%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP172^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 08:07:03 AM UTC 2026
% Result : Theorem 232.54s 61.17s
% Output : Refutation 228.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP172^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:09:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.57/1.21 % [INFO] Parsing done (437ms).
% 2.57/1.23 % [INFO] Running in sequential loop mode.
% 3.57/1.61 % [INFO] eprover registered as external prover.
% 3.57/1.62 % [INFO] Scanning for conjecture ...
% 3.77/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 342 axioms. Running axiom selection ...
% 4.35/1.91 % [INFO] Axiom selection finished. Selected 326 axioms (removed 16 axioms).
% 4.88/2.12 % [INFO] Problem is higher-order (TPTP THF).
% 5.35/2.15 % [INFO] Type checking passed.
% 5.35/2.15 % [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 ...
% 232.54/61.16 % External prover 'e' found a proof!
% 232.54/61.16 % [INFO] Killing All external provers ...
% 232.54/61.17 % Time passed: 60842ms (effective reasoning time: 59930ms)
% 232.54/61.17 % 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)>
% 232.54/61.17 % Axioms used in derivation (326): fact_281_insert__Nil, fact_251_list__induct4, fact_322_append1__eq__conv, fact_172_not__None__eq, fact_133_add_Oleft__commute, fact_225_neq__Nil__conv, fact_46_RDocument_Oupdate__convs_I4_J, fact_148_add__is__1, fact_18_RObject_Ocases__scheme, fact_56_object__more__extend__id, fact_53_RObject_Oselect__convs_I2_J, fact_80_option_Osize_I3_J, fact_29_nat__induct, fact_132_add__left__imp__eq, fact_131_add__right__imp__eq, fact_83_list_Osize_I3_J, fact_296_bind_Obind__lzero, fact_51_size__neq__size__imp__neq, fact_189_option_OdiscI, fact_128_add__is__0, fact_260_list__induct3, fact_65_RDocument_Ofold__congs_I6_J, fact_297_bind_Obind__lzero, fact_11_RObject_Oinduct, fact_273_n__lists__Nil, fact_121_add__cancel__right__left, fact_5_RObject_Oext__inject, fact_157_option_Osize__gen_I2_J, fact_110_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none, fact_7_old_Onat_Oinject, fact_134_add_Ocommute, fact_317_append__is__Nil__conv, fact_150_gen__length__code_I1_J, fact_294_bind__split, fact_35_document__ptr_Osize_I3_J, fact_240_sorted__wrt_Oinduct, fact_95_document__ptr_Odistinct_I1_J, fact_22_old_Onat_Oinducts, fact_179_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__some, fact_52_RObject_Oselect__convs_I2_J, fact_41_mem__Collect__eq, fact_247_list__induct4, fact_59_RDocument_Oselect__convs_I5_J, fact_293_bind__split, fact_295_bind__split, fact_154_triangle__Suc, fact_163_option_Oinject, fact_191_option_Oexhaust, fact_253_list__induct4, fact_248_list__induct4, fact_214_get__object__ptr__simp2, fact_199_combine__options__cases, fact_140_add_Ocomm__neutral, fact_144_add__Suc__shift, fact_118_zero__eq__add__iff__both__eq__0, fact_266_list__induct2, fact_77_length__0__conv, fact_26_Suc__neq__Zero, fact_298_bind_Obind__lzero, fact_254_list__induct4, fact_92_neq__if__length__neq, fact_209_splice_Osimps_I1_J, fact_81_option_Osize_I3_J, fact_331_rev__nonempty__induct, fact_171_not__Some__eq, fact_206_split__Nil__iff, fact_109_document__ptr_Osize__gen_I2_J, fact_223_list_Oinducts, fact_267_list__induct2, fact_231_splice_Oinduct, fact_117_add__left__cancel, fact_34_document__ptr_Osize__gen_I1_J, fact_196_split__option__all, fact_120_add__cancel__right__right, fact_20_RDocument_Oext__induct, fact_184_option_Odistinct_I1_J, fact_48_size__neq__size__imp__neq, fact_9_RDocument_Oinduct__scheme, fact_315_Nil__is__append__conv, fact_220_list_OdiscI, fact_319_append_Oright__neutral, fact_175_not__None__eq, fact_265_list__induct2, fact_249_list__induct4, fact_102_option_Osize__neq, fact_320_set__decode__inverse, fact_129_gen__length__def, fact_137_group__cancel_Oadd1, fact_84_list_Osize_I3_J, fact_219_list_OdiscI, fact_91_neq__if__length__neq, fact_287_nths__empty, fact_210_splice_Osimps_I1_J, fact_274_n__lists_Osimps_I1_J, fact_75_length__0__conv, fact_321_append1__eq__conv, fact_16_RObject_Oinduct__scheme, fact_6_nat_Oinject, fact_332_rev__nonempty__induct, fact_108_length__code, fact_313_self__append__conv2, fact_156_add__0__iff, fact_263_list__induct3, fact_230_list__induct2_H, fact_224_list_Oinducts, fact_30_nat_OdiscI, fact_50_size__neq__size__imp__neq, fact_164_option_Oinject, fact_252_list__induct4, fact_8_RDocument_Ocases__scheme, fact_217_list_Odistinct_I1_J, fact_222_list_Oexhaust, fact_68_RDocument_Ounfold__congs_I5_J, fact_258_list__induct3, fact_310_append__self__conv2, fact_329_append__eq__Cons__conv, fact_264_list__induct3, fact_291_bind__split__asm, fact_337_append_Oleft__neutral, fact_136_group__cancel_Oadd2, fact_246_list__nonempty__induct, fact_23_old_Onat_Oexhaust, fact_235_shuffles_Oinduct, fact_99_RObject_Oselect__convs_I1_J, fact_185_option_OdiscI, fact_282_nths__singleton, fact_47_size__neq__size__imp__neq, fact_17_RObject_Oinduct__scheme, fact_149_gen__length__code_I1_J, fact_292_bind__split, fact_183_option_Odistinct_I1_J, fact_301_set__decode__zero, fact_193_option_Oinducts, fact_180_option_Odistinct_I1_J, fact_328_Cons__eq__append__conv, conj_2, fact_107_length__code, fact_278_subseqs_Osimps_I1_J, fact_335_append__Nil, fact_14_n__not__Suc__n, fact_145_add__eq__self__zero, fact_176_not__None__eq, fact_135_add_Oassoc, fact_94_Ex__list__of__length, fact_1_cast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r__inject, fact_111_list__ex1__simps_I1_J, fact_302_length__append__singleton, fact_85_list_Osize_I3_J, fact_66_RDocument_Ounfold__congs_I3_J, fact_327_Cons__eq__append__conv, fact_250_list__induct4, fact_333_eq__Nil__appendI, fact_239_sorted__wrt_Oinduct, fact_227_list__induct2_H, fact_208_splice__Nil2, fact_64_RDocument_Ounfold__congs_I6_J, fact_4_RObject_Oext__inject, fact_192_option_Oinducts, fact_195_split__option__ex, fact_28_diff__induct, fact_138_add__mono__thms__linordered__semiring_I4_J, fact_284_nths__nil, fact_309_self__append__conv, fact_27_zero__induct, fact_3_RDocument_Oext__inject, fact_104_option_Osize__gen_I1_J, fact_270_splice_Oelims, fact_119_add__eq__0__iff__both__eq__0, fact_256_list__induct4, fact_325_rev__exhaust, fact_70_RDocument_Ofold__congs_I4_J, fact_124_add_Oright__neutral, fact_10_bot__nat__def, fact_272_n__lists__Nil, fact_279_subseqs_Osimps_I1_J, fact_197_split__option__all, fact_61_RDocument_Oselect__convs_I3_J, fact_160_option_Osize__gen_I2_J, fact_241_remdups__adj_Oinduct, fact_178_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__inv, fact_280_insert__Nil, fact_255_list__induct4, fact_221_list_Oexhaust, fact_289_bind__split__asm, fact_97_document__ptr_Oexhaust, fact_236_shuffles_Oinduct, fact_31_old_Onat_Odistinct_I1_J, fact_25_Zero__neq__Suc, fact_62_RDocument_Oselect__convs_I2_J, fact_153_Euclid__induct, fact_143_nat__arith_Osuc1, fact_45_RDocument_Oupdate__convs_I3_J, fact_306_append__self__conv, fact_307_append__self__conv, fact_130_gen__length__def, fact_261_list__induct3, fact_42_Collect__mem__eq, fact_89_RObject_Osurjective, fact_212_count__list_Osimps_I1_J, fact_73_RDocument_Ofold__congs_I2_J, fact_285_nths__nil, fact_33_nat_Odistinct_I1_J, fact_318_append_Oright__neutral, fact_242_remdups__adj_Oinduct, fact_275_n__lists_Osimps_I1_J, fact_122_add__cancel__left__right, fact_54_document__ptr_Osize__neq, fact_229_list__induct2_H, fact_24_Zero__not__Suc, fact_204_get__document__ptr__simp, fact_336_append__Nil, fact_207_splice__Nil2, fact_125_add_Oleft__neutral, fact_286_nths__empty, fact_288_bind__split__asm, fact_98_RObject_Oselect__convs_I1_J, fact_188_option_OdiscI, fact_39_object__empty, fact_232_splice_Oinduct, fact_74_length__0__conv, fact_152_gen__length__code_I1_J, fact_100_RObject_Oequality, fact_244_successively_Oinduct, fact_334_eq__Nil__appendI, fact_49_size__neq__size__imp__neq, fact_238_remdups__adj_Ocases, fact_93_Ex__list__of__length, fact_303_length__append__singleton, fact_155_verit__sum__simplify, fact_233_induct__list012, fact_79_RDocument_Oequality, fact_177_triangle__0, fact_299_bind_Obind__lzero, fact_259_list__induct3, fact_142_add__Suc, fact_316_append__is__Nil__conv, conj_1, fact_290_bind__split__asm, fact_324_rev__induct, fact_338_append_Oleft__neutral, fact_283_nths__singleton, fact_60_RDocument_Oselect__convs_I4_J, fact_276_product__lists_Osimps_I1_J, fact_44_RDocument_Oupdate__convs_I2_J, fact_19_RObject_Ocases__scheme, fact_269_splice_Oelims, fact_36_put_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def, fact_147_one__is__add, fact_123_add__cancel__left__left, fact_314_Nil__is__append__conv, fact_162_option_Oinject, fact_0_cast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t__inject, fact_116_add__right__cancel, fact_226_neq__Nil__conv, fact_21_not0__implies__Suc, fact_312_self__append__conv2, fact_300_set__encode__empty, fact_201_combine__options__cases, fact_228_list__induct2_H, fact_88_RObject_Osurjective, fact_216_transpose_Ocases, fact_112_list__ex1__simps_I1_J, fact_170_not__Some__eq, fact_114_list__ex1__simps_I1_J, fact_76_length__0__conv, fact_243_successively_Oinduct, fact_63_RDocument_Oselect__convs_I1_J, fact_90_document__ptr_Oinject_I2_J, fact_277_product__lists_Osimps_I1_J, fact_200_combine__options__cases, fact_127_Nat_Oadd__0__right, fact_32_old_Onat_Odistinct_I2_J, fact_87_document__ptr_Osize_I4_J, fact_101_RObject_Oequality, fact_257_list__induct3, fact_262_list__induct3, fact_69_RDocument_Ofold__congs_I3_J, fact_58_is__document__ptr__ref, fact_105_option_Osize__gen_I1_J, fact_237_remdups__adj_Ocases, fact_2_document__ptr_Oinject_I1_J, fact_308_self__append__conv, fact_103_option_Osize__neq, fact_141_comm__monoid__add__class_Oadd__0, fact_38_list__decode_Ocases, fact_190_option_Oexhaust, fact_167_not__Some__eq, fact_213_count__list_Osimps_I1_J, fact_215_transpose_Ocases, fact_12_RObject_Ocases, fact_78_RDocument_Osurjective, fact_268_list__induct2, fact_15_Suc__inject, fact_218_list_Odistinct_I1_J, fact_126_add__Suc__right, fact_40_object__empty, fact_323_rev__induct, fact_205_split__Nil__iff, fact_72_RDocument_Ounfold__congs_I2_J, fact_139_ab__semigroup__add__class_Oadd__ac_I1_J, conj_0, fact_67_RDocument_Ounfold__congs_I4_J, fact_13_zero__reorient, fact_115_is__document__kind__def, fact_245_list__nonempty__induct, fact_326_rev__exhaust, fact_194_split__option__ex, fact_146_plus__nat_Oadd__0, fact_43_RDocument_Oupdate__convs_I1_J, fact_161_option_Osize__gen_I2_J, fact_198_combine__options__cases, fact_234_induct__list012, fact_305_append__Nil2, fact_311_append__self__conv2, fact_96_document__ptr_Oinduct, fact_37_exists__least__lemma, fact_106_option_Osize__gen_I1_J, fact_304_append__Nil2, fact_113_list__ex1__simps_I1_J, fact_71_RDocument_Ofold__congs_I5_J, fact_55_object__more__extend__id, fact_330_append__eq__Cons__conv, fact_86_list_Osize_I3_J, fact_57_RDocument_Oupdate__convs_I5_J, fact_151_gen__length__code_I1_J, fact_82_option_Osize_I3_J
% 232.54/61.17 % No. of inferences in proof: 941
% 232.54/61.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 60842 ms resp. 59930 ms w/o parsing
% 228.49/61.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 228.49/61.55 thf(heap_S1465075775_j_k_l_type, type, heap_S1465075775_j_k_l: $tType).
% 228.49/61.55 thf(option1749760295_j_k_l_type, type, option1749760295_j_k_l: $tType).
% 228.49/61.55 thf(rObjec1413572695_j_k_l_type, type, rObjec1413572695_j_k_l: $tType).
% 228.49/61.55 thf(object945351580_d_e_f_type, type, object945351580_d_e_f: $tType).
% 228.49/61.55 thf(option841825948on_j_k_type, type, option841825948on_j_k: $tType).
% 228.49/61.55 thf(rObjec1617416918on_j_k_type, type, rObjec1617416918on_j_k: $tType).
% 228.49/61.55 thf(rDocum326988203on_j_k_type, type, rDocum326988203on_j_k: $tType).
% 228.49/61.55 thf(list_l118626078tr_b_c_type, type, list_l118626078tr_b_c: $tType).
% 228.49/61.55 thf(list_n282880152tr_b_c_type, type, list_n282880152tr_b_c: $tType).
% 228.49/61.55 thf(node_p1234578834tr_b_c_type, type, node_p1234578834tr_b_c: $tType).
% 228.49/61.55 thf(option2026120038on_j_k_type, type, option2026120038on_j_k: $tType).
% 228.49/61.55 thf(option1330818496tr_d_e_type, type, option1330818496tr_d_e: $tType).
% 228.49/61.55 thf(fset_d1663890464tr_d_e_type, type, fset_d1663890464tr_d_e: $tType).
% 228.49/61.55 thf(sum_su1221287958on_j_k_type, type, sum_su1221287958on_j_k: $tType).
% 228.49/61.55 thf(docume1935157360tr_d_e_type, type, docume1935157360tr_d_e: $tType).
% 228.49/61.55 thf(sum_su1576157353tr_d_e_type, type, sum_su1576157353tr_d_e: $tType).
% 228.49/61.55 thf(rObjec103300152t_unit_type, type, rObjec103300152t_unit: $tType).
% 228.49/61.55 thf(option_element_ptr_a_type, type, option_element_ptr_a: $tType).
% 228.49/61.55 thf(list_list_char_type, type, list_list_char: $tType).
% 228.49/61.55 thf(element_ptr_a_type, type, element_ptr_a: $tType).
% 228.49/61.55 thf(list_char_type, type, list_char: $tType).
% 228.49/61.55 thf(set_nat_type, type, set_nat: $tType).
% 228.49/61.55 thf(product_unit_type, type, product_unit: $tType).
% 228.49/61.55 thf(char_type, type, char: $tType).
% 228.49/61.55 thf(nat_type, type, nat: $tType).
% 228.49/61.55 thf(rDocum427676485on_j_k_decl, type, rDocum427676485on_j_k: (product_unit > (list_char > (option_element_ptr_a > (list_n282880152tr_b_c > (option2026120038on_j_k > rDocum326988203on_j_k)))))).
% 228.49/61.55 thf(discon866287741on_j_k_decl, type, discon866287741on_j_k: (rObjec1617416918on_j_k > list_n282880152tr_b_c)).
% 228.49/61.55 thf(discon442323090on_j_k_decl, type, discon442323090on_j_k: ((list_n282880152tr_b_c > list_n282880152tr_b_c) > (rObjec1617416918on_j_k > rObjec1617416918on_j_k))).
% 228.49/61.55 thf(doctyp814403297on_j_k_decl, type, doctyp814403297on_j_k: (rObjec1617416918on_j_k > list_char)).
% 228.49/61.55 thf(doctyp68000440on_j_k_decl, type, doctyp68000440on_j_k: ((list_char > list_char) > (rObjec1617416918on_j_k > rObjec1617416918on_j_k))).
% 228.49/61.55 thf(docume1175131570on_j_k_decl, type, docume1175131570on_j_k: (rObjec1617416918on_j_k > option_element_ptr_a)).
% 228.49/61.55 thf(docume244715269on_j_k_decl, type, docume244715269on_j_k: ((option_element_ptr_a > option_element_ptr_a) > (rObjec1617416918on_j_k > rObjec1617416918on_j_k))).
% 228.49/61.55 thf(more_c1453068134on_j_k_decl, type, more_c1453068134on_j_k: (rObjec1617416918on_j_k > option2026120038on_j_k)).
% 228.49/61.55 thf(more_u1044474223_c_a_b_decl, type, more_u1044474223_c_a_b: ((option2026120038on_j_k > option2026120038on_j_k) > (rObjec1617416918on_j_k > rObjec1617416918on_j_k))).
% 228.49/61.55 thf(nothin757132294on_j_k_decl, type, nothin757132294on_j_k: (rObjec1617416918on_j_k > product_unit)).
% 228.49/61.55 thf(nothin1105341917on_j_k_decl, type, nothin1105341917on_j_k: ((product_unit > product_unit) > (rObjec1617416918on_j_k > rObjec1617416918on_j_k))).
% 228.49/61.55 thf(cast_D1252964113_h_i_l_decl, type, cast_D1252964113_h_i_l: (rObjec1617416918on_j_k > rObjec1413572695_j_k_l)).
% 228.49/61.55 thf(cast_O1034441233_j_k_l_decl, type, cast_O1034441233_j_k_l: (rObjec1413572695_j_k_l > option841825948on_j_k)).
% 228.49/61.55 thf(docume1070804385_j_k_l_decl, type, docume1070804385_j_k_l: (heap_S1465075775_j_k_l > fset_d1663890464tr_d_e)).
% 228.49/61.55 thf(get_D_1192261494_j_k_l_decl, type, get_D_1192261494_j_k_l: (docume1935157360tr_d_e > (heap_S1465075775_j_k_l > option841825948on_j_k))).
% 228.49/61.55 thf(is_doc1417632087_j_k_l_decl, type, is_doc1417632087_j_k_l: (rObjec1413572695_j_k_l > $o)).
% 228.49/61.55 thf(put_D_2126422573_h_i_l_decl, type, put_D_2126422573_h_i_l: (docume1935157360tr_d_e > (rObjec1617416918on_j_k > (heap_S1465075775_j_k_l > heap_S1465075775_j_k_l)))).
% 228.49/61.55 thf(cast_d1608273229_b_c_f_decl, type, cast_d1608273229_b_c_f: (docume1935157360tr_d_e > object945351580_d_e_f)).
% 228.49/61.55 thf(docume1825929374tr_d_e_decl, type, docume1825929374tr_d_e: (sum_su1576157353tr_d_e > docume1935157360tr_d_e)).
% 228.49/61.55 thf(docume1511108976tr_d_e_decl, type, docume1511108976tr_d_e: (nat > docume1935157360tr_d_e)).
% 228.49/61.55 thf(docume1799427087tr_d_e_decl, type, docume1799427087tr_d_e: ((sum_su1576157353tr_d_e > nat) > (docume1935157360tr_d_e > nat))).
% 228.49/61.55 thf(is_doc2037328342tr_d_e_decl, type, is_doc2037328342tr_d_e: (docume1935157360tr_d_e > $o)).
% 228.49/61.55 thf(plus_plus_nat_decl, type, plus_plus_nat: (nat > (nat > nat))).
% 228.49/61.55 thf(zero_zero_nat_decl, type, zero_zero_nat: nat).
% 228.49/61.55 thf(append846395565tr_b_c_decl, type, append846395565tr_b_c: (list_n282880152tr_b_c > (list_n282880152tr_b_c > list_n282880152tr_b_c))).
% 228.49/61.55 thf(append_char_decl, type, append_char: (list_char > (list_char > list_char))).
% 228.49/61.55 thf(count_2128515342tr_b_c_decl, type, count_2128515342tr_b_c: (list_n282880152tr_b_c > (node_p1234578834tr_b_c > nat))).
% 228.49/61.55 thf(count_list_char_decl, type, count_list_char: (list_char > (char > nat))).
% 228.49/61.55 thf(gen_le170886571tr_b_c_decl, type, gen_le170886571tr_b_c: (nat > (list_l118626078tr_b_c > nat))).
% 228.49/61.55 thf(gen_length_list_char_decl, type, gen_length_list_char: (nat > (list_list_char > nat))).
% 228.49/61.55 thf(gen_le955068453tr_b_c_decl, type, gen_le955068453tr_b_c: (nat > (list_n282880152tr_b_c > nat))).
% 228.49/61.55 thf(gen_length_char_decl, type, gen_length_char: (nat > (list_char > nat))).
% 228.49/61.55 thf(insert678865070tr_b_c_decl, type, insert678865070tr_b_c: (node_p1234578834tr_b_c > (list_n282880152tr_b_c > list_n282880152tr_b_c))).
% 228.49/61.55 thf(insert_char_decl, type, insert_char: (char > (list_char > list_char))).
% 228.49/61.55 thf(cons_l1809994318tr_b_c_decl, type, cons_l1809994318tr_b_c: (list_n282880152tr_b_c > (list_l118626078tr_b_c > list_l118626078tr_b_c))).
% 228.49/61.55 thf(cons_list_char_decl, type, cons_list_char: (list_char > (list_list_char > list_list_char))).
% 228.49/61.55 thf(cons_n413985352tr_b_c_decl, type, cons_n413985352tr_b_c: (node_p1234578834tr_b_c > (list_n282880152tr_b_c > list_n282880152tr_b_c))).
% 228.49/61.55 thf(cons_char_decl, type, cons_char: (char > (list_char > list_char))).
% 228.49/61.55 thf(nil_li198338206tr_b_c_decl, type, nil_li198338206tr_b_c: list_l118626078tr_b_c).
