)))),inference(simp,[status(thm)],[21030])).
% 159.48/36.23 thf(89,axiom,((! [A:nat]: ? [B:list_a]: ((size_size_list_a @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Ex__list__of__length)).
% 159.48/36.23 thf(630,plain,((! [A:nat]: ? [B:list_a]: ((size_size_list_a @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
% 159.48/36.23 thf(631,plain,(! [A:nat] : (((size_size_list_a @ (sk35 @ A)) = A))),inference(cnf,[status(esa)],[630])).
% 159.48/36.23 thf(632,plain,(! [A:nat] : (((size_size_list_a @ (sk35 @ A)) = A))),inference(lifteq,[status(thm)],[631])).
% 159.48/36.23 thf(1618,plain,(! [A:nat] : (~ (($true)) | ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ (suc @ A) @ A)))),inference(paramod_ordered,[status(thm)],[589,390])).
% 159.48/36.23 thf(1619,plain,(! [A:nat] : (((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ (suc @ A) @ A)))),inference(simp,[status(thm)],[1618])).
% 159.48/36.23 thf(1624,plain,(! [A:nat] : (((size_size_list_a @ xs) != (suc @ A)) | ((size_size_list_a @ ys) != A))),inference(simp,[status(thm)],[1619])).
% 159.48/36.23 thf(1630,plain,(((size_size_list_a @ xs) != (suc @ (size_size_list_a @ ys)))),inference(simp,[status(thm)],[1624])).
% 159.48/36.23 thf(1810,plain,(! [A:nat] : ((A != (suc @ (size_size_list_a @ ys))) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ xs)))),inference(paramod_ordered,[status(thm)],[632,1630])).
% 159.48/36.23 thf(1823,plain,(((sk35 @ (suc @ (size_size_list_a @ ys))) != xs)),inference(simp,[status(thm)],[1810])).
% 159.48/36.23 thf(115,axiom,((! [A:nat,B:(nat > (nat > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:nat]: (B @ C @ D)))) = (? [C:list_nat]: (((size_size_list_nat @ C) = A) & ! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_nat @ C @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Skolem__list__nth)).
% 159.48/36.23 thf(730,plain,((! [A:nat,B:(nat > (nat > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:nat]: (B @ C @ D)))) = (? [C:list_nat]: (((size_size_list_nat @ C) = A) & ! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_nat @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
% 159.48/36.23 thf(20806,plain,(! [B:list_a,A:nat] : ((A != sk1) | ((rev_a @ B) != ys) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ B)))),inference(paramod_ordered,[status(thm)],[632,8639])).
% 159.48/36.23 thf(20807,plain,(! [A:nat] : ((A != sk1) | ((rev_a @ (sk35 @ A)) != ys))),inference(pattern_uni,[status(thm)],[20806:[bind(A, $thf(C)),bind(B, $thf(sk35 @ C))]])).
% 159.48/36.23 thf(20813,plain,(((rev_a @ (sk35 @ sk1)) != ys)),inference(simp,[status(thm)],[20807])).
% 159.48/36.23 thf(118,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (B != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_ge__less__neq__conv)).
% 159.48/36.23 thf(737,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
% 159.48/36.23 thf(738,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))))),inference(lifteq,[status(thm)],[737])).
% 159.48/36.23 thf(117,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_dual__order_Oorder__iff__strict)).
% 159.48/36.23 thf(735,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
% 159.48/36.23 thf(736,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(lifteq,[status(thm)],[735])).
% 159.48/36.23 thf(1439,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))))),inference(rewrite,[status(thm)],[738,736])).
% 159.48/36.23 thf(161,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_le__eq__less__or__eq)).
% 159.48/36.23 thf(883,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
% 159.48/36.23 thf(884,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(lifteq,[status(thm)],[883])).
% 159.48/36.23 thf(1319,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(rewrite,[status(thm)],[884,736])).
% 159.48/36.23 thf(1442,plain,(((^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B)))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) != (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(paramod_ordered,[status(thm)],[1439,1319])).
% 159.48/36.23 thf(1443,plain,(((^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(pattern_uni,[status(thm)],[1442:[]])).
% 159.48/36.23 thf(120,axiom,((! [A:nat,B:list_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((nth_nat @ (rev_nat @ B) @ A) = (nth_nat @ B @ (minus_minus_nat @ (size_size_list_nat @ B) @ (suc @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_rev__nth)).
% 159.48/36.23 thf(741,plain,((! [A:nat,B:list_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((nth_nat @ (rev_nat @ B) @ A) = (nth_nat @ B @ (minus_minus_nat @ (size_size_list_nat @ B) @ (suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
% 159.48/36.23 thf(228,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ C @ B)) => ((ord_less_nat @ B @ A) => (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_nat__diff__right__cancel__eq1)).
% 159.48/36.23 thf(1142,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ C @ B)) => ((ord_less_nat @ B @ A) => (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
% 159.48/36.23 thf(62,axiom,((! [A:(nat > $o),B:list_nat]: ((list_ex_nat @ A @ (rev_nat @ B)) = (list_ex_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_list__ex__rev)).
% 159.48/36.23 thf(523,plain,((! [A:(nat > $o),B:list_nat]: ((list_ex_nat @ (A) @ (rev_nat @ B)) = (list_ex_nat @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
% 159.48/36.23 thf(125,axiom,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__imp__triv)).
% 159.48/36.23 thf(762,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)],[125])).
% 159.48/36.23 thf(46,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((C @ D) => (C @ (suc @ D))))) => (C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_nat__induct__at__least)).
% 159.48/36.23 thf(440,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((C @ D) => (C @ (suc @ D))))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
% 159.48/36.23 thf(59,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_41_order__subst1)).
% 159.48/36.23 thf(511,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)],[59])).
% 159.48/36.23 thf(6,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_diff__diff__cancel)).
% 159.48/36.23 thf(269,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 159.48/36.23 thf(101,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_less__le)).
% 159.48/36.23 thf(677,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
% 159.48/36.23 thf(34,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_30_antisym__conv)).
% 159.48/36.23 thf(385,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)],[34])).
% 159.48/36.23 thf(30,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_32_order_Otrans)).
% 159.48/36.23 thf(371,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)],[30])).
% 159.48/36.23 thf(372,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)],[371])).
% 159.48/36.23 thf(373,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)],[372])).
% 159.48/36.23 thf(22076,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_nat @ A @ (suc @ B))) | (~ (ord_less_nat @ B @ (suc @ C))) | (ord_less_nat @ A @ (suc @ C)))),inference(rewrite,[status(thm)],[373,20819])).
% 159.48/36.23 thf(8368,plain,(! [B:nat,A:nat] : (((ord_less_nat @ B @ A) = (~ (($true)))) | ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ A @ B)))),inference(paramod_ordered,[status(thm)],[589,761])).
% 159.48/36.23 thf(8369,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ B @ A)) | ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ A @ B)))),inference(simp,[status(thm)],[8368])).
% 159.48/36.23 thf(8370,plain,((~ (ord_less_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs)))),inference(pattern_uni,[status(thm)],[8369:[bind(A, $thf(size_size_list_a @ xs)),bind(B, $thf(size_size_list_a @ ys))]])).
% 159.48/36.23 thf(122,axiom,((! [A:(list_nat > $o),B:list_nat]: ((! [C:list_nat]: ((! [D:list_nat]: ((ord_less_nat @ (size_size_list_nat @ D) @ (size_size_list_nat @ C)) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_length__induct)).
% 159.48/36.23 thf(747,plain,((! [A:(list_nat > $o),B:list_nat]: ((! [C:list_nat]: ((! [D:list_nat]: ((ord_less_nat @ (size_size_list_nat @ D) @ (size_size_list_nat @ C)) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
% 159.48/36.23 thf(247,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_not__less)).
% 159.48/36.23 thf(1222,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
% 159.48/36.23 thf(99,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_140_minf_I8_J)).
% 159.48/36.23 thf(670,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)],[99])).
% 159.48/36.23 thf(127,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_pinf_I3_J)).
% 159.48/36.23 thf(768,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
% 159.48/36.23 thf(769,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ (sk51 @ A) @ B)) | (~ (B = A)))),inference(cnf,[status(esa)],[768])).
% 159.48/36.23 thf(770,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ (sk51 @ A) @ B)))),inference(lifteq,[status(thm)],[769])).
% 159.48/36.23 thf(771,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk51 @ A) @ A)))),inference(simp,[status(thm)],[770])).
% 159.48/36.23 thf(8380,plain,(! [C:nat,B:nat,A:nat] : ((~ (~ (ord_less_eq_nat @ A @ B))) | ((ord_less_nat @ B @ A) != (ord_less_nat @ (sk51 @ C) @ C)))),inference(paramod_ordered,[status(thm)],[761,771])).
% 159.48/36.23 thf(8381,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | ((ord_less_nat @ B @ A) != (ord_less_nat @ (sk51 @ C) @ C)))),inference(simp,[status(thm)],[8380])).
% 159.48/36.23 thf(8382,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ (sk51 @ A)))),inference(pattern_uni,[status(thm)],[8381:[bind(A, $thf(A)),bind(B, $thf(sk51 @ A)),bind(C, $thf(A))]])).
% 159.48/36.23 thf(194,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_gt__ex)).
% 159.48/36.23 thf(989,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
% 159.48/36.23 thf(990,plain,(! [A:nat] : ((ord_less_nat @ A @ (sk72 @ A)))),inference(cnf,[status(esa)],[989])).
% 159.48/36.23 thf(8362,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | ((ord_less_nat @ B @ A) != (ord_less_nat @ C @ (sk72 @ C))))),inference(paramod_ordered,[status(thm)],[761,990])).
% 159.48/36.23 thf(8363,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | ((ord_less_nat @ B @ A) != (ord_less_nat @ C @ (sk72 @ C))))),inference(simp,[status(thm)],[8362])).
% 159.48/36.23 thf(8364,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ (sk72 @ A) @ A)))),inference(pattern_uni,[status(thm)],[8363:[bind(A, $thf(sk72 @ D)),bind(B, $thf(D)),bind(C, $thf(D))]])).
% 159.48/36.23 thf(8492,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ (sk72 @ A) @ A)))),inference(simp,[status(thm)],[8364])).
% 159.48/36.23 thf(12933,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ A @ (sk51 @ A)) != (ord_less_eq_nat @ (sk72 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[8382,8492])).
% 159.48/36.23 thf(12934,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ A @ (sk51 @ A)) != (ord_less_eq_nat @ (sk72 @ B) @ B)))),inference(simp,[status(thm)],[12933])).
% 159.48/36.23 thf(12994,plain,(! [B:nat,A:nat] : ((A != (sk72 @ B)) | ((sk51 @ A) != B))),inference(simp,[status(thm)],[12934])).
% 159.48/36.23 thf(13029,plain,(! [A:nat] : (((sk51 @ (sk72 @ A)) != A))),inference(simp,[status(thm)],[12994])).
% 159.48/36.23 thf(225,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_less__imp__not__less)).
% 159.48/36.23 thf(1127,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
% 159.48/36.23 thf(131,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_116_le__neq__trans)).
% 159.48/36.23 thf(782,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)],[131])).
% 159.48/36.23 thf(162,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_le__imp__less__Suc)).
% 159.48/36.23 thf(885,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
% 159.48/36.23 thf(13,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_le__refl)).
% 159.48/36.23 thf(303,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 159.48/36.23 thf(304,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ A))),inference(cnf,[status(esa)],[303])).
% 159.48/36.23 thf(270,plain,(! [B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A))),inference(cnf,[status(esa)],[269])).
% 159.48/36.23 thf(271,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | (~ (ord_less_eq_nat @ A @ B)))),inference(lifteq,[status(thm)],[270])).
% 159.48/36.23 thf(1357,plain,(! [C:nat,B:nat,A:nat] : (((minus_minus_nat @ C @ (minus_minus_nat @ C @ B)) = B) | ~ (($true)) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[304,271])).
% 159.48/36.23 thf(1358,plain,(! [C:nat,B:nat,A:nat] : (((minus_minus_nat @ C @ (minus_minus_nat @ C @ B)) = B) | ((ord_less_eq_nat @ A @ A) != (ord_less_eq_nat @ B @ C)))),inference(simp,[status(thm)],[1357])).
% 159.48/36.23 thf(1359,plain,(! [A:nat] : (((minus_minus_nat @ A @ (minus_minus_nat @ A @ A)) = A))),inference(pattern_uni,[status(thm)],[1358:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(A))]])).
% 159.48/36.23 thf(244,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_dual__order_Ostrict__iff__order)).
% 159.48/36.23 thf(1214,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
% 159.48/36.23 thf(1215,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (B = A))))),inference(lifteq,[status(thm)],[1214])).
% 159.48/36.23 thf(20845,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) & ~ (B = A))))),inference(rewrite,[status(thm)],[1215,20819])).
% 159.48/36.23 thf(72,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_eq__imp__le)).
% 159.48/36.23 thf(565,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
% 159.48/36.23 thf(78,axiom,((list_asc_nat = linorder_sorted_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_list__ord__le__sorted__eq)).
% 159.48/36.23 thf(584,plain,(((list_asc_nat) = (linorder_sorted_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
% 159.48/36.23 thf(585,plain,(((linorder_sorted_nat) = (list_asc_nat))),inference(lifteq,[status(thm)],[584])).
% 159.48/36.23 thf(1287,plain,(! [A:list_nat] : (((linorder_sorted_nat @ A) = (list_asc_nat @ A)))),inference(func_ext,[status(esa)],[585])).
% 159.48/36.23 thf(111,axiom,((((=) @ list_a) = (^ [A:list_a,B:list_a]: (((size_size_list_a @ A) = (size_size_list_a @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ A)) => ((nth_a @ A @ C) = (nth_a @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_list__eq__iff__nth__eq)).
% 159.48/36.23 thf(719,plain,((((=) @ list_a) = (^ [A:list_a,B:list_a]: (((size_size_list_a @ A) = (size_size_list_a @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ A)) => ((nth_a @ A @ C) = (nth_a @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
% 159.48/36.23 thf(132,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_96_order_Onot__eq__order__implies__strict)).
% 159.48/36.23 thf(785,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)],[132])).
% 159.48/36.23 thf(174,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_47_exists__least__iff)).
% 159.48/36.23 thf(916,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)],[174])).
% 159.48/36.23 thf(917,plain,(((^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))) = ((?) @ nat))),inference(lifteq,[status(thm)],[916])).
% 159.48/36.23 thf(206,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_76_infinite__descent)).
% 159.48/36.23 thf(1055,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])).
% 159.48/36.23 thf(113,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_less__not__refl2)).
% 159.48/36.23 thf(724,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
% 159.48/36.23 thf(50,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_diff__le__self)).
% 159.48/36.23 thf(471,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
% 159.48/36.23 thf(472,plain,(! [B:nat,A:nat] : ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(cnf,[status(esa)],[471])).
% 159.48/36.23 thf(8534,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1)))),inference(paramod_ordered,[status(thm)],[472,8352])).
% 159.48/36.23 thf(8535,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1)))),inference(simp,[status(thm)],[8534])).
% 159.48/36.23 thf(8585,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ A @ B) != (size_size_list_a @ xs)) | (A != sk1))),inference(simp,[status(thm)],[8535])).
% 159.48/36.23 thf(8610,plain,(! [A:nat] : (((minus_minus_nat @ sk1 @ A) != (size_size_list_a @ xs)))),inference(simp,[status(thm)],[8585])).
% 159.48/36.23 thf(137,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_lift__Suc__mono__less)).
% 159.48/36.23 thf(802,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
% 159.48/36.23 thf(22,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_order__refl)).
% 159.48/36.23 thf(344,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 159.48/36.23 thf(1762,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ (sk51 @ A) @ A) != (ord_less_nat @ sk1 @ (size_size_list_a @ xs))))),inference(paramod_ordered,[status(thm)],[259,771])).
% 159.48/36.23 thf(1763,plain,(! [A:nat] : (((ord_less_nat @ (sk51 @ A) @ A) != (ord_less_nat @ sk1 @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[1762])).
% 159.48/36.23 thf(1764,plain,(! [A:nat] : (((sk51 @ A) != sk1) | (A != (size_size_list_a @ xs)))),inference(simp,[status(thm)],[1763])).
% 159.48/36.23 thf(1765,plain,(((sk51 @ (size_size_list_a @ xs)) != sk1)),inference(simp,[status(thm)],[1764])).
% 159.48/36.23 thf(1807,plain,(! [A:nat] : (((sk51 @ A) != sk1) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ xs)))),inference(paramod_ordered,[status(thm)],[632,1765])).
% 159.48/36.23 thf(1832,plain,(! [A:nat] : (((sk51 @ A) != sk1) | ((sk35 @ A) != xs))),inference(simp,[status(thm)],[1807])).
% 159.48/36.23 thf(26,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_22_dual__order_Otrans)).
% 159.48/36.23 thf(357,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)],[26])).
% 159.48/36.23 thf(235,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_115_antisym__conv1)).
% 159.48/36.23 thf(1191,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)],[235])).
% 159.48/36.23 thf(68,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq_nat @ A @ B) => ((! [D:nat]: (C @ D @ D)) => ((! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_transitive__stepwise__le)).
% 159.48/36.23 thf(542,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq_nat @ A @ B) => ((! [D:nat]: (C @ D @ D)) => ((! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
% 159.48/36.23 thf(1937,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ (sk63 @ A) @ A) != (ord_less_nat @ sk1 @ (size_size_list_a @ xs))))),inference(paramod_ordered,[status(thm)],[259,910])).
% 159.48/36.23 thf(1938,plain,(! [A:nat] : (((ord_less_nat @ (sk63 @ A) @ A) != (ord_less_nat @ sk1 @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[1937])).
% 159.48/36.23 thf(1940,plain,(! [A:nat] : (((sk63 @ A) != sk1) | (A != (size_size_list_a @ xs)))),inference(simp,[status(thm)],[1938])).
% 159.48/36.23 thf(1942,plain,(((sk63 @ (size_size_list_a @ xs)) != sk1)),inference(simp,[status(thm)],[1940])).
% 159.48/36.23 thf(2480,plain,(! [A:list_a] : (((sk63 @ (size_size_list_a @ A)) != sk1) | ((size_size_list_a @ (rev_a @ A)) != (size_size_list_a @ xs)))),inference(paramod_ordered,[status(thm)],[904,1942])).
% 159.48/36.23 thf(2497,plain,(! [A:list_a] : (((sk63 @ (size_size_list_a @ A)) != sk1) | ((rev_a @ A) != xs))),inference(simp,[status(thm)],[2480])).
% 159.48/36.23 thf(2698,plain,(! [B:list_a,A:nat] : (((sk63 @ A) != sk1) | ((rev_a @ B) != xs) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ B)))),inference(paramod_ordered,[status(thm)],[632,2497])).
% 159.48/36.23 thf(2699,plain,(! [A:nat] : (((sk63 @ A) != sk1) | ((rev_a @ (sk35 @ A)) != xs))),inference(pattern_uni,[status(thm)],[2698:[bind(A, $thf(C)),bind(B, $thf(sk35 @ C))]])).
% 159.48/36.23 thf(2703,plain,(! [A:nat] : (((sk63 @ A) != sk1) | ((rev_a @ (sk35 @ A)) != xs))),inference(simp,[status(thm)],[2699])).
% 159.48/36.23 thf(70,axiom,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_verit__la__disequality)).
% 159.48/36.23 thf(559,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
% 159.48/36.23 thf(2823,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | ~ (($true)) | ((ord_less_eq_nat @ B @ A) != (ord_less_eq_nat @ (suc @ C) @ C)))),inference(paramod_ordered,[status(thm)],[296,390])).
% 159.48/36.23 thf(2824,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | ((ord_less_eq_nat @ B @ A) != (ord_less_eq_nat @ (suc @ C) @ C)))),inference(simp,[status(thm)],[2823])).
% 159.48/36.23 thf(2825,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ (suc @ A)))),inference(pattern_uni,[status(thm)],[2824:[bind(A, $thf(A)),bind(B, $thf(suc @ A)),bind(C, $thf(A))]])).
% 159.48/36.23 thf(20004,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_nat @ A @ B) | ((ord_less_eq_nat @ (suc @ A) @ B) != (ord_less_eq_nat @ C @ (suc @ C))))),inference(paramod_ordered,[status(thm)],[1068,2825])).
% 159.48/36.23 thf(20005,plain,(! [A:nat] : ((ord_less_nat @ A @ (suc @ (suc @ A))))),inference(pattern_uni,[status(thm)],[20004:[bind(A, $thf(F)),bind(B, $thf(suc @ (suc @ F))),bind(C, $thf(suc @ F))]])).
% 159.48/36.23 thf(20289,plain,(! [A:nat] : ((ord_less_nat @ A @ (suc @ (suc @ A))))),inference(simp,[status(thm)],[20005])).
% 159.48/36.23 thf(20839,plain,((~ (ord_less_nat @ (size_size_list_a @ xs) @ (suc @ sk1)))),inference(rewrite,[status(thm)],[8352,20819])).
% 159.48/36.23 thf(20959,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ (suc @ A))) != (ord_less_nat @ (size_size_list_a @ xs) @ (suc @ sk1))))),inference(paramod_ordered,[status(thm)],[20289,20839])).
% 159.48/36.23 thf(20960,plain,(! [A:nat] : (((ord_less_nat @ A @ (suc @ (suc @ A))) != (ord_less_nat @ (size_size_list_a @ xs) @ (suc @ sk1))))),inference(simp,[status(thm)],[20959])).
% 159.48/36.23 thf(20976,plain,(! [A:nat] : ((A != (size_size_list_a @ xs)) | ((suc @ (suc @ A)) != (suc @ sk1)))),inference(simp,[status(thm)],[20960])).
% 159.48/36.23 thf(20981,plain,(((suc @ (suc @ (size_size_list_a @ xs))) != (suc @ sk1))),inference(simp,[status(thm)],[20976])).
% 159.48/36.23 thf(2847,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ A @ (suc @ A)) != (ord_less_eq_nat @ (suc @ B) @ B)))),inference(paramod_ordered,[status(thm)],[2825,390])).
% 159.48/36.23 thf(2848,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ A @ (suc @ A)) != (ord_less_eq_nat @ (suc @ B) @ B)))),inference(simp,[status(thm)],[2847])).
% 159.48/36.23 thf(2854,plain,(! [B:nat,A:nat] : ((A != (suc @ B)) | ((suc @ A) != B))),inference(simp,[status(thm)],[2848])).
% 159.48/36.23 thf(2857,plain,(! [A:nat] : (((suc @ (suc @ A)) != A))),inference(simp,[status(thm)],[2854])).
% 159.48/36.23 thf(8542,plain,(! [A:nat] : (~ (($true)) | ((ord_less_eq_nat @ A @ (suc @ A)) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1)))),inference(paramod_ordered,[status(thm)],[2825,8352])).
% 159.48/36.23 thf(8543,plain,(! [A:nat] : (((ord_less_eq_nat @ A @ (suc @ A)) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1)))),inference(simp,[status(thm)],[8542])).
% 159.48/36.23 thf(8593,plain,(! [A:nat] : ((A != (size_size_list_a @ xs)) | ((suc @ A) != sk1))),inference(simp,[status(thm)],[8543])).
% 159.48/36.23 thf(8615,plain,(((suc @ (size_size_list_a @ xs)) != sk1)),inference(simp,[status(thm)],[8593])).
% 159.48/36.23 thf(18,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((ord_less_eq_nat @ B @ D) => ((A @ D) => (A @ (suc @ D))))) => ((ord_less_eq_nat @ B @ C) => (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_nat__induct_H)).
% 159.48/36.23 thf(316,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((ord_less_eq_nat @ B @ D) => ((A @ D) => (A @ (suc @ D))))) => ((ord_less_eq_nat @ B @ C) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 159.48/36.23 thf(1809,plain,(! [A:nat] : ((ord_less_nat @ sk1 @ A) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ xs)))),inference(paramod_ordered,[status(thm)],[632,259])).
% 159.48/36.23 thf(1825,plain,(! [A:nat] : ((ord_less_nat @ sk1 @ A) | ((sk35 @ A) != xs))),inference(simp,[status(thm)],[1809])).
% 159.48/36.23 thf(21,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_23_linorder__wlog)).
% 159.48/36.23 thf(337,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)],[21])).
% 159.48/36.23 thf(338,plain,((! [A:(nat > (nat > $o))]: ((! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (A @ B @ C))) => ((! [B:nat,C:nat]: ((A @ C @ B) => (A @ B @ C))) => (! [B:nat,C:nat]: (A @ B @ C)))))),inference(miniscope,[status(thm)],[337])).
% 159.48/36.23 thf(339,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((((ord_less_eq_nat @ (sk8 @ (A)) @ (sk9 @ (A))) | (A @ (sk11 @ (A)) @ (sk10 @ (A))) | (A @ B @ C)) & ((ord_less_eq_nat @ (sk8 @ (A)) @ (sk9 @ (A))) | ~ (A @ (sk10 @ (A)) @ (sk11 @ (A))) | (A @ B @ C)) & (~ (A @ (sk8 @ (A)) @ (sk9 @ (A))) | (A @ (sk11 @ (A)) @ (sk10 @ (A))) | (A @ B @ C)) & (~ (A @ (sk8 @ (A)) @ (sk9 @ (A))) | ~ (A @ (sk10 @ (A)) @ (sk11 @ (A))) | (A @ B @ C))))),inference(cnf,[status(esa)],[338])).
% 159.48/36.23 thf(340,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((ord_less_eq_nat @ (sk8 @ (A)) @ (sk9 @ (A))) | (A @ (sk11 @ (A)) @ (sk10 @ (A))) | (A @ B @ C))),inference(cnfConj,[status(thm)],[339])).
% 159.48/36.23 thf(10897,plain,((ord_less_eq_nat @ (sk8 @ (^ [A:nat,B:nat]: (($false)))) @ (sk9 @ (^ [A:nat,B:nat]: (($false))))) | ($false) | ($false)),inference(prim_subst,[status(thm)],[340:[bind(A, $thf(^ [D:nat,E:nat]: (($false))))]])).
% 159.48/36.23 thf(11201,plain,((ord_less_eq_nat @ (sk8 @ (^ [A:nat,B:nat]: (($false)))) @ (sk9 @ (^ [A:nat,B:nat]: (($false)))))),inference(simp,[status(thm)],[10897])).
% 159.48/36.23 thf(11426,plain,(! [B:nat,A:nat] : (((ord_less_nat @ B @ A) = (~ (($true)))) | ((ord_less_eq_nat @ (sk8 @ (^ [C:nat,D:nat]: (($false)))) @ (sk9 @ (^ [C:nat,D:nat]: (($false))))) != (ord_less_eq_nat @ A @ B)))),inference(paramod_ordered,[status(thm)],[11201,761])).
% 159.48/36.23 thf(11427,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ B @ A)) | ((ord_less_eq_nat @ (sk8 @ (^ [C:nat,D:nat]: (($false)))) @ (sk9 @ (^ [C:nat,D:nat]: (($false))))) != (ord_less_eq_nat @ A @ B)))),inference(simp,[status(thm)],[11426])).
% 159.48/36.23 thf(11428,plain,((~ (ord_less_nat @ (sk9 @ (^ [A:nat,B:nat]: (($false)))) @ (sk8 @ (^ [A:nat,B:nat]: (($false))))))),inference(pattern_uni,[status(thm)],[11427:[bind(A, $thf(sk8 @ (^ [C:nat,D:nat]: (($false))))),bind(B, $thf(sk9 @ (^ [C:nat,D:nat]: (($false)))))]])).
% 159.48/36.23 thf(11605,plain,(! [A:nat] : (((sk35 @ A) != xs) | ~ (($true)) | ((ord_less_nat @ sk1 @ A) != (ord_less_nat @ (sk9 @ (^ [B:nat,C:nat]: (($false)))) @ (sk8 @ (^ [B:nat,C:nat]: (($false)))))))),inference(paramod_ordered,[status(thm)],[1825,11428])).
% 159.48/36.23 thf(11606,plain,(! [A:nat] : (((sk35 @ A) != xs) | ((ord_less_nat @ sk1 @ A) != (ord_less_nat @ (sk9 @ (^ [B:nat,C:nat]: (($false)))) @ (sk8 @ (^ [B:nat,C:nat]: (($false)))))))),inference(simp,[status(thm)],[11605])).
% 159.48/36.23 thf(11678,plain,(! [A:nat] : (((sk35 @ A) != xs) | ((sk9 @ (^ [B:nat,C:nat]: (($false)))) != sk1) | (A != (sk8 @ (^ [B:nat,C:nat]: (($false))))))),inference(simp,[status(thm)],[11606])).
% 159.48/36.23 thf(11716,plain,(((sk35 @ (sk8 @ (^ [A:nat,B:nat]: (($false))))) != xs) | ((sk9 @ (^ [A:nat,B:nat]: (($false)))) != sk1)),inference(simp,[status(thm)],[11678])).
% 159.48/36.23 thf(260,plain,((~ ((nth_a @ xs @ sk1) = (nth_a @ ys @ sk1)))),inference(cnfConj,[status(thm)],[258])).
% 159.48/36.23 thf(261,plain,(((nth_a @ ys @ sk1) != (nth_a @ xs @ sk1))),inference(lifteq,[status(thm)],[260])).
% 159.48/36.23 thf(8674,plain,(! [B:nat,A:nat] : (((ord_less_nat @ B @ A) = (~ (($true)))) | ((ord_less_eq_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_eq_nat @ A @ B)))),inference(paramod_ordered,[status(thm)],[8548,761])).
% 159.48/36.23 thf(8675,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ B @ A)) | ((ord_less_eq_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_eq_nat @ A @ B)))),inference(simp,[status(thm)],[8674])).
% 159.48/36.23 thf(8676,plain,((~ (ord_less_nat @ (size_size_list_a @ xs) @ sk1))),inference(pattern_uni,[status(thm)],[8675:[bind(A, $thf(sk1)),bind(B, $thf(size_size_list_a @ xs))]])).
% 159.48/36.23 thf(9715,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (size_size_list_a @ xs) @ sk1)))),inference(paramod_ordered,[status(thm)],[990,8676])).
% 159.48/36.23 thf(9716,plain,(! [A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (size_size_list_a @ xs) @ sk1)))),inference(simp,[status(thm)],[9715])).
% 159.48/36.23 thf(9746,plain,(! [A:nat] : ((A != (size_size_list_a @ xs)) | ((sk72 @ A) != sk1))),inference(simp,[status(thm)],[9716])).
% 159.48/36.23 thf(9768,plain,(((sk72 @ (size_size_list_a @ xs)) != sk1)),inference(simp,[status(thm)],[9746])).
% 159.48/36.23 thf(142,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_63_less__trans)).
% 159.48/36.23 thf(817,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)],[142])).
% 159.48/36.23 thf(39,axiom,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) != (size_size_list_nat @ B)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_size__neq__size__imp__neq)).
% 159.48/36.23 thf(421,plain,((! [A:list_nat,B:list_nat]: ((~ ((size_size_list_nat @ A) = (size_size_list_nat @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
% 159.48/36.23 thf(123,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_109_le__imp__less__or__eq)).
% 159.48/36.23 thf(756,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)],[123])).
% 159.48/36.23 thf(220,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_153_minf_I5_J)).
% 159.48/36.23 thf(1109,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)],[220])).
% 159.48/36.23 thf(53,axiom,((! [A:nat]: ? [B:list_nat]: ((size_size_list_nat @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Ex__list__of__length)).
% 159.48/36.23 thf(485,plain,((! [A:nat]: ? [B:list_nat]: ((size_size_list_nat @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
% 159.48/36.23 thf(25,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_le__diff__iff_H)).
% 159.48/36.23 thf(353,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 159.48/36.23 thf(255,axiom,((linorder_sorted_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ (suc @ B) @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ (suc @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_sorted__iff__nth__Suc)).
% 159.48/36.23 thf(1283,plain,(((linorder_sorted_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ (suc @ B) @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])).
% 159.48/36.23 thf(170,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_less__imp__le__nat)).
% 159.48/36.23 thf(905,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
% 159.48/36.23 thf(231,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_122_order__le__less__subst1)).
% 159.48/36.23 thf(1151,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)],[231])).
% 159.48/36.23 thf(179,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_108_less__le__not__le)).
% 159.48/36.23 thf(937,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)],[179])).
% 159.48/36.23 thf(29,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_40_order__subst2)).
% 159.48/36.23 thf(366,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)],[29])).
% 159.48/36.23 thf(367,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)],[366])).
% 159.48/36.23 thf(368,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 @ (sk12 @ D @ (C) @ B @ A) @ (sk13 @ 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 @ (sk12 @ D @ (C) @ B @ A)) @ (C @ (sk13 @ D @ (C) @ B @ A))) | (ord_less_eq_nat @ (C @ A) @ D))))),inference(cnf,[status(esa)],[367])).
% 159.48/36.23 thf(369,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 @ (sk12 @ D @ (C) @ B @ A) @ (sk13 @ D @ (C) @ B @ A)) | (ord_less_eq_nat @ (C @ A) @ D))),inference(cnfConj,[status(thm)],[368])).
% 159.48/36.23 thf(21060,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_nat @ A @ (suc @ B))) | (~ (ord_less_nat @ (C @ B) @ (suc @ D))) | (ord_less_nat @ (sk12 @ D @ (C) @ B @ A) @ (suc @ (sk13 @ D @ (C) @ B @ A))) | (ord_less_nat @ (C @ A) @ (suc @ D)))),inference(rewrite,[status(thm)],[369,20819])).
% 159.48/36.23 thf(11615,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (sk9 @ (^ [B:nat,C:nat]: (($false)))) @ (sk8 @ (^ [B:nat,C:nat]: (($false)))))))),inference(paramod_ordered,[status(thm)],[990,11428])).
% 159.48/36.23 thf(11616,plain,(! [A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (sk9 @ (^ [B:nat,C:nat]: (($false)))) @ (sk8 @ (^ [B:nat,C:nat]: (($false)))))))),inference(simp,[status(thm)],[11615])).