% 228.49/61.55 thf(nil_list_char_decl, type, nil_list_char: list_list_char).
% 228.49/61.55 thf(nil_no279930520tr_b_c_decl, type, nil_no279930520tr_b_c: list_n282880152tr_b_c).
% 228.49/61.55 thf(nil_char_decl, type, nil_char: list_char).
% 228.49/61.55 thf(list_e529904353tr_b_c_decl, type, list_e529904353tr_b_c: ((list_n282880152tr_b_c > $o) > (list_l118626078tr_b_c > $o))).
% 228.49/61.55 thf(list_ex1_list_char_decl, type, list_ex1_list_char: ((list_char > $o) > (list_list_char > $o))).
% 228.49/61.55 thf(list_e469495899tr_b_c_decl, type, list_e469495899tr_b_c: ((node_p1234578834tr_b_c > $o) > (list_n282880152tr_b_c > $o))).
% 228.49/61.55 thf(list_ex1_char_decl, type, list_ex1_char: ((char > $o) > (list_char > $o))).
% 228.49/61.55 thf(n_list1807568544tr_b_c_decl, type, n_list1807568544tr_b_c: (nat > (list_n282880152tr_b_c > list_l118626078tr_b_c))).
% 228.49/61.55 thf(n_lists_char_decl, type, n_lists_char: (nat > (list_char > list_list_char))).
% 228.49/61.55 thf(nths_n1256675478tr_b_c_decl, type, nths_n1256675478tr_b_c: (list_n282880152tr_b_c > (set_nat > list_n282880152tr_b_c))).
% 228.49/61.55 thf(nths_char_decl, type, nths_char: (list_char > (set_nat > list_char))).
% 228.49/61.55 thf(produc1509350401tr_b_c_decl, type, produc1509350401tr_b_c: (list_l118626078tr_b_c > list_l118626078tr_b_c)).
% 228.49/61.55 thf(product_lists_char_decl, type, product_lists_char: (list_list_char > list_list_char)).
% 228.49/61.55 thf(splice1294941035tr_b_c_decl, type, splice1294941035tr_b_c: (list_n282880152tr_b_c > (list_n282880152tr_b_c > list_n282880152tr_b_c))).
% 228.49/61.55 thf(splice_char_decl, type, splice_char: (list_char > (list_char > list_char))).
% 228.49/61.55 thf(subseq1828679783tr_b_c_decl, type, subseq1828679783tr_b_c: (list_n282880152tr_b_c > list_l118626078tr_b_c)).
% 228.49/61.55 thf(subseqs_char_decl, type, subseqs_char: (list_char > list_list_char)).
% 228.49/61.55 thf(suc_decl, type, suc: (nat > nat)).
% 228.49/61.55 thf(size_s724035844tr_d_e_decl, type, size_s724035844tr_d_e: (docume1935157360tr_d_e > nat)).
% 228.49/61.55 thf(size_s9369994tr_b_c_decl, type, size_s9369994tr_b_c: (list_l118626078tr_b_c > nat)).
% 228.49/61.55 thf(size_s2008079621t_char_decl, type, size_s2008079621t_char: (list_list_char > nat)).
% 228.49/61.55 thf(size_s2106487044tr_b_c_decl, type, size_s2106487044tr_b_c: (list_n282880152tr_b_c > nat)).
% 228.49/61.55 thf(size_size_list_char_decl, type, size_size_list_char: (list_char > nat)).
% 228.49/61.55 thf(size_s1129684517_ptr_a_decl, type, size_s1129684517_ptr_a: (option_element_ptr_a > nat)).
% 228.49/61.55 thf(size_s7667464on_j_k_decl, type, size_s7667464on_j_k: (option841825948on_j_k > nat)).
% 228.49/61.55 thf(size_s1129069050on_j_k_decl, type, size_s1129069050on_j_k: (option2026120038on_j_k > nat)).
% 228.49/61.55 thf(nat_set_decode_decl, type, nat_set_decode: (nat > set_nat)).
% 228.49/61.55 thf(nat_set_encode_decl, type, nat_set_encode: (set_nat > nat)).
% 228.49/61.55 thf(nat_triangle_decl, type, nat_triangle: (nat > nat)).
% 228.49/61.55 thf(rObjec1303043984on_j_k_decl, type, rObjec1303043984on_j_k: (product_unit > (rDocum326988203on_j_k > rObjec1617416918on_j_k))).
% 228.49/61.55 thf(rObjec730108904t_unit_decl, type, rObjec730108904t_unit: (product_unit > (product_unit > rObjec103300152t_unit))).
% 228.49/61.55 thf(extend1066431834on_j_k_decl, type, extend1066431834on_j_k: (rObjec103300152t_unit > (rDocum326988203on_j_k > rObjec1617416918on_j_k))).
% 228.49/61.55 thf(extend_Product_unit_decl, type, extend_Product_unit: (rObjec103300152t_unit > (product_unit > rObjec103300152t_unit))).
% 228.49/61.55 thf(more_R1625109589on_j_k_decl, type, more_R1625109589on_j_k: (rObjec1617416918on_j_k > rDocum326988203on_j_k)).
% 228.49/61.55 thf(more_Product_unit_decl, type, more_Product_unit: (rObjec103300152t_unit > product_unit)).
% 228.49/61.55 thf(nothin1567949605on_j_k_decl, type, nothin1567949605on_j_k: (rObjec1617416918on_j_k > product_unit)).
% 228.49/61.55 thf(nothing_Product_unit_decl, type, nothing_Product_unit: (rObjec103300152t_unit > product_unit)).
% 228.49/61.55 thf(get_O_623850005_j_k_l_decl, type, get_O_623850005_j_k_l: (object945351580_d_e_f > (heap_S1465075775_j_k_l > option1749760295_j_k_l))).
% 228.49/61.55 thf(put_O_834343516_j_k_l_decl, type, put_O_834343516_j_k_l: (object945351580_d_e_f > (rObjec1413572695_j_k_l > (heap_S1465075775_j_k_l > heap_S1465075775_j_k_l)))).
% 228.49/61.55 thf(bind_e22036734_ptr_a_decl, type, bind_e22036734_ptr_a: (option_element_ptr_a > ((element_ptr_a > option_element_ptr_a) > option_element_ptr_a))).
% 228.49/61.55 thf(bind_e1012152651on_j_k_decl, type, bind_e1012152651on_j_k: (option_element_ptr_a > ((element_ptr_a > option2026120038on_j_k) > option2026120038on_j_k))).
% 228.49/61.55 thf(bind_S287509021_ptr_a_decl, type, bind_S287509021_ptr_a: (option2026120038on_j_k > ((sum_su1221287958on_j_k > option_element_ptr_a) > option_element_ptr_a))).
% 228.49/61.55 thf(bind_S607117548on_j_k_decl, type, bind_S607117548on_j_k: (option2026120038on_j_k > ((sum_su1221287958on_j_k > option2026120038on_j_k) > option2026120038on_j_k))).
% 228.49/61.55 thf(none_element_ptr_a_decl, type, none_element_ptr_a: option_element_ptr_a).
% 228.49/61.55 thf(none_R1587534007on_j_k_decl, type, none_R1587534007on_j_k: option841825948on_j_k).
% 228.49/61.55 thf(none_S1393028981on_j_k_decl, type, none_S1393028981on_j_k: option2026120038on_j_k).
% 228.49/61.55 thf(some_element_ptr_a_decl, type, some_element_ptr_a: (element_ptr_a > option_element_ptr_a)).
% 228.49/61.55 thf(some_R67702331on_j_k_decl, type, some_R67702331on_j_k: (rObjec1617416918on_j_k > option841825948on_j_k)).
% 228.49/61.55 thf(some_S1960742641on_j_k_decl, type, some_S1960742641on_j_k: (sum_su1221287958on_j_k > option2026120038on_j_k)).
% 228.49/61.55 thf(size_o1591053974_ptr_a_decl, type, size_o1591053974_ptr_a: ((element_ptr_a > nat) > (option_element_ptr_a > nat))).
% 228.49/61.55 thf(size_o26122489on_j_k_decl, type, size_o26122489on_j_k: ((rObjec1617416918on_j_k > nat) > (option841825948on_j_k > nat))).
% 228.49/61.55 thf(size_o1777465779on_j_k_decl, type, size_o1777465779on_j_k: ((sum_su1221287958on_j_k > nat) > (option2026120038on_j_k > nat))).
% 228.49/61.55 thf(bot_bo1111241908tr_d_e_decl, type, bot_bo1111241908tr_d_e: fset_d1663890464tr_d_e).
% 228.49/61.55 thf(bot_bot_nat_decl, type, bot_bot_nat: nat).
% 228.49/61.55 thf(bot_bot_set_nat_decl, type, bot_bot_set_nat: set_nat).
% 228.49/61.55 thf(product_Unity_decl, type, product_Unity: product_unit).
% 228.49/61.55 thf(collect_nat_decl, type, collect_nat: ((nat > $o) > set_nat)).
% 228.49/61.55 thf(type_w92696601_j_k_l_decl, type, type_w92696601_j_k_l: (heap_S1465075775_j_k_l > $o)).
% 228.49/61.55 thf(member_nat_decl, type, member_nat: (nat > (set_nat > $o))).
% 228.49/61.55 thf(h_decl, type, h: heap_S1465075775_j_k_l).
% 228.49/61.55 thf(h2_decl, type, h2: heap_S1465075775_j_k_l).
% 228.49/61.55 thf(sk1_decl, type, sk1: (nat > (nat > nat))).
% 228.49/61.55 thf(sk2_decl, type, sk2: (nat > (nat > nat))).
% 228.49/61.55 thf(sk3_decl, type, sk3: ((nat > (nat > $o)) > nat)).
% 228.49/61.55 thf(sk4_decl, type, sk4: ((nat > (nat > $o)) > nat)).
% 228.49/61.55 thf(sk5_decl, type, sk5: ((nat > (nat > $o)) > nat)).
% 228.49/61.55 thf(sk6_decl, type, sk6: ((nat > (nat > $o)) > nat)).
% 228.49/61.55 thf(sk7_decl, type, sk7: ((nat > (nat > $o)) > nat)).
% 228.49/61.55 thf(sk8_decl, type, sk8: (nat > nat)).
% 228.49/61.55 thf(sk9_decl, type, sk9: ((nat > $o) > nat)).
% 228.49/61.55 thf(sk11_decl, type, sk11: ((nat > $o) > nat)).
% 228.49/61.55 thf(sk23_decl, type, sk23: (nat > list_char)).
% 228.49/61.55 thf(sk27_decl, type, sk27: (nat > list_n282880152tr_b_c)).
% 228.49/61.55 thf(sk164_decl, type, sk164: (rObjec103300152t_unit > product_unit)).
% 228.49/61.55 thf(sk1_def, definition, sk1 = (@+ [A:(nat > (nat > nat))]: ! [B:nat,C:nat]: ((A @ B @ (plus_plus_nat @ B @ C)) = C)) ).
% 228.49/61.55 thf(sk2_def, definition, sk2 = (@+ [A:(nat > (nat > nat))]: ! [B:nat,C:nat]: ((A @ C @ (plus_plus_nat @ B @ C)) = B)) ).
% 228.49/61.55 thf(sk3_def, definition, sk3 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ (! [C:nat]: ((A @ B @ C) = (A @ C @ B))))) ).
% 228.49/61.55 thf(sk4_def, definition, sk4 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ ((A @ (sk3 @ A) @ B) = (A @ B @ (sk3 @ A))))) ).
% 228.49/61.55 thf(sk5_def, definition, sk5 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ (A @ B @ zero_zero_nat))) ).
% 228.49/61.55 thf(sk6_def, definition, sk6 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ (! [C:nat]: ((A @ B @ C) => (A @ B @ (plus_plus_nat @ B @ C)))))) ).
% 228.49/61.55 thf(sk7_def, definition, sk7 = (^ [A:(nat > (nat > $o))]: (@+ [B:nat]: ~ ((A @ (sk6 @ A) @ B) => (A @ (sk6 @ A) @ (plus_plus_nat @ (sk6 @ A) @ B))))) ).
% 228.49/61.55 thf(sk8_def, definition, sk8 = (@+ [A:(nat > nat)]: ! [B:nat]: ((A @ (suc @ B)) = B)) ).
% 228.49/61.55 thf(sk9_def, definition, sk9 = (^ [A:(nat > $o)]: (@+ [B:nat]: ~ ((A @ B) => (A @ (suc @ B))))) ).
% 228.49/61.55 thf(sk11_def, definition, sk11 = (^ [A:(nat > $o)]: (@+ [B:nat]: ~ ((A @ B) => (A @ (suc @ B))))) ).
% 228.49/61.55 thf(sk23_def, definition, sk23 = (^ [A:nat]: (@+ [B:list_char]: ((size_size_list_char @ B) = A))) ).
% 228.49/61.55 thf(sk27_def, definition, sk27 = (^ [A:nat]: (@+ [B:list_n282880152tr_b_c]: ((size_s2106487044tr_b_c @ B) = A))) ).
% 228.49/61.55 thf(sk164_def, definition, sk164 = (^ [A:rObjec103300152t_unit]: (@+ [B:product_unit]: (A = (rObjec730108904t_unit @ B @ product_Unity)))) ).
% 228.49/61.55 thf(83,axiom,(((docume1070804385_j_k_l @ h) = bot_bo1111241908tr_d_e)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 228.49/61.55 thf(645,plain,(((docume1070804385_j_k_l @ h) = bot_bo1111241908tr_d_e)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
% 228.49/61.55 thf(124,axiom,((! [A:nat]: ((A != zero_zero_nat) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_not0__implies__Suc)).
% 228.49/61.55 thf(809,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])).
% 228.49/61.55 thf(224,axiom,((! [A:list_n282880152tr_b_c]: ((splice1294941035tr_b_c @ A @ nil_no279930520tr_b_c) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_splice__Nil2)).
% 228.49/61.55 thf(1337,plain,((! [A:list_n282880152tr_b_c]: ((splice1294941035tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
% 228.49/61.55 thf(192,axiom,((! [A:(option2026120038on_j_k > $o),B:option_element_ptr_a,C:(element_ptr_a > option2026120038on_j_k)]: ((A @ (bind_e1012152651on_j_k @ B @ C)) = (((B = none_element_ptr_a) => (A @ none_S1393028981on_j_k)) & ! [D:element_ptr_a]: ((B = (some_element_ptr_a @ D)) => (A @ (C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_bind__split)).
% 228.49/61.55 thf(1168,plain,((! [A:(option2026120038on_j_k > $o),B:option_element_ptr_a,C:(element_ptr_a > option2026120038on_j_k)]: ((A @ (bind_e1012152651on_j_k @ B @ (C))) = (((B = none_element_ptr_a) => (A @ none_S1393028981on_j_k)) & ! [D:element_ptr_a]: ((B = (some_element_ptr_a @ D)) => (A @ (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
% 228.49/61.55 thf(246,axiom,((! [A:list_n282880152tr_b_c,B:list_char,C:list_char,D:list_n282880152tr_b_c,E:(list_n282880152tr_b_c > (list_char > (list_char > (list_n282880152tr_b_c > $o))))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_s2106487044tr_b_c @ D)) => ((E @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_no279930520tr_b_c) => ((! [F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c,H:char,I:list_char,J:char,K:list_char,L:node_p1234578834tr_b_c,M:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_s2106487044tr_b_c @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_n413985352tr_b_c @ F @ G) @ (cons_char @ H @ I) @ (cons_char @ J @ K) @ (cons_n413985352tr_b_c @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_list__induct4)).
% 228.49/61.55 thf(1454,plain,((! [A:list_n282880152tr_b_c,B:list_char,C:list_char,D:list_n282880152tr_b_c,E:(list_n282880152tr_b_c > (list_char > (list_char > (list_n282880152tr_b_c > $o))))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_s2106487044tr_b_c @ D)) => ((E @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_no279930520tr_b_c) => ((! [F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c,H:char,I:list_char,J:char,K:list_char,L:node_p1234578834tr_b_c,M:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_s2106487044tr_b_c @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_n413985352tr_b_c @ F @ G) @ (cons_char @ H @ I) @ (cons_char @ J @ K) @ (cons_n413985352tr_b_c @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])).
% 228.49/61.55 thf(180,axiom,(((subseq1828679783tr_b_c @ nil_no279930520tr_b_c) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_subseqs_Osimps_I1_J)).
% 228.49/61.55 thf(1121,plain,(((subseq1828679783tr_b_c @ nil_no279930520tr_b_c) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])).
% 228.49/61.55 thf(1122,plain,(((cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c) = (subseq1828679783tr_b_c @ nil_no279930520tr_b_c))),inference(lifteq,[status(thm)],[1121])).
% 228.49/61.55 thf(170,axiom,(((produc1509350401tr_b_c @ nil_li198338206tr_b_c) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_product__lists_Osimps_I1_J)).
% 228.49/61.55 thf(1066,plain,(((produc1509350401tr_b_c @ nil_li198338206tr_b_c) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
% 228.49/61.55 thf(1067,plain,(((cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c) = (produc1509350401tr_b_c @ nil_li198338206tr_b_c))),inference(lifteq,[status(thm)],[1066])).
% 228.49/61.55 thf(1995,plain,(((subseq1828679783tr_b_c @ nil_no279930520tr_b_c) = (produc1509350401tr_b_c @ nil_li198338206tr_b_c))),inference(rewrite,[status(thm)],[1122,1067])).
% 228.49/61.55 thf(8,axiom,((! [A:nat]: ((nat_set_encode @ (nat_set_decode @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_set__decode__inverse)).
% 228.49/61.55 thf(347,plain,((! [A:nat]: ((nat_set_encode @ (nat_set_decode @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 228.49/61.55 thf(131,axiom,((! [A:nat]: (is_doc2037328342tr_d_e @ (docume1511108976tr_d_e @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_is__document__ptr__ref)).
% 228.49/61.55 thf(845,plain,((! [A:nat]: (is_doc2037328342tr_d_e @ (docume1511108976tr_d_e @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])).
% 228.49/61.55 thf(846,plain,(! [A:nat] : ((is_doc2037328342tr_d_e @ (docume1511108976tr_d_e @ A)))),inference(cnf,[status(esa)],[845])).
% 228.49/61.55 thf(4,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_add__Suc__shift)).
% 228.49/61.55 thf(333,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 228.49/61.55 thf(143,axiom,((! [A:list_char,B:list_char]: ((A = B) => (A = (append_char @ nil_char @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_eq__Nil__appendI)).
% 228.49/61.55 thf(890,plain,((! [A:list_char,B:list_char]: ((A = B) => (A = (append_char @ nil_char @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
% 228.49/61.55 thf(891,plain,(! [B:list_char,A:list_char] : ((~ (A = B)) | (A = (append_char @ nil_char @ B)))),inference(cnf,[status(esa)],[890])).
% 228.49/61.55 thf(892,plain,(! [B:list_char,A:list_char] : ((A != B) | (A = (append_char @ nil_char @ B)))),inference(lifteq,[status(thm)],[891])).
% 228.49/61.55 thf(893,plain,(! [A:list_char] : (((append_char @ nil_char @ A) = A))),inference(simp,[status(thm)],[892])).
% 228.49/61.55 thf(152,axiom,((is_doc1417632087_j_k_l = (^ [A:rObjec1413572695_j_k_l]: ((cast_O1034441233_j_k_l @ A) != none_R1587534007on_j_k)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_is__document__kind__def)).
% 228.49/61.55 thf(940,plain,(((is_doc1417632087_j_k_l) = (^ [A:rObjec1413572695_j_k_l]: ~ ((cast_O1034441233_j_k_l @ A) = none_R1587534007on_j_k)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
% 228.49/61.55 thf(941,plain,(((is_doc1417632087_j_k_l) = (^ [A:rObjec1413572695_j_k_l]: ~ ((cast_O1034441233_j_k_l @ A) = none_R1587534007on_j_k)))),inference(lifteq,[status(thm)],[940])).
% 228.49/61.55 thf(60,axiom,((! [A:(sum_su1221287958on_j_k > nat),B:sum_su1221287958on_j_k]: ((size_o1777465779on_j_k @ A @ (some_S1960742641on_j_k @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_option_Osize__gen_I2_J)).
% 228.49/61.55 thf(555,plain,((! [A:(sum_su1221287958on_j_k > nat),B:sum_su1221287958on_j_k]: ((size_o1777465779on_j_k @ (A) @ (some_S1960742641on_j_k @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
% 228.49/61.55 thf(88,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_nat_Odistinct_I1_J)).
% 228.49/61.55 thf(666,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
% 228.49/61.55 thf(45,axiom,(((size_s7667464on_j_k @ none_R1587534007on_j_k) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_option_Osize_I3_J)).
% 228.49/61.55 thf(481,plain,(((size_s7667464on_j_k @ none_R1587534007on_j_k) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
% 228.49/61.55 thf(9,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_add__cancel__right__right)).
% 228.49/61.55 thf(350,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 228.49/61.55 thf(351,plain,(! [B:nat,A:nat] : (((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(cnf,[status(esa)],[350])).
% 228.49/61.55 thf(352,plain,(! [B:nat,A:nat] : (((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(lifteq,[status(thm)],[351])).
% 228.49/61.55 thf(295,axiom,((! [A:list_char,B:list_char,C:list_char,D:list_n282880152tr_b_c,E:(list_char > (list_char > (list_char > (list_n282880152tr_b_c > $o))))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_s2106487044tr_b_c @ D)) => ((E @ nil_char @ nil_char @ nil_char @ nil_no279930520tr_b_c) => ((! [F:char,G:list_char,H:char,I:list_char,J:char,K:list_char,L:node_p1234578834tr_b_c,M:list_n282880152tr_b_c]: (((size_size_list_char @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_s2106487044tr_b_c @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_char @ H @ I) @ (cons_char @ J @ K) @ (cons_n413985352tr_b_c @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_list__induct4)).
% 228.49/61.55 thf(1750,plain,((! [A:list_char,B:list_char,C:list_char,D:list_n282880152tr_b_c,E:(list_char > (list_char > (list_char > (list_n282880152tr_b_c > $o))))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_s2106487044tr_b_c @ D)) => ((E @ nil_char @ nil_char @ nil_char @ nil_no279930520tr_b_c) => ((! [F:char,G:list_char,H:char,I:list_char,J:char,K:list_char,L:node_p1234578834tr_b_c,M:list_n282880152tr_b_c]: (((size_size_list_char @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_s2106487044tr_b_c @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_char @ H @ I) @ (cons_char @ J @ K) @ (cons_n413985352tr_b_c @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])).
% 228.49/61.55 thf(239,axiom,((! [A:option2026120038on_j_k,B:(option2026120038on_j_k > (option_element_ptr_a > $o)),C:option_element_ptr_a]: (((A = none_S1393028981on_j_k) => (B @ A @ C)) => (((C = none_element_ptr_a) => (B @ A @ C)) => ((! [D:sum_su1221287958on_j_k,E:element_ptr_a]: ((A = (some_S1960742641on_j_k @ D)) => ((C = (some_element_ptr_a @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_combine__options__cases)).