% 159.48/36.23 thf(11667,plain,(! [A:nat] : ((A != (sk9 @ (^ [B:nat,C:nat]: (($false))))) | ((sk72 @ A) != (sk8 @ (^ [B:nat,C:nat]: (($false))))))),inference(simp,[status(thm)],[11616])).
% 159.48/36.23 thf(11709,plain,(((sk72 @ (sk9 @ (^ [A:nat,B:nat]: (($false))))) != (sk8 @ (^ [A:nat,B:nat]: (($false)))))),inference(simp,[status(thm)],[11667])).
% 159.48/36.23 thf(23,axiom,((! [A:list_nat,B:list_nat]: (((rev_nat @ A) = B) = (A = (rev_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_rev__swap)).
% 159.48/36.23 thf(346,plain,((! [A:list_nat,B:list_nat]: (((rev_nat @ A) = B) = (A = (rev_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 159.48/36.23 thf(347,plain,(! [B:list_nat,A:list_nat] : ((((rev_nat @ A) = B) = (A = (rev_nat @ B))))),inference(cnf,[status(esa)],[346])).
% 159.48/36.23 thf(348,plain,(! [B:list_nat,A:list_nat] : ((((rev_nat @ A) = B) = (A = (rev_nat @ B))))),inference(lifteq,[status(thm)],[347])).
% 159.48/36.23 thf(82,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_less__imp__not__eq)).
% 159.48/36.23 thf(592,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
% 159.48/36.23 thf(593,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ A @ B)) | (~ (A = B)))),inference(cnf,[status(esa)],[592])).
% 159.48/36.23 thf(594,plain,(! [B:nat,A:nat] : ((A != B) | (~ (ord_less_nat @ A @ B)))),inference(lifteq,[status(thm)],[593])).
% 159.48/36.23 thf(595,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ A)))),inference(simp,[status(thm)],[594])).
% 159.48/36.23 thf(1330,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_nat @ A @ A)))),inference(paramod_ordered,[status(thm)],[259,595])).
% 159.48/36.23 thf(1331,plain,(! [A:nat] : (((ord_less_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_nat @ A @ A)))),inference(simp,[status(thm)],[1330])).
% 159.48/36.23 thf(1332,plain,(! [A:nat] : ((sk1 != A) | ((size_size_list_a @ xs) != A))),inference(simp,[status(thm)],[1331])).
% 159.48/36.23 thf(1333,plain,(((size_size_list_a @ xs) != sk1)),inference(simp,[status(thm)],[1332])).
% 159.48/36.23 thf(2481,plain,(! [A:list_a] : (((size_size_list_a @ A) != sk1) | ((size_size_list_a @ (rev_a @ A)) != (size_size_list_a @ xs)))),inference(paramod_ordered,[status(thm)],[904,1333])).
% 159.48/36.23 thf(2505,plain,(! [A:list_a] : (((size_size_list_a @ A) != sk1) | ((rev_a @ A) != xs))),inference(simp,[status(thm)],[2481])).
% 159.48/36.23 thf(2524,plain,(! [B:list_a,A:list_a] : (((size_size_list_a @ A) != sk1) | ((rev_a @ B) != xs) | ((size_size_list_a @ (rev_a @ A)) != (size_size_list_a @ B)))),inference(paramod_ordered,[status(thm)],[904,2505])).
% 159.48/36.23 thf(2525,plain,(! [A:list_a] : (((size_size_list_a @ A) != sk1) | ((rev_a @ (rev_a @ A)) != xs))),inference(pattern_uni,[status(thm)],[2524:[bind(A, $thf(C)),bind(B, $thf(rev_a @ C))]])).
% 159.48/36.23 thf(2531,plain,(! [A:list_a] : (((size_size_list_a @ A) != sk1) | ((rev_a @ (rev_a @ A)) != xs))),inference(simp,[status(thm)],[2525])).
% 159.48/36.23 thf(44,axiom,((! [A:list_a]: ((rev_a @ (rev_a @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_rev__rev__ident)).
% 159.48/36.23 thf(435,plain,((! [A:list_a]: ((rev_a @ (rev_a @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
% 159.48/36.23 thf(436,plain,(! [A:list_a] : (((rev_a @ (rev_a @ A)) = A))),inference(cnf,[status(esa)],[435])).
% 159.48/36.23 thf(437,plain,(! [A:list_a] : (((rev_a @ (rev_a @ A)) = A))),inference(lifteq,[status(thm)],[436])).
% 159.48/36.23 thf(2861,plain,(! [A:list_a] : (((size_size_list_a @ A) != sk1) | (A != xs))),inference(rewrite,[status(thm)],[2531,437])).
% 159.48/36.23 thf(185,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_not__less__less__Suc__eq)).
% 159.48/36.23 thf(956,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
% 159.48/36.23 thf(96,axiom,((! [A:list_nat]: ((linorder_sorted_nat @ (rev_nat @ A)) = (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_sorted__rev__iff__nth__mono)).
% 159.48/36.23 thf(660,plain,((! [A:list_nat]: ((linorder_sorted_nat @ (rev_nat @ A)) = (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
% 159.48/36.23 thf(138,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_minf_I4_J)).
% 159.48/36.23 thf(805,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
% 159.48/36.23 thf(806,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ B @ (sk53 @ A))) | (~ (B = A)))),inference(cnf,[status(esa)],[805])).
% 159.48/36.23 thf(807,plain,(! [B:nat,A:nat] : ((B != A) | (~ (ord_less_nat @ B @ (sk53 @ A))))),inference(lifteq,[status(thm)],[806])).
% 159.48/36.23 thf(808,plain,(! [A:nat] : ((~ (ord_less_nat @ A @ (sk53 @ A))))),inference(simp,[status(thm)],[807])).
% 159.48/36.23 thf(1965,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ B @ (sk53 @ B))))),inference(paramod_ordered,[status(thm)],[990,808])).
% 159.48/36.23 thf(1966,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ B @ (sk53 @ B))))),inference(simp,[status(thm)],[1965])).
% 159.48/36.23 thf(1971,plain,(! [B:nat,A:nat] : ((A != B) | ((sk72 @ A) != (sk53 @ B)))),inference(simp,[status(thm)],[1966])).
% 159.48/36.23 thf(1975,plain,(! [A:nat] : (((sk72 @ A) != (sk53 @ A)))),inference(simp,[status(thm)],[1971])).
% 159.48/36.23 thf(252,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => ((! [D:nat]: ((B = (suc @ D)) => (C @ D))) => ((! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_strict__inc__induct)).
% 159.48/36.23 thf(1242,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => ((! [D:nat]: ((B = (suc @ D)) => (C @ D))) => ((! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])).
% 159.48/36.23 thf(154,axiom,((list_strict_asc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_list__strict__asc__trans)).
% 159.48/36.23 thf(849,plain,(((list_strict_asc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
% 159.48/36.23 thf(8312,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_nat @ C @ B) = (~ (($true)))) | ((ord_less_eq_nat @ A @ (suc @ A)) != (ord_less_eq_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[2825,761])).
% 159.48/36.23 thf(8313,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_nat @ C @ B)) | ((ord_less_eq_nat @ A @ (suc @ A)) != (ord_less_eq_nat @ B @ C)))),inference(simp,[status(thm)],[8312])).
% 159.48/36.23 thf(8314,plain,(! [A:nat] : ((~ (ord_less_nat @ (suc @ A) @ A)))),inference(pattern_uni,[status(thm)],[8313:[bind(A, $thf(D)),bind(B, $thf(D)),bind(C, $thf(suc @ D))]])).
% 159.48/36.23 thf(8523,plain,(! [A:nat] : ((~ (ord_less_nat @ (suc @ A) @ A)))),inference(simp,[status(thm)],[8314])).
% 159.48/36.23 thf(15,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_25_order__trans)).
% 159.48/36.23 thf(307,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)],[15])).
% 159.48/36.23 thf(211,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_less__Suc__eq)).
% 159.48/36.23 thf(1074,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])).
% 159.48/36.23 thf(240,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_Suc__lessD)).
% 159.48/36.23 thf(1206,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
% 159.48/36.23 thf(176,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_less__irrefl__nat)).
% 159.48/36.23 thf(920,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])).
% 159.48/36.23 thf(64,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_diff__commute)).
% 159.48/36.23 thf(529,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
% 159.48/36.23 thf(8287,plain,(! [D:nat,C:nat,B:nat,A:nat] : (((ord_less_nat @ D @ C) = (~ (($true)))) | ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ C @ D)))),inference(paramod_ordered,[status(thm)],[472,761])).
% 159.48/36.23 thf(8288,plain,(! [D:nat,C:nat,B:nat,A:nat] : ((~ (ord_less_nat @ D @ C)) | ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ C @ D)))),inference(simp,[status(thm)],[8287])).
% 159.48/36.23 thf(8289,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ A @ (minus_minus_nat @ A @ B))))),inference(pattern_uni,[status(thm)],[8288:[bind(A, $thf(E)),bind(B, $thf(F)),bind(C, $thf(minus_minus_nat @ E @ F)),bind(D, $thf(E))]])).
% 159.48/36.23 thf(8499,plain,(! [B:nat,A:nat] : ((~ (ord_less_nat @ A @ (minus_minus_nat @ A @ B))))),inference(simp,[status(thm)],[8289])).
% 159.48/36.23 thf(19418,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ B @ (minus_minus_nat @ B @ C))))),inference(paramod_ordered,[status(thm)],[990,8499])).
% 159.48/36.23 thf(19419,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ B @ (minus_minus_nat @ B @ C))))),inference(simp,[status(thm)],[19418])).
% 159.48/36.23 thf(19469,plain,(! [C:nat,B:nat,A:nat] : ((A != B) | ((sk72 @ A) != (minus_minus_nat @ B @ C)))),inference(simp,[status(thm)],[19419])).
% 159.48/36.23 thf(19502,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ A @ B) != (sk72 @ A)))),inference(simp,[status(thm)],[19469])).
% 159.48/36.23 thf(238,axiom,((! [A:list_a,B:list_a,C:(nat > a),D:(nat > a)]: (((size_size_list_a @ A) = (size_size_list_a @ B)) => (((listIn1312259492pend_a @ A @ C) = (listIn1312259492pend_a @ B @ D)) = ((A = B) & (C = D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_i__append__eq__i__append__conv)).
% 159.48/36.23 thf(1199,plain,((! [A:list_a,B:list_a,C:(nat > a),D:(nat > a)]: (((size_size_list_a @ A) = (size_size_list_a @ B)) => (((listIn1312259492pend_a @ A @ C) = (listIn1312259492pend_a @ B @ D)) = ((A = B) & ((C) = (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
% 159.48/36.23 thf(33,axiom,((! [A:list_nat,B:list_nat,C:(nat > nat),D:(nat > nat)]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => (((listIn923761578nd_nat @ A @ C) = (listIn923761578nd_nat @ B @ D)) = ((A = B) & (C = D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_i__append__eq__i__append__conv)).
% 159.48/36.23 thf(381,plain,((! [A:list_nat,B:list_nat,C:(nat > nat),D:(nat > nat)]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => (((listIn923761578nd_nat @ A @ C) = (listIn923761578nd_nat @ B @ D)) = ((A = B) & ((C) = (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 159.48/36.23 thf(230,axiom,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_lessI)).
% 159.48/36.23 thf(1149,plain,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
% 159.48/36.23 thf(1150,plain,(! [A:nat] : ((ord_less_nat @ A @ (suc @ A)))),inference(cnf,[status(esa)],[1149])).
% 159.48/36.23 thf(2079,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ (sk63 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[1150,910])).
% 159.48/36.23 thf(2080,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ (sk63 @ B) @ B)))),inference(simp,[status(thm)],[2079])).
% 159.48/36.23 thf(2088,plain,(! [B:nat,A:nat] : ((A != (sk63 @ B)) | ((suc @ A) != B))),inference(simp,[status(thm)],[2080])).
% 159.48/36.23 thf(2093,plain,(! [A:nat] : (((suc @ (sk63 @ A)) != A))),inference(simp,[status(thm)],[2088])).
% 159.48/36.23 thf(205,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_nat @ A @ B) => ((! [D:nat]: (C @ D @ (suc @ D))) => ((! [D:nat,E:nat,F:nat]: ((ord_less_nat @ D @ E) => ((ord_less_nat @ E @ F) => ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))))) => (C @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_less__Suc__induct)).
% 159.48/36.23 thf(1047,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_nat @ A @ B) => ((! [D:nat]: (C @ D @ (suc @ D))) => ((! [D:nat,E:nat,F:nat]: ((ord_less_nat @ D @ E) => ((ord_less_nat @ E @ F) => ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))))) => (C @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
% 159.48/36.23 thf(136,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_dual__order_Ostrict__implies__not__eq)).
% 159.48/36.23 thf(798,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])).
% 159.48/36.23 thf(20,axiom,((! [A:(a > $o),B:list_a]: ((list_ex_a @ A @ (rev_a @ B)) = (list_ex_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_list__ex__rev)).
% 159.48/36.23 thf(334,plain,((! [A:(a > $o),B:list_a]: ((list_ex_a @ (A) @ (rev_a @ B)) = (list_ex_a @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 159.48/36.23 thf(216,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_49_order_Ostrict__trans)).
% 159.48/36.23 thf(1091,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)],[216])).
% 159.48/36.23 thf(12,axiom,((! [A:list_nat]: ((rev_nat @ (rev_nat @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_rev__rev__ident)).
% 159.48/36.23 thf(300,plain,((! [A:list_nat]: ((rev_nat @ (rev_nat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 159.48/36.23 thf(301,plain,(! [A:list_nat] : (((rev_nat @ (rev_nat @ A)) = A))),inference(cnf,[status(esa)],[300])).
% 159.48/36.23 thf(302,plain,(! [A:list_nat] : (((rev_nat @ (rev_nat @ A)) = A))),inference(lifteq,[status(thm)],[301])).
% 159.48/36.23 thf(84,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((ord_less_nat @ D @ B) => ((C @ D) => (C @ (suc @ D)))))) => (C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_dec__induct)).
% 159.48/36.23 thf(598,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((ord_less_nat @ D @ B) => ((C @ D) => (C @ (suc @ D)))))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
% 159.48/36.23 thf(143,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_nat__less__le)).
% 159.48/36.23 thf(820,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
% 159.48/36.23 thf(11,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_20_dual__order_Oantisym)).
% 159.48/36.23 thf(297,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)],[11])).
% 159.48/36.23 thf(42,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_Suc__diff__diff)).
% 159.48/36.23 thf(429,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
% 159.48/36.23 thf(141,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_dual__order_Oasym)).
% 159.48/36.23 thf(815,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
% 159.48/36.23 thf(37,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_85_le__antisym)).
% 159.48/36.23 thf(407,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)],[37])).
% 159.48/36.23 thf(105,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_69_neqE)).
% 159.48/36.23 thf(693,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)],[105])).
% 159.48/36.23 thf(8,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_31_le__cases3)).
% 159.48/36.23 thf(275,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)],[8])).
% 159.48/36.23 thf(133,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_68_neq__iff)).
% 159.48/36.23 thf(788,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)],[133])).
% 159.48/36.23 thf(153,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (A != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_le__greater__neq__conv)).
% 159.48/36.23 thf(847,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
% 159.48/36.23 thf(54,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_Suc__inject)).
% 159.48/36.23 thf(488,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
% 159.48/36.23 thf(489,plain,(! [B:nat,A:nat] : ((~ ((suc @ A) = (suc @ B))) | (A = B))),inference(cnf,[status(esa)],[488])).
% 159.48/36.23 thf(490,plain,(! [B:nat,A:nat] : (((suc @ A) != (suc @ B)) | (A = B))),inference(lifteq,[status(thm)],[489])).
% 159.48/36.23 thf(491,plain,((? [A:(nat > nat)]: ! [B:nat]: ((A @ (suc @ B)) = B))),inference(detectInverse,[status(thm)],[490])).
% 159.48/36.23 thf(492,plain,(! [A:nat] : (((sk23 @ (suc @ A)) = A))),inference(cnf,[status(esa)],[491])).
% 159.48/36.23 thf(2433,plain,(! [A:nat] : (((sk23 @ (suc @ A)) = A))),inference(lifteq,[status(thm)],[492])).
% 159.48/36.23 thf(21950,plain,(~ (($true)) | ((ord_less_nat @ (size_size_list_a @ xs) @ (suc @ (size_size_list_a @ ys))) != (ord_less_nat @ (size_size_list_a @ xs) @ (suc @ sk1)))),inference(paramod_ordered,[status(thm)],[20873,20839])).
% 159.48/36.23 thf(21951,plain,(((ord_less_nat @ (size_size_list_a @ xs) @ (suc @ (size_size_list_a @ ys))) != (ord_less_nat @ (size_size_list_a @ xs) @ (suc @ sk1)))),inference(simp,[status(thm)],[21950])).
% 159.48/36.23 thf(21993,plain,(((size_size_list_a @ xs) != (size_size_list_a @ xs)) | ((suc @ (size_size_list_a @ ys)) != (suc @ sk1))),inference(simp,[status(thm)],[21951])).
% 159.48/36.23 thf(22015,plain,(((suc @ (size_size_list_a @ ys)) != (suc @ sk1))),inference(simp,[status(thm)],[21993])).
% 159.48/36.23 thf(848,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))))),inference(lifteq,[status(thm)],[847])).
% 159.48/36.23 thf(1457,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))))),inference(rewrite,[status(thm)],[848,736])).
% 159.48/36.23 thf(1808,plain,(! [A:nat] : ((A != sk1) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ xs)))),inference(paramod_ordered,[status(thm)],[632,1333])).
% 159.48/36.23 thf(1819,plain,(((sk35 @ sk1) != xs)),inference(simp,[status(thm)],[1808])).
% 159.48/36.23 thf(164,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (((suc @ A) != B) => (ord_less_nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_Suc__lessI)).
% 159.48/36.23 thf(889,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((~ ((suc @ A) = B)) => (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
% 159.48/36.23 thf(233,axiom,((list_strict_desc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_list__strict__desc__trans)).
% 159.48/36.23 thf(1159,plain,(((list_strict_desc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
% 159.48/36.23 thf(103,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_73_ord__less__eq__subst)).
% 159.48/36.23 thf(682,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)],[103])).
% 159.48/36.23 thf(254,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_154_minf_I7_J)).
% 159.48/36.23 thf(1281,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)],[254])).
% 159.48/36.23 thf(108,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ C @ B)) => ((ord_less_nat @ B @ C) => (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_nat__diff__right__cancel__eq2)).
% 159.48/36.23 thf(710,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ C @ B)) => ((ord_less_nat @ B @ C) => (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
% 159.48/36.23 thf(151,axiom,((! [A:nat]: ((listIn1312259492pend_a @ xs @ f @ A) = (listIn1312259492pend_a @ ys @ g @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 159.48/36.23 thf(842,plain,((! [A:nat]: ((listIn1312259492pend_a @ xs @ (f) @ A) = (listIn1312259492pend_a @ ys @ (g) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
% 159.48/36.23 thf(12915,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ (sk72 @ C) @ C)))),inference(paramod_ordered,[status(thm)],[472,8492])).
% 159.48/36.23 thf(12916,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ (sk72 @ C) @ C)))),inference(simp,[status(thm)],[12915])).
% 159.48/36.23 thf(12985,plain,(! [C:nat,B:nat,A:nat] : (((minus_minus_nat @ A @ B) != (sk72 @ C)) | (A != C))),inference(simp,[status(thm)],[12916])).
% 159.48/36.23 thf(13063,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ B @ A) != (sk72 @ B)))),inference(simp,[status(thm)],[12985])).
% 159.48/36.23 thf(219,axiom,((! [A:nat,B:list_a]: ((ord_less_nat @ A @ (size_size_list_a @ B)) => ((nth_a @ (rev_a @ B) @ A) = (nth_a @ B @ (minus_minus_nat @ (size_size_list_a @ B) @ (suc @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_rev__nth)).
% 159.48/36.23 thf(1106,plain,((! [A:nat,B:list_a]: ((ord_less_nat @ A @ (size_size_list_a @ B)) => ((nth_a @ (rev_a @ B) @ A) = (nth_a @ B @ (minus_minus_nat @ (size_size_list_a @ B) @ (suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
% 159.48/36.23 thf(55,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Suc__le__D)).
% 159.48/36.23 thf(493,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
% 159.48/36.23 thf(242,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_less__SucI)).
% 159.48/36.23 thf(1210,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
% 159.48/36.23 thf(215,axiom,((list_desc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_list__desc__trans__le)).
% 159.48/36.23 thf(1089,plain,(((list_desc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])).
% 159.48/36.23 thf(93,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ (suc @ A)) & (B @ C))) = ((B @ A) | ? [C:nat]: ((ord_less_nat @ C @ A) & (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Ex__less__Suc)).
% 159.48/36.23 thf(650,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ (suc @ A)) & (B @ C))) = ((B @ A) | ? [C:nat]: ((ord_less_nat @ C @ A) & (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
% 159.48/36.23 thf(207,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_dual__order_Ostrict__implies__order)).
% 159.48/36.23 thf(1064,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
% 159.48/36.23 thf(191,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_106_order_Ostrict__trans1)).
% 159.48/36.23 thf(980,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)],[191])).
% 159.48/36.23 thf(199,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Suc__less__SucD)).
% 159.48/36.23 thf(1006,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])).
% 159.48/36.23 thf(223,axiom,((! [A:list_a,B:list_a]: (((size_size_list_a @ A) = (size_size_list_a @ B)) => ((! [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ A)) => ((nth_a @ A @ C) = (nth_a @ B @ C)))) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_nth__equalityI)).
% 159.48/36.23 thf(1118,plain,((! [A:list_a,B:list_a]: (((size_size_list_a @ A) = (size_size_list_a @ B)) => ((! [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ A)) => ((nth_a @ A @ C) = (nth_a @ B @ C)))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
% 159.48/36.23 thf(57,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_38_ord__le__eq__subst)).
% 159.48/36.23 thf(499,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)],[57])).
% 159.48/36.23 thf(221,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_72_order__less__subst1)).
% 159.48/36.23 thf(1111,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)],[221])).
% 159.48/36.23 thf(249,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_less__Suc__eq__le)).
% 159.48/36.23 thf(1227,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])).
% 159.48/36.23 thf(1160,plain,(((list_strict_desc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)))))))),inference(lifteq,[status(thm)],[1159])).
% 159.48/36.23 thf(1460,plain,(((^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B)))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) != (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(paramod_ordered,[status(thm)],[1457,1319])).
% 159.48/36.23 thf(1461,plain,(((^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(pattern_uni,[status(thm)],[1460:[]])).
% 159.48/36.23 thf(8685,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | ~ (($true)) | ((ord_less_eq_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_eq_nat @ A @ B)))),inference(paramod_ordered,[status(thm)],[8548,271])).
% 159.48/36.23 thf(8686,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | ((ord_less_eq_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_eq_nat @ A @ B)))),inference(simp,[status(thm)],[8685])).
% 159.48/36.23 thf(8687,plain,(((minus_minus_nat @ (size_size_list_a @ xs) @ (minus_minus_nat @ (size_size_list_a @ xs) @ sk1)) = sk1)),inference(pattern_uni,[status(thm)],[8686:[bind(A, $thf(sk1)),bind(B, $thf(size_size_list_a @ xs))]])).
% 159.48/36.23 thf(63,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_diff__le__mono2)).
% 159.48/36.23 thf(526,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
% 159.48/36.23 thf(317,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((! [C:nat]: ((ord_less_eq_nat @ B @ C) => ((A @ C) => (A @ (suc @ C))))) => (! [C:nat]: ((ord_less_eq_nat @ B @ C) => (A @ C))))))),inference(miniscope,[status(thm)],[316])).
% 159.48/36.23 thf(318,plain,(! [C:nat,B:nat,A:(nat > $o)] : (((~ (A @ B) | (ord_less_eq_nat @ B @ (sk7 @ B @ (A))) | ~ (ord_less_eq_nat @ B @ C) | (A @ C)) & (~ (A @ B) | (A @ (sk7 @ B @ (A))) | ~ (ord_less_eq_nat @ B @ C) | (A @ C)) & (~ (A @ B) | ~ (A @ (suc @ (sk7 @ B @ (A)))) | ~ (ord_less_eq_nat @ B @ C) | (A @ C))))),inference(cnf,[status(esa)],[317])).
% 159.48/36.23 thf(319,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (ord_less_eq_nat @ B @ (sk7 @ B @ (A))) | (~ (ord_less_eq_nat @ B @ C)) | (A @ C))),inference(cnfConj,[status(thm)],[318])).
% 159.48/36.23 thf(8705,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (ord_less_eq_nat @ B @ (sk7 @ B @ (A))) | ~ (($true)) | (A @ C) | ((ord_less_eq_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_eq_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[8548,319])).
% 159.48/36.23 thf(8706,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (ord_less_eq_nat @ B @ (sk7 @ B @ (A))) | (A @ C) | ((ord_less_eq_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_eq_nat @ B @ C)))),inference(simp,[status(thm)],[8705])).
% 159.48/36.23 thf(8707,plain,(! [A:(nat > $o)] : ((~ (A @ sk1)) | (ord_less_eq_nat @ sk1 @ (sk7 @ sk1 @ (A))) | (A @ (size_size_list_a @ xs)))),inference(pattern_uni,[status(thm)],[8706:[bind(A, $thf(A)),bind(B, $thf(sk1)),bind(C, $thf(size_size_list_a @ xs))]])).
% 159.48/36.23 thf(8722,plain,((~ (sk1 = sk1)) | (ord_less_eq_nat @ sk1 @ (sk7 @ sk1 @ ((=) @ nat @ sk1))) | (sk1 = (size_size_list_a @ xs))),inference(replace_leibeq,[status(thm)],[8707:[bind(A, $thf((=) @ nat @ sk1))]])).
% 159.48/36.23 thf(8724,plain,((sk1 != sk1) | ((size_size_list_a @ xs) = sk1) | (ord_less_eq_nat @ sk1 @ (sk7 @ sk1 @ ((=) @ nat @ sk1)))),inference(lifteq,[status(thm)],[8722])).
% 159.48/36.23 thf(8732,plain,((ord_less_eq_nat @ sk1 @ (sk7 @ sk1 @ ((=) @ nat @ sk1))) | ((size_size_list_a @ xs) = sk1)),inference(pattern_uni,[status(thm)],[8724:[]])).
% 159.48/36.23 thf(320,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (A @ (sk7 @ B @ (A))) | (~ (ord_less_eq_nat @ B @ C)) | (A @ C))),inference(cnfConj,[status(thm)],[318])).
% 159.48/36.23 thf(323,plain,(! [B:nat,A:nat] : ((~ (A = A)) | (A = (sk7 @ A @ ((=) @ nat @ A))) | (~ (ord_less_eq_nat @ A @ B)) | (A = B))),inference(replace_leibeq,[status(thm)],[320:[bind(A, $thf((=) @ nat @ B))]])).
% 159.48/36.23 thf(327,plain,(! [B:nat,A:nat] : ((A != A) | ((sk7 @ A @ ((=) @ nat @ A)) = A) | (A = B) | (~ (ord_less_eq_nat @ A @ B)))),inference(lifteq,[status(thm)],[323])).
% 159.48/36.23 thf(328,plain,(! [B:nat,A:nat] : (((sk7 @ A @ ((=) @ nat @ A)) = A) | (A = B) | (~ (ord_less_eq_nat @ A @ B)))),inference(simp,[status(thm)],[327])).
% 159.48/36.23 thf(8677,plain,(! [B:nat,A:nat] : (((sk7 @ A @ ((=) @ nat @ A)) = A) | (A = B) | ~ (($true)) | ((ord_less_eq_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_eq_nat @ A @ B)))),inference(paramod_ordered,[status(thm)],[8548,328])).
% 159.48/36.23 thf(8678,plain,(! [B:nat,A:nat] : (((sk7 @ A @ ((=) @ nat @ A)) = A) | (A = B) | ((ord_less_eq_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_eq_nat @ A @ B)))),inference(simp,[status(thm)],[8677])).
% 159.48/36.23 thf(8679,plain,(((sk7 @ sk1 @ ((=) @ nat @ sk1)) = sk1) | ((size_size_list_a @ xs) = sk1)),inference(pattern_uni,[status(thm)],[8678:[bind(A, $thf(sk1)),bind(B, $thf(size_size_list_a @ xs))]])).
% 159.48/36.23 thf(9906,plain,(((sk7 @ sk1 @ ((=) @ nat @ sk1)) = sk1)),inference(simplifyReflect,[status(thm)],[8679,1333])).
% 159.48/36.23 thf(11980,plain,((ord_less_eq_nat @ sk1 @ sk1) | ((size_size_list_a @ xs) = sk1)),inference(rewrite,[status(thm)],[8732,9906])).
% 159.48/36.23 thf(11981,plain,((ord_less_eq_nat @ sk1 @ sk1)),inference(simplifyReflect,[status(thm)],[11980,1333])).
% 159.48/36.23 thf(12929,plain,(! [A:nat] : (~ (($true)) | ((ord_less_eq_nat @ (sk72 @ A) @ A) != (ord_less_eq_nat @ sk1 @ sk1)))),inference(paramod_ordered,[status(thm)],[11981,8492])).
% 159.48/36.23 thf(12930,plain,(! [A:nat] : (((ord_less_eq_nat @ (sk72 @ A) @ A) != (ord_less_eq_nat @ sk1 @ sk1)))),inference(simp,[status(thm)],[12929])).
% 159.48/36.23 thf(12989,plain,(! [A:nat] : (((sk72 @ A) != sk1) | (A != sk1))),inference(simp,[status(thm)],[12930])).
% 159.48/36.23 thf(13066,plain,(((sk72 @ sk1) != sk1)),inference(simp,[status(thm)],[12989])).
% 159.48/36.23 thf(81,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ A @ C)) => (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_nat__diff__left__cancel__less)).
% 159.48/36.23 thf(590,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ A @ C)) => (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
% 159.48/36.23 thf(12938,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | ~ (($true)) | ((ord_less_eq_nat @ B @ A) != (ord_less_eq_nat @ (sk72 @ C) @ C)))),inference(paramod_ordered,[status(thm)],[296,8492])).
% 159.48/36.23 thf(12939,plain,(! [C:nat,B:nat,A:nat] : ((ord_less_eq_nat @ A @ B) | ((ord_less_eq_nat @ B @ A) != (ord_less_eq_nat @ (sk72 @ C) @ C)))),inference(simp,[status(thm)],[12938])).
% 159.48/36.23 thf(12940,plain,(! [A:nat] : ((ord_less_eq_nat @ A @ (sk72 @ A)))),inference(pattern_uni,[status(thm)],[12939:[bind(A, $thf(A)),bind(B, $thf(sk72 @ A)),bind(C, $thf(A))]])).
% 159.48/36.23 thf(15784,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_nat @ C @ B) = (~ (($true)))) | ((ord_less_eq_nat @ A @ (sk72 @ A)) != (ord_less_eq_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[12940,761])).
% 159.48/36.23 thf(15785,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_nat @ C @ B)) | ((ord_less_eq_nat @ A @ (sk72 @ A)) != (ord_less_eq_nat @ B @ C)))),inference(simp,[status(thm)],[15784])).
% 159.48/36.23 thf(15786,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk72 @ A) @ A)))),inference(pattern_uni,[status(thm)],[15785:[bind(A, $thf(D)),bind(B, $thf(D)),bind(C, $thf(sk72 @ D))]])).
% 159.48/36.23 thf(15897,plain,(! [A:nat] : ((~ (ord_less_nat @ (sk72 @ A) @ A)))),inference(simp,[status(thm)],[15786])).
% 159.48/36.23 thf(102,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Suc__less__eq)).
% 159.48/36.23 thf(679,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])).
% 159.48/36.23 thf(213,axiom,((! [A:list_nat]: ((linorder_sorted_nat @ (rev_nat @ A)) = (! [B:nat]: ((ord_less_nat @ (suc @ B) @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ (suc @ B)) @ (nth_nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_sorted__rev__iff__nth__Suc)).
% 159.48/36.23 thf(1082,plain,((! [A:list_nat]: ((linorder_sorted_nat @ (rev_nat @ A)) = (! [B:nat]: ((ord_less_nat @ (suc @ B) @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ (suc @ B)) @ (nth_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
% 159.48/36.23 thf(20953,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (size_size_list_a @ xs) @ (suc @ sk1))))),inference(paramod_ordered,[status(thm)],[990,20839])).
% 159.48/36.23 thf(20954,plain,(! [A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (size_size_list_a @ xs) @ (suc @ sk1))))),inference(simp,[status(thm)],[20953])).
% 159.48/36.23 thf(20962,plain,(! [A:nat] : ((A != (size_size_list_a @ xs)) | ((sk72 @ A) != (suc @ sk1)))),inference(simp,[status(thm)],[20954])).
% 159.48/36.23 thf(20979,plain,(((sk72 @ (size_size_list_a @ xs)) != (suc @ sk1))),inference(simp,[status(thm)],[20962])).
% 159.48/36.23 thf(15798,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ A @ (sk72 @ A)) != (ord_less_eq_nat @ (sk72 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[12940,8492])).
% 159.48/36.23 thf(15799,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ A @ (sk72 @ A)) != (ord_less_eq_nat @ (sk72 @ B) @ B)))),inference(simp,[status(thm)],[15798])).
% 159.48/36.23 thf(15875,plain,(! [B:nat,A:nat] : ((A != (sk72 @ B)) | ((sk72 @ A) != B))),inference(simp,[status(thm)],[15799])).
% 159.48/36.23 thf(15882,plain,(! [A:nat] : (((sk72 @ (sk72 @ A)) != A))),inference(simp,[status(thm)],[15875])).
% 159.48/36.23 thf(167,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_less__eq__Suc__le)).
% 159.48/36.23 thf(897,plain,(((ord_less_nat) = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
% 159.48/36.23 thf(898,plain,(((^ [A:nat]: (ord_less_eq_nat @ (suc @ A))) = (ord_less_nat))),inference(lifteq,[status(thm)],[897])).