% 228.49/61.55 thf(1406,plain,((! [A:option2026120038on_j_k,B:(option2026120038on_j_k > (option_element_ptr_a > $o)),C:option_element_ptr_a]: (((A = none_S1393028981on_j_k) => (B @ A @ C)) => (((C = none_element_ptr_a) => (B @ A @ C)) => ((! [D:sum_su1221287958on_j_k,E:element_ptr_a]: ((A = (some_S1960742641on_j_k @ D)) => ((C = (some_element_ptr_a @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
% 228.49/61.55 thf(93,axiom,((! [A:sum_su1576157353tr_d_e]: ((size_s724035844tr_d_e @ (docume1825929374tr_d_e @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_document__ptr_Osize_I4_J)).
% 228.49/61.55 thf(681,plain,((! [A:sum_su1576157353tr_d_e]: ((size_s724035844tr_d_e @ (docume1825929374tr_d_e @ A)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
% 228.49/61.55 thf(682,plain,(! [A:sum_su1576157353tr_d_e] : (((size_s724035844tr_d_e @ (docume1825929374tr_d_e @ A)) = (suc @ zero_zero_nat)))),inference(cnf,[status(esa)],[681])).
% 228.49/61.55 thf(683,plain,(! [A:sum_su1576157353tr_d_e] : (((size_s724035844tr_d_e @ (docume1825929374tr_d_e @ A)) = (suc @ zero_zero_nat)))),inference(lifteq,[status(thm)],[682])).
% 228.49/61.55 thf(105,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:option_element_ptr_a,D:(option_element_ptr_a > option_element_ptr_a),E:(option_element_ptr_a > option_element_ptr_a)]: ((A = B) => (((docume1175131570on_j_k @ B) = C) => ((! [F:option_element_ptr_a]: ((F = C) => ((D @ F) = (E @ F)))) => ((docume244715269on_j_k @ D @ A) = (docume244715269on_j_k @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_RDocument_Ounfold__congs_I4_J)).
% 228.49/61.55 thf(730,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:option_element_ptr_a,D:(option_element_ptr_a > option_element_ptr_a),E:(option_element_ptr_a > option_element_ptr_a)]: ((A = B) => (((docume1175131570on_j_k @ B) = C) => ((! [F:option_element_ptr_a]: ((F = C) => ((D @ F) = (E @ F)))) => ((docume244715269on_j_k @ (D) @ A) = (docume244715269on_j_k @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
% 228.49/61.55 thf(171,axiom,((! [A:list_char]: ((A != nil_char) = (? [B:char,C:list_char]: (A = (cons_char @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_neq__Nil__conv)).
% 228.49/61.55 thf(1068,plain,((! [A:list_char]: ((~ (A = nil_char)) = (? [B:char,C:list_char]: (A = (cons_char @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
% 228.49/61.55 thf(172,axiom,((! [A:set_nat]: ((nths_char @ nil_char @ A) = nil_char))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_nths__nil)).
% 228.49/61.55 thf(1071,plain,((! [A:set_nat]: ((nths_char @ nil_char @ A) = nil_char))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
% 228.49/61.55 thf(1072,plain,(! [A:set_nat] : (((nths_char @ nil_char @ A) = nil_char))),inference(cnf,[status(esa)],[1071])).
% 228.49/61.55 thf(1073,plain,(! [A:set_nat] : (((nths_char @ nil_char @ A) = nil_char))),inference(lifteq,[status(thm)],[1072])).
% 228.49/61.55 thf(199,axiom,((! [A:list_list_char]: ((A != nil_list_char) => ((! [B:list_list_char]: (A != (cons_list_char @ nil_char @ B))) => (~ (! [B:char,C:list_char,D:list_list_char]: (A != (cons_list_char @ (cons_char @ B @ C) @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_transpose_Ocases)).
% 228.49/61.55 thf(1205,plain,((! [A:list_list_char]: ((~ (A = nil_list_char)) => ((! [B:list_list_char]: ~ (A = (cons_list_char @ nil_char @ B))) => (~ (! [B:char,C:list_char,D:list_list_char]: ~ (A = (cons_list_char @ (cons_char @ B @ C) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])).
% 228.49/61.55 thf(18,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_add__left__cancel)).
% 228.49/61.55 thf(377,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 228.49/61.55 thf(378,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(cnf,[status(esa)],[377])).
% 228.49/61.55 thf(379,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(lifteq,[status(thm)],[378])).
% 228.49/61.55 thf(71,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ A) != (size_s2106487044tr_b_c @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_size__neq__size__imp__neq)).
% 228.49/61.55 thf(597,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((~ ((size_s2106487044tr_b_c @ A) = (size_s2106487044tr_b_c @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
% 228.49/61.55 thf(54,axiom,((! [A:rObjec103300152t_unit]: ~ (! [B:product_unit,C:product_unit]: (A != (rObjec730108904t_unit @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_RObject_Ocases__scheme)).
% 228.49/61.55 thf(523,plain,((! [A:rObjec103300152t_unit]: ~ (! [B:product_unit,C:product_unit]: ~ (A = (rObjec730108904t_unit @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
% 228.49/61.55 thf(66,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)) | ((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_one__is__add)).
% 228.49/61.55 thf(582,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)) | ((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
% 228.49/61.55 thf(76,axiom,((! [A:docume1935157360tr_d_e]: ((size_s724035844tr_d_e @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_document__ptr_Osize__neq)).
% 228.49/61.55 thf(614,plain,((! [A:docume1935157360tr_d_e]: ~ ((size_s724035844tr_d_e @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
% 228.49/61.55 thf(91,axiom,((! [A:nat]: ((gen_le170886571tr_b_c @ A @ nil_li198338206tr_b_c) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_gen__length__code_I1_J)).
% 228.49/61.55 thf(675,plain,((! [A:nat]: ((gen_le170886571tr_b_c @ A @ nil_li198338206tr_b_c) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])).
% 228.49/61.55 thf(676,plain,(! [A:nat] : (((gen_le170886571tr_b_c @ A @ nil_li198338206tr_b_c) = A))),inference(cnf,[status(esa)],[675])).
% 228.49/61.55 thf(677,plain,(! [A:nat] : (((gen_le170886571tr_b_c @ A @ nil_li198338206tr_b_c) = A))),inference(lifteq,[status(thm)],[676])).
% 228.49/61.55 thf(174,axiom,((! [A:(list_char > $o),B:list_char]: ((A @ nil_char) => ((! [C:char,D:list_char]: ((A @ D) => (A @ (cons_char @ C @ D)))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_list_Oinducts)).
% 228.49/61.55 thf(1078,plain,((! [A:(list_char > $o),B:list_char]: ((A @ nil_char) => ((! [C:char,D:list_char]: ((A @ D) => (A @ (cons_char @ C @ D)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
% 228.49/61.55 thf(20,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_add__0__iff)).
% 228.49/61.55 thf(384,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 228.49/61.55 thf(185,axiom,((! [A:list_n282880152tr_b_c]: ((append846395565tr_b_c @ A @ nil_no279930520tr_b_c) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_append_Oright__neutral)).
% 228.49/61.55 thf(1135,plain,((! [A:list_n282880152tr_b_c]: ((append846395565tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
% 228.49/61.55 thf(1136,plain,(! [A:list_n282880152tr_b_c] : (((append846395565tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(cnf,[status(esa)],[1135])).
% 228.49/61.55 thf(1137,plain,(! [A:list_n282880152tr_b_c] : (((append846395565tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(lifteq,[status(thm)],[1136])).
% 228.49/61.55 thf(7,axiom,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_triangle__Suc)).
% 228.49/61.55 thf(344,plain,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 228.49/61.55 thf(345,plain,(! [A:nat] : (((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),inference(cnf,[status(esa)],[344])).
% 228.49/61.55 thf(346,plain,(! [A:nat] : (((plus_plus_nat @ (nat_triangle @ A) @ (suc @ A)) = (nat_triangle @ (suc @ A))))),inference(lifteq,[status(thm)],[345])).
% 228.49/61.55 thf(6,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_add__Suc__right)).
% 228.49/61.55 thf(341,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 228.49/61.55 thf(342,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),inference(cnf,[status(esa)],[341])).
% 228.49/61.55 thf(343,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),inference(lifteq,[status(thm)],[342])).
% 228.49/61.55 thf(2020,plain,(! [A:nat] : (((suc @ (plus_plus_nat @ (nat_triangle @ A) @ A)) = (nat_triangle @ (suc @ A))))),inference(rewrite,[status(thm)],[346,343])).
% 228.49/61.55 thf(122,axiom,(((nat_triangle @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_triangle__0)).
% 228.49/61.55 thf(802,plain,(((nat_triangle @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
% 228.49/61.55 thf(803,plain,(((nat_triangle @ zero_zero_nat) = zero_zero_nat)),inference(lifteq,[status(thm)],[802])).
% 228.49/61.55 thf(2034,plain,(! [A:nat] : (((suc @ (plus_plus_nat @ zero_zero_nat @ A)) = (nat_triangle @ (suc @ A))) | ((nat_triangle @ zero_zero_nat) != (nat_triangle @ A)))),inference(paramod_ordered,[status(thm)],[803,2020])).
% 228.49/61.55 thf(2035,plain,(((suc @ (plus_plus_nat @ zero_zero_nat @ zero_zero_nat)) = (nat_triangle @ (suc @ zero_zero_nat)))),inference(pattern_uni,[status(thm)],[2034:[bind(A, $thf(zero_zero_nat))]])).
% 228.49/61.55 thf(49,axiom,((! [A:nat,B:nat]: ((A = (suc @ B)) => (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_nat_OdiscI)).
% 228.49/61.55 thf(498,plain,((! [A:nat,B:nat]: ((A = (suc @ B)) => (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
% 228.49/61.55 thf(499,plain,((! [A:nat]: ((? [B:nat]: (A = (suc @ B))) => (~ (A = zero_zero_nat))))),inference(miniscope,[status(thm)],[498])).
% 228.49/61.55 thf(500,plain,(! [B:nat,A:nat] : ((~ (A = (suc @ B))) | (~ (A = zero_zero_nat)))),inference(cnf,[status(esa)],[499])).
% 228.49/61.55 thf(501,plain,(! [B:nat,A:nat] : ((A != (suc @ B)) | (A != zero_zero_nat))),inference(lifteq,[status(thm)],[500])).
% 228.49/61.55 thf(502,plain,(! [A:nat] : (((suc @ A) != zero_zero_nat))),inference(simp,[status(thm)],[501])).
% 228.49/61.55 thf(2030,plain,(! [B:nat,A:nat] : (((nat_triangle @ (suc @ A)) != zero_zero_nat) | ((suc @ (plus_plus_nat @ (nat_triangle @ A) @ A)) != (suc @ B)))),inference(paramod_ordered,[status(thm)],[2020,502])).
% 228.49/61.55 thf(2031,plain,(! [A:nat] : (((nat_triangle @ (suc @ A)) != zero_zero_nat))),inference(pattern_uni,[status(thm)],[2030:[bind(A, $thf(D)),bind(B, $thf(plus_plus_nat @ (nat_triangle @ D) @ D))]])).
% 228.49/61.55 thf(2049,plain,(! [A:nat] : (((nat_triangle @ (suc @ A)) != zero_zero_nat))),inference(simp,[status(thm)],[2031])).
% 228.49/61.55 thf(2051,plain,(! [B:nat,A:nat] : (((nat_triangle @ (nat_triangle @ (suc @ A))) != zero_zero_nat) | ((suc @ (plus_plus_nat @ (nat_triangle @ A) @ A)) != (suc @ B)))),inference(paramod_ordered,[status(thm)],[2020,2049])).
% 228.49/61.55 thf(2052,plain,(! [A:nat] : (((nat_triangle @ (nat_triangle @ (suc @ A))) != zero_zero_nat))),inference(pattern_uni,[status(thm)],[2051:[bind(A, $thf(D)),bind(B, $thf(plus_plus_nat @ (nat_triangle @ D) @ D))]])).
% 228.49/61.55 thf(2058,plain,(! [A:nat] : (((nat_triangle @ (nat_triangle @ (suc @ A))) != zero_zero_nat))),inference(simp,[status(thm)],[2052])).
% 228.49/61.55 thf(2087,plain,(! [A:nat] : (((nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ zero_zero_nat)))) != zero_zero_nat) | ((suc @ (plus_plus_nat @ zero_zero_nat @ zero_zero_nat)) != (suc @ A)))),inference(paramod_ordered,[status(thm)],[2035,2058])).
% 228.49/61.55 thf(2088,plain,(((nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ zero_zero_nat)))) != zero_zero_nat)),inference(pattern_uni,[status(thm)],[2087:[bind(A, $thf(plus_plus_nat @ zero_zero_nat @ zero_zero_nat))]])).
% 228.49/61.55 thf(2160,plain,(((nat_triangle @ (nat_triangle @ (suc @ (plus_plus_nat @ zero_zero_nat @ zero_zero_nat)))) != zero_zero_nat) | ((nat_triangle @ (suc @ zero_zero_nat)) != (nat_triangle @ (suc @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[2035,2088])).
% 228.49/61.55 thf(2161,plain,(((nat_triangle @ (nat_triangle @ (suc @ (plus_plus_nat @ zero_zero_nat @ zero_zero_nat)))) != zero_zero_nat)),inference(pattern_uni,[status(thm)],[2160:[]])).
% 228.49/61.55 thf(10,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_add_Oleft__neutral)).
% 228.49/61.55 thf(353,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 228.49/61.55 thf(354,plain,(! [A:nat] : (((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(cnf,[status(esa)],[353])).
% 228.49/61.55 thf(355,plain,(! [A:nat] : (((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(lifteq,[status(thm)],[354])).
% 228.49/61.55 thf(2351,plain,(((nat_triangle @ (nat_triangle @ (suc @ zero_zero_nat))) != zero_zero_nat)),inference(rewrite,[status(thm)],[2161,355])).
% 228.49/61.55 thf(2354,plain,(! [A:nat] : (((nat_triangle @ (suc @ (plus_plus_nat @ (nat_triangle @ A) @ A))) != zero_zero_nat) | ((nat_triangle @ (suc @ A)) != (nat_triangle @ (suc @ zero_zero_nat))))),inference(paramod_ordered,[status(thm)],[2020,2351])).
% 228.49/61.55 thf(2355,plain,(((nat_triangle @ (suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat))) != zero_zero_nat)),inference(pattern_uni,[status(thm)],[2354:[bind(A, $thf(zero_zero_nat))]])).
% 228.49/61.55 thf(22,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Nat_Oadd__0__right)).
% 228.49/61.55 thf(392,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 228.49/61.55 thf(393,plain,(! [A:nat] : (((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(cnf,[status(esa)],[392])).
% 228.49/61.55 thf(394,plain,(! [A:nat] : (((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(lifteq,[status(thm)],[393])).
% 228.49/61.55 thf(2491,plain,(((nat_triangle @ (suc @ (nat_triangle @ zero_zero_nat))) != zero_zero_nat)),inference(rewrite,[status(thm)],[2355,394])).
% 228.49/61.55 thf(2493,plain,(! [A:nat] : (((suc @ (plus_plus_nat @ (nat_triangle @ A) @ A)) != zero_zero_nat) | ((nat_triangle @ (suc @ A)) != (nat_triangle @ (suc @ (nat_triangle @ zero_zero_nat)))))),inference(paramod_ordered,[status(thm)],[2020,2491])).
% 228.49/61.55 thf(2494,plain,(((suc @ (plus_plus_nat @ (nat_triangle @ (nat_triangle @ zero_zero_nat)) @ (nat_triangle @ zero_zero_nat))) != zero_zero_nat)),inference(pattern_uni,[status(thm)],[2493:[bind(A, $thf(nat_triangle @ zero_zero_nat))]])).
% 228.49/61.55 thf(2607,plain,(((suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat)) != zero_zero_nat)),inference(rewrite,[status(thm)],[2494,803])).
% 228.49/61.55 thf(40,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Suc__inject)).
% 228.49/61.55 thf(455,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
% 228.49/61.55 thf(456,plain,(! [B:nat,A:nat] : ((~ ((suc @ A) = (suc @ B))) | (A = B))),inference(cnf,[status(esa)],[455])).
% 228.49/61.55 thf(457,plain,(! [B:nat,A:nat] : (((suc @ A) != (suc @ B)) | (A = B))),inference(lifteq,[status(thm)],[456])).
% 228.49/61.55 thf(458,plain,((? [A:(nat > nat)]: ! [B:nat]: ((A @ (suc @ B)) = B))),inference(detectInverse,[status(thm)],[457])).
% 228.49/61.55 thf(459,plain,(! [A:nat] : (((sk8 @ (suc @ A)) = A))),inference(cnf,[status(esa)],[458])).
% 228.49/61.55 thf(4884,plain,(! [A:nat] : (((sk8 @ (suc @ A)) = A))),inference(lifteq,[status(thm)],[459])).
% 228.49/61.55 thf(120,axiom,(((nat_set_encode @ bot_bot_set_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_set__encode__empty)).
% 228.49/61.55 thf(797,plain,(((nat_set_encode @ bot_bot_set_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
% 228.49/61.55 thf(206,axiom,((! [A:option2026120038on_j_k]: ((! [B:sum_su1221287958on_j_k]: (A != (some_S1960742641on_j_k @ B))) = (A = none_S1393028981on_j_k)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_not__Some__eq)).
% 228.49/61.55 thf(1233,plain,((! [A:option2026120038on_j_k]: ((! [B:sum_su1221287958on_j_k]: ~ (A = (some_S1960742641on_j_k @ B))) = (A = none_S1393028981on_j_k)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])).
% 228.49/61.55 thf(126,axiom,((! [A:(rObjec103300152t_unit > $o),B:rObjec103300152t_unit]: ((! [C:product_unit,D:product_unit]: (A @ (rObjec730108904t_unit @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_RObject_Oinduct__scheme)).
% 228.49/61.55 thf(814,plain,((! [A:(rObjec103300152t_unit > $o),B:rObjec103300152t_unit]: ((! [C:product_unit,D:product_unit]: (A @ (rObjec730108904t_unit @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
% 228.49/61.55 thf(97,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_zero__reorient)).
% 228.49/61.55 thf(698,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
% 228.49/61.55 thf(327,axiom,((! [A:list_char,B:(list_char > $o)]: ((A != nil_char) => ((! [C:char]: (B @ (cons_char @ C @ nil_char))) => ((! [C:char,D:list_char]: ((D != nil_char) => ((B @ D) => (B @ (cons_char @ C @ D))))) => (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_list__nonempty__induct)).
% 228.49/61.55 thf(1919,plain,((! [A:list_char,B:(list_char > $o)]: ((~ (A = nil_char)) => ((! [C:char]: (B @ (cons_char @ C @ nil_char))) => ((! [C:char,D:list_char]: ((~ (D = nil_char)) => ((B @ D) => (B @ (cons_char @ C @ D))))) => (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])).
% 228.49/61.55 thf(225,axiom,((! [A:list_n282880152tr_b_c]: ((splice1294941035tr_b_c @ nil_no279930520tr_b_c @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_splice_Osimps_I1_J)).
% 228.49/61.55 thf(1340,plain,((! [A:list_n282880152tr_b_c]: ((splice1294941035tr_b_c @ nil_no279930520tr_b_c @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
% 228.49/61.55 thf(1341,plain,(! [A:list_n282880152tr_b_c] : (((splice1294941035tr_b_c @ nil_no279930520tr_b_c @ A) = A))),inference(cnf,[status(esa)],[1340])).
% 228.49/61.55 thf(1342,plain,(! [A:list_n282880152tr_b_c] : (((splice1294941035tr_b_c @ nil_no279930520tr_b_c @ A) = A))),inference(lifteq,[status(thm)],[1341])).
% 228.49/61.55 thf(278,axiom,((! [A:product_unit,B:rDocum326988203on_j_k]: ((nothin1567949605on_j_k @ (rObjec1303043984on_j_k @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_RObject_Oselect__convs_I1_J)).
% 228.49/61.55 thf(1640,plain,((! [A:product_unit,B:rDocum326988203on_j_k]: ((nothin1567949605on_j_k @ (rObjec1303043984on_j_k @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])).
% 228.49/61.55 thf(2165,plain,(! [A:nat] : (((nat_triangle @ (nat_triangle @ (suc @ (plus_plus_nat @ (nat_triangle @ A) @ A)))) != zero_zero_nat) | ((nat_triangle @ (suc @ A)) != (nat_triangle @ (suc @ zero_zero_nat))))),inference(paramod_ordered,[status(thm)],[2020,2088])).
% 228.49/61.55 thf(2166,plain,(((nat_triangle @ (nat_triangle @ (suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat)))) != zero_zero_nat)),inference(pattern_uni,[status(thm)],[2165:[bind(A, $thf(zero_zero_nat))]])).
% 228.49/61.55 thf(2524,plain,(((nat_triangle @ (nat_triangle @ (suc @ (nat_triangle @ zero_zero_nat)))) != zero_zero_nat)),inference(rewrite,[status(thm)],[2166,394])).
% 228.49/61.55 thf(2528,plain,(! [A:nat] : (((nat_triangle @ (suc @ (plus_plus_nat @ (nat_triangle @ A) @ A))) != zero_zero_nat) | ((nat_triangle @ (suc @ A)) != (nat_triangle @ (suc @ (nat_triangle @ zero_zero_nat)))))),inference(paramod_ordered,[status(thm)],[2020,2524])).
% 228.49/61.55 thf(2529,plain,(((nat_triangle @ (suc @ (plus_plus_nat @ (nat_triangle @ (nat_triangle @ zero_zero_nat)) @ (nat_triangle @ zero_zero_nat)))) != zero_zero_nat)),inference(pattern_uni,[status(thm)],[2528:[bind(A, $thf(nat_triangle @ zero_zero_nat))]])).
% 228.49/61.55 thf(3313,plain,(((nat_triangle @ (suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat))) != zero_zero_nat)),inference(rewrite,[status(thm)],[2529,803])).
% 228.49/61.55 thf(169,axiom,((! [A:char,B:list_char,C:list_char,D:list_char]: (((cons_char @ A @ B) = (append_char @ C @ D)) = (((C = nil_char) & ((cons_char @ A @ B) = D)) | ? [E:list_char]: (((cons_char @ A @ E) = C) & (B = (append_char @ E @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Cons__eq__append__conv)).
% 228.49/61.55 thf(1063,plain,((! [A:char,B:list_char,C:list_char,D:list_char]: (((cons_char @ A @ B) = (append_char @ C @ D)) = (((C = nil_char) & ((cons_char @ A @ B) = D)) | ? [E:list_char]: (((cons_char @ A @ E) = C) & (B = (append_char @ E @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
% 228.49/61.55 thf(89,axiom,((! [A:sum_su1221287958on_j_k,B:sum_su1221287958on_j_k]: (((some_S1960742641on_j_k @ A) = (some_S1960742641on_j_k @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_option_Oinject)).
% 228.49/61.55 thf(670,plain,((! [A:sum_su1221287958on_j_k,B:sum_su1221287958on_j_k]: (((some_S1960742641on_j_k @ A) = (some_S1960742641on_j_k @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
% 228.49/61.55 thf(231,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((A = (append846395565tr_b_c @ B @ A)) = (B = nil_no279930520tr_b_c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_self__append__conv2)).
% 228.49/61.55 thf(1359,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((A = (append846395565tr_b_c @ B @ A)) = (B = nil_no279930520tr_b_c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])).
% 228.49/61.55 thf(320,axiom,((! [A:(list_char > $o),B:list_char]: ((A @ nil_char) => ((! [C:char,D:list_char]: ((A @ D) => (A @ (append_char @ D @ (cons_char @ C @ nil_char))))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_rev__induct)).
% 228.49/61.55 thf(1887,plain,((! [A:(list_char > $o),B:list_char]: ((A @ nil_char) => ((! [C:char,D:list_char]: ((A @ D) => (A @ (append_char @ D @ (cons_char @ C @ nil_char))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])).
% 228.49/61.55 thf(85,axiom,((size_s2106487044tr_b_c = (gen_le955068453tr_b_c @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_length__code)).
% 228.49/61.55 thf(651,plain,(((size_s2106487044tr_b_c) = (gen_le955068453tr_b_c @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
% 228.49/61.55 thf(323,axiom,((! [A:list_char,B:char,C:list_char]: ((A = (cons_char @ B @ C)) => (A != nil_char)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_list_OdiscI)).
% 228.49/61.55 thf(1904,plain,((! [A:list_char,B:char,C:list_char]: ((A = (cons_char @ B @ C)) => (~ (A = nil_char))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])).
% 228.49/61.55 thf(287,axiom,((! [A:char,B:list_char]: (nil_char != (cons_char @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_list_Odistinct_I1_J)).
% 228.49/61.55 thf(1700,plain,((! [A:char,B:list_char]: ~ (nil_char = (cons_char @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])).
% 228.49/61.55 thf(1701,plain,((~ (? [A:char,B:list_char]: (nil_char = (cons_char @ A @ B))))),inference(miniscope,[status(thm)],[1700])).
% 228.49/61.55 thf(1702,plain,(! [B:list_char,A:char] : ((~ (nil_char = (cons_char @ A @ B))))),inference(cnf,[status(esa)],[1701])).
% 228.49/61.55 thf(1703,plain,(! [B:list_char,A:char] : (((cons_char @ A @ B) != nil_char))),inference(lifteq,[status(thm)],[1702])).
% 228.49/61.55 thf(204,axiom,((! [A:list_char]: ((splice_char @ nil_char @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_splice_Osimps_I1_J)).
% 228.49/61.55 thf(1226,plain,((! [A:list_char]: ((splice_char @ nil_char @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
% 228.49/61.55 thf(1227,plain,(! [A:list_char] : (((splice_char @ nil_char @ A) = A))),inference(cnf,[status(esa)],[1226])).
% 228.49/61.55 thf(1228,plain,(! [A:list_char] : (((splice_char @ nil_char @ A) = A))),inference(lifteq,[status(thm)],[1227])).
% 228.49/61.55 thf(275,axiom,((! [A:(sum_su1221287958on_j_k > nat)]: ((size_o1777465779on_j_k @ A @ none_S1393028981on_j_k) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_option_Osize__gen_I1_J)).
% 228.49/61.55 thf(1623,plain,((! [A:(sum_su1221287958on_j_k > nat)]: ((size_o1777465779on_j_k @ (A) @ none_S1393028981on_j_k) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])).
% 228.49/61.55 thf(103,axiom,((! [A:element_ptr_a,B:element_ptr_a]: (((some_element_ptr_a @ A) = (some_element_ptr_a @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_option_Oinject)).
% 228.49/61.55 thf(724,plain,((! [A:element_ptr_a,B:element_ptr_a]: (((some_element_ptr_a @ A) = (some_element_ptr_a @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
% 228.49/61.55 thf(50,axiom,(((nat_set_decode @ zero_zero_nat) = bot_bot_set_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_set__decode__zero)).
% 228.49/61.55 thf(503,plain,(((nat_set_decode @ zero_zero_nat) = bot_bot_set_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
% 228.49/61.55 thf(504,plain,(((nat_set_decode @ zero_zero_nat) = bot_bot_set_nat)),inference(lifteq,[status(thm)],[503])).
% 228.49/61.55 thf(184,axiom,((! [A:list_char,B:char]: ((size_size_list_char @ (append_char @ A @ (cons_char @ B @ nil_char))) = (suc @ (size_size_list_char @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_length__append__singleton)).
% 228.49/61.55 thf(1132,plain,((! [A:list_char,B:char]: ((size_size_list_char @ (append_char @ A @ (cons_char @ B @ nil_char))) = (suc @ (size_size_list_char @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
% 228.49/61.55 thf(41,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k]: (((some_R67702331on_j_k @ A) = (some_R67702331on_j_k @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_option_Oinject)).
% 228.49/61.55 thf(460,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k]: (((some_R67702331on_j_k @ A) = (some_R67702331on_j_k @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
% 228.49/61.55 thf(68,axiom,((! [A:(rObjec1617416918on_j_k > nat)]: ((size_o26122489on_j_k @ A @ none_R1587534007on_j_k) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_option_Osize__gen_I1_J)).
% 228.49/61.55 thf(587,plain,((! [A:(rObjec1617416918on_j_k > nat)]: ((size_o26122489on_j_k @ (A) @ none_R1587534007on_j_k) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
% 228.49/61.55 thf(24,axiom,((! [A:(sum_su1576157353tr_d_e > nat),B:sum_su1576157353tr_d_e]: ((docume1799427087tr_d_e @ A @ (docume1825929374tr_d_e @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_document__ptr_Osize__gen_I2_J)).
% 228.49/61.55 thf(400,plain,((! [A:(sum_su1576157353tr_d_e > nat),B:sum_su1576157353tr_d_e]: ((docume1799427087tr_d_e @ (A) @ (docume1825929374tr_d_e @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 228.49/61.55 thf(401,plain,(! [B:sum_su1576157353tr_d_e,A:(sum_su1576157353tr_d_e > nat)] : (((docume1799427087tr_d_e @ (A) @ (docume1825929374tr_d_e @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(cnf,[status(esa)],[400])).
% 228.49/61.55 thf(402,plain,(! [B:sum_su1576157353tr_d_e,A:(sum_su1576157353tr_d_e > nat)] : (((docume1799427087tr_d_e @ (A) @ (docume1825929374tr_d_e @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(lifteq,[status(thm)],[401])).
% 228.49/61.55 thf(3403,plain,(! [B:sum_su1576157353tr_d_e,A:(sum_su1576157353tr_d_e > nat)] : (((docume1799427087tr_d_e @ (A) @ (docume1825929374tr_d_e @ B)) = (suc @ (plus_plus_nat @ (A @ B) @ zero_zero_nat))))),inference(rewrite,[status(thm)],[402,343])).
% 228.49/61.55 thf(3408,plain,(! [B:sum_su1576157353tr_d_e,A:(sum_su1576157353tr_d_e > nat)] : (((docume1799427087tr_d_e @ (A) @ (docume1825929374tr_d_e @ B)) != zero_zero_nat) | ((suc @ (plus_plus_nat @ (A @ B) @ zero_zero_nat)) != (suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat))))),inference(paramod_ordered,[status(thm)],[3403,2607])).
% 228.49/61.55 thf(3505,plain,(! [A:sum_su1576157353tr_d_e] : (((docume1799427087tr_d_e @ (^ [B:sum_su1576157353tr_d_e]: (nat_triangle @ zero_zero_nat)) @ (docume1825929374tr_d_e @ A)) != zero_zero_nat))),inference(pre_uni,[status(thm)],[3408:[bind(A, $thf(^ [C:sum_su1576157353tr_d_e]: (nat_triangle @ zero_zero_nat))),bind(B, $thf(B))]])).
% 228.49/61.55 thf(3572,plain,(! [A:sum_su1576157353tr_d_e] : (((docume1799427087tr_d_e @ (^ [B:sum_su1576157353tr_d_e]: (nat_triangle @ zero_zero_nat)) @ (docume1825929374tr_d_e @ A)) != zero_zero_nat))),inference(simp,[status(thm)],[3505])).
% 228.49/61.55 thf(3612,plain,(! [A:sum_su1576157353tr_d_e] : (((docume1799427087tr_d_e @ (^ [B:sum_su1576157353tr_d_e]: (zero_zero_nat)) @ (docume1825929374tr_d_e @ A)) != zero_zero_nat))),inference(rewrite,[status(thm)],[3572,803])).
% 228.49/61.55 thf(251,axiom,((((!) @ option_element_ptr_a) = (^ [A:(option_element_ptr_a > $o)]: ((A @ none_element_ptr_a) & ! [B:element_ptr_a]: (A @ (some_element_ptr_a @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_split__option__all)).
% 228.49/61.55 thf(1479,plain,((((!) @ option_element_ptr_a) = (^ [A:(option_element_ptr_a > $o)]: ((A @ none_element_ptr_a) & ! [B:element_ptr_a]: (A @ (some_element_ptr_a @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])).
% 228.49/61.55 thf(178,axiom,((! [A:list_n282880152tr_b_c,B:node_p1234578834tr_b_c]: ((size_s2106487044tr_b_c @ (append846395565tr_b_c @ A @ (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c))) = (suc @ (size_s2106487044tr_b_c @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_length__append__singleton)).
% 228.49/61.55 thf(1115,plain,((! [A:list_n282880152tr_b_c,B:node_p1234578834tr_b_c]: ((size_s2106487044tr_b_c @ (append846395565tr_b_c @ A @ (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c))) = (suc @ (size_s2106487044tr_b_c @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
% 228.49/61.55 thf(232,axiom,(((size_s1129069050on_j_k @ none_S1393028981on_j_k) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_option_Osize_I3_J)).
% 228.49/61.55 thf(1362,plain,(((size_s1129069050on_j_k @ none_S1393028981on_j_k) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
% 228.49/61.55 thf(81,axiom,((! [A:list_char,B:list_char]: (((size_size_list_char @ A) != (size_size_list_char @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_neq__if__length__neq)).
% 228.49/61.55 thf(638,plain,((! [A:list_char,B:list_char]: ((~ ((size_size_list_char @ A) = (size_size_list_char @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
% 228.49/61.55 thf(134,axiom,((! [A:option2026120038on_j_k]: ((size_s1129069050on_j_k @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_option_Osize__neq)).
% 228.49/61.55 thf(853,plain,((! [A:option2026120038on_j_k]: ~ ((size_s1129069050on_j_k @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
% 228.49/61.55 thf(288,axiom,((! [A:node_p1234578834tr_b_c,B:list_n282880152tr_b_c]: (nil_no279930520tr_b_c != (cons_n413985352tr_b_c @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_list_Odistinct_I1_J)).
% 228.49/61.55 thf(1704,plain,((! [A:node_p1234578834tr_b_c,B:list_n282880152tr_b_c]: ~ (nil_no279930520tr_b_c = (cons_n413985352tr_b_c @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])).
% 228.49/61.55 thf(31,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => ((! [D:nat]: (A @ D @ zero_zero_nat)) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ D @ (plus_plus_nat @ D @ E)))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Euclid__induct)).
% 228.49/61.55 thf(421,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => ((! [D:nat]: (A @ D @ zero_zero_nat)) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ D @ (plus_plus_nat @ D @ E)))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 228.49/61.55 thf(109,axiom,((gen_le955068453tr_b_c = (^ [A:nat,B:list_n282880152tr_b_c]: (plus_plus_nat @ A @ (size_s2106487044tr_b_c @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_gen__length__def)).
% 228.49/61.55 thf(756,plain,(((gen_le955068453tr_b_c) = (^ [A:nat,B:list_n282880152tr_b_c]: (plus_plus_nat @ A @ (size_s2106487044tr_b_c @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
% 228.49/61.55 thf(290,axiom,((! [A:list_char,B:list_char]: (((append_char @ A @ B) = A) = (B = nil_char)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_append__self__conv)).
% 228.49/61.55 thf(1714,plain,((! [A:list_char,B:list_char]: (((append_char @ A @ B) = A) = (B = nil_char)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])).
% 228.49/61.55 thf(306,axiom,((! [A:list_char]: ((nths_char @ A @ bot_bot_set_nat) = nil_char))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_nths__empty)).
% 228.49/61.55 thf(1809,plain,((! [A:list_char]: ((nths_char @ A @ bot_bot_set_nat) = nil_char))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])).
% 228.49/61.55 thf(1810,plain,(! [A:list_char] : (((nths_char @ A @ bot_bot_set_nat) = nil_char))),inference(cnf,[status(esa)],[1809])).
% 228.49/61.55 thf(1811,plain,(! [A:list_char] : (((nths_char @ A @ bot_bot_set_nat) = nil_char))),inference(lifteq,[status(thm)],[1810])).
% 228.49/61.55 thf(324,axiom,((! [A:list_char]: ((splice_char @ A @ nil_char) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_splice__Nil2)).
% 228.49/61.55 thf(1909,plain,((! [A:list_char]: ((splice_char @ A @ nil_char) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])).
% 228.49/61.55 thf(1910,plain,(! [A:list_char] : (((splice_char @ A @ nil_char) = A))),inference(cnf,[status(esa)],[1909])).
% 228.49/61.55 thf(1911,plain,(! [A:list_char] : (((splice_char @ A @ nil_char) = A))),inference(lifteq,[status(thm)],[1910])).
% 228.49/61.55 thf(17,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add__cancel__left__left)).
% 228.49/61.55 thf(374,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 228.49/61.55 thf(375,plain,(! [B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(cnf,[status(esa)],[374])).
% 228.49/61.55 thf(376,plain,(! [B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(lifteq,[status(thm)],[375])).
% 228.49/61.55 thf(646,plain,(((docume1070804385_j_k_l @ h) = bot_bo1111241908tr_d_e)),inference(lifteq,[status(thm)],[645])).
% 228.49/61.55 thf(312,axiom,((! [A:(node_p1234578834tr_b_c > $o)]: ~ (list_e469495899tr_b_c @ A @ nil_no279930520tr_b_c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_list__ex1__simps_I1_J)).
% 228.49/61.55 thf(1828,plain,((! [A:(node_p1234578834tr_b_c > $o)]: ~ (list_e469495899tr_b_c @ (A) @ nil_no279930520tr_b_c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])).
% 228.49/61.55 thf(151,axiom,((! [A:(option_element_ptr_a > $o),B:option_element_ptr_a,C:(element_ptr_a > option_element_ptr_a)]: ((A @ (bind_e22036734_ptr_a @ B @ C)) = (~ (((B = none_element_ptr_a) & ~ (A @ none_element_ptr_a)) | ? [D:element_ptr_a]: ((B = (some_element_ptr_a @ D)) & ~ (A @ (C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_bind__split__asm)).
% 228.49/61.55 thf(937,plain,((! [A:(option_element_ptr_a > $o),B:option_element_ptr_a,C:(element_ptr_a > option_element_ptr_a)]: ((A @ (bind_e22036734_ptr_a @ B @ (C))) = (~ (((B = none_element_ptr_a) & ~ (A @ none_element_ptr_a)) | ? [D:element_ptr_a]: ((B = (some_element_ptr_a @ D)) & ~ (A @ (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
% 228.49/61.55 thf(215,axiom,((! [A:list_char,B:char,C:list_char,D:char]: (((append_char @ A @ (cons_char @ B @ nil_char)) = (append_char @ C @ (cons_char @ D @ nil_char))) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_append1__eq__conv)).
% 228.49/61.55 thf(1283,plain,((! [A:list_char,B:char,C:list_char,D:char]: (((append_char @ A @ (cons_char @ B @ nil_char)) = (append_char @ C @ (cons_char @ D @ nil_char))) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])).
% 228.49/61.55 thf(128,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_old_Onat_Odistinct_I2_J)).
% 228.49/61.55 thf(821,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])).
% 228.49/61.55 thf(236,axiom,((! [A:(list_char > $o),B:list_char]: ((A @ nil_char) => ((! [C:char]: (A @ (cons_char @ C @ nil_char))) => ((! [C:char,D:char,E:list_char]: (((C = D) => (A @ (cons_char @ C @ E))) => (((C != D) => (A @ (cons_char @ D @ E))) => (A @ (cons_char @ C @ (cons_char @ D @ E)))))) => (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_remdups__adj_Oinduct)).
% 228.49/61.55 thf(1383,plain,((! [A:(list_char > $o),B:list_char]: ((A @ nil_char) => ((! [C:char]: (A @ (cons_char @ C @ nil_char))) => ((! [C:char,D:char,E:list_char]: (((C = D) => (A @ (cons_char @ C @ E))) => (((~ (C = D)) => (A @ (cons_char @ D @ E))) => (A @ (cons_char @ C @ (cons_char @ D @ E)))))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
% 228.49/61.55 thf(64,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat]: (A @ D @ zero_zero_nat)) => ((! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_diff__induct)).
% 228.49/61.55 thf(574,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat]: (A @ D @ zero_zero_nat)) => ((! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
% 228.49/61.55 thf(23,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_add__right__imp__eq)).
% 228.49/61.55 thf(395,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 228.49/61.55 thf(396,plain,(! [C:nat,B:nat,A:nat] : ((~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B))) | (A = C))),inference(cnf,[status(esa)],[395])).
% 228.49/61.55 thf(397,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ A @ B) != (plus_plus_nat @ C @ B)) | (A = C))),inference(lifteq,[status(thm)],[396])).
% 228.49/61.55 thf(201,axiom,((! [A:(rObjec103300152t_unit > $o),B:rObjec103300152t_unit]: ((! [C:product_unit]: (A @ (rObjec730108904t_unit @ C @ product_Unity))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_RObject_Oinduct)).
% 228.49/61.55 thf(1215,plain,((! [A:(rObjec103300152t_unit > $o),B:rObjec103300152t_unit]: ((! [C:product_unit]: (A @ (rObjec730108904t_unit @ C @ product_Unity))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
% 228.49/61.55 thf(244,axiom,((! [A:list_char]: ((A != nil_char) => (~ (! [B:char,C:list_char]: (A != (cons_char @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_list_Oexhaust)).
% 228.49/61.55 thf(1447,plain,((! [A:list_char]: ((~ (A = nil_char)) => (~ (! [B:char,C:list_char]: ~ (A = (cons_char @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
% 228.49/61.55 thf(138,axiom,((! [A:rObjec1617416918on_j_k]: (A = (rObjec1303043984on_j_k @ (nothin1567949605on_j_k @ A) @ (rDocum427676485on_j_k @ (nothin757132294on_j_k @ A) @ (doctyp814403297on_j_k @ A) @ (docume1175131570on_j_k @ A) @ (discon866287741on_j_k @ A) @ (more_c1453068134on_j_k @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_RDocument_Osurjective)).
% 228.49/61.55 thf(866,plain,((! [A:rObjec1617416918on_j_k]: (A = (rObjec1303043984on_j_k @ (nothin1567949605on_j_k @ A) @ (rDocum427676485on_j_k @ (nothin757132294on_j_k @ A) @ (doctyp814403297on_j_k @ A) @ (docume1175131570on_j_k @ A) @ (discon866287741on_j_k @ A) @ (more_c1453068134on_j_k @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
% 228.49/61.55 thf(302,axiom,((! [A:node_p1234578834tr_b_c]: ((count_2128515342tr_b_c @ nil_no279930520tr_b_c @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_count__list_Osimps_I1_J)).
% 228.49/61.55 thf(1796,plain,((! [A:node_p1234578834tr_b_c]: ((count_2128515342tr_b_c @ nil_no279930520tr_b_c @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])).
% 228.49/61.55 thf(274,axiom,((! [A:(sum_su1221287958on_j_k > option_element_ptr_a)]: ((bind_S287509021_ptr_a @ none_S1393028981on_j_k @ A) = none_element_ptr_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_bind_Obind__lzero)).
% 228.49/61.55 thf(1620,plain,((! [A:(sum_su1221287958on_j_k > option_element_ptr_a)]: ((bind_S287509021_ptr_a @ none_S1393028981on_j_k @ (A)) = none_element_ptr_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])).
% 228.49/61.55 thf(1621,plain,(! [A:(sum_su1221287958on_j_k > option_element_ptr_a)] : (((bind_S287509021_ptr_a @ none_S1393028981on_j_k @ (A)) = none_element_ptr_a))),inference(cnf,[status(esa)],[1620])).
% 228.49/61.55 thf(1622,plain,(! [A:(sum_su1221287958on_j_k > option_element_ptr_a)] : (((bind_S287509021_ptr_a @ none_S1393028981on_j_k @ (A)) = none_element_ptr_a))),inference(lifteq,[status(thm)],[1621])).
% 228.49/61.55 thf(227,axiom,((! [A:list_n282880152tr_b_c]: ((A != nil_no279930520tr_b_c) => (~ (! [B:list_n282880152tr_b_c,C:node_p1234578834tr_b_c]: (A != (append846395565tr_b_c @ B @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_rev__exhaust)).
% 228.49/61.55 thf(1345,plain,((! [A:list_n282880152tr_b_c]: ((~ (A = nil_no279930520tr_b_c)) => (~ (! [B:list_n282880152tr_b_c,C:node_p1234578834tr_b_c]: ~ (A = (append846395565tr_b_c @ B @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])).
% 228.49/61.55 thf(55,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:list_n282880152tr_b_c,D:(list_n282880152tr_b_c > list_n282880152tr_b_c),E:(list_n282880152tr_b_c > list_n282880152tr_b_c)]: ((A = B) => (((discon866287741on_j_k @ B) = C) => ((! [F:list_n282880152tr_b_c]: ((F = C) => ((D @ F) = (E @ F)))) => ((discon442323090on_j_k @ D @ A) = (discon442323090on_j_k @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_RDocument_Ounfold__congs_I5_J)).
% 228.49/61.55 thf(527,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:list_n282880152tr_b_c,D:(list_n282880152tr_b_c > list_n282880152tr_b_c),E:(list_n282880152tr_b_c > list_n282880152tr_b_c)]: ((A = B) => (((discon866287741on_j_k @ B) = C) => ((! [F:list_n282880152tr_b_c]: ((F = C) => ((D @ F) = (E @ F)))) => ((discon442323090on_j_k @ (D) @ A) = (discon442323090on_j_k @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
% 228.49/61.55 thf(32,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_add__mono__thms__linordered__semiring_I4_J)).