% 159.48/36.23 thf(1304,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) = (ord_less_nat)) | ((^ [A:nat]: (ord_less_eq_nat @ (suc @ A))) != (ord_less_eq_nat))),inference(paramod_ordered,[status(thm)],[736,898])).
% 159.48/36.23 thf(1306,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) = (ord_less_nat)) | ((^ [A:nat,B:nat]: (suc @ A)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: (B)) != (^ [A:nat,B:nat]: (B)))),inference(simp,[status(thm)],[1304])).
% 159.48/36.23 thf(1308,plain,(((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) = (ord_less_nat)) | ((^ [A:nat,B:nat]: (suc @ A)) != (^ [A:nat,B:nat]: (A)))),inference(simp,[status(thm)],[1306])).
% 159.48/36.23 thf(1643,plain,(((^ [A:nat,B:nat]: (suc @ A)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (ord_less_nat)) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) != (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(paramod_ordered,[status(thm)],[1308,1319])).
% 159.48/36.23 thf(1644,plain,(((^ [A:nat,B:nat]: (suc @ A)) != (^ [A:nat,B:nat]: (A))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))) = (ord_less_nat))),inference(pattern_uni,[status(thm)],[1643:[]])).
% 159.48/36.23 thf(21010,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs))) != (ord_less_nat @ A @ (sk53 @ A))))),inference(paramod_ordered,[status(thm)],[20894,808])).
% 159.48/36.23 thf(21011,plain,(! [A:nat] : (((ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs))) != (ord_less_nat @ A @ (sk53 @ A))))),inference(simp,[status(thm)],[21010])).
% 159.48/36.23 thf(21034,plain,(! [A:nat] : ((sk1 != A) | ((sk53 @ A) != (suc @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[21011])).
% 159.48/36.23 thf(21042,plain,(((sk53 @ sk1) != (suc @ (size_size_list_a @ xs)))),inference(simp,[status(thm)],[21034])).
% 159.48/36.23 thf(150,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_121_order__le__less__subst2)).
% 159.48/36.23 thf(837,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)],[150])).
% 159.48/36.23 thf(48,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_full__nat__induct)).
% 159.48/36.23 thf(457,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
% 159.48/36.23 thf(197,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_not__le__imp__less)).
% 159.48/36.23 thf(1002,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
% 159.48/36.23 thf(73,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_le__SucE)).
% 159.48/36.23 thf(569,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
% 159.48/36.23 thf(163,axiom,((list_ex_a = (^ [A:(a > $o),B:list_a]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ B)) & (A @ (nth_a @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_list__ex__length)).
% 159.48/36.23 thf(887,plain,(((list_ex_a) = (^ [A:(a > $o),B:list_a]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ B)) & (A @ (nth_a @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
% 159.48/36.23 thf(888,plain,(((list_ex_a) = (^ [A:(a > $o),B:list_a]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ B)) & (A @ (nth_a @ B @ C)))))),inference(lifteq,[status(thm)],[887])).
% 159.48/36.23 thf(1478,plain,(! [A:(a > $o)] : (((list_ex_a @ A) = (^ [B:list_a]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ B)) & (A @ (nth_a @ B @ C))))))),inference(func_ext,[status(esa)],[888])).
% 159.48/36.23 thf(1963,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (sk63 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[990,910])).
% 159.48/36.23 thf(1964,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (sk63 @ B) @ B)))),inference(simp,[status(thm)],[1963])).
% 159.48/36.23 thf(1970,plain,(! [B:nat,A:nat] : ((A != (sk63 @ B)) | ((sk72 @ A) != B))),inference(simp,[status(thm)],[1964])).
% 159.48/36.23 thf(1974,plain,(! [A:nat] : (((sk72 @ (sk63 @ A)) != A))),inference(simp,[status(thm)],[1970])).
% 159.48/36.23 thf(9834,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs))))),inference(paramod_ordered,[status(thm)],[990,8370])).
% 159.48/36.23 thf(9835,plain,(! [A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[9834])).
% 159.48/36.23 thf(9870,plain,(! [A:nat] : ((A != (size_size_list_a @ ys)) | ((sk72 @ A) != (size_size_list_a @ xs)))),inference(simp,[status(thm)],[9835])).
% 159.48/36.23 thf(9893,plain,(((sk72 @ (size_size_list_a @ ys)) != (size_size_list_a @ xs))),inference(simp,[status(thm)],[9870])).
% 159.48/36.23 thf(172,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = ((B @ A) & ! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_All__less__Suc)).
% 159.48/36.23 thf(911,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = ((B @ A) & ! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
% 159.48/36.23 thf(112,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_order_Ostrict__trans2)).
% 159.48/36.23 thf(721,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
% 159.48/36.23 thf(1977,plain,(! [B:nat,A:nat] : (((sk35 @ A) != xs) | ~ (($true)) | ((ord_less_nat @ sk1 @ A) != (ord_less_nat @ B @ (sk96 @ B))))),inference(paramod_ordered,[status(thm)],[1825,1148])).
% 159.48/36.23 thf(1978,plain,(! [B:nat,A:nat] : (((sk35 @ A) != xs) | ((ord_less_nat @ sk1 @ A) != (ord_less_nat @ B @ (sk96 @ B))))),inference(simp,[status(thm)],[1977])).
% 159.48/36.23 thf(1979,plain,(((sk35 @ (sk96 @ sk1)) != xs)),inference(pattern_uni,[status(thm)],[1978:[bind(A, $thf(sk96 @ sk1)),bind(B, $thf(sk1))]])).
% 159.48/36.23 thf(130,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_114_antisym__conv2)).
% 159.48/36.23 thf(779,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)],[130])).
% 159.48/36.23 thf(343,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((~ (A @ (sk8 @ (A)) @ (sk9 @ (A)))) | (~ (A @ (sk10 @ (A)) @ (sk11 @ (A)))) | (A @ B @ C))),inference(cnfConj,[status(thm)],[339])).
% 159.48/36.23 thf(5,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ C) @ (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_lift__Suc__antimono__le)).
% 159.48/36.23 thf(266,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ C) @ (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 159.48/36.23 thf(58,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_36_antisym)).
% 159.48/36.23 thf(508,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)],[58])).
% 159.48/36.23 thf(95,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_45_dual__order_Ostrict__trans)).
% 159.48/36.23 thf(657,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)],[95])).
% 159.48/36.23 thf(126,axiom,((! [A:list_nat,B:nat,C:nat]: ((linorder_sorted_nat @ A) => ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_sorted__nth__mono)).
% 159.48/36.23 thf(765,plain,((! [A:list_nat,B:nat,C:nat]: ((linorder_sorted_nat @ A) => ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
% 159.48/36.23 thf(256,axiom,((list_ex_nat = (^ [A:(nat > $o),B:list_nat]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ B)) & (A @ (nth_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_list__ex__length)).
% 159.48/36.23 thf(1285,plain,(((list_ex_nat) = (^ [A:(nat > $o),B:list_nat]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ B)) & (A @ (nth_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])).
% 159.48/36.23 thf(1286,plain,(((list_ex_nat) = (^ [A:(nat > $o),B:list_nat]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ B)) & (A @ (nth_nat @ B @ C)))))),inference(lifteq,[status(thm)],[1285])).
% 159.48/36.23 thf(11471,plain,(! [A:nat] : (~ (($true)) | ((ord_less_eq_nat @ (sk8 @ (^ [B:nat,C:nat]: (($false)))) @ (sk9 @ (^ [B:nat,C:nat]: (($false))))) != (ord_less_eq_nat @ (suc @ A) @ A)))),inference(paramod_ordered,[status(thm)],[11201,390])).
% 159.48/36.23 thf(11472,plain,(! [A:nat] : (((ord_less_eq_nat @ (sk8 @ (^ [B:nat,C:nat]: (($false)))) @ (sk9 @ (^ [B:nat,C:nat]: (($false))))) != (ord_less_eq_nat @ (suc @ A) @ A)))),inference(simp,[status(thm)],[11471])).
% 159.48/36.23 thf(11512,plain,(! [A:nat] : (((sk8 @ (^ [B:nat,C:nat]: (($false)))) != (suc @ A)) | ((sk9 @ (^ [B:nat,C:nat]: (($false)))) != A))),inference(simp,[status(thm)],[11472])).
% 159.48/36.23 thf(11576,plain,(((sk8 @ (^ [A:nat,B:nat]: (($false)))) != (suc @ (sk9 @ (^ [A:nat,B:nat]: (($false))))))),inference(simp,[status(thm)],[11512])).
% 159.48/36.23 thf(184,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ C)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_less__diff__imp__less)).
% 159.48/36.23 thf(953,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ C)) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
% 159.48/36.23 thf(79,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_62_less__linear)).
% 159.48/36.23 thf(586,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)],[79])).
% 159.48/36.23 thf(178,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_143_pinf_I1_J)).
% 159.48/36.23 thf(926,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)],[178])).
% 159.48/36.23 thf(90,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Suc__mono)).
% 159.48/36.23 thf(633,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
% 159.48/36.23 thf(27,axiom,((! [A:list_a,B:list_a]: (((rev_a @ A) = B) = (A = (rev_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_rev__swap)).
% 159.48/36.23 thf(360,plain,((! [A:list_a,B:list_a]: (((rev_a @ A) = B) = (A = (rev_a @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
% 159.48/36.23 thf(69,axiom,((! [A:list_nat]: ((list_strict_desc_nat @ A) => (list_desc_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_list__strict__desc__imp__list__desc)).
% 159.48/36.23 thf(557,plain,((! [A:list_nat]: ((list_strict_desc_nat @ A) => (list_desc_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
% 159.48/36.23 thf(558,plain,(! [A:list_nat] : ((~ (list_strict_desc_nat @ A)) | (list_desc_nat @ A))),inference(cnf,[status(esa)],[557])).
% 159.48/36.23 thf(210,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) => (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_less__antisym)).
% 159.48/36.23 thf(1071,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])).
% 159.48/36.23 thf(188,axiom,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => ((! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C)))) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_nth__equalityI)).
% 159.48/36.23 thf(965,plain,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => ((! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C)))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
% 159.48/36.23 thf(40,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_84_nat__le__linear)).
% 159.48/36.23 thf(425,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)],[40])).
% 159.48/36.23 thf(8637,plain,(! [A:nat] : ((A != sk1) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ ys)))),inference(paramod_ordered,[status(thm)],[632,8626])).
% 159.48/36.23 thf(8641,plain,(((sk35 @ sk1) != ys)),inference(simp,[status(thm)],[8637])).
% 159.48/36.23 thf(218,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) => ((~ (ord_less_nat @ A @ B)) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_less__SucE)).
% 159.48/36.23 thf(1103,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) => ((~ (ord_less_nat @ A @ B)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
% 159.48/36.23 thf(145,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Suc__leI)).
% 159.48/36.23 thf(824,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
% 159.48/36.23 thf(4,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_37_eq__iff)).
% 159.48/36.23 thf(264,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 159.48/36.23 thf(157,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_55_less__induct)).
% 159.48/36.23 thf(856,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)],[157])).
% 159.48/36.23 thf(116,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__asym)).
% 159.48/36.23 thf(733,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
% 159.48/36.23 thf(128,axiom,((! [A:nat,B:list_a,C:(nat > a)]: ((ord_less_nat @ A @ (size_size_list_a @ B)) => ((listIn1312259492pend_a @ B @ C @ A) = (nth_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_i__append__nth1)).
% 159.48/36.23 thf(772,plain,((! [A:nat,B:list_a,C:(nat > a)]: ((ord_less_nat @ A @ (size_size_list_a @ B)) => ((listIn1312259492pend_a @ B @ (C) @ A) = (nth_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])).
% 159.48/36.23 thf(224,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less_nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Suc__less__eq2)).
% 159.48/36.23 thf(1124,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
% 159.48/36.23 thf(71,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_not__less__eq__eq)).
% 159.48/36.23 thf(562,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
% 159.48/36.23 thf(190,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_120_order__less__le__subst1)).
% 159.48/36.23 thf(975,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)],[190])).
% 159.48/36.23 thf(146,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_leI)).
% 159.48/36.23 thf(826,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
% 159.48/36.23 thf(76,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_87_le__trans)).
% 159.48/36.23 thf(577,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)],[76])).
% 159.48/36.23 thf(36,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_83_Nat_Oex__has__greatest__nat)).
% 159.48/36.23 thf(391,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) => (? [D:nat]: ((A @ D) & ! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
% 159.48/36.23 thf(74,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_order__class_Oorder_Oantisym)).
% 159.48/36.23 thf(572,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])).
% 159.48/36.23 thf(49,axiom,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_ord__eq__le__trans)).
% 159.48/36.23 thf(466,plain,((! [A:nat,B:nat,C:nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
% 159.48/36.23 thf(20864,plain,((ord_less_nat @ (sk8 @ (^ [A:nat,B:nat]: (($false)))) @ (suc @ (sk9 @ (^ [A:nat,B:nat]: (($false))))))),inference(rewrite,[status(thm)],[11201,20819])).
% 159.48/36.23 thf(20448,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ (suc @ A))) != (ord_less_nat @ (size_size_list_a @ xs) @ sk1)))),inference(paramod_ordered,[status(thm)],[20289,8676])).
% 159.48/36.23 thf(20449,plain,(! [A:nat] : (((ord_less_nat @ A @ (suc @ (suc @ A))) != (ord_less_nat @ (size_size_list_a @ xs) @ sk1)))),inference(simp,[status(thm)],[20448])).
% 159.48/36.23 thf(20489,plain,(! [A:nat] : ((A != (size_size_list_a @ xs)) | ((suc @ (suc @ A)) != sk1))),inference(simp,[status(thm)],[20449])).
% 159.48/36.23 thf(20518,plain,(((suc @ (suc @ (size_size_list_a @ xs))) != sk1)),inference(simp,[status(thm)],[20489])).
% 159.48/36.23 thf(1354,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | ~ (($true)) | ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ A @ B)))),inference(paramod_ordered,[status(thm)],[589,271])).
% 159.48/36.23 thf(1355,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ A @ B)))),inference(simp,[status(thm)],[1354])).
% 159.48/36.23 thf(1356,plain,(((minus_minus_nat @ (size_size_list_a @ ys) @ (minus_minus_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs))) = (size_size_list_a @ xs))),inference(pattern_uni,[status(thm)],[1355:[bind(A, $thf(size_size_list_a @ xs)),bind(B, $thf(size_size_list_a @ ys))]])).
% 159.48/36.23 thf(100,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_19_less__mono__imp__le__mono)).
% 159.48/36.23 thf(672,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)],[100])).
% 159.48/36.23 thf(109,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_101_dual__order_Ostrict__trans2)).
% 159.48/36.23 thf(713,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)],[109])).
% 159.48/36.23 thf(56,axiom,((! [A:list_nat]: ((size_size_list_nat @ (rev_nat @ A)) = (size_size_list_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_length__rev)).
% 159.48/36.23 thf(496,plain,((! [A:list_nat]: ((size_size_list_nat @ (rev_nat @ A)) = (size_size_list_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
% 159.48/36.23 thf(497,plain,(! [A:list_nat] : (((size_size_list_nat @ (rev_nat @ A)) = (size_size_list_nat @ A)))),inference(cnf,[status(esa)],[496])).
% 159.48/36.23 thf(498,plain,(! [A:list_nat] : (((size_size_list_nat @ (rev_nat @ A)) = (size_size_list_nat @ A)))),inference(lifteq,[status(thm)],[497])).
% 159.48/36.23 thf(2482,plain,(! [A:list_a] : ((ord_less_nat @ sk1 @ (size_size_list_a @ A)) | ((size_size_list_a @ (rev_a @ A)) != (size_size_list_a @ xs)))),inference(paramod_ordered,[status(thm)],[904,259])).
% 159.48/36.23 thf(2510,plain,(! [A:list_a] : ((ord_less_nat @ sk1 @ (size_size_list_a @ A)) | ((rev_a @ A) != xs))),inference(simp,[status(thm)],[2482])).
% 159.48/36.23 thf(236,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ A @ C)) => ((ord_less_nat @ C @ A) => (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_nat__diff__left__cancel__eq2)).
% 159.48/36.23 thf(1194,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ A @ C)) => ((ord_less_nat @ C @ A) => (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
% 159.48/36.23 thf(2526,plain,(! [B:list_a,A:nat] : ((A != sk1) | ((rev_a @ B) != xs) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ B)))),inference(paramod_ordered,[status(thm)],[632,2505])).
% 159.48/36.23 thf(2527,plain,(! [A:nat] : ((A != sk1) | ((rev_a @ (sk35 @ A)) != xs))),inference(pattern_uni,[status(thm)],[2526:[bind(A, $thf(C)),bind(B, $thf(sk35 @ C))]])).
% 159.48/36.23 thf(2532,plain,(((rev_a @ (sk35 @ sk1)) != xs)),inference(simp,[status(thm)],[2527])).
% 159.48/36.23 thf(2536,plain,(! [A:list_a] : ((A != xs) | ((rev_a @ (rev_a @ A)) != (rev_a @ (sk35 @ sk1))))),inference(paramod_ordered,[status(thm)],[437,2532])).