% 228.49/61.55 thf(428,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (C = D)) => ((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
% 228.49/61.55 thf(198,axiom,((! [A:rObjec1617416918on_j_k]: ~ (! [B:product_unit,C:rDocum326988203on_j_k]: (A != (rObjec1303043984on_j_k @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_RObject_Ocases__scheme)).
% 228.49/61.55 thf(1201,plain,((! [A:rObjec1617416918on_j_k]: ~ (! [B:product_unit,C:rDocum326988203on_j_k]: ~ (A = (rObjec1303043984on_j_k @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
% 228.49/61.55 thf(286,axiom,((! [A:rObjec1617416918on_j_k]: (A = (rObjec1303043984on_j_k @ (nothin1567949605on_j_k @ A) @ (more_R1625109589on_j_k @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_RObject_Osurjective)).
% 228.49/61.55 thf(1697,plain,((! [A:rObjec1617416918on_j_k]: (A = (rObjec1303043984on_j_k @ (nothin1567949605on_j_k @ A) @ (more_R1625109589on_j_k @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])).
% 228.49/61.55 thf(209,axiom,((! [A:list_char,B:list_char,C:list_char]: (((splice_char @ A @ B) = C) => (((A = nil_char) => (C != B)) => (~ (! [D:char,E:list_char]: ((A = (cons_char @ D @ E)) => (C != (cons_char @ D @ (splice_char @ B @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_splice_Oelims)).
% 228.49/61.55 thf(1242,plain,((! [A:list_char,B:list_char,C:list_char]: (((splice_char @ A @ B) = C) => (((A = nil_char) => (~ (C = B))) => (~ (! [D:char,E:list_char]: ((A = (cons_char @ D @ E)) => (~ (C = (cons_char @ D @ (splice_char @ B @ E))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
% 228.49/61.55 thf(173,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((A = B) => (A = (append846395565tr_b_c @ nil_no279930520tr_b_c @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_eq__Nil__appendI)).
% 228.49/61.55 thf(1074,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((A = B) => (A = (append846395565tr_b_c @ nil_no279930520tr_b_c @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])).
% 228.49/61.55 thf(39,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_add__cancel__right__left)).
% 228.49/61.55 thf(452,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
% 228.49/61.55 thf(19,axiom,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus_nat @ B @ C)) => ((suc @ A) = (plus_plus_nat @ B @ (suc @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_nat__arith_Osuc1)).
% 228.49/61.55 thf(380,plain,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus_nat @ B @ C)) => ((suc @ A) = (plus_plus_nat @ B @ (suc @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 228.49/61.55 thf(153,axiom,((! [A:option2026120038on_j_k,B:(option2026120038on_j_k > (option2026120038on_j_k > $o)),C:option2026120038on_j_k]: (((A = none_S1393028981on_j_k) => (B @ A @ C)) => (((C = none_S1393028981on_j_k) => (B @ A @ C)) => ((! [D:sum_su1221287958on_j_k,E:sum_su1221287958on_j_k]: ((A = (some_S1960742641on_j_k @ D)) => ((C = (some_S1960742641on_j_k @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_combine__options__cases)).
% 228.49/61.55 thf(942,plain,((! [A:option2026120038on_j_k,B:(option2026120038on_j_k > (option2026120038on_j_k > $o)),C:option2026120038on_j_k]: (((A = none_S1393028981on_j_k) => (B @ A @ C)) => (((C = none_S1393028981on_j_k) => (B @ A @ C)) => ((! [D:sum_su1221287958on_j_k,E:sum_su1221287958on_j_k]: ((A = (some_S1960742641on_j_k @ D)) => ((C = (some_S1960742641on_j_k @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
% 228.49/61.55 thf(92,axiom,((! [A:nat]: ? [B:list_n282880152tr_b_c]: ((size_s2106487044tr_b_c @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Ex__list__of__length)).
% 228.49/61.55 thf(678,plain,((! [A:nat]: ? [B:list_n282880152tr_b_c]: ((size_s2106487044tr_b_c @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
% 228.49/61.55 thf(111,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Zero__not__Suc)).
% 228.49/61.55 thf(761,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
% 228.49/61.55 thf(14,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_add_Oassoc)).
% 228.49/61.55 thf(366,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 228.49/61.55 thf(248,axiom,((! [A:list_n282880152tr_b_c,B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c,D:node_p1234578834tr_b_c]: (((append846395565tr_b_c @ A @ (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c)) = (append846395565tr_b_c @ C @ (cons_n413985352tr_b_c @ D @ nil_no279930520tr_b_c))) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_append1__eq__conv)).
% 228.49/61.55 thf(1470,plain,((! [A:list_n282880152tr_b_c,B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c,D:node_p1234578834tr_b_c]: (((append846395565tr_b_c @ A @ (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c)) = (append846395565tr_b_c @ C @ (cons_n413985352tr_b_c @ D @ nil_no279930520tr_b_c))) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])).
% 228.49/61.55 thf(289,axiom,((! [A:(option2026120038on_j_k > $o),B:option2026120038on_j_k]: ((A @ none_S1393028981on_j_k) => ((! [C:sum_su1221287958on_j_k]: (A @ (some_S1960742641on_j_k @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_option_Oinducts)).
% 228.49/61.55 thf(1708,plain,((! [A:(option2026120038on_j_k > $o),B:option2026120038on_j_k]: ((A @ none_S1393028981on_j_k) => ((! [C:sum_su1221287958on_j_k]: (A @ (some_S1960742641on_j_k @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])).
% 228.49/61.55 thf(292,axiom,((! [A:rObjec1617416918on_j_k]: ~ (! [B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: (A != (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_RDocument_Ocases__scheme)).
% 228.49/61.55 thf(1730,plain,((! [A:rObjec1617416918on_j_k]: ~ (! [B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ~ (A = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])).
% 228.49/61.55 thf(798,plain,(((nat_set_encode @ bot_bot_set_nat) = zero_zero_nat)),inference(lifteq,[status(thm)],[797])).
% 228.49/61.55 thf(166,axiom,((((?) @ option2026120038on_j_k) = (^ [A:(option2026120038on_j_k > $o)]: ((A @ none_S1393028981on_j_k) | ? [B:sum_su1221287958on_j_k]: (A @ (some_S1960742641on_j_k @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_split__option__ex)).
% 228.49/61.55 thf(1056,plain,((((?) @ option2026120038on_j_k) = (^ [A:(option2026120038on_j_k > $o)]: ((A @ none_S1393028981on_j_k) | ? [B:sum_su1221287958on_j_k]: (A @ (some_S1960742641on_j_k @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
% 228.49/61.55 thf(1057,plain,(((^ [A:(option2026120038on_j_k > $o)]: ((A @ none_S1393028981on_j_k) | ? [B:sum_su1221287958on_j_k]: (A @ (some_S1960742641on_j_k @ B)))) = ((?) @ option2026120038on_j_k))),inference(lifteq,[status(thm)],[1056])).
% 228.49/61.55 thf(190,axiom,((! [A:list_char]: (((size_size_list_char @ A) = zero_zero_nat) = (A = nil_char)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_length__0__conv)).
% 228.49/61.55 thf(1163,plain,((! [A:list_char]: (((size_size_list_char @ A) = zero_zero_nat) = (A = nil_char)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])).
% 228.49/61.55 thf(321,axiom,((! [A:(sum_su1221287958on_j_k > option2026120038on_j_k)]: ((bind_S607117548on_j_k @ none_S1393028981on_j_k @ A) = none_S1393028981on_j_k))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_bind_Obind__lzero)).
% 228.49/61.55 thf(1898,plain,((! [A:(sum_su1221287958on_j_k > option2026120038on_j_k)]: ((bind_S607117548on_j_k @ none_S1393028981on_j_k @ (A)) = none_S1393028981on_j_k))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])).
% 228.49/61.55 thf(1899,plain,(! [A:(sum_su1221287958on_j_k > option2026120038on_j_k)] : (((bind_S607117548on_j_k @ none_S1393028981on_j_k @ (A)) = none_S1393028981on_j_k))),inference(cnf,[status(esa)],[1898])).
% 228.49/61.55 thf(1900,plain,(! [A:(sum_su1221287958on_j_k > option2026120038on_j_k)] : (((bind_S607117548on_j_k @ none_S1393028981on_j_k @ (A)) = none_S1393028981on_j_k))),inference(lifteq,[status(thm)],[1899])).
% 228.49/61.55 thf(175,axiom,((! [A:char]: ((count_list_char @ nil_char @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_count__list_Osimps_I1_J)).
% 228.49/61.55 thf(1089,plain,((! [A:char]: ((count_list_char @ nil_char @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
% 228.49/61.55 thf(1090,plain,(! [A:char] : (((count_list_char @ nil_char @ A) = zero_zero_nat))),inference(cnf,[status(esa)],[1089])).
% 228.49/61.55 thf(1091,plain,(! [A:char] : (((count_list_char @ nil_char @ A) = zero_zero_nat))),inference(lifteq,[status(thm)],[1090])).
% 228.49/61.55 thf(229,axiom,((! [A:(element_ptr_a > nat)]: ((size_o1591053974_ptr_a @ A @ none_element_ptr_a) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_option_Osize__gen_I1_J)).
% 228.49/61.55 thf(1353,plain,((! [A:(element_ptr_a > nat)]: ((size_o1591053974_ptr_a @ (A) @ none_element_ptr_a) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])).
% 228.49/61.55 thf(1354,plain,(! [A:(element_ptr_a > nat)] : (((size_o1591053974_ptr_a @ (A) @ none_element_ptr_a) = (suc @ zero_zero_nat)))),inference(cnf,[status(esa)],[1353])).
% 228.49/61.55 thf(1355,plain,(! [A:(element_ptr_a > nat)] : (((size_o1591053974_ptr_a @ (A) @ none_element_ptr_a) = (suc @ zero_zero_nat)))),inference(lifteq,[status(thm)],[1354])).
% 228.49/61.55 thf(194,axiom,((! [A:option_element_ptr_a]: ((A != none_element_ptr_a) = (? [B:element_ptr_a]: (A = (some_element_ptr_a @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_not__None__eq)).
% 228.49/61.55 thf(1174,plain,((! [A:option_element_ptr_a]: ((~ (A = none_element_ptr_a)) = (? [B:element_ptr_a]: (A = (some_element_ptr_a @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
% 228.49/61.55 thf(127,axiom,((bot_bot_nat = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_bot__nat__def)).
% 228.49/61.55 thf(819,plain,((bot_bot_nat = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
% 228.49/61.55 thf(820,plain,((bot_bot_nat = zero_zero_nat)),inference(lifteq,[status(thm)],[819])).
% 228.49/61.55 thf(203,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((A = (append846395565tr_b_c @ A @ B)) = (B = nil_no279930520tr_b_c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_self__append__conv)).
% 228.49/61.55 thf(1223,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((A = (append846395565tr_b_c @ A @ B)) = (B = nil_no279930520tr_b_c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
% 228.49/61.55 thf(144,axiom,((! [A:product_unit,B:rDocum326988203on_j_k]: ((more_R1625109589on_j_k @ (rObjec1303043984on_j_k @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_RObject_Oselect__convs_I2_J)).
% 228.49/61.55 thf(894,plain,((! [A:product_unit,B:rDocum326988203on_j_k]: ((more_R1625109589on_j_k @ (rObjec1303043984on_j_k @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
% 228.49/61.55 thf(129,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((! [C:nat]: ((A @ (suc @ C)) => (A @ C))) => (A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_zero__induct)).
% 228.49/61.55 thf(825,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((! [C:nat]: ((A @ (suc @ C)) => (A @ C))) => (A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
% 228.49/61.55 thf(226,axiom,((h2 = (put_O_834343516_j_k_l @ (cast_d1608273229_b_c_f @ (docume1511108976tr_d_e @ (suc @ zero_zero_nat))) @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k))) @ h))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 228.49/61.55 thf(1343,plain,((h2 = (put_O_834343516_j_k_l @ (cast_d1608273229_b_c_f @ (docume1511108976tr_d_e @ (suc @ zero_zero_nat))) @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k))) @ h))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
% 228.49/61.55 thf(181,axiom,((! [A:list_char]: ((append_char @ A @ nil_char) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_append__Nil2)).
% 228.49/61.55 thf(1123,plain,((! [A:list_char]: ((append_char @ A @ nil_char) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])).
% 228.49/61.55 thf(348,plain,(! [A:nat] : (((nat_set_encode @ (nat_set_decode @ A)) = A))),inference(cnf,[status(esa)],[347])).
% 228.49/61.55 thf(349,plain,(! [A:nat] : (((nat_set_encode @ (nat_set_decode @ A)) = A))),inference(lifteq,[status(thm)],[348])).
% 228.49/61.55 thf(132,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_nat_Oinject)).
% 228.49/61.55 thf(847,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
% 228.49/61.55 thf(315,axiom,((! [A:list_char,B:list_char,C:list_char,D:(list_char > (list_char > (list_char > $o)))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => ((D @ nil_char @ nil_char @ nil_char) => ((! [E:char,F:list_char,G:char,H:list_char,I:char,J:list_char]: (((size_size_list_char @ F) = (size_size_list_char @ H)) => (((size_size_list_char @ H) = (size_size_list_char @ J)) => ((D @ F @ H @ J) => (D @ (cons_char @ E @ F) @ (cons_char @ G @ H) @ (cons_char @ I @ J)))))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_list__induct3)).
% 228.49/61.55 thf(1837,plain,((! [A:list_char,B:list_char,C:list_char,D:(list_char > (list_char > (list_char > $o)))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => ((D @ nil_char @ nil_char @ nil_char) => ((! [E:char,F:list_char,G:char,H:list_char,I:char,J:list_char]: (((size_size_list_char @ F) = (size_size_list_char @ H)) => (((size_size_list_char @ H) = (size_size_list_char @ J)) => ((D @ F @ H @ J) => (D @ (cons_char @ E @ F) @ (cons_char @ G @ H) @ (cons_char @ I @ J)))))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])).
% 228.49/61.55 thf(12,axiom,((! [A:sum_su1576157353tr_d_e,B:sum_su1576157353tr_d_e]: (((docume1825929374tr_d_e @ A) = (docume1825929374tr_d_e @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_document__ptr_Oinject_I2_J)).
% 228.49/61.55 thf(359,plain,((! [A:sum_su1576157353tr_d_e,B:sum_su1576157353tr_d_e]: (((docume1825929374tr_d_e @ A) = (docume1825929374tr_d_e @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 228.49/61.55 thf(360,plain,(! [B:sum_su1576157353tr_d_e,A:sum_su1576157353tr_d_e] : ((((docume1825929374tr_d_e @ A) = (docume1825929374tr_d_e @ B)) = (A = B)))),inference(cnf,[status(esa)],[359])).
% 228.49/61.55 thf(361,plain,(! [B:sum_su1576157353tr_d_e,A:sum_su1576157353tr_d_e] : ((((docume1825929374tr_d_e @ A) = (docume1825929374tr_d_e @ B)) = (A = B)))),inference(lifteq,[status(thm)],[360])).
% 228.49/61.55 thf(34,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_add_Oleft__commute)).
% 228.49/61.55 thf(435,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
% 228.49/61.55 thf(1,conjecture,((is_doc1417632087_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3)).
% 228.49/61.55 thf(2,negated_conjecture,((~ (is_doc1417632087_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k)))))),inference(neg_conjecture,[status(cth)],[1])).
% 228.49/61.55 thf(329,plain,((~ (is_doc1417632087_j_k_l @ (cast_D1252964113_h_i_l @ (rObjec1303043984on_j_k @ product_Unity @ (rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 228.49/61.55 thf(87,axiom,((! [A:nat]: ((gen_length_list_char @ A @ nil_list_char) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_gen__length__code_I1_J)).
% 228.49/61.55 thf(663,plain,((! [A:nat]: ((gen_length_list_char @ A @ nil_list_char) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
% 228.49/61.55 thf(664,plain,(! [A:nat] : (((gen_length_list_char @ A @ nil_list_char) = A))),inference(cnf,[status(esa)],[663])).
% 228.49/61.55 thf(665,plain,(! [A:nat] : (((gen_length_list_char @ A @ nil_list_char) = A))),inference(lifteq,[status(thm)],[664])).
% 228.49/61.55 thf(309,axiom,((! [A:product_unit,B:rDocum326988203on_j_k,C:product_unit,D:rDocum326988203on_j_k]: (((rObjec1303043984on_j_k @ A @ B) = (rObjec1303043984on_j_k @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_RObject_Oext__inject)).
% 228.49/61.55 thf(1819,plain,((! [A:product_unit,B:rDocum326988203on_j_k,C:product_unit,D:rDocum326988203on_j_k]: (((rObjec1303043984on_j_k @ A @ B) = (rObjec1303043984on_j_k @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])).
% 228.49/61.55 thf(142,axiom,((! [A:nat]: ((gen_le955068453tr_b_c @ A @ nil_no279930520tr_b_c) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_gen__length__code_I1_J)).
% 228.49/61.55 thf(887,plain,((! [A:nat]: ((gen_le955068453tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
% 228.49/61.55 thf(888,plain,(! [A:nat] : (((gen_le955068453tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(cnf,[status(esa)],[887])).
% 228.49/61.55 thf(889,plain,(! [A:nat] : (((gen_le955068453tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(lifteq,[status(thm)],[888])).
% 228.49/61.55 thf(300,axiom,((! [A:(option_element_ptr_a > option_element_ptr_a),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((docume244715269on_j_k @ A @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ (A @ E) @ F @ G))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_RDocument_Oupdate__convs_I3_J)).
% 228.49/61.55 thf(1787,plain,((! [A:(option_element_ptr_a > option_element_ptr_a),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((docume244715269on_j_k @ (A) @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ (A @ E) @ F @ G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])).
% 228.49/61.55 thf(757,plain,(((gen_le955068453tr_b_c) = (^ [A:nat,B:list_n282880152tr_b_c]: (plus_plus_nat @ A @ (size_s2106487044tr_b_c @ B))))),inference(lifteq,[status(thm)],[756])).
% 228.49/61.55 thf(196,axiom,((! [A:(char > $o)]: ~ (list_ex1_char @ A @ nil_char))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_list__ex1__simps_I1_J)).
% 228.49/61.55 thf(1195,plain,((! [A:(char > $o)]: ~ (list_ex1_char @ (A) @ nil_char))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
% 228.49/61.55 thf(182,axiom,((! [A:(element_ptr_a > option_element_ptr_a)]: ((bind_e22036734_ptr_a @ none_element_ptr_a @ A) = none_element_ptr_a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_bind_Obind__lzero)).
% 228.49/61.55 thf(1126,plain,((! [A:(element_ptr_a > option_element_ptr_a)]: ((bind_e22036734_ptr_a @ none_element_ptr_a @ (A)) = none_element_ptr_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
% 228.49/61.55 thf(1127,plain,(! [A:(element_ptr_a > option_element_ptr_a)] : (((bind_e22036734_ptr_a @ none_element_ptr_a @ (A)) = none_element_ptr_a))),inference(cnf,[status(esa)],[1126])).
% 228.49/61.55 thf(1128,plain,(! [A:(element_ptr_a > option_element_ptr_a)] : (((bind_e22036734_ptr_a @ none_element_ptr_a @ (A)) = none_element_ptr_a))),inference(lifteq,[status(thm)],[1127])).
% 228.49/61.55 thf(217,axiom,((! [A:list_char,B:list_char]: (((append_char @ A @ B) = B) = (A = nil_char)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_append__self__conv2)).
% 228.49/61.55 thf(1291,plain,((! [A:list_char,B:list_char]: (((append_char @ A @ B) = B) = (A = nil_char)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])).
% 228.49/61.55 thf(100,axiom,((! [A:option_element_ptr_a]: ((size_s1129684517_ptr_a @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_option_Osize__neq)).
% 228.49/61.55 thf(707,plain,((! [A:option_element_ptr_a]: ~ ((size_s1129684517_ptr_a @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])).
% 228.49/61.55 thf(708,plain,((~ (? [A:option_element_ptr_a]: ((size_s1129684517_ptr_a @ A) = zero_zero_nat)))),inference(miniscope,[status(thm)],[707])).
% 228.49/61.55 thf(709,plain,(! [A:option_element_ptr_a] : ((~ ((size_s1129684517_ptr_a @ A) = zero_zero_nat)))),inference(cnf,[status(esa)],[708])).
% 228.49/61.55 thf(710,plain,(! [A:option_element_ptr_a] : (((size_s1129684517_ptr_a @ A) != zero_zero_nat))),inference(lifteq,[status(thm)],[709])).
% 228.49/61.55 thf(258,axiom,(((size_s1129684517_ptr_a @ none_element_ptr_a) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_option_Osize_I3_J)).
% 228.49/61.55 thf(1523,plain,(((size_s1129684517_ptr_a @ none_element_ptr_a) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])).
% 228.49/61.55 thf(1524,plain,(((size_s1129684517_ptr_a @ none_element_ptr_a) = (suc @ zero_zero_nat))),inference(lifteq,[status(thm)],[1523])).
% 228.49/61.55 thf(1982,plain,(! [A:option_element_ptr_a] : (((suc @ zero_zero_nat) != zero_zero_nat) | ((size_s1129684517_ptr_a @ none_element_ptr_a) != (size_s1129684517_ptr_a @ A)))),inference(paramod_ordered,[status(thm)],[1524,710])).
% 228.49/61.55 thf(1983,plain,(((suc @ zero_zero_nat) != zero_zero_nat)),inference(pattern_uni,[status(thm)],[1982:[bind(A, $thf(none_element_ptr_a))]])).
% 228.49/61.55 thf(318,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:(list_n282880152tr_b_c > (list_n282880152tr_b_c > $o))]: (((size_s2106487044tr_b_c @ A) = (size_s2106487044tr_b_c @ B)) => ((C @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ E) = (size_s2106487044tr_b_c @ G)) => ((C @ E @ G) => (C @ (cons_n413985352tr_b_c @ D @ E) @ (cons_n413985352tr_b_c @ F @ G))))) => (C @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_list__induct2)).
% 228.49/61.55 thf(1856,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:(list_n282880152tr_b_c > (list_n282880152tr_b_c > $o))]: (((size_s2106487044tr_b_c @ A) = (size_s2106487044tr_b_c @ B)) => ((C @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ E) = (size_s2106487044tr_b_c @ G)) => ((C @ E @ G) => (C @ (cons_n413985352tr_b_c @ D @ E) @ (cons_n413985352tr_b_c @ F @ G))))) => (C @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])).
% 228.49/61.55 thf(25,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_add_Ocomm__neutral)).
% 228.49/61.55 thf(403,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 228.49/61.55 thf(139,axiom,((! [A:(list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)),B:list_n282880152tr_b_c,C:list_n282880152tr_b_c]: ((! [D:list_n282880152tr_b_c]: (A @ nil_no279930520tr_b_c @ D)) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:list_n282880152tr_b_c]: ((A @ F @ E) => (A @ (cons_n413985352tr_b_c @ D @ E) @ F))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_splice_Oinduct)).
% 228.49/61.55 thf(869,plain,((! [A:(list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)),B:list_n282880152tr_b_c,C:list_n282880152tr_b_c]: ((! [D:list_n282880152tr_b_c]: (A @ nil_no279930520tr_b_c @ D)) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:list_n282880152tr_b_c]: ((A @ F @ E) => (A @ (cons_n413985352tr_b_c @ D @ E) @ F))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
% 228.49/61.55 thf(135,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_old_Onat_Oinject)).
% 228.49/61.55 thf(857,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])).
% 228.49/61.55 thf(96,axiom,((type_w92696601_j_k_l @ h)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 228.49/61.55 thf(697,plain,((type_w92696601_j_k_l @ h)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
% 228.49/61.55 thf(140,axiom,((((!) @ option2026120038on_j_k) = (^ [A:(option2026120038on_j_k > $o)]: ((A @ none_S1393028981on_j_k) & ! [B:sum_su1221287958on_j_k]: (A @ (some_S1960742641on_j_k @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_split__option__all)).
% 228.49/61.55 thf(874,plain,((((!) @ option2026120038on_j_k) = (^ [A:(option2026120038on_j_k > $o)]: ((A @ none_S1393028981on_j_k) & ! [B:sum_su1221287958on_j_k]: (A @ (some_S1960742641on_j_k @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
% 228.49/61.55 thf(187,axiom,((! [A:(list_char > list_char),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((doctyp68000440on_j_k @ A @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ (A @ D) @ E @ F @ G))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_RDocument_Oupdate__convs_I2_J)).
% 228.49/61.55 thf(1143,plain,((! [A:(list_char > list_char),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((doctyp68000440on_j_k @ (A) @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ (A @ D) @ E @ F @ G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])).
% 228.49/61.55 thf(317,axiom,((! [A:(list_n282880152tr_b_c > (list_char > $o)),B:list_n282880152tr_b_c,C:list_char]: ((A @ nil_no279930520tr_b_c @ nil_char) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (A @ (cons_n413985352tr_b_c @ D @ E) @ nil_char)) => ((! [D:char,E:list_char]: (A @ nil_no279930520tr_b_c @ (cons_char @ D @ E))) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:char,G:list_char]: ((A @ E @ G) => (A @ (cons_n413985352tr_b_c @ D @ E) @ (cons_char @ F @ G)))) => (A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_list__induct2_H)).
% 228.49/61.55 thf(1851,plain,((! [A:(list_n282880152tr_b_c > (list_char > $o)),B:list_n282880152tr_b_c,C:list_char]: ((A @ nil_no279930520tr_b_c @ nil_char) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (A @ (cons_n413985352tr_b_c @ D @ E) @ nil_char)) => ((! [D:char,E:list_char]: (A @ nil_no279930520tr_b_c @ (cons_char @ D @ E))) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:char,G:list_char]: ((A @ E @ G) => (A @ (cons_n413985352tr_b_c @ D @ E) @ (cons_char @ F @ G)))) => (A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])).
% 228.49/61.55 thf(211,axiom,((! [A:rObjec1413572695_j_k_l,B:rObjec1617416918on_j_k]: (((cast_O1034441233_j_k_l @ A) = (some_R67702331on_j_k @ B)) = ((cast_D1252964113_h_i_l @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__some)).
% 228.49/61.55 thf(1259,plain,((! [A:rObjec1413572695_j_k_l,B:rObjec1617416918on_j_k]: (((cast_O1034441233_j_k_l @ A) = (some_R67702331on_j_k @ B)) = ((cast_D1252964113_h_i_l @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])).
% 228.49/61.55 thf(262,axiom,((! [A:rObjec1617416918on_j_k]: ((cast_O1034441233_j_k_l @ (cast_D1252964113_h_i_l @ A)) = (some_R67702331on_j_k @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__inv)).
% 228.49/61.55 thf(1534,plain,((! [A:rObjec1617416918on_j_k]: ((cast_O1034441233_j_k_l @ (cast_D1252964113_h_i_l @ A)) = (some_R67702331on_j_k @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])).
% 228.49/61.55 thf(162,axiom,((! [A:list_char,B:list_n282880152tr_b_c,C:list_char,D:list_char,E:(list_char > (list_n282880152tr_b_c > (list_char > (list_char > $o))))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_size_list_char @ D)) => ((E @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_char) => ((! [F:char,G:list_char,H:node_p1234578834tr_b_c,I:list_n282880152tr_b_c,J:char,K:list_char,L:char,M:list_char]: (((size_size_list_char @ G) = (size_s2106487044tr_b_c @ I)) => (((size_s2106487044tr_b_c @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_n413985352tr_b_c @ H @ I) @ (cons_char @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_list__induct4)).
% 228.49/61.55 thf(1017,plain,((! [A:list_char,B:list_n282880152tr_b_c,C:list_char,D:list_char,E:(list_char > (list_n282880152tr_b_c > (list_char > (list_char > $o))))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_size_list_char @ D)) => ((E @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_char) => ((! [F:char,G:list_char,H:node_p1234578834tr_b_c,I:list_n282880152tr_b_c,J:char,K:list_char,L:char,M:list_char]: (((size_size_list_char @ G) = (size_s2106487044tr_b_c @ I)) => (((size_s2106487044tr_b_c @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_n413985352tr_b_c @ H @ I) @ (cons_char @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
% 228.49/61.55 thf(314,axiom,((! [A:list_n282880152tr_b_c]: ((n_list1807568544tr_b_c @ zero_zero_nat @ A) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_n__lists_Osimps_I1_J)).
% 228.49/61.55 thf(1834,plain,((! [A:list_n282880152tr_b_c]: ((n_list1807568544tr_b_c @ zero_zero_nat @ A) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])).
% 228.49/61.55 thf(1835,plain,(! [A:list_n282880152tr_b_c] : (((n_list1807568544tr_b_c @ zero_zero_nat @ A) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c)))),inference(cnf,[status(esa)],[1834])).
% 228.49/61.55 thf(1836,plain,(! [A:list_n282880152tr_b_c] : (((n_list1807568544tr_b_c @ zero_zero_nat @ A) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c)))),inference(lifteq,[status(thm)],[1835])).
% 228.49/61.55 thf(2685,plain,(! [A:list_n282880152tr_b_c] : (((n_list1807568544tr_b_c @ zero_zero_nat @ A) = (produc1509350401tr_b_c @ nil_li198338206tr_b_c)))),inference(rewrite,[status(thm)],[1836,1067])).
% 228.49/61.55 thf(176,axiom,((! [A:option_element_ptr_a,B:element_ptr_a]: ((A = (some_element_ptr_a @ B)) => (A != none_element_ptr_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_option_OdiscI)).
% 228.49/61.55 thf(1092,plain,((! [A:option_element_ptr_a,B:element_ptr_a]: ((A = (some_element_ptr_a @ B)) => (~ (A = none_element_ptr_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])).
% 228.49/61.55 thf(1093,plain,((! [A:option_element_ptr_a]: ((? [B:element_ptr_a]: (A = (some_element_ptr_a @ B))) => (~ (A = none_element_ptr_a))))),inference(miniscope,[status(thm)],[1092])).
% 228.49/61.55 thf(1094,plain,(! [B:element_ptr_a,A:option_element_ptr_a] : ((~ (A = (some_element_ptr_a @ B))) | (~ (A = none_element_ptr_a)))),inference(cnf,[status(esa)],[1093])).
% 228.49/61.55 thf(1095,plain,(! [B:element_ptr_a,A:option_element_ptr_a] : ((A != (some_element_ptr_a @ B)) | (A != none_element_ptr_a))),inference(lifteq,[status(thm)],[1094])).
% 228.49/61.55 thf(1096,plain,(! [A:element_ptr_a] : (((some_element_ptr_a @ A) != none_element_ptr_a))),inference(simp,[status(thm)],[1095])).
% 228.49/61.55 thf(284,axiom,((! [A:set_nat,B:char]: (((member_nat @ zero_zero_nat @ A) => ((nths_char @ (cons_char @ B @ nil_char) @ A) = (cons_char @ B @ nil_char))) & ((~ (member_nat @ zero_zero_nat @ A)) => ((nths_char @ (cons_char @ B @ nil_char) @ A) = nil_char))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_nths__singleton)).
% 228.49/61.55 thf(1672,plain,((! [A:set_nat,B:char]: (((member_nat @ zero_zero_nat @ A) => ((nths_char @ (cons_char @ B @ nil_char) @ A) = (cons_char @ B @ nil_char))) & ((~ (member_nat @ zero_zero_nat @ A)) => ((nths_char @ (cons_char @ B @ nil_char) @ A) = nil_char))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])).
% 228.49/61.55 thf(186,axiom,((! [A:((node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)) > (list_n282880152tr_b_c > $o)),B:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),C:list_n282880152tr_b_c]: ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o))]: (A @ D @ nil_no279930520tr_b_c)) => ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c]: ((A @ D @ F) => (A @ D @ (cons_n413985352tr_b_c @ E @ F)))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_sorted__wrt_Oinduct)).
% 228.49/61.55 thf(1138,plain,((! [A:((node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)) > (list_n282880152tr_b_c > $o)),B:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),C:list_n282880152tr_b_c]: ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o))]: (A @ (D) @ nil_no279930520tr_b_c)) => ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c]: ((A @ (D) @ F) => (A @ (D) @ (cons_n413985352tr_b_c @ E @ F)))) => (A @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])).
% 228.49/61.55 thf(11,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_add__is__0)).
% 228.49/61.55 thf(356,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 228.49/61.55 thf(115,axiom,((! [A:(list_char > $o)]: ~ (list_ex1_list_char @ A @ nil_list_char))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_list__ex1__simps_I1_J)).
% 228.49/61.55 thf(781,plain,((! [A:(list_char > $o)]: ~ (list_ex1_list_char @ (A) @ nil_list_char))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
% 228.49/61.55 thf(782,plain,((~ (? [A:(list_char > $o)]: (list_ex1_list_char @ (A) @ nil_list_char)))),inference(miniscope,[status(thm)],[781])).
% 228.49/61.55 thf(783,plain,(! [A:(list_char > $o)] : ((~ (list_ex1_list_char @ (A) @ nil_list_char)))),inference(cnf,[status(esa)],[782])).
% 228.49/61.55 thf(30,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_add__right__cancel)).
% 228.49/61.55 thf(418,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 228.49/61.55 thf(419,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(cnf,[status(esa)],[418])).
% 228.49/61.55 thf(420,plain,(! [C:nat,B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(lifteq,[status(thm)],[419])).
% 228.49/61.55 thf(179,axiom,((! [A:list_char,B:list_char]: ((A = (append_char @ A @ B)) = (B = nil_char)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_self__append__conv)).
% 228.49/61.55 thf(1118,plain,((! [A:list_char,B:list_char]: ((A = (append_char @ A @ B)) = (B = nil_char)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
% 228.49/61.55 thf(222,axiom,((! [A:rObjec1413572695_j_k_l]: (((cast_O1034441233_j_k_l @ A) = none_R1587534007on_j_k) = (~ (? [B:rObjec1617416918on_j_k]: ((cast_D1252964113_h_i_l @ B) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none)).
% 228.49/61.55 thf(1329,plain,((! [A:rObjec1413572695_j_k_l]: (((cast_O1034441233_j_k_l @ A) = none_R1587534007on_j_k) = (~ (? [B:rObjec1617416918on_j_k]: ((cast_D1252964113_h_i_l @ B) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
% 228.49/61.55 thf(240,axiom,((! [A:element_ptr_a]: (none_element_ptr_a != (some_element_ptr_a @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_option_Odistinct_I1_J)).
% 228.49/61.55 thf(1424,plain,((! [A:element_ptr_a]: ~ (none_element_ptr_a = (some_element_ptr_a @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
% 228.49/61.55 thf(82,axiom,((! [A:rObjec103300152t_unit,B:product_unit]: ((more_Product_unit @ (extend_Product_unit @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_object__more__extend__id)).
% 228.49/61.55 thf(642,plain,((! [A:rObjec103300152t_unit,B:product_unit]: ((more_Product_unit @ (extend_Product_unit @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
% 228.49/61.55 thf(69,axiom,((! [A:option_element_ptr_a,B:option_element_ptr_a]: (((size_s1129684517_ptr_a @ A) != (size_s1129684517_ptr_a @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_size__neq__size__imp__neq)).
% 228.49/61.55 thf(590,plain,((! [A:option_element_ptr_a,B:option_element_ptr_a]: ((~ ((size_s1129684517_ptr_a @ A) = (size_s1129684517_ptr_a @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
% 228.49/61.55 thf(48,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:list_n282880152tr_b_c,D:(list_n282880152tr_b_c > list_n282880152tr_b_c),E:(list_n282880152tr_b_c > list_n282880152tr_b_c)]: ((A = B) => (((discon866287741on_j_k @ B) = C) => ((! [F:list_n282880152tr_b_c]: ((C = F) => ((D @ F) = (E @ F)))) => ((discon442323090on_j_k @ D @ A) = (discon442323090on_j_k @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_RDocument_Ofold__congs_I5_J)).
% 228.49/61.55 thf(489,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:list_n282880152tr_b_c,D:(list_n282880152tr_b_c > list_n282880152tr_b_c),E:(list_n282880152tr_b_c > list_n282880152tr_b_c)]: ((A = B) => (((discon866287741on_j_k @ B) = C) => ((! [F:list_n282880152tr_b_c]: ((C = F) => ((D @ F) = (E @ F)))) => ((discon442323090on_j_k @ (D) @ A) = (discon442323090on_j_k @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
% 228.49/61.55 thf(311,axiom,((! [A:list_char]: ((n_lists_char @ zero_zero_nat @ A) = (cons_list_char @ nil_char @ nil_list_char)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_n__lists_Osimps_I1_J)).
% 228.49/61.55 thf(1825,plain,((! [A:list_char]: ((n_lists_char @ zero_zero_nat @ A) = (cons_list_char @ nil_char @ nil_list_char)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])).
% 228.49/61.55 thf(84,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_list__decode_Ocases)).
% 228.49/61.55 thf(647,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
% 228.49/61.55 thf(159,axiom,((((?) @ option_element_ptr_a) = (^ [A:(option_element_ptr_a > $o)]: ((A @ none_element_ptr_a) | ? [B:element_ptr_a]: (A @ (some_element_ptr_a @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_split__option__ex)).
% 228.49/61.55 thf(985,plain,((((?) @ option_element_ptr_a) = (^ [A:(option_element_ptr_a > $o)]: ((A @ none_element_ptr_a) | ? [B:element_ptr_a]: (A @ (some_element_ptr_a @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
% 228.49/61.55 thf(98,axiom,((! [A:option841825948on_j_k]: ((! [B:rObjec1617416918on_j_k]: (A != (some_R67702331on_j_k @ B))) = (A = none_R1587534007on_j_k)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_not__Some__eq)).
% 228.49/61.55 thf(701,plain,((! [A:option841825948on_j_k]: ((! [B:rObjec1617416918on_j_k]: ~ (A = (some_R67702331on_j_k @ B))) = (A = none_R1587534007on_j_k)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
% 228.49/61.55 thf(189,axiom,((! [A:list_n282880152tr_b_c,B:list_char,C:list_char,D:list_char,E:(list_n282880152tr_b_c > (list_char > (list_char > (list_char > $o))))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_size_list_char @ D)) => ((E @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_char) => ((! [F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c,H:char,I:list_char,J:char,K:list_char,L:char,M:list_char]: (((size_s2106487044tr_b_c @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_n413985352tr_b_c @ F @ G) @ (cons_char @ H @ I) @ (cons_char @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_list__induct4)).
% 228.49/61.55 thf(1150,plain,((! [A:list_n282880152tr_b_c,B:list_char,C:list_char,D:list_char,E:(list_n282880152tr_b_c > (list_char > (list_char > (list_char > $o))))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_size_list_char @ D)) => ((E @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_char) => ((! [F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c,H:char,I:list_char,J:char,K:list_char,L:char,M:list_char]: (((size_s2106487044tr_b_c @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_n413985352tr_b_c @ F @ G) @ (cons_char @ H @ I) @ (cons_char @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
% 228.49/61.55 thf(245,axiom,((! [A:product_unit,B:list_char,C:option_element_ptr_a,D:list_n282880152tr_b_c,E:option2026120038on_j_k,F:product_unit,G:list_char,H:option_element_ptr_a,I:list_n282880152tr_b_c,J:option2026120038on_j_k]: (((rDocum427676485on_j_k @ A @ B @ C @ D @ E) = (rDocum427676485on_j_k @ F @ G @ H @ I @ J)) = ((A = F) & (B = G) & (C = H) & (D = I) & (E = J))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_RDocument_Oext__inject)).
% 228.49/61.55 thf(1451,plain,((! [A:product_unit,B:list_char,C:option_element_ptr_a,D:list_n282880152tr_b_c,E:option2026120038on_j_k,F:product_unit,G:list_char,H:option_element_ptr_a,I:list_n282880152tr_b_c,J:option2026120038on_j_k]: (((rDocum427676485on_j_k @ A @ B @ C @ D @ E) = (rDocum427676485on_j_k @ F @ G @ H @ I @ J)) = ((A = F) & (B = G) & (C = H) & (D = I) & (E = J))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
% 228.49/61.55 thf(235,axiom,((put_D_2126422573_h_i_l = (^ [A:docume1935157360tr_d_e,B:rObjec1617416918on_j_k]: (put_O_834343516_j_k_l @ (cast_d1608273229_b_c_f @ A) @ (cast_D1252964113_h_i_l @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_put_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def)).
% 228.49/61.55 thf(1381,plain,(((put_D_2126422573_h_i_l) = (^ [A:docume1935157360tr_d_e,B:rObjec1617416918on_j_k]: (put_O_834343516_j_k_l @ (cast_d1608273229_b_c_f @ A) @ (cast_D1252964113_h_i_l @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])).
% 228.49/61.55 thf(1382,plain,(((^ [A:docume1935157360tr_d_e,B:rObjec1617416918on_j_k]: (put_O_834343516_j_k_l @ (cast_d1608273229_b_c_f @ A) @ (cast_D1252964113_h_i_l @ B))) = (put_D_2126422573_h_i_l))),inference(lifteq,[status(thm)],[1381])).
% 228.49/61.55 thf(313,axiom,((! [A:set_nat]: ((nths_n1256675478tr_b_c @ nil_no279930520tr_b_c @ A) = nil_no279930520tr_b_c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_nths__nil)).
% 228.49/61.55 thf(1831,plain,((! [A:set_nat]: ((nths_n1256675478tr_b_c @ nil_no279930520tr_b_c @ A) = nil_no279930520tr_b_c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])).
% 228.49/61.55 thf(167,axiom,((! [A:(element_ptr_a > option2026120038on_j_k)]: ((bind_e1012152651on_j_k @ none_element_ptr_a @ A) = none_S1393028981on_j_k))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_bind_Obind__lzero)).
% 228.49/61.55 thf(1058,plain,((! [A:(element_ptr_a > option2026120038on_j_k)]: ((bind_e1012152651on_j_k @ none_element_ptr_a @ (A)) = none_S1393028981on_j_k))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
% 228.49/61.55 thf(1059,plain,(! [A:(element_ptr_a > option2026120038on_j_k)] : (((bind_e1012152651on_j_k @ none_element_ptr_a @ (A)) = none_S1393028981on_j_k))),inference(cnf,[status(esa)],[1058])).
% 228.49/61.55 thf(1060,plain,(! [A:(element_ptr_a > option2026120038on_j_k)] : (((bind_e1012152651on_j_k @ none_element_ptr_a @ (A)) = none_S1393028981on_j_k))),inference(lifteq,[status(thm)],[1059])).
% 228.49/61.55 thf(303,axiom,((! [A:(option2026120038on_j_k > $o),B:option2026120038on_j_k,C:(sum_su1221287958on_j_k > option2026120038on_j_k)]: ((A @ (bind_S607117548on_j_k @ B @ C)) = (((B = none_S1393028981on_j_k) => (A @ none_S1393028981on_j_k)) & ! [D:sum_su1221287958on_j_k]: ((B = (some_S1960742641on_j_k @ D)) => (A @ (C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_bind__split)).
% 228.49/61.55 thf(1799,plain,((! [A:(option2026120038on_j_k > $o),B:option2026120038on_j_k,C:(sum_su1221287958on_j_k > option2026120038on_j_k)]: ((A @ (bind_S607117548on_j_k @ B @ (C))) = (((B = none_S1393028981on_j_k) => (A @ none_S1393028981on_j_k)) & ! [D:sum_su1221287958on_j_k]: ((B = (some_S1960742641on_j_k @ D)) => (A @ (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])).
% 228.49/61.55 thf(161,axiom,((! [A:list_n282880152tr_b_c,B:(list_n282880152tr_b_c > $o)]: ((A != nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c]: (B @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))) => ((! [C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: ((D != nil_no279930520tr_b_c) => ((B @ D) => (B @ (cons_n413985352tr_b_c @ C @ D))))) => (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_list__nonempty__induct)).
% 228.49/61.55 thf(1002,plain,((! [A:list_n282880152tr_b_c,B:(list_n282880152tr_b_c > $o)]: ((~ (A = nil_no279930520tr_b_c)) => ((! [C:node_p1234578834tr_b_c]: (B @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))) => ((! [C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: ((~ (D = nil_no279930520tr_b_c)) => ((B @ D) => (B @ (cons_n413985352tr_b_c @ C @ D))))) => (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
% 228.49/61.55 thf(319,axiom,((! [A:list_char,B:list_n282880152tr_b_c,C:list_char,D:list_n282880152tr_b_c,E:(list_char > (list_n282880152tr_b_c > (list_char > (list_n282880152tr_b_c > $o))))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_s2106487044tr_b_c @ D)) => ((E @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c) => ((! [F:char,G:list_char,H:node_p1234578834tr_b_c,I:list_n282880152tr_b_c,J:char,K:list_char,L:node_p1234578834tr_b_c,M:list_n282880152tr_b_c]: (((size_size_list_char @ G) = (size_s2106487044tr_b_c @ I)) => (((size_s2106487044tr_b_c @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_s2106487044tr_b_c @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_n413985352tr_b_c @ H @ I) @ (cons_char @ J @ K) @ (cons_n413985352tr_b_c @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_list__induct4)).