% 159.48/36.23 thf(2538,plain,(((sk35 @ sk1) != (rev_a @ xs))),inference(simp,[status(thm)],[2536])).
% 159.48/36.23 thf(7,axiom,((! [A:list_nat,B:list_nat]: (((rev_nat @ A) = (rev_nat @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_rev__is__rev__conv)).
% 159.48/36.23 thf(272,plain,((! [A:list_nat,B:list_nat]: (((rev_nat @ A) = (rev_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 159.48/36.23 thf(273,plain,(! [B:list_nat,A:list_nat] : ((((rev_nat @ A) = (rev_nat @ B)) = (A = B)))),inference(cnf,[status(esa)],[272])).
% 159.48/36.23 thf(274,plain,(! [B:list_nat,A:list_nat] : ((((rev_nat @ A) = (rev_nat @ B)) = (A = B)))),inference(lifteq,[status(thm)],[273])).
% 159.48/36.23 thf(361,plain,(! [B:list_a,A:list_a] : ((((rev_a @ A) = B) = (A = (rev_a @ B))))),inference(cnf,[status(esa)],[360])).
% 159.48/36.23 thf(362,plain,(! [B:list_a,A:list_a] : ((((rev_a @ A) = B) = (A = (rev_a @ B))))),inference(lifteq,[status(thm)],[361])).
% 159.48/36.23 thf(11436,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | ~ (($true)) | ((ord_less_eq_nat @ (sk8 @ (^ [C:nat,D:nat]: (($false)))) @ (sk9 @ (^ [C:nat,D:nat]: (($false))))) != (ord_less_eq_nat @ A @ B)))),inference(paramod_ordered,[status(thm)],[11201,271])).
% 159.48/36.23 thf(11437,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | ((ord_less_eq_nat @ (sk8 @ (^ [C:nat,D:nat]: (($false)))) @ (sk9 @ (^ [C:nat,D:nat]: (($false))))) != (ord_less_eq_nat @ A @ B)))),inference(simp,[status(thm)],[11436])).
% 159.48/36.23 thf(11438,plain,(((minus_minus_nat @ (sk9 @ (^ [A:nat,B:nat]: (($false)))) @ (minus_minus_nat @ (sk9 @ (^ [A:nat,B:nat]: (($false)))) @ (sk8 @ (^ [A:nat,B:nat]: (($false)))))) = (sk8 @ (^ [A:nat,B:nat]: (($false)))))),inference(pattern_uni,[status(thm)],[11437:[bind(A, $thf(sk8 @ (^ [C:nat,D:nat]: (($false))))),bind(B, $thf(sk9 @ (^ [C:nat,D:nat]: (($false)))))]])).
% 159.48/36.23 thf(32,axiom,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) != (size_size_list_nat @ B)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_neq__if__length__neq)).
% 159.48/36.23 thf(377,plain,((! [A:list_nat,B:list_nat]: ((~ ((size_size_list_nat @ A) = (size_size_list_nat @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
% 159.48/36.23 thf(1811,plain,(! [A:nat] : (((suc @ A) != (size_size_list_a @ xs)) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ ys)))),inference(paramod_ordered,[status(thm)],[632,1630])).
% 159.48/36.23 thf(1821,plain,(! [A:nat] : (((suc @ A) != (size_size_list_a @ xs)) | ((sk35 @ A) != ys))),inference(simp,[status(thm)],[1811])).
% 159.48/36.23 thf(86,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_75_linorder__neqE__nat)).
% 159.48/36.23 thf(621,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)],[86])).
% 159.48/36.23 thf(61,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_diff__Suc__Suc)).
% 159.48/36.23 thf(520,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
% 159.48/36.23 thf(1292,plain,((ys != xs) | (sk1 != sk1)),inference(simp,[status(thm)],[261])).
% 159.48/36.23 thf(1293,plain,((ys != xs)),inference(simp,[status(thm)],[1292])).
% 159.48/36.23 thf(202,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_119_order__less__le__subst2)).
% 159.48/36.23 thf(1029,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)],[202])).
% 159.48/36.23 thf(166,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_less__not__sym)).
% 159.48/36.23 thf(895,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
% 159.48/36.23 thf(192,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_less__irrefl)).
% 159.48/36.23 thf(983,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
% 159.48/36.23 thf(1925,plain,(! [A:nat] : (((sk35 @ (suc @ A)) != xs) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ ys)))),inference(paramod_ordered,[status(thm)],[632,1823])).
% 159.48/36.23 thf(1926,plain,(! [A:nat] : (((sk35 @ (suc @ A)) != xs) | ((sk35 @ A) != ys))),inference(simp,[status(thm)],[1925])).
% 159.48/36.23 thf(186,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_18_le__neq__implies__less)).
% 159.48/36.23 thf(959,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)],[186])).
% 159.48/36.23 thf(155,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ A @ C)) => ((ord_less_nat @ B @ A) => (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_nat__diff__left__cancel__eq1)).
% 159.48/36.23 thf(851,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ A @ B) = (minus_minus_nat @ A @ C)) => ((ord_less_nat @ B @ A) => (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
% 159.48/36.23 thf(45,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_Suc__leD)).
% 159.48/36.23 thf(438,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
% 159.48/36.23 thf(94,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_lift__Suc__mono__less__iff)).
% 159.48/36.23 thf(653,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
% 159.48/36.23 thf(1961,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (sk51 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[990,771])).
% 159.48/36.23 thf(1962,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (sk51 @ B) @ B)))),inference(simp,[status(thm)],[1961])).
% 159.48/36.23 thf(1969,plain,(! [B:nat,A:nat] : ((A != (sk51 @ B)) | ((sk72 @ A) != B))),inference(simp,[status(thm)],[1962])).
% 159.48/36.23 thf(1973,plain,(! [A:nat] : (((sk72 @ (sk51 @ A)) != A))),inference(simp,[status(thm)],[1969])).
% 159.48/36.23 thf(181,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ B @ C) => (A != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_less__ge__neq__conv)).
% 159.48/36.23 thf(944,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ B @ C) => (~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])).
% 159.48/36.23 thf(945,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ B @ C) => (~ (A = C)))))),inference(lifteq,[status(thm)],[944])).
% 159.48/36.23 thf(20828,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ (suc @ C)) => (~ (A = C)))))),inference(rewrite,[status(thm)],[945,20819])).
% 159.48/36.23 thf(47,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_le__SucI)).
% 159.48/36.23 thf(455,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
% 159.48/36.23 thf(193,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_102_dual__order_Ostrict__trans1)).
% 159.48/36.23 thf(986,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)],[193])).
% 159.48/36.23 thf(14,axiom,((! [A:list_nat]: ((list_strict_asc_nat @ A) => (list_asc_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_list__strict__asc__imp__list__asc)).
% 159.48/36.23 thf(305,plain,((! [A:list_nat]: ((list_strict_asc_nat @ A) => (list_asc_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 159.48/36.23 thf(306,plain,(! [A:list_nat] : ((~ (list_strict_asc_nat @ A)) | (list_asc_nat @ A))),inference(cnf,[status(esa)],[305])).
% 159.48/36.23 thf(20937,plain,(! [A:list_a] : ((A != ys) | ((rev_a @ (rev_a @ A)) != (rev_a @ (sk35 @ sk1))))),inference(paramod_ordered,[status(thm)],[437,20813])).
% 159.48/36.23 thf(20939,plain,(((sk35 @ sk1) != (rev_a @ ys))),inference(simp,[status(thm)],[20937])).
% 159.48/36.23 thf(1288,plain,(! [A:nat] : (((ord_less_eq_nat @ (suc @ A)) = (ord_less_nat @ A)))),inference(func_ext,[status(esa)],[898])).
% 159.48/36.23 thf(1302,plain,(! [A:nat] : (((ord_less_eq_nat @ A) = (^ [B:nat]: ((ord_less_nat @ A @ B) | (B = A)))))),inference(func_ext,[status(esa)],[736])).
% 159.48/36.23 thf(7366,plain,(! [A:nat] : (((^ [B:nat]: ((ord_less_nat @ (suc @ A) @ B) | (B = (suc @ A)))) = (ord_less_nat @ A)))),inference(rewrite,[status(thm)],[1288,1302])).
% 159.48/36.23 thf(51,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_39_ord__eq__le__subst)).
% 159.48/36.23 thf(473,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)],[51])).
% 159.48/36.23 thf(203,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_144_pinf_I2_J)).
% 159.48/36.23 thf(1034,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
% 159.48/36.23 thf(2077,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ (sk51 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[1150,771])).
% 159.48/36.23 thf(2078,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ (sk51 @ B) @ B)))),inference(simp,[status(thm)],[2077])).
% 159.48/36.23 thf(2091,plain,(! [B:nat,A:nat] : ((A != (sk51 @ B)) | ((suc @ A) != B))),inference(simp,[status(thm)],[2078])).
% 159.48/36.23 thf(2096,plain,(! [A:nat] : (((suc @ (sk51 @ A)) != A))),inference(simp,[status(thm)],[2091])).
% 159.48/36.23 thf(1466,plain,(((^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C))))) | ((^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))) != (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(paramod_ordered,[status(thm)],[1457,1439])).
% 159.48/36.23 thf(1467,plain,(((^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (A = C)))) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B = C)))))),inference(pattern_uni,[status(thm)],[1466:[]])).
% 159.48/36.23 thf(135,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) => (ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_diff__less__mono2)).
% 159.48/36.23 thf(795,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) => (ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])).
% 159.48/36.23 thf(31,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_lift__Suc__mono__le)).
% 159.48/36.23 thf(374,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 159.48/36.23 thf(370,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 @ (sk12 @ D @ (C) @ B @ A)) @ (C @ (sk13 @ D @ (C) @ B @ A)))) | (ord_less_eq_nat @ (C @ A) @ D))),inference(cnfConj,[status(thm)],[368])).
% 159.48/36.23 thf(21512,plain,(! [D:nat,C:(nat > nat),B:nat,A:nat] : ((~ (ord_less_nat @ A @ (suc @ B))) | (~ (ord_less_nat @ (C @ B) @ (suc @ D))) | (~ (ord_less_nat @ (C @ (sk12 @ D @ (C) @ B @ A)) @ (suc @ (C @ (sk13 @ D @ (C) @ B @ A))))) | (ord_less_nat @ (C @ A) @ (suc @ D)))),inference(rewrite,[status(thm)],[370,20819])).
% 159.48/36.23 thf(140,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_44_not__less__iff__gr__or__eq)).
% 159.48/36.23 thf(812,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)],[140])).
% 159.48/36.23 thf(20944,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ (size_size_list_a @ xs) @ (suc @ sk1))))),inference(paramod_ordered,[status(thm)],[1150,20839])).
% 159.48/36.23 thf(20945,plain,(! [A:nat] : (((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ (size_size_list_a @ xs) @ (suc @ sk1))))),inference(simp,[status(thm)],[20944])).
% 159.48/36.23 thf(20971,plain,(! [A:nat] : ((A != (size_size_list_a @ xs)) | ((suc @ A) != (suc @ sk1)))),inference(simp,[status(thm)],[20945])).
% 159.48/36.23 thf(20980,plain,(((suc @ (size_size_list_a @ xs)) != (suc @ sk1))),inference(simp,[status(thm)],[20971])).
% 159.48/36.23 thf(180,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_71_order__less__subst2)).
% 159.48/36.23 thf(939,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)],[180])).
% 159.48/36.23 thf(342,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((~ (A @ (sk8 @ (A)) @ (sk9 @ (A)))) | (A @ (sk11 @ (A)) @ (sk10 @ (A))) | (A @ B @ C))),inference(cnfConj,[status(thm)],[339])).
% 159.48/36.23 thf(239,axiom,((! [A:nat,B:(nat > (a > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:a]: (B @ C @ D)))) = (? [C:list_a]: (((size_size_list_a @ C) = A) & ! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_a @ C @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Skolem__list__nth)).
% 159.48/36.23 thf(1203,plain,((! [A:nat,B:(nat > (a > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:a]: (B @ C @ D)))) = (? [C:list_a]: (((size_size_list_a @ C) = A) & ! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_a @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
% 159.48/36.23 thf(241,axiom,((linorder_sorted_nat = (^ [A:list_nat]: ! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_sorted__iff__nth__mono)).
% 159.48/36.23 thf(1208,plain,(((linorder_sorted_nat) = (^ [A:list_nat]: ! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
% 159.48/36.23 thf(97,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_not__less__eq)).
% 159.48/36.23 thf(663,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
% 159.48/36.23 thf(5408,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (A @ (sk7 @ B @ (A))) | ~ (($true)) | (A @ C) | ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[589,320])).
% 159.48/36.23 thf(5409,plain,(! [C:nat,B:nat,A:(nat > $o)] : ((~ (A @ B)) | (A @ (sk7 @ B @ (A))) | (A @ C) | ((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys)) != (ord_less_eq_nat @ B @ C)))),inference(simp,[status(thm)],[5408])).
% 159.48/36.23 thf(5410,plain,(! [A:(nat > $o)] : ((~ (A @ (size_size_list_a @ xs))) | (A @ (sk7 @ (size_size_list_a @ xs) @ (A))) | (A @ (size_size_list_a @ ys)))),inference(pattern_uni,[status(thm)],[5409:[bind(A, $thf(A)),bind(B, $thf(size_size_list_a @ xs)),bind(C, $thf(size_size_list_a @ ys))]])).
% 159.48/36.23 thf(5599,plain,((~ ((size_size_list_a @ xs) = (size_size_list_a @ xs))) | ((size_size_list_a @ xs) = (sk7 @ (size_size_list_a @ xs) @ ((=) @ nat @ (size_size_list_a @ xs)))) | ((size_size_list_a @ xs) = (size_size_list_a @ ys))),inference(replace_leibeq,[status(thm)],[5410:[bind(A, $thf((=) @ nat @ (size_size_list_a @ xs)))]])).
% 159.48/36.23 thf(5712,plain,(((size_size_list_a @ xs) != (size_size_list_a @ xs)) | ((sk7 @ (size_size_list_a @ xs) @ ((=) @ nat @ (size_size_list_a @ xs))) = (size_size_list_a @ xs)) | ((size_size_list_a @ ys) = (size_size_list_a @ xs))),inference(lifteq,[status(thm)],[5599])).
% 159.48/36.23 thf(5785,plain,(((size_size_list_a @ ys) = (size_size_list_a @ xs)) | ((sk7 @ (size_size_list_a @ xs) @ ((=) @ nat @ (size_size_list_a @ xs))) = (size_size_list_a @ xs))),inference(pattern_uni,[status(thm)],[5712:[]])).
% 159.48/36.23 thf(92,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__asym_H)).
% 159.48/36.23 thf(648,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
% 159.48/36.23 thf(486,plain,(! [A:nat] : (((size_size_list_nat @ (sk22 @ A)) = A))),inference(cnf,[status(esa)],[485])).
% 159.48/36.23 thf(487,plain,(! [A:nat] : (((size_size_list_nat @ (sk22 @ A)) = A))),inference(lifteq,[status(thm)],[486])).
% 159.48/36.23 thf(85,axiom,((! [A:list_a,B:nat,C:(nat > a)]: ((ord_less_eq_nat @ (size_size_list_a @ A) @ B) => ((listIn1312259492pend_a @ A @ C @ B) = (C @ (minus_minus_nat @ B @ (size_size_list_a @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_i__append__nth2)).
% 159.48/36.23 thf(617,plain,((! [A:list_a,B:nat,C:(nat > a)]: ((ord_less_eq_nat @ (size_size_list_a @ A) @ B) => ((listIn1312259492pend_a @ A @ (C) @ B) = (C @ (minus_minus_nat @ B @ (size_size_list_a @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
% 159.48/36.23 thf(60,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_le__diff__iff)).
% 159.48/36.23 thf(516,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
% 159.48/36.23 thf(524,plain,(! [B:list_nat,A:(nat > $o)] : (((list_ex_nat @ (A) @ (rev_nat @ B)) = (list_ex_nat @ (A) @ B)))),inference(cnf,[status(esa)],[523])).
% 159.48/36.23 thf(525,plain,(! [B:list_nat,A:(nat > $o)] : (((list_ex_nat @ (A) @ (rev_nat @ B)) = (list_ex_nat @ (A) @ B)))),inference(lifteq,[status(thm)],[524])).
% 159.48/36.23 thf(77,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_eq__refl)).
% 159.48/36.23 thf(580,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
% 159.48/36.23 thf(232,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_less__imp__diff__less)).
% 159.48/36.23 thf(1156,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
% 159.48/36.23 thf(189,axiom,((! [A:list_a,B:list_a]: (((size_size_list_a @ A) != (size_size_list_a @ B)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_size__neq__size__imp__neq)).
% 159.48/36.23 thf(971,plain,((! [A:list_a,B:list_a]: ((~ ((size_size_list_a @ A) = (size_size_list_a @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
% 159.48/36.23 thf(8332,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | ((sk35 @ C) != xs) | ((ord_less_nat @ B @ A) != (ord_less_nat @ sk1 @ C)))),inference(paramod_ordered,[status(thm)],[761,1825])).