% 228.49/61.55 thf(1874,plain,((! [A:list_char,B:list_n282880152tr_b_c,C:list_char,D:list_n282880152tr_b_c,E:(list_char > (list_n282880152tr_b_c > (list_char > (list_n282880152tr_b_c > $o))))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_s2106487044tr_b_c @ D)) => ((E @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c) => ((! [F:char,G:list_char,H:node_p1234578834tr_b_c,I:list_n282880152tr_b_c,J:char,K:list_char,L:node_p1234578834tr_b_c,M:list_n282880152tr_b_c]: (((size_size_list_char @ G) = (size_s2106487044tr_b_c @ I)) => (((size_s2106487044tr_b_c @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_s2106487044tr_b_c @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_n413985352tr_b_c @ H @ I) @ (cons_char @ J @ K) @ (cons_n413985352tr_b_c @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])).
% 228.49/61.55 thf(16,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_add__Suc)).
% 228.49/61.55 thf(371,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 228.49/61.55 thf(259,axiom,((! [A:option_element_ptr_a]: ((! [B:element_ptr_a]: (A != (some_element_ptr_a @ B))) = (A = none_element_ptr_a)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_not__Some__eq)).
% 228.49/61.55 thf(1525,plain,((! [A:option_element_ptr_a]: ((! [B:element_ptr_a]: ~ (A = (some_element_ptr_a @ B))) = (A = none_element_ptr_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])).
% 228.49/61.55 thf(1826,plain,(! [A:list_char] : (((n_lists_char @ zero_zero_nat @ A) = (cons_list_char @ nil_char @ nil_list_char)))),inference(cnf,[status(esa)],[1825])).
% 228.49/61.55 thf(1827,plain,(! [A:list_char] : (((n_lists_char @ zero_zero_nat @ A) = (cons_list_char @ nil_char @ nil_list_char)))),inference(lifteq,[status(thm)],[1826])).
% 228.49/61.55 thf(168,axiom,(((product_lists_char @ nil_list_char) = (cons_list_char @ nil_char @ nil_list_char))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_product__lists_Osimps_I1_J)).
% 228.49/61.55 thf(1061,plain,(((product_lists_char @ nil_list_char) = (cons_list_char @ nil_char @ nil_list_char))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])).
% 228.49/61.55 thf(1062,plain,(((cons_list_char @ nil_char @ nil_list_char) = (product_lists_char @ nil_list_char))),inference(lifteq,[status(thm)],[1061])).
% 228.49/61.55 thf(2634,plain,(! [A:list_char] : (((n_lists_char @ zero_zero_nat @ A) = (product_lists_char @ nil_list_char)))),inference(rewrite,[status(thm)],[1827,1062])).
% 228.49/61.55 thf(149,axiom,((! [A:(rObjec1617416918on_j_k > $o),B:rObjec1617416918on_j_k]: ((! [C:product_unit,D:product_unit,E:list_char,F:option_element_ptr_a,G:list_n282880152tr_b_c,H:option2026120038on_j_k]: (A @ (rObjec1303043984on_j_k @ C @ (rDocum427676485on_j_k @ D @ E @ F @ G @ H)))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_RDocument_Oinduct__scheme)).
% 228.49/61.55 thf(921,plain,((! [A:(rObjec1617416918on_j_k > $o),B:rObjec1617416918on_j_k]: ((! [C:product_unit,D:product_unit,E:list_char,F:option_element_ptr_a,G:list_n282880152tr_b_c,H:option2026120038on_j_k]: (A @ (rObjec1303043984on_j_k @ C @ (rDocum427676485on_j_k @ D @ E @ F @ G @ H)))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
% 228.49/61.55 thf(112,axiom,((! [A:option2026120038on_j_k,B:option2026120038on_j_k]: (((size_s1129069050on_j_k @ A) != (size_s1129069050on_j_k @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_size__neq__size__imp__neq)).
% 228.49/61.55 thf(765,plain,((! [A:option2026120038on_j_k,B:option2026120038on_j_k]: ((~ ((size_s1129069050on_j_k @ A) = (size_s1129069050on_j_k @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
% 228.49/61.55 thf(216,axiom,((! [A:(list_char > (list_char > $o)),B:list_char,C:list_char]: ((! [D:list_char]: (A @ nil_char @ D)) => ((! [D:char,E:list_char,F:list_char]: ((A @ F @ E) => (A @ (cons_char @ D @ E) @ F))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_splice_Oinduct)).
% 228.49/61.55 thf(1286,plain,((! [A:(list_char > (list_char > $o)),B:list_char,C:list_char]: ((! [D:list_char]: (A @ nil_char @ D)) => ((! [D:char,E:list_char,F:list_char]: ((A @ F @ E) => (A @ (cons_char @ D @ E) @ F))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
% 228.49/61.55 thf(90,axiom,(((size_s9369994tr_b_c @ nil_li198338206tr_b_c) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_list_Osize_I3_J)).
% 228.49/61.55 thf(673,plain,(((size_s9369994tr_b_c @ nil_li198338206tr_b_c) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
% 228.49/61.55 thf(674,plain,(((size_s9369994tr_b_c @ nil_li198338206tr_b_c) = zero_zero_nat)),inference(lifteq,[status(thm)],[673])).
% 228.49/61.55 thf(150,axiom,((! [A:list_char,B:list_n282880152tr_b_c,C:list_char,D:(list_char > (list_n282880152tr_b_c > (list_char > $o)))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_size_list_char @ C)) => ((D @ nil_char @ nil_no279930520tr_b_c @ nil_char) => ((! [E:char,F:list_char,G:node_p1234578834tr_b_c,H:list_n282880152tr_b_c,I:char,J:list_char]: (((size_size_list_char @ F) = (size_s2106487044tr_b_c @ H)) => (((size_s2106487044tr_b_c @ H) = (size_size_list_char @ J)) => ((D @ F @ H @ J) => (D @ (cons_char @ E @ F) @ (cons_n413985352tr_b_c @ G @ H) @ (cons_char @ I @ J)))))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_list__induct3)).
% 228.49/61.55 thf(926,plain,((! [A:list_char,B:list_n282880152tr_b_c,C:list_char,D:(list_char > (list_n282880152tr_b_c > (list_char > $o)))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_size_list_char @ C)) => ((D @ nil_char @ nil_no279930520tr_b_c @ nil_char) => ((! [E:char,F:list_char,G:node_p1234578834tr_b_c,H:list_n282880152tr_b_c,I:char,J:list_char]: (((size_size_list_char @ F) = (size_s2106487044tr_b_c @ H)) => (((size_s2106487044tr_b_c @ H) = (size_size_list_char @ J)) => ((D @ F @ H @ J) => (D @ (cons_char @ E @ F) @ (cons_n413985352tr_b_c @ G @ H) @ (cons_char @ I @ J)))))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
% 228.49/61.55 thf(61,axiom,((! [A:docume1935157360tr_d_e]: ((! [B:nat]: (A != (docume1511108976tr_d_e @ B))) => (~ (! [B:sum_su1576157353tr_d_e]: (A != (docume1825929374tr_d_e @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_document__ptr_Oexhaust)).
% 228.49/61.55 thf(558,plain,((! [A:docume1935157360tr_d_e]: ((! [B:nat]: ~ (A = (docume1511108976tr_d_e @ B))) => (~ (! [B:sum_su1576157353tr_d_e]: ~ (A = (docume1825929374tr_d_e @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
% 228.49/61.55 thf(119,axiom,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Collect__mem__eq)).
% 228.49/61.55 thf(794,plain,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
% 228.49/61.55 thf(67,axiom,((gen_length_char = (^ [A:nat,B:list_char]: (plus_plus_nat @ A @ (size_size_list_char @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_gen__length__def)).
% 228.49/61.55 thf(585,plain,(((gen_length_char) = (^ [A:nat,B:list_char]: (plus_plus_nat @ A @ (size_size_list_char @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
% 228.49/61.55 thf(586,plain,(((gen_length_char) = (^ [A:nat,B:list_char]: (plus_plus_nat @ A @ (size_size_list_char @ B))))),inference(lifteq,[status(thm)],[585])).
% 228.49/61.55 thf(77,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:list_char,D:(list_char > list_char),E:(list_char > list_char)]: ((A = B) => (((doctyp814403297on_j_k @ B) = C) => ((! [F:list_char]: ((C = F) => ((D @ F) = (E @ F)))) => ((doctyp68000440on_j_k @ D @ A) = (doctyp68000440on_j_k @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_RDocument_Ofold__congs_I3_J)).
% 228.49/61.55 thf(618,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:list_char,D:(list_char > list_char),E:(list_char > list_char)]: ((A = B) => (((doctyp814403297on_j_k @ B) = C) => ((! [F:list_char]: ((C = F) => ((D @ F) = (E @ F)))) => ((doctyp68000440on_j_k @ (D) @ A) = (doctyp68000440on_j_k @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
% 228.49/61.55 thf(188,axiom,((! [A:list_char]: ((A != nil_char) => ((! [B:char]: (A != (cons_char @ B @ nil_char))) => (~ (! [B:char,C:char,D:list_char]: (A != (cons_char @ B @ (cons_char @ C @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_remdups__adj_Ocases)).
% 228.49/61.55 thf(1146,plain,((! [A:list_char]: ((~ (A = nil_char)) => ((! [B:char]: ~ (A = (cons_char @ B @ nil_char))) => (~ (! [B:char,C:char,D:list_char]: ~ (A = (cons_char @ B @ (cons_char @ C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
% 228.49/61.55 thf(285,axiom,((! [A:(list_n282880152tr_b_c > $o),B:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c]: (A @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))) => ((! [C:node_p1234578834tr_b_c,D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (((C = D) => (A @ (cons_n413985352tr_b_c @ C @ E))) => (((C != D) => (A @ (cons_n413985352tr_b_c @ D @ E))) => (A @ (cons_n413985352tr_b_c @ C @ (cons_n413985352tr_b_c @ D @ E)))))) => (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_remdups__adj_Oinduct)).
% 228.49/61.55 thf(1680,plain,((! [A:(list_n282880152tr_b_c > $o),B:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c]: (A @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))) => ((! [C:node_p1234578834tr_b_c,D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (((C = D) => (A @ (cons_n413985352tr_b_c @ C @ E))) => (((~ (C = D)) => (A @ (cons_n413985352tr_b_c @ D @ E))) => (A @ (cons_n413985352tr_b_c @ C @ (cons_n413985352tr_b_c @ D @ E)))))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])).
% 228.49/61.55 thf(398,plain,((? [A:(nat > (nat > nat))]: ! [B:nat,C:nat]: ((A @ C @ (plus_plus_nat @ B @ C)) = B))),inference(detectInverse,[status(thm)],[397])).
% 228.49/61.55 thf(399,plain,(! [B:nat,A:nat] : (((sk2 @ B @ (plus_plus_nat @ A @ B)) = A))),inference(cnf,[status(esa)],[398])).
% 228.49/61.55 thf(3358,plain,(! [B:nat,A:nat] : (((sk2 @ B @ (plus_plus_nat @ A @ B)) = A))),inference(lifteq,[status(thm)],[399])).
% 228.49/61.55 thf(854,plain,((~ (? [A:option2026120038on_j_k]: ((size_s1129069050on_j_k @ A) = zero_zero_nat)))),inference(miniscope,[status(thm)],[853])).
% 228.49/61.55 thf(855,plain,(! [A:option2026120038on_j_k] : ((~ ((size_s1129069050on_j_k @ A) = zero_zero_nat)))),inference(cnf,[status(esa)],[854])).
% 228.49/61.55 thf(856,plain,(! [A:option2026120038on_j_k] : (((size_s1129069050on_j_k @ A) != zero_zero_nat))),inference(lifteq,[status(thm)],[855])).
% 228.49/61.55 thf(63,axiom,((! [A:nat]: ((size_s724035844tr_d_e @ (docume1511108976tr_d_e @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_document__ptr_Osize_I3_J)).
% 228.49/61.55 thf(571,plain,((! [A:nat]: ((size_s724035844tr_d_e @ (docume1511108976tr_d_e @ A)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
% 228.49/61.55 thf(572,plain,(! [A:nat] : (((size_s724035844tr_d_e @ (docume1511108976tr_d_e @ A)) = (suc @ zero_zero_nat)))),inference(cnf,[status(esa)],[571])).
% 228.49/61.55 thf(573,plain,(! [A:nat] : (((size_s724035844tr_d_e @ (docume1511108976tr_d_e @ A)) = (suc @ zero_zero_nat)))),inference(lifteq,[status(thm)],[572])).
% 228.49/61.55 thf(37,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_add__cancel__left__right)).
% 228.49/61.55 thf(444,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
% 228.49/61.55 thf(72,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)) | ((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_add__is__1)).
% 228.49/61.55 thf(601,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)) | ((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
% 228.49/61.56 thf(28,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_zero__eq__add__iff__both__eq__0)).
% 228.49/61.56 thf(412,plain,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 228.49/61.56 thf(62,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:product_unit,D:(product_unit > product_unit),E:(product_unit > product_unit)]: ((A = B) => (((nothin757132294on_j_k @ B) = C) => ((! [F:product_unit]: ((C = F) => ((D @ F) = (E @ F)))) => ((nothin1105341917on_j_k @ D @ A) = (nothin1105341917on_j_k @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_RDocument_Ofold__congs_I2_J)).
% 228.49/61.56 thf(562,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:product_unit,D:(product_unit > product_unit),E:(product_unit > product_unit)]: ((A = B) => (((nothin757132294on_j_k @ B) = C) => ((! [F:product_unit]: ((C = F) => ((D @ F) = (E @ F)))) => ((nothin1105341917on_j_k @ (D) @ A) = (nothin1105341917on_j_k @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
% 228.49/61.56 thf(1832,plain,(! [A:set_nat] : (((nths_n1256675478tr_b_c @ nil_no279930520tr_b_c @ A) = nil_no279930520tr_b_c))),inference(cnf,[status(esa)],[1831])).
% 228.49/61.56 thf(1833,plain,(! [A:set_nat] : (((nths_n1256675478tr_b_c @ nil_no279930520tr_b_c @ A) = nil_no279930520tr_b_c))),inference(lifteq,[status(thm)],[1832])).
% 228.49/61.56 thf(44,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__induct)).
% 228.49/61.56 thf(470,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
% 228.49/61.56 thf(471,plain,((! [A:(nat > $o)]: ((A @ zero_zero_nat) => ((! [B:nat]: ((A @ B) => (A @ (suc @ B)))) => (! [B:nat]: (A @ B)))))),inference(miniscope,[status(thm)],[470])).
% 228.49/61.56 thf(472,plain,(! [B:nat,A:(nat > $o)] : (((~ (A @ zero_zero_nat) | (A @ (sk9 @ (A))) | (A @ B)) & (~ (A @ zero_zero_nat) | ~ (A @ (suc @ (sk9 @ (A)))) | (A @ B))))),inference(cnf,[status(esa)],[471])).
% 228.49/61.56 thf(473,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero_zero_nat)) | (A @ (sk9 @ (A))) | (A @ B))),inference(cnfConj,[status(thm)],[472])).
% 228.49/61.56 thf(475,plain,(! [A:nat] : ((~ (zero_zero_nat = zero_zero_nat)) | (zero_zero_nat = (sk9 @ ((=) @ nat @ zero_zero_nat))) | (zero_zero_nat = A))),inference(replace_leibeq,[status(thm)],[473:[bind(A, $thf((=) @ nat @ zero_zero_nat))]])).
% 228.49/61.56 thf(477,plain,(! [A:nat] : ((zero_zero_nat != zero_zero_nat) | ((sk9 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat) | (zero_zero_nat = A))),inference(lifteq,[status(thm)],[475])).
% 228.49/61.56 thf(478,plain,(! [A:nat] : (((sk9 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat) | (zero_zero_nat = A))),inference(simp,[status(thm)],[477])).
% 228.49/61.56 thf(2725,plain,(! [A:nat] : (((sk9 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat) | (zero_zero_nat != zero_zero_nat) | (A != (suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat))))),inference(paramod_ordered,[status(thm)],[478,2607])).
% 228.49/61.56 thf(2726,plain,(! [A:nat] : (((sk9 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat) | (A != (suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat))))),inference(simp,[status(thm)],[2725])).
% 228.49/61.56 thf(2727,plain,(((sk9 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat)),inference(pattern_uni,[status(thm)],[2726:[bind(A, $thf(suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat)))]])).
% 228.49/61.56 thf(299,axiom,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((more_c1453068134on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = F))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_RDocument_Oselect__convs_I5_J)).
% 228.49/61.56 thf(1784,plain,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((more_c1453068134on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = F))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])).
% 228.49/61.56 thf(1124,plain,(! [A:list_char] : (((append_char @ A @ nil_char) = A))),inference(cnf,[status(esa)],[1123])).
% 228.49/61.56 thf(1125,plain,(! [A:list_char] : (((append_char @ A @ nil_char) = A))),inference(lifteq,[status(thm)],[1124])).
% 228.49/61.56 thf(114,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:option_element_ptr_a,D:(option_element_ptr_a > option_element_ptr_a),E:(option_element_ptr_a > option_element_ptr_a)]: ((A = B) => (((docume1175131570on_j_k @ B) = C) => ((! [F:option_element_ptr_a]: ((C = F) => ((D @ F) = (E @ F)))) => ((docume244715269on_j_k @ D @ A) = (docume244715269on_j_k @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_RDocument_Ofold__congs_I4_J)).
% 228.49/61.56 thf(772,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:option_element_ptr_a,D:(option_element_ptr_a > option_element_ptr_a),E:(option_element_ptr_a > option_element_ptr_a)]: ((A = B) => (((docume1175131570on_j_k @ B) = C) => ((! [F:option_element_ptr_a]: ((C = F) => ((D @ F) = (E @ F)))) => ((docume244715269on_j_k @ (D) @ A) = (docume244715269on_j_k @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
% 228.49/61.56 thf(282,axiom,((! [A:list_char,B:list_n282880152tr_b_c,C:(list_char > (list_n282880152tr_b_c > $o))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => ((C @ nil_char @ nil_no279930520tr_b_c) => ((! [D:char,E:list_char,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: (((size_size_list_char @ E) = (size_s2106487044tr_b_c @ G)) => ((C @ E @ G) => (C @ (cons_char @ D @ E) @ (cons_n413985352tr_b_c @ F @ G))))) => (C @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_list__induct2)).
% 228.49/61.56 thf(1652,plain,((! [A:list_char,B:list_n282880152tr_b_c,C:(list_char > (list_n282880152tr_b_c > $o))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => ((C @ nil_char @ nil_no279930520tr_b_c) => ((! [D:char,E:list_char,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: (((size_size_list_char @ E) = (size_s2106487044tr_b_c @ G)) => ((C @ E @ G) => (C @ (cons_char @ D @ E) @ (cons_n413985352tr_b_c @ F @ G))))) => (C @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])).
% 228.49/61.56 thf(107,axiom,((! [A:object945351580_d_e_f,B:docume1935157360tr_d_e,C:rObjec1413572695_j_k_l,D:heap_S1465075775_j_k_l]: (((A = (cast_d1608273229_b_c_f @ B)) => ((get_D_1192261494_j_k_l @ B @ (put_O_834343516_j_k_l @ A @ C @ D)) = (cast_O1034441233_j_k_l @ C))) & ((A != (cast_d1608273229_b_c_f @ B)) => ((get_D_1192261494_j_k_l @ B @ (put_O_834343516_j_k_l @ A @ C @ D)) = (get_D_1192261494_j_k_l @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_get__document__ptr__simp)).
% 228.49/61.56 thf(743,plain,((! [A:object945351580_d_e_f,B:docume1935157360tr_d_e,C:rObjec1413572695_j_k_l,D:heap_S1465075775_j_k_l]: (((A = (cast_d1608273229_b_c_f @ B)) => ((get_D_1192261494_j_k_l @ B @ (put_O_834343516_j_k_l @ A @ C @ D)) = (cast_O1034441233_j_k_l @ C))) & ((~ (A = (cast_d1608273229_b_c_f @ B))) => ((get_D_1192261494_j_k_l @ B @ (put_O_834343516_j_k_l @ A @ C @ D)) = (get_D_1192261494_j_k_l @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
% 228.49/61.56 thf(65,axiom,((! [A:rObjec103300152t_unit]: (A = (rObjec730108904t_unit @ (nothing_Product_unit @ A) @ (more_Product_unit @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_RObject_Osurjective)).
% 228.49/61.56 thf(579,plain,((! [A:rObjec103300152t_unit]: (A = (rObjec730108904t_unit @ (nothing_Product_unit @ A) @ (more_Product_unit @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
% 228.49/61.56 thf(238,axiom,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((nothin757132294on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_RDocument_Oselect__convs_I1_J)).
% 228.49/61.56 thf(1403,plain,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((nothin757132294on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
% 228.49/61.56 thf(875,plain,(((^ [A:(option2026120038on_j_k > $o)]: ((A @ none_S1393028981on_j_k) & ! [B:sum_su1221287958on_j_k]: (A @ (some_S1960742641on_j_k @ B)))) = ((!) @ option2026120038on_j_k))),inference(lifteq,[status(thm)],[874])).
% 228.49/61.56 thf(101,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:option2026120038on_j_k,D:(option2026120038on_j_k > option2026120038on_j_k),E:(option2026120038on_j_k > option2026120038on_j_k)]: ((A = B) => (((more_c1453068134on_j_k @ B) = C) => ((! [F:option2026120038on_j_k]: ((C = F) => ((D @ F) = (E @ F)))) => ((more_u1044474223_c_a_b @ D @ A) = (more_u1044474223_c_a_b @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_RDocument_Ofold__congs_I6_J)).
% 228.49/61.56 thf(711,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:option2026120038on_j_k,D:(option2026120038on_j_k > option2026120038on_j_k),E:(option2026120038on_j_k > option2026120038on_j_k)]: ((A = B) => (((more_c1453068134on_j_k @ B) = C) => ((! [F:option2026120038on_j_k]: ((C = F) => ((D @ F) = (E @ F)))) => ((more_u1044474223_c_a_b @ (D) @ A) = (more_u1044474223_c_a_b @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
% 228.49/61.56 thf(210,axiom,((! [A:rObjec103300152t_unit]: ((rObjec730108904t_unit @ product_Unity @ (more_Product_unit @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_object__empty)).
% 228.49/61.56 thf(1256,plain,((! [A:rObjec103300152t_unit]: ((rObjec730108904t_unit @ product_Unity @ (more_Product_unit @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])).
% 228.49/61.56 thf(241,axiom,((! [A:node_p1234578834tr_b_c,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c,D:list_n282880152tr_b_c]: (((cons_n413985352tr_b_c @ A @ B) = (append846395565tr_b_c @ C @ D)) = (((C = nil_no279930520tr_b_c) & ((cons_n413985352tr_b_c @ A @ B) = D)) | ? [E:list_n282880152tr_b_c]: (((cons_n413985352tr_b_c @ A @ E) = C) & (B = (append846395565tr_b_c @ E @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_Cons__eq__append__conv)).