% 159.48/36.23 thf(8333,plain,(! [C:nat,B:nat,A:nat] : ((~ (ord_less_eq_nat @ A @ B)) | ((sk35 @ C) != xs) | ((ord_less_nat @ B @ A) != (ord_less_nat @ sk1 @ C)))),inference(simp,[status(thm)],[8332])).
% 159.48/36.23 thf(8334,plain,(! [A:nat] : ((~ (ord_less_eq_nat @ A @ sk1)) | ((sk35 @ A) != xs))),inference(pattern_uni,[status(thm)],[8333:[bind(A, $thf(A)),bind(B, $thf(sk1)),bind(C, $thf(A))]])).
% 159.48/36.23 thf(16137,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | ((sk35 @ C) != xs) | ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ C @ sk1)))),inference(paramod_ordered,[status(thm)],[472,8334])).
% 159.48/36.23 thf(16138,plain,(! [C:nat,B:nat,A:nat] : (((sk35 @ C) != xs) | ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ C @ sk1)))),inference(simp,[status(thm)],[16137])).
% 159.48/36.23 thf(16139,plain,(! [A:nat] : (((sk35 @ (minus_minus_nat @ sk1 @ A)) != xs))),inference(pattern_uni,[status(thm)],[16138:[bind(A, $thf(sk1)),bind(B, $thf(E)),bind(C, $thf(minus_minus_nat @ sk1 @ E))]])).
% 159.48/36.23 thf(16266,plain,(! [A:nat] : (((sk35 @ (minus_minus_nat @ sk1 @ A)) != xs))),inference(simp,[status(thm)],[16139])).
% 159.48/36.23 thf(20404,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ (suc @ A))) != (ord_less_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs))))),inference(paramod_ordered,[status(thm)],[20289,8370])).
% 159.48/36.23 thf(20405,plain,(! [A:nat] : (((ord_less_nat @ A @ (suc @ (suc @ A))) != (ord_less_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[20404])).
% 159.48/36.23 thf(20490,plain,(! [A:nat] : ((A != (size_size_list_a @ ys)) | ((suc @ (suc @ A)) != (size_size_list_a @ xs)))),inference(simp,[status(thm)],[20405])).
% 159.48/36.23 thf(20519,plain,(((suc @ (suc @ (size_size_list_a @ ys))) != (size_size_list_a @ xs))),inference(simp,[status(thm)],[20490])).
% 159.48/36.23 thf(20635,plain,(! [A:nat] : ((A != (suc @ (suc @ (size_size_list_a @ ys)))) | ((size_size_list_a @ (sk35 @ A)) != (size_size_list_a @ xs)))),inference(paramod_ordered,[status(thm)],[632,20519])).
% 159.48/36.23 thf(20645,plain,(((sk35 @ (suc @ (suc @ (size_size_list_a @ ys)))) != xs)),inference(simp,[status(thm)],[20635])).
% 159.48/36.23 thf(1935,plain,(! [B:nat,A:nat] : (((sk35 @ A) != xs) | ~ (($true)) | ((ord_less_nat @ sk1 @ A) != (ord_less_nat @ (sk63 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[1825,910])).
% 159.48/36.23 thf(1936,plain,(! [B:nat,A:nat] : (((sk35 @ A) != xs) | ((ord_less_nat @ sk1 @ A) != (ord_less_nat @ (sk63 @ B) @ B)))),inference(simp,[status(thm)],[1935])).
% 159.48/36.23 thf(1939,plain,(! [B:nat,A:nat] : (((sk35 @ A) != xs) | ((sk63 @ B) != sk1) | (A != B))),inference(simp,[status(thm)],[1936])).
% 159.48/36.23 thf(1941,plain,(! [A:nat] : (((sk35 @ A) != xs) | ((sk63 @ A) != sk1))),inference(simp,[status(thm)],[1939])).
% 159.48/36.23 thf(119,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_pinf_I5_J)).
% 159.48/36.23 thf(739,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
% 159.48/36.23 thf(21014,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ (sk51 @ A) @ A) != (ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs)))))),inference(paramod_ordered,[status(thm)],[20894,771])).
% 159.48/36.23 thf(21015,plain,(! [A:nat] : (((ord_less_nat @ (sk51 @ A) @ A) != (ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs)))))),inference(simp,[status(thm)],[21014])).
% 159.48/36.23 thf(21029,plain,(! [A:nat] : (((sk51 @ A) != sk1) | (A != (suc @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[21015])).
% 159.48/36.23 thf(21039,plain,(((sk51 @ (suc @ (size_size_list_a @ xs))) != sk1)),inference(simp,[status(thm)],[21029])).
% 159.48/36.23 thf(250,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_17_less__or__eq__imp__le)).
% 159.48/36.23 thf(1230,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)],[250])).
% 159.48/36.23 thf(16,axiom,((! [A:list_nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ B) => ((listIn923761578nd_nat @ A @ C @ B) = (C @ (minus_minus_nat @ B @ (size_size_list_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_i__append__nth2)).
% 159.48/36.23 thf(310,plain,((! [A:list_nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ B) => ((listIn923761578nd_nat @ A @ (C) @ B) = (C @ (minus_minus_nat @ B @ (size_size_list_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 159.48/36.23 thf(196,axiom,((! [A:(list_a > $o),B:list_a]: ((! [C:list_a]: ((! [D:list_a]: ((ord_less_nat @ (size_size_list_a @ D) @ (size_size_list_a @ C)) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_length__induct)).
% 159.48/36.23 thf(993,plain,((! [A:(list_a > $o),B:list_a]: ((! [C:list_a]: ((! [D:list_a]: ((ord_less_nat @ (size_size_list_a @ D) @ (size_size_list_a @ C)) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
% 159.48/36.23 thf(129,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_not__le)).
% 159.48/36.23 thf(776,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
% 159.48/36.23 thf(14523,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (suc @ B) @ B)))),inference(paramod_ordered,[status(thm)],[990,8523])).
% 159.48/36.23 thf(14524,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ (suc @ B) @ B)))),inference(simp,[status(thm)],[14523])).
% 159.48/36.23 thf(14549,plain,(! [B:nat,A:nat] : ((A != (suc @ B)) | ((sk72 @ A) != B))),inference(simp,[status(thm)],[14524])).
% 159.48/36.23 thf(14594,plain,(! [A:nat] : (((sk72 @ (suc @ A)) != A))),inference(simp,[status(thm)],[14549])).
% 159.48/36.23 thf(12045,plain,(! [A:nat] : (~ (($true)) | ((ord_less_eq_nat @ (suc @ A) @ A) != (ord_less_eq_nat @ sk1 @ sk1)))),inference(paramod_ordered,[status(thm)],[11981,390])).
% 159.48/36.23 thf(12046,plain,(! [A:nat] : (((ord_less_eq_nat @ (suc @ A) @ A) != (ord_less_eq_nat @ sk1 @ sk1)))),inference(simp,[status(thm)],[12045])).
% 159.48/36.23 thf(12068,plain,(! [A:nat] : (((suc @ A) != sk1) | (A != sk1))),inference(simp,[status(thm)],[12046])).
% 159.48/36.23 thf(12088,plain,(((suc @ sk1) != sk1)),inference(simp,[status(thm)],[12068])).
% 159.48/36.23 thf(160,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_149_minf_I1_J)).
% 159.48/36.23 thf(872,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) & (C @ F)) = ((B @ F) & (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
% 159.48/36.23 thf(248,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_pinf_I6_J)).
% 159.48/36.23 thf(1225,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])).
% 159.48/36.23 thf(107,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_less__not__refl)).
% 159.48/36.23 thf(707,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
% 159.48/36.23 thf(4288,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ (suc @ C) @ C)))),inference(paramod_ordered,[status(thm)],[472,390])).
% 159.48/36.23 thf(4289,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A) != (ord_less_eq_nat @ (suc @ C) @ C)))),inference(simp,[status(thm)],[4288])).
% 159.48/36.23 thf(4302,plain,(! [C:nat,B:nat,A:nat] : (((minus_minus_nat @ A @ B) != (suc @ C)) | (A != C))),inference(simp,[status(thm)],[4289])).
% 159.48/36.23 thf(4314,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ B @ A) != (suc @ B)))),inference(simp,[status(thm)],[4302])).
% 159.48/36.23 thf(2081,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ B @ (sk53 @ B))))),inference(paramod_ordered,[status(thm)],[1150,808])).
% 159.48/36.23 thf(2082,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ B @ (sk53 @ B))))),inference(simp,[status(thm)],[2081])).
% 159.48/36.23 thf(2087,plain,(! [B:nat,A:nat] : ((A != B) | ((suc @ A) != (sk53 @ B)))),inference(simp,[status(thm)],[2082])).
% 159.48/36.23 thf(2092,plain,(! [A:nat] : (((sk53 @ A) != (suc @ A)))),inference(simp,[status(thm)],[2087])).
% 159.48/36.23 thf(1982,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ B @ (sk96 @ B))))),inference(paramod_ordered,[status(thm)],[990,1148])).
% 159.48/36.23 thf(1983,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ B @ (sk96 @ B))))),inference(simp,[status(thm)],[1982])).
% 159.48/36.23 thf(1985,plain,(! [B:nat,A:nat] : ((A != B) | ((sk72 @ A) != (sk96 @ B)))),inference(simp,[status(thm)],[1983])).
% 159.48/36.23 thf(1987,plain,(! [A:nat] : (((sk96 @ A) != (sk72 @ A)))),inference(simp,[status(thm)],[1985])).
% 159.48/36.23 thf(134,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_order_Ostrict__implies__not__eq)).
% 159.48/36.23 thf(791,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
% 159.48/36.23 thf(20997,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ (sk72 @ A) @ A) != (ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs)))))),inference(paramod_ordered,[status(thm)],[20894,15897])).
% 159.48/36.23 thf(20998,plain,(! [A:nat] : (((ord_less_nat @ (sk72 @ A) @ A) != (ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs)))))),inference(simp,[status(thm)],[20997])).
% 159.48/36.23 thf(21032,plain,(! [A:nat] : (((sk72 @ A) != sk1) | (A != (suc @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[20998])).
% 159.48/36.23 thf(21041,plain,(((sk72 @ (suc @ (size_size_list_a @ xs))) != sk1)),inference(simp,[status(thm)],[21032])).
% 159.48/36.23 thf(253,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ B) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D))))) => (C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_inc__induct)).
% 159.48/36.23 thf(1262,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ B) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D))))) => (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])).
% 159.48/36.23 thf(214,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_less__imp__not__eq2)).
% 159.48/36.23 thf(1085,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
% 159.48/36.23 thf(246,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__imp__neq)).
% 159.48/36.23 thf(1218,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])).
% 159.48/36.23 thf(1931,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_nat @ A @ (sk53 @ A))))),inference(paramod_ordered,[status(thm)],[259,808])).
% 159.48/36.23 thf(1932,plain,(! [A:nat] : (((ord_less_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_nat @ A @ (sk53 @ A))))),inference(simp,[status(thm)],[1931])).
% 159.48/36.23 thf(1933,plain,(! [A:nat] : ((sk1 != A) | ((sk53 @ A) != (size_size_list_a @ xs)))),inference(simp,[status(thm)],[1932])).
% 159.48/36.23 thf(1934,plain,(((sk53 @ sk1) != (size_size_list_a @ xs))),inference(simp,[status(thm)],[1933])).
% 159.48/36.23 thf(10482,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ A @ (sk51 @ A)) != (ord_less_eq_nat @ (suc @ B) @ B)))),inference(paramod_ordered,[status(thm)],[8382,390])).
% 159.48/36.23 thf(10483,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ A @ (sk51 @ A)) != (ord_less_eq_nat @ (suc @ B) @ B)))),inference(simp,[status(thm)],[10482])).
% 159.48/36.23 thf(10510,plain,(! [B:nat,A:nat] : ((A != (suc @ B)) | ((sk51 @ A) != B))),inference(simp,[status(thm)],[10483])).
% 159.48/36.23 thf(10531,plain,(! [A:nat] : (((sk51 @ (suc @ A)) != A))),inference(simp,[status(thm)],[10510])).
% 159.48/36.23 thf(217,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_77_nat__less__induct)).
% 159.48/36.23 thf(1094,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)],[217])).
% 159.48/36.23 thf(200,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_less__imp__le)).
% 159.48/36.23 thf(1008,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
% 159.48/36.23 thf(17,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_dual__order_Orefl)).
% 159.48/36.23 thf(314,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 159.48/36.23 thf(195,axiom,((((=) @ list_nat) = (^ [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_list__eq__iff__nth__eq)).
% 159.48/36.23 thf(991,plain,((((=) @ list_nat) = (^ [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
% 159.48/36.23 thf(2483,plain,(! [A:list_a] : (((sk51 @ (size_size_list_a @ A)) != sk1) | ((size_size_list_a @ (rev_a @ A)) != (size_size_list_a @ xs)))),inference(paramod_ordered,[status(thm)],[904,1765])).
% 159.48/36.23 thf(2500,plain,(! [A:list_a] : (((sk51 @ (size_size_list_a @ A)) != sk1) | ((rev_a @ A) != xs))),inference(simp,[status(thm)],[2483])).
% 159.48/36.23 thf(121,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_54_antisym__conv3)).
% 159.48/36.23 thf(744,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)],[121])).
% 159.48/36.23 thf(335,plain,(! [B:list_a,A:(a > $o)] : (((list_ex_a @ (A) @ (rev_a @ B)) = (list_ex_a @ (A) @ B)))),inference(cnf,[status(esa)],[334])).
% 159.48/36.23 thf(336,plain,(! [B:list_a,A:(a > $o)] : (((list_ex_a @ (A) @ (rev_a @ B)) = (list_ex_a @ (A) @ B)))),inference(lifteq,[status(thm)],[335])).
% 159.48/36.23 thf(152,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_142_pinf_I8_J)).
% 159.48/36.23 thf(845,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)],[152])).
% 159.48/36.23 thf(88,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_112_le__less__trans)).
% 159.48/36.23 thf(627,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)],[88])).
% 159.48/36.23 thf(67,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((ord_less_eq_nat @ A @ B) | (A = (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_le__Suc__eq)).
% 159.48/36.23 thf(539,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((ord_less_eq_nat @ A @ B) | (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
% 159.48/36.23 thf(52,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_diff__le__mono)).
% 159.48/36.23 thf(482,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
% 159.48/36.23 thf(245,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_leD)).
% 159.48/36.23 thf(1216,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
% 159.48/36.23 thf(201,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_46_linorder__less__wlog)).
% 159.48/36.23 thf(1010,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat]: (A @ D @ D)) => ((! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
% 159.48/36.23 thf(843,plain,(! [A:nat] : (((listIn1312259492pend_a @ xs @ (f) @ A) = (listIn1312259492pend_a @ ys @ (g) @ A)))),inference(cnf,[status(esa)],[842])).
% 159.48/36.23 thf(844,plain,(! [A:nat] : (((listIn1312259492pend_a @ ys @ (g) @ A) = (listIn1312259492pend_a @ xs @ (f) @ A)))),inference(lifteq,[status(thm)],[843])).
% 159.48/36.23 thf(678,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(lifteq,[status(thm)],[677])).
% 159.48/36.23 thf(20846,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) & ~ (A = B))))),inference(rewrite,[status(thm)],[678,20819])).
% 159.48/36.23 thf(11415,plain,(~ (($true)) | ((ord_less_eq_nat @ (sk8 @ (^ [A:nat,B:nat]: (($false)))) @ (sk9 @ (^ [A:nat,B:nat]: (($false))))) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1))),inference(paramod_ordered,[status(thm)],[11201,8352])).
% 159.48/36.24 thf(11416,plain,(((ord_less_eq_nat @ (sk8 @ (^ [A:nat,B:nat]: (($false)))) @ (sk9 @ (^ [A:nat,B:nat]: (($false))))) != (ord_less_eq_nat @ (size_size_list_a @ xs) @ sk1))),inference(simp,[status(thm)],[11415])).
% 159.48/36.24 thf(11514,plain,(((sk8 @ (^ [A:nat,B:nat]: (($false)))) != (size_size_list_a @ xs)) | ((sk9 @ (^ [A:nat,B:nat]: (($false)))) != sk1)),inference(simp,[status(thm)],[11416])).
% 159.48/36.24 thf(182,axiom,((! [A:list_a,B:list_a]: (((size_size_list_a @ A) != (size_size_list_a @ B)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_neq__if__length__neq)).
% 159.48/36.24 thf(946,plain,((! [A:list_a,B:list_a]: ((~ ((size_size_list_a @ A) = (size_size_list_a @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
% 159.48/36.24 thf(212,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_59_ord__less__eq__trans)).
% 159.48/36.24 thf(1077,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)],[212])).
% 159.48/36.24 thf(243,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) => (B != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_greater__le__neq__conv)).
% 159.48/36.24 thf(1212,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) => (~ (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])).
% 159.48/36.24 thf(168,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_51_linorder__cases)).
% 159.48/36.24 thf(899,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)],[168])).
% 159.48/36.24 thf(2085,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ B @ (sk96 @ B))))),inference(paramod_ordered,[status(thm)],[1150,1148])).
% 159.48/36.24 thf(2086,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ B @ (sk96 @ B))))),inference(simp,[status(thm)],[2085])).
% 159.48/36.24 thf(2090,plain,(! [B:nat,A:nat] : ((A != B) | ((suc @ A) != (sk96 @ B)))),inference(simp,[status(thm)],[2086])).
% 159.48/36.24 thf(2095,plain,(! [A:nat] : (((sk96 @ A) != (suc @ A)))),inference(simp,[status(thm)],[2090])).
% 159.48/36.24 thf(66,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_nat_Oinject)).
% 159.48/36.24 thf(536,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
% 159.48/36.24 thf(204,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ C @ B)) => (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_nat__diff__right__cancel__less)).
% 159.48/36.24 thf(1045,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ C @ B)) => (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
% 159.48/36.24 thf(9,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_27_ord__le__eq__trans)).
% 159.48/36.24 thf(290,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)],[9])).
% 159.48/36.24 thf(173,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_order_Ostrict__iff__order)).
% 159.48/36.24 thf(914,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])).
% 159.48/36.24 thf(110,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_dual__order_Oirrefl)).
% 159.48/36.24 thf(716,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
% 159.48/36.24 thf(234,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_133_complete__interval)).
% 159.48/36.24 thf(1161,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)],[234])).
% 159.48/36.24 thf(222,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_le__less)).
% 159.48/36.24 thf(1116,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
% 159.48/36.24 thf(227,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_74_ord__eq__less__subst)).
% 159.48/36.24 thf(1133,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)],[227])).
% 159.48/36.24 thf(43,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_old_Onat_Oinject)).
% 159.48/36.24 thf(432,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
% 159.48/36.24 thf(159,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (B != (suc @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_Suc__lessE)).
% 159.48/36.24 thf(867,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (~ (B = (suc @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
% 159.48/36.24 thf(158,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_order_Oasym)).
% 159.48/36.24 thf(865,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
% 159.48/36.24 thf(148,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_order_Ostrict__implies__order)).
% 159.48/36.24 thf(833,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
% 159.48/36.24 thf(38,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ (suc @ D)) => (A @ D))) => (A @ (minus_minus_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_zero__induct__lemma)).
% 159.48/36.24 thf(410,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((A @ (suc @ D)) => (A @ D))) => (A @ (minus_minus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
% 159.48/36.24 thf(183,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ (suc @ A)) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_le__less__Suc__eq)).
% 159.48/36.24 thf(950,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ (suc @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
% 159.48/36.24 thf(149,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_minf_I6_J)).
% 159.48/36.24 thf(835,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
% 159.48/36.24 thf(3,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_order__class_Oorder_Oeq__iff)).
% 159.48/36.24 thf(262,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 159.48/36.24 thf(156,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_le__less__linear)).
% 159.48/36.24 thf(854,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
% 159.48/36.24 thf(1980,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_nat @ A @ (sk96 @ A))))),inference(paramod_ordered,[status(thm)],[259,1148])).
% 159.48/36.24 thf(1981,plain,(! [A:nat] : (((ord_less_nat @ sk1 @ (size_size_list_a @ xs)) != (ord_less_nat @ A @ (sk96 @ A))))),inference(simp,[status(thm)],[1980])).
% 159.48/36.24 thf(1984,plain,(! [A:nat] : ((sk1 != A) | ((sk96 @ A) != (size_size_list_a @ xs)))),inference(simp,[status(thm)],[1981])).
% 159.48/36.24 thf(1986,plain,(((sk96 @ sk1) != (size_size_list_a @ xs))),inference(simp,[status(thm)],[1984])).
% 159.48/36.24 thf(175,axiom,((list_asc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_list__asc__trans)).
% 159.48/36.24 thf(918,plain,(((list_asc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
% 159.48/36.24 thf(237,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_order_Oorder__iff__strict)).
% 159.48/36.24 thf(1197,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
% 159.48/36.24 thf(147,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_60_ord__eq__less__trans)).
% 159.48/36.24 thf(828,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)],[147])).
% 159.48/36.24 thf(91,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_132_nat__descend__induct)).
% 159.48/36.24 thf(635,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)],[91])).
% 159.48/36.24 thf(65,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_Nat_Odiff__diff__eq)).
% 159.48/36.24 thf(532,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
% 159.48/36.24 thf(106,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_150_minf_I2_J)).
% 159.48/36.24 thf(696,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
% 159.48/36.24 thf(720,plain,(((^ [A:list_a,B:list_a]: (((size_size_list_a @ A) = (size_size_list_a @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_a @ A)) => ((nth_a @ A @ C) = (nth_a @ B @ C))))) = ((=) @ list_a))),inference(lifteq,[status(thm)],[719])).
% 159.48/36.24 thf(12927,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ A @ (suc @ A)) != (ord_less_eq_nat @ (sk72 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[2825,8492])).
% 159.48/36.24 thf(12928,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ A @ (suc @ A)) != (ord_less_eq_nat @ (sk72 @ B) @ B)))),inference(simp,[status(thm)],[12927])).
% 159.48/36.24 thf(12993,plain,(! [B:nat,A:nat] : ((A != (sk72 @ B)) | ((suc @ A) != B))),inference(simp,[status(thm)],[12928])).
% 159.48/36.24 thf(13028,plain,(! [A:nat] : (((suc @ (sk72 @ A)) != A))),inference(simp,[status(thm)],[12993])).
% 159.48/36.24 thf(12956,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_eq_nat @ A @ (sk63 @ A)) != (ord_less_eq_nat @ (sk72 @ B) @ B)))),inference(paramod_ordered,[status(thm)],[8331,8492])).
% 159.48/36.24 thf(12957,plain,(! [B:nat,A:nat] : (((ord_less_eq_nat @ A @ (sk63 @ A)) != (ord_less_eq_nat @ (sk72 @ B) @ B)))),inference(simp,[status(thm)],[12956])).
% 159.48/36.24 thf(12991,plain,(! [B:nat,A:nat] : ((A != (sk72 @ B)) | ((sk63 @ A) != B))),inference(simp,[status(thm)],[12957])).
% 159.48/36.24 thf(13068,plain,(! [A:nat] : (((sk63 @ (sk72 @ A)) != A))),inference(simp,[status(thm)],[12991])).
% 159.48/36.24 thf(114,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_148_pinf_I7_J)).
% 159.48/36.24 thf(728,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)],[114])).
% 159.48/36.24 thf(251,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((B != (suc @ A)) => (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (B != (suc @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_Nat_OlessE)).
% 159.48/36.24 thf(1236,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((~ (B = (suc @ A))) => (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (~ (B = (suc @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])).
% 159.48/36.24 thf(226,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_less__not__refl3)).
% 159.48/36.24 thf(1129,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
% 159.48/36.24 thf(75,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_21_dual__order_Oeq__iff)).
% 159.48/36.24 thf(575,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)],[75])).
% 159.48/36.24 thf(41,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_35_linear)).
% 159.48/36.24 thf(427,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)],[41])).
% 159.48/36.24 thf(1532,plain,(! [A:(nat > $o)] : (((list_ex_nat @ A) = (^ [B:list_nat]: ? [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ B)) & (A @ (nth_nat @ B @ C))))))),inference(func_ext,[status(esa)],[1286])).
% 159.48/36.24 thf(83,axiom,((list_desc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_list__desc__trans)).
% 159.48/36.24 thf(596,plain,(((list_desc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
% 159.48/36.24 thf(19407,plain,(! [C:nat,B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ B @ (minus_minus_nat @ B @ C))))),inference(paramod_ordered,[status(thm)],[1150,8499])).
% 159.48/36.24 thf(19408,plain,(! [C:nat,B:nat,A:nat] : (((ord_less_nat @ A @ (suc @ A)) != (ord_less_nat @ B @ (minus_minus_nat @ B @ C))))),inference(simp,[status(thm)],[19407])).
% 159.48/36.24 thf(19454,plain,(! [C:nat,B:nat,A:nat] : ((A != B) | ((suc @ A) != (minus_minus_nat @ B @ C)))),inference(simp,[status(thm)],[19408])).
% 159.48/36.24 thf(19528,plain,(! [B:nat,A:nat] : (((minus_minus_nat @ A @ B) != (suc @ A)))),inference(simp,[status(thm)],[19454])).
% 159.48/36.24 thf(1967,plain,(! [B:nat,A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ B @ B)))),inference(paramod_ordered,[status(thm)],[990,595])).
% 159.48/36.24 thf(1968,plain,(! [B:nat,A:nat] : (((ord_less_nat @ A @ (sk72 @ A)) != (ord_less_nat @ B @ B)))),inference(simp,[status(thm)],[1967])).
% 159.48/36.24 thf(1972,plain,(! [B:nat,A:nat] : ((A != B) | ((sk72 @ A) != B))),inference(simp,[status(thm)],[1968])).
% 159.48/36.24 thf(1976,plain,(! [A:nat] : (((sk72 @ A) != A))),inference(simp,[status(thm)],[1972])).
% 159.48/36.24 thf(992,plain,(((^ [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C))))) = ((=) @ list_nat))),inference(lifteq,[status(thm)],[991])).
% 159.48/36.24 thf(144,axiom,((list_asc_nat = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_list__asc__trans__le)).
% 159.48/36.24 thf(822,plain,(((list_asc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
% 159.48/36.24 thf(850,plain,(((list_strict_asc_nat) = (^ [A:list_nat]: ! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B)))))))),inference(lifteq,[status(thm)],[849])).
% 159.48/36.24 thf(198,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_Suc__le__lessD)).
% 159.48/36.24 thf(1004,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
% 159.48/36.24 thf(20452,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ A @ (suc @ (suc @ A))) != (ord_less_nat @ (sk9 @ (^ [B:nat,C:nat]: (($false)))) @ (sk8 @ (^ [B:nat,C:nat]: (($false)))))))),inference(paramod_ordered,[status(thm)],[20289,11428])).
% 159.48/36.24 thf(20453,plain,(! [A:nat] : (((ord_less_nat @ A @ (suc @ (suc @ A))) != (ord_less_nat @ (sk9 @ (^ [B:nat,C:nat]: (($false)))) @ (sk8 @ (^ [B:nat,C:nat]: (($false)))))))),inference(simp,[status(thm)],[20452])).
% 159.48/36.24 thf(20479,plain,(! [A:nat] : ((A != (sk9 @ (^ [B:nat,C:nat]: (($false))))) | ((suc @ (suc @ A)) != (sk8 @ (^ [B:nat,C:nat]: (($false))))))),inference(simp,[status(thm)],[20453])).
% 159.48/36.24 thf(20548,plain,(((suc @ (suc @ (sk9 @ (^ [A:nat,B:nat]: (($false)))))) != (sk8 @ (^ [A:nat,B:nat]: (($false)))))),inference(simp,[status(thm)],[20479])).
% 159.48/36.24 thf(104,axiom,((linorder_sorted_nat = (^ [A:list_nat]: ! [B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_sorted__iff__nth__mono__less)).
% 159.48/36.24 thf(691,plain,(((linorder_sorted_nat) = (^ [A:list_nat]: ! [B:nat,C:nat]: ((ord_less_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ B) @ (nth_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
% 159.48/36.24 thf(1928,plain,(! [B:nat,A:nat] : (((sk35 @ A) != xs) | ~ (($true)) | ((ord_less_nat @ sk1 @ A) != (ord_less_nat @ B @ (sk53 @ B))))),inference(paramod_ordered,[status(thm)],[1825,808])).
% 159.48/36.24 thf(1929,plain,(! [B:nat,A:nat] : (((sk35 @ A) != xs) | ((ord_less_nat @ sk1 @ A) != (ord_less_nat @ B @ (sk53 @ B))))),inference(simp,[status(thm)],[1928])).
% 159.48/36.24 thf(1930,plain,(((sk35 @ (sk53 @ sk1)) != xs)),inference(pattern_uni,[status(thm)],[1929:[bind(A, $thf(sk53 @ sk1)),bind(B, $thf(sk1))]])).
% 159.48/36.24 thf(87,axiom,((! [A:list_nat,B:nat,C:nat]: ((linorder_sorted_nat @ (rev_nat @ A)) => ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_sorted__rev__nth__mono)).
% 159.48/36.24 thf(624,plain,((! [A:list_nat,B:nat,C:nat]: ((linorder_sorted_nat @ (rev_nat @ A)) => ((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
% 159.48/36.24 thf(21966,plain,(~ (($true)) | ((ord_less_nat @ (size_size_list_a @ xs) @ (suc @ (size_size_list_a @ ys))) != (ord_less_nat @ (size_size_list_a @ xs) @ sk1))),inference(paramod_ordered,[status(thm)],[20873,8676])).
% 159.48/36.24 thf(21967,plain,(((ord_less_nat @ (size_size_list_a @ xs) @ (suc @ (size_size_list_a @ ys))) != (ord_less_nat @ (size_size_list_a @ xs) @ sk1))),inference(simp,[status(thm)],[21966])).
% 159.48/36.24 thf(22006,plain,(((size_size_list_a @ xs) != (size_size_list_a @ xs)) | ((suc @ (size_size_list_a @ ys)) != sk1)),inference(simp,[status(thm)],[21967])).
% 159.48/36.24 thf(22022,plain,(((suc @ (size_size_list_a @ ys)) != sk1)),inference(simp,[status(thm)],[22006])).
% 159.48/36.24 thf(177,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_82_nat__neq__iff)).
% 159.48/36.24 thf(923,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)],[177])).
% 159.48/36.24 thf(20993,plain,(! [A:nat] : (~ (($true)) | ((ord_less_nat @ (sk63 @ A) @ A) != (ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs)))))),inference(paramod_ordered,[status(thm)],[20894,910])).
% 159.48/36.24 thf(20994,plain,(! [A:nat] : (((ord_less_nat @ (sk63 @ A) @ A) != (ord_less_nat @ sk1 @ (suc @ (size_size_list_a @ xs)))))),inference(simp,[status(thm)],[20993])).
% 159.48/36.24 thf(21022,plain,(! [A:nat] : (((sk63 @ A) != sk1) | (A != (suc @ (size_size_list_a @ xs))))),inference(simp,[status(thm)],[20994])).
% 159.48/36.24 thf(21044,plain,(((sk63 @ (suc @ (size_size_list_a @ xs))) != sk1)),inference(simp,[status(thm)],[21022])).
% 159.48/36.24 thf(209,axiom,((! [A:list_nat]: ((list_strict_asc_nat @ A) => (! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_list__strict__asc__trans__le)).
% 159.48/36.24 thf(1069,plain,((! [A:list_nat]: ((list_strict_asc_nat @ A) => (! [B:nat]: ((ord_less_nat @ B @ (size_size_list_nat @ A)) => (! [C:nat]: ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (nth_nat @ A @ C) @ (nth_nat @ A @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
% 159.48/36.24 thf(37010,plain,(($false)),inference(e,[status(thm)],[809,10410,333,962,8639,666,352,20873,892,21040,1823,730,20813,1443,741,1142,523,762,440,511,269,677,385,22076,8370,747,1222,670,13029,1127,782,885,1359,20845,565,257,1287,719,785,917,1055,724,20894,8610,802,344,1832,357,1191,542,2703,559,20981,2857,8615,316,11716,261,9768,817,902,1319,421,756,1109,485,353,1283,905,1151,937,21060,11709,348,2861,956,660,20839,1975,1242,849,8523,307,1074,1206,920,529,19502,1199,381,2093,366,1047,798,334,910,1091,302,349,598,820,297,429,815,407,693,630,275,788,916,847,20819,2433,22015,435,1457,1819,889,1159,682,1281,710,842,13063,1106,493,1210,1089,650,1064,980,1006,388,1118,499,989,1111,1227,471,1160,488,1461,8687,526,13066,8499,1214,590,15897,679,1082,20979,15882,1942,1644,21042,837,1825,457,1002,569,371,1150,1478,1974,9893,911,2505,2497,721,1979,779,1333,343,266,805,508,657,765,1286,11576,953,586,926,633,360,558,1071,8626,888,965,425,8641,1103,824,264,856,733,584,772,1124,259,562,904,975,826,577,391,572,466,1765,20864,20518,1356,672,713,498,2510,1194,2538,274,362,737,303,11438,1439,377,990,1630,1821,621,520,1149,1293,1029,895,983,1926,959,768,1066,8676,851,438,653,1973,20828,455,883,986,306,20939,7366,473,1034,2096,944,1467,795,374,21512,812,20980,939,342,1145,1203,1208,589,663,5785,648,487,617,516,525,557,580,295,1156,887,971,16266,20645,1941,739,21039,1230,310,993,776,14594,12088,872,1225,707,11428,4314,2092,1987,791,331,21041,1262,1085,808,907,1285,1218,1934,10531,1094,1008,314,20519,595,991,2500,744,20289,336,845,627,363,539,482,759,1216,1010,844,771,20846,11514,2532,946,632,9906,1308,1077,1212,272,899,2095,346,536,1045,290,914,716,1161,1116,1133,300,432,1148,867,865,735,833,410,950,835,262,854,1986,305,918,437,897,1197,828,635,532,696,720,13028,13068,728,1236,1129,575,427,1532,596,19528,1976,992,822,850,1004,20548,691,1930,624,22022,337,923,592,21044,496,1069])).
% 159.48/36.24 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 159.48/36.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------