% 228.49/61.56 thf(1428,plain,((! [A:node_p1234578834tr_b_c,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c,D:list_n282880152tr_b_c]: (((cons_n413985352tr_b_c @ A @ B) = (append846395565tr_b_c @ C @ D)) = (((C = nil_no279930520tr_b_c) & ((cons_n413985352tr_b_c @ A @ B) = D)) | ? [E:list_n282880152tr_b_c]: (((cons_n413985352tr_b_c @ A @ E) = C) & (B = (append846395565tr_b_c @ E @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
% 228.49/61.56 thf(1705,plain,((~ (? [A:node_p1234578834tr_b_c,B:list_n282880152tr_b_c]: (nil_no279930520tr_b_c = (cons_n413985352tr_b_c @ A @ B))))),inference(miniscope,[status(thm)],[1704])).
% 228.49/61.56 thf(1706,plain,(! [B:list_n282880152tr_b_c,A:node_p1234578834tr_b_c] : ((~ (nil_no279930520tr_b_c = (cons_n413985352tr_b_c @ A @ B))))),inference(cnf,[status(esa)],[1705])).
% 228.49/61.56 thf(1707,plain,(! [B:list_n282880152tr_b_c,A:node_p1234578834tr_b_c] : (((cons_n413985352tr_b_c @ A @ B) != nil_no279930520tr_b_c))),inference(lifteq,[status(thm)],[1706])).
% 228.49/61.56 thf(208,axiom,((! [A:(list_n282880152tr_b_c > list_n282880152tr_b_c),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((discon442323090on_j_k @ A @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ (A @ F) @ G))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_RDocument_Oupdate__convs_I4_J)).
% 228.49/61.56 thf(1239,plain,((! [A:(list_n282880152tr_b_c > list_n282880152tr_b_c),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((discon442323090on_j_k @ (A) @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ (A @ F) @ G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
% 228.49/61.56 thf(223,axiom,((! [A:option2026120038on_j_k,B:sum_su1221287958on_j_k]: ((A = (some_S1960742641on_j_k @ B)) => (A != none_S1393028981on_j_k)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_option_OdiscI)).
% 228.49/61.56 thf(1332,plain,((! [A:option2026120038on_j_k,B:sum_su1221287958on_j_k]: ((A = (some_S1960742641on_j_k @ B)) => (~ (A = none_S1393028981on_j_k))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
% 228.49/61.56 thf(296,axiom,((! [A:nat]: ((gen_length_char @ A @ nil_char) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_gen__length__code_I1_J)).
% 228.49/61.56 thf(1763,plain,((! [A:nat]: ((gen_length_char @ A @ nil_char) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])).
% 228.49/61.56 thf(1764,plain,(! [A:nat] : (((gen_length_char @ A @ nil_char) = A))),inference(cnf,[status(esa)],[1763])).
% 228.49/61.56 thf(1765,plain,(! [A:nat] : (((gen_length_char @ A @ nil_char) = A))),inference(lifteq,[status(thm)],[1764])).
% 228.49/61.56 thf(123,axiom,((! [A:(docume1935157360tr_d_e > $o),B:docume1935157360tr_d_e]: ((! [C:nat]: (A @ (docume1511108976tr_d_e @ C))) => ((! [C:sum_su1576157353tr_d_e]: (A @ (docume1825929374tr_d_e @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_document__ptr_Oinduct)).
% 228.49/61.56 thf(804,plain,((! [A:(docume1935157360tr_d_e > $o),B:docume1935157360tr_d_e]: ((! [C:nat]: (A @ (docume1511108976tr_d_e @ C))) => ((! [C:sum_su1576157353tr_d_e]: (A @ (docume1825929374tr_d_e @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
% 228.49/61.56 thf(230,axiom,((! [A:list_n282880152tr_b_c]: ((nths_n1256675478tr_b_c @ A @ bot_bot_set_nat) = nil_no279930520tr_b_c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_nths__empty)).
% 228.49/61.56 thf(1356,plain,((! [A:list_n282880152tr_b_c]: ((nths_n1256675478tr_b_c @ A @ bot_bot_set_nat) = nil_no279930520tr_b_c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
% 228.49/61.56 thf(57,axiom,((! [A:list_list_char]: (((size_s2008079621t_char @ A) = zero_zero_nat) = (A = nil_list_char)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_length__0__conv)).
% 228.49/61.56 thf(540,plain,((! [A:list_list_char]: (((size_s2008079621t_char @ A) = zero_zero_nat) = (A = nil_list_char)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
% 228.49/61.56 thf(21,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_group__cancel_Oadd2)).
% 228.49/61.56 thf(387,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
% 228.49/61.56 thf(388,plain,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus_nat @ B @ C)) => (! [D:nat]: ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))))))),inference(miniscope,[status(thm)],[387])).
% 228.49/61.56 thf(389,plain,(! [D:nat,C:nat,B:nat,A:nat] : ((~ (A = (plus_plus_nat @ B @ C))) | ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))))),inference(cnf,[status(esa)],[388])).
% 228.49/61.56 thf(390,plain,(! [D:nat,C:nat,B:nat,A:nat] : ((A != (plus_plus_nat @ B @ C)) | ((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))))),inference(lifteq,[status(thm)],[389])).
% 228.49/61.56 thf(391,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ C @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ A @ (plus_plus_nat @ C @ B))))),inference(simp,[status(thm)],[390])).
% 228.49/61.56 thf(256,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((n_lists_char @ A @ nil_char) = (cons_list_char @ nil_char @ nil_list_char))) & ((A != zero_zero_nat) => ((n_lists_char @ A @ nil_char) = nil_list_char))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_n__lists__Nil)).
% 228.49/61.56 thf(1503,plain,((! [A:nat]: (((A = zero_zero_nat) => ((n_lists_char @ A @ nil_char) = (cons_list_char @ nil_char @ nil_list_char))) & ((~ (A = zero_zero_nat)) => ((n_lists_char @ A @ nil_char) = nil_list_char))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])).
% 228.49/61.56 thf(75,axiom,((! [A:(element_ptr_a > nat),B:element_ptr_a]: ((size_o1591053974_ptr_a @ A @ (some_element_ptr_a @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_option_Osize__gen_I2_J)).
% 228.49/61.56 thf(611,plain,((! [A:(element_ptr_a > nat),B:element_ptr_a]: ((size_o1591053974_ptr_a @ (A) @ (some_element_ptr_a @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])).
% 228.49/61.56 thf(117,axiom,((! [A:product_unit,B:product_unit,C:product_unit,D:product_unit]: (((rObjec730108904t_unit @ A @ B) = (rObjec730108904t_unit @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_RObject_Oext__inject)).
% 228.49/61.56 thf(787,plain,((! [A:product_unit,B:product_unit,C:product_unit,D:product_unit]: (((rObjec730108904t_unit @ A @ B) = (rObjec730108904t_unit @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
% 228.49/61.56 thf(1257,plain,(! [A:rObjec103300152t_unit] : (((rObjec730108904t_unit @ product_Unity @ (more_Product_unit @ A)) = A))),inference(cnf,[status(esa)],[1256])).
% 228.49/61.56 thf(1258,plain,(! [A:rObjec103300152t_unit] : (((rObjec730108904t_unit @ product_Unity @ (more_Product_unit @ A)) = A))),inference(lifteq,[status(thm)],[1257])).
% 228.49/61.56 thf(99,axiom,((! [A:nat,B:nat]: (((docume1511108976tr_d_e @ A) = (docume1511108976tr_d_e @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_document__ptr_Oinject_I1_J)).
% 228.49/61.56 thf(704,plain,((! [A:nat,B:nat]: (((docume1511108976tr_d_e @ A) = (docume1511108976tr_d_e @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])).
% 228.49/61.56 thf(73,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k]: (((nothin1567949605on_j_k @ A) = (nothin1567949605on_j_k @ B)) => (((nothin757132294on_j_k @ A) = (nothin757132294on_j_k @ B)) => (((doctyp814403297on_j_k @ A) = (doctyp814403297on_j_k @ B)) => (((docume1175131570on_j_k @ A) = (docume1175131570on_j_k @ B)) => (((discon866287741on_j_k @ A) = (discon866287741on_j_k @ B)) => (((more_c1453068134on_j_k @ A) = (more_c1453068134on_j_k @ B)) => (A = B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_RDocument_Oequality)).
% 228.49/61.56 thf(604,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k]: (((nothin1567949605on_j_k @ A) = (nothin1567949605on_j_k @ B)) => (((nothin757132294on_j_k @ A) = (nothin757132294on_j_k @ B)) => (((doctyp814403297on_j_k @ A) = (doctyp814403297on_j_k @ B)) => (((docume1175131570on_j_k @ A) = (docume1175131570on_j_k @ B)) => (((discon866287741on_j_k @ A) = (discon866287741on_j_k @ B)) => (((more_c1453068134on_j_k @ A) = (more_c1453068134on_j_k @ B)) => (A = B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
% 228.49/61.56 thf(200,axiom,((! [A:(option_element_ptr_a > $o),B:option_element_ptr_a]: ((A @ none_element_ptr_a) => ((! [C:element_ptr_a]: (A @ (some_element_ptr_a @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_option_Oinducts)).
% 228.49/61.56 thf(1209,plain,((! [A:(option_element_ptr_a > $o),B:option_element_ptr_a]: ((A @ none_element_ptr_a) => ((! [C:element_ptr_a]: (A @ (some_element_ptr_a @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
% 228.49/61.56 thf(26,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_add_Oright__neutral)).
% 228.49/61.56 thf(406,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 228.49/61.56 thf(5,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_add__left__imp__eq)).
% 228.49/61.56 thf(336,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 228.49/61.56 thf(337,plain,(! [C:nat,B:nat,A:nat] : ((~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))) | (B = C))),inference(cnf,[status(esa)],[336])).
% 228.49/61.56 thf(338,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ A @ B) != (plus_plus_nat @ A @ C)) | (B = C))),inference(lifteq,[status(thm)],[337])).
% 228.49/61.56 thf(339,plain,((? [A:(nat > (nat > nat))]: ! [B:nat,C:nat]: ((A @ B @ (plus_plus_nat @ B @ C)) = C))),inference(detectInverse,[status(thm)],[338])).
% 228.49/61.56 thf(340,plain,(! [B:nat,A:nat] : (((sk1 @ A @ (plus_plus_nat @ A @ B)) = B))),inference(cnf,[status(esa)],[339])).
% 228.49/61.56 thf(1987,plain,(! [B:nat,A:nat] : (((sk1 @ A @ (plus_plus_nat @ A @ B)) = B))),inference(lifteq,[status(thm)],[340])).
% 228.49/61.56 thf(2414,plain,(! [C:nat,B:nat,A:nat] : (((sk1 @ B @ A) = C) | ((plus_plus_nat @ A @ zero_zero_nat) != (plus_plus_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[394,1987])).
% 228.49/61.56 thf(2415,plain,(! [A:nat] : (((sk1 @ A @ A) = zero_zero_nat))),inference(pattern_uni,[status(thm)],[2414:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(zero_zero_nat))]])).
% 228.49/61.56 thf(116,axiom,((! [A:(list_n282880152tr_b_c > $o)]: ~ (list_e529904353tr_b_c @ A @ nil_li198338206tr_b_c))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_list__ex1__simps_I1_J)).
% 228.49/61.56 thf(784,plain,((! [A:(list_n282880152tr_b_c > $o)]: ~ (list_e529904353tr_b_c @ (A) @ nil_li198338206tr_b_c))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
% 228.49/61.56 thf(305,axiom,((! [A:list_n282880152tr_b_c]: ((A != nil_no279930520tr_b_c) = (? [B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c]: (A = (cons_n413985352tr_b_c @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_neq__Nil__conv)).
% 228.49/61.56 thf(1806,plain,((! [A:list_n282880152tr_b_c]: ((~ (A = nil_no279930520tr_b_c)) = (? [B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c]: (A = (cons_n413985352tr_b_c @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])).
% 228.49/61.56 thf(228,axiom,((! [A:rObjec103300152t_unit]: ~ (! [B:product_unit]: (A != (rObjec730108904t_unit @ B @ product_Unity))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_RObject_Ocases)).
% 228.49/61.56 thf(1349,plain,((! [A:rObjec103300152t_unit]: ~ (! [B:product_unit]: ~ (A = (rObjec730108904t_unit @ B @ product_Unity))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
% 228.49/61.56 thf(13,axiom,((! [A:docume1935157360tr_d_e,B:docume1935157360tr_d_e]: (((size_s724035844tr_d_e @ A) != (size_s724035844tr_d_e @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_size__neq__size__imp__neq)).
% 228.49/61.56 thf(362,plain,((! [A:docume1935157360tr_d_e,B:docume1935157360tr_d_e]: ((~ ((size_s724035844tr_d_e @ A) = (size_s724035844tr_d_e @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 228.49/61.56 thf(267,axiom,((! [A:list_char,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c,D:(list_char > (list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_s2106487044tr_b_c @ C)) => ((D @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [E:char,F:list_char,G:node_p1234578834tr_b_c,H:list_n282880152tr_b_c,I:node_p1234578834tr_b_c,J:list_n282880152tr_b_c]: (((size_size_list_char @ F) = (size_s2106487044tr_b_c @ H)) => (((size_s2106487044tr_b_c @ H) = (size_s2106487044tr_b_c @ J)) => ((D @ F @ H @ J) => (D @ (cons_char @ E @ F) @ (cons_n413985352tr_b_c @ G @ H) @ (cons_n413985352tr_b_c @ I @ J)))))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_list__induct3)).
% 228.49/61.56 thf(1571,plain,((! [A:list_char,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c,D:(list_char > (list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_s2106487044tr_b_c @ C)) => ((D @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [E:char,F:list_char,G:node_p1234578834tr_b_c,H:list_n282880152tr_b_c,I:node_p1234578834tr_b_c,J:list_n282880152tr_b_c]: (((size_size_list_char @ F) = (size_s2106487044tr_b_c @ H)) => (((size_s2106487044tr_b_c @ H) = (size_s2106487044tr_b_c @ J)) => ((D @ F @ H @ J) => (D @ (cons_char @ E @ F) @ (cons_n413985352tr_b_c @ G @ H) @ (cons_n413985352tr_b_c @ I @ J)))))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])).
% 228.49/61.56 thf(137,axiom,((! [A:(option_element_ptr_a > $o),B:option2026120038on_j_k,C:(sum_su1221287958on_j_k > option_element_ptr_a)]: ((A @ (bind_S287509021_ptr_a @ B @ C)) = (((B = none_S1393028981on_j_k) => (A @ none_element_ptr_a)) & ! [D:sum_su1221287958on_j_k]: ((B = (some_S1960742641on_j_k @ D)) => (A @ (C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_bind__split)).
% 228.49/61.56 thf(863,plain,((! [A:(option_element_ptr_a > $o),B:option2026120038on_j_k,C:(sum_su1221287958on_j_k > option_element_ptr_a)]: ((A @ (bind_S287509021_ptr_a @ B @ (C))) = (((B = none_S1393028981on_j_k) => (A @ none_element_ptr_a)) & ! [D:sum_su1221287958on_j_k]: ((B = (some_S1960742641on_j_k @ D)) => (A @ (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
% 228.49/61.56 thf(2245,plain,(! [C:nat,B:nat,A:nat] : (((sk1 @ B @ A) = C) | ((plus_plus_nat @ zero_zero_nat @ A) != (plus_plus_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[355,1987])).
% 228.49/61.56 thf(2246,plain,(! [A:nat] : (((sk1 @ zero_zero_nat @ A) = A))),inference(pattern_uni,[status(thm)],[2245:[bind(A, $thf(A)),bind(B, $thf(zero_zero_nat)),bind(C, $thf(A))]])).
% 228.49/61.56 thf(255,axiom,((! [A:list_n282880152tr_b_c,B:list_char,C:list_char,D:(list_n282880152tr_b_c > (list_char > (list_char > $o)))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => ((D @ nil_no279930520tr_b_c @ nil_char @ nil_char) => ((! [E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c,G:char,H:list_char,I:char,J:list_char]: (((size_s2106487044tr_b_c @ F) = (size_size_list_char @ H)) => (((size_size_list_char @ H) = (size_size_list_char @ J)) => ((D @ F @ H @ J) => (D @ (cons_n413985352tr_b_c @ E @ F) @ (cons_char @ G @ H) @ (cons_char @ I @ J)))))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_list__induct3)).
% 228.49/61.56 thf(1492,plain,((! [A:list_n282880152tr_b_c,B:list_char,C:list_char,D:(list_n282880152tr_b_c > (list_char > (list_char > $o)))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => ((D @ nil_no279930520tr_b_c @ nil_char @ nil_char) => ((! [E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c,G:char,H:list_char,I:char,J:list_char]: (((size_s2106487044tr_b_c @ F) = (size_size_list_char @ H)) => (((size_size_list_char @ H) = (size_size_list_char @ J)) => ((D @ F @ H @ J) => (D @ (cons_n413985352tr_b_c @ E @ F) @ (cons_char @ G @ H) @ (cons_char @ I @ J)))))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])).
% 228.49/61.56 thf(271,axiom,((! [A:list_n282880152tr_b_c,B:list_char,C:list_n282880152tr_b_c,D:(list_n282880152tr_b_c > (list_char > (list_n282880152tr_b_c > $o)))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => ((D @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c) => ((! [E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c,G:char,H:list_char,I:node_p1234578834tr_b_c,J:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ F) = (size_size_list_char @ H)) => (((size_size_list_char @ H) = (size_s2106487044tr_b_c @ J)) => ((D @ F @ H @ J) => (D @ (cons_n413985352tr_b_c @ E @ F) @ (cons_char @ G @ H) @ (cons_n413985352tr_b_c @ I @ J)))))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_list__induct3)).
% 228.49/61.56 thf(1603,plain,((! [A:list_n282880152tr_b_c,B:list_char,C:list_n282880152tr_b_c,D:(list_n282880152tr_b_c > (list_char > (list_n282880152tr_b_c > $o)))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => ((D @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c) => ((! [E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c,G:char,H:list_char,I:node_p1234578834tr_b_c,J:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ F) = (size_size_list_char @ H)) => (((size_size_list_char @ H) = (size_s2106487044tr_b_c @ J)) => ((D @ F @ H @ J) => (D @ (cons_n413985352tr_b_c @ E @ F) @ (cons_char @ G @ H) @ (cons_n413985352tr_b_c @ I @ J)))))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])).
% 228.49/61.56 thf(79,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ A) != (size_s2106487044tr_b_c @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_neq__if__length__neq)).
% 228.49/61.56 thf(631,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((~ ((size_s2106487044tr_b_c @ A) = (size_s2106487044tr_b_c @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
% 228.49/61.56 thf(59,axiom,((! [A:(sum_su1576157353tr_d_e > nat),B:nat]: ((docume1799427087tr_d_e @ A @ (docume1511108976tr_d_e @ B)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_document__ptr_Osize__gen_I1_J)).
% 228.49/61.56 thf(552,plain,((! [A:(sum_su1576157353tr_d_e > nat),B:nat]: ((docume1799427087tr_d_e @ (A) @ (docume1511108976tr_d_e @ B)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
% 228.49/61.56 thf(70,axiom,((! [A:nat]: ? [B:list_char]: ((size_size_list_char @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Ex__list__of__length)).
% 228.49/61.56 thf(594,plain,((! [A:nat]: ? [B:list_char]: ((size_size_list_char @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
% 228.49/61.56 thf(46,axiom,((! [A:rObjec103300152t_unit,B:rObjec103300152t_unit]: (((nothing_Product_unit @ A) = (nothing_Product_unit @ B)) => (((more_Product_unit @ A) = (more_Product_unit @ B)) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_RObject_Oequality)).
% 228.49/61.56 thf(483,plain,((! [A:rObjec103300152t_unit,B:rObjec103300152t_unit]: (((nothing_Product_unit @ A) = (nothing_Product_unit @ B)) => (((more_Product_unit @ A) = (more_Product_unit @ B)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
% 228.49/61.56 thf(53,axiom,((! [A:(rObjec1617416918on_j_k > nat),B:rObjec1617416918on_j_k]: ((size_o26122489on_j_k @ A @ (some_R67702331on_j_k @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_option_Osize__gen_I2_J)).
% 228.49/61.56 thf(520,plain,((! [A:(rObjec1617416918on_j_k > nat),B:rObjec1617416918on_j_k]: ((size_o26122489on_j_k @ (A) @ (some_R67702331on_j_k @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
% 228.49/61.56 thf(147,axiom,((! [A:(option2026120038on_j_k > $o),B:option_element_ptr_a,C:(element_ptr_a > option2026120038on_j_k)]: ((A @ (bind_e1012152651on_j_k @ B @ C)) = (~ (((B = none_element_ptr_a) & ~ (A @ none_S1393028981on_j_k)) | ? [D:element_ptr_a]: ((B = (some_element_ptr_a @ D)) & ~ (A @ (C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_bind__split__asm)).
% 228.49/61.56 thf(915,plain,((! [A:(option2026120038on_j_k > $o),B:option_element_ptr_a,C:(element_ptr_a > option2026120038on_j_k)]: ((A @ (bind_e1012152651on_j_k @ B @ (C))) = (~ (((B = none_element_ptr_a) & ~ (A @ none_S1393028981on_j_k)) | ? [D:element_ptr_a]: ((B = (some_element_ptr_a @ D)) & ~ (A @ (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
% 228.49/61.56 thf(113,axiom,((! [A:product_unit,B:product_unit]: ((more_Product_unit @ (rObjec730108904t_unit @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_RObject_Oselect__convs_I2_J)).
% 228.49/61.56 thf(769,plain,((! [A:product_unit,B:product_unit]: ((more_Product_unit @ (rObjec730108904t_unit @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
% 228.49/61.56 thf(3,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_ab__semigroup__add__class_Oadd__ac_I1_J)).
% 228.49/61.56 thf(330,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 228.49/61.56 thf(110,axiom,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_mem__Collect__eq)).
% 228.49/61.56 thf(758,plain,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
% 228.49/61.56 thf(1338,plain,(! [A:list_n282880152tr_b_c] : (((splice1294941035tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(cnf,[status(esa)],[1337])).
% 228.49/61.56 thf(1339,plain,(! [A:list_n282880152tr_b_c] : (((splice1294941035tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(lifteq,[status(thm)],[1338])).
% 228.49/61.56 thf(121,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k]: (((nothin1567949605on_j_k @ A) = (nothin1567949605on_j_k @ B)) => (((more_R1625109589on_j_k @ A) = (more_R1625109589on_j_k @ B)) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_RObject_Oequality)).
% 228.49/61.56 thf(799,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k]: (((nothin1567949605on_j_k @ A) = (nothin1567949605on_j_k @ B)) => (((more_R1625109589on_j_k @ A) = (more_R1625109589on_j_k @ B)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
% 228.49/61.56 thf(195,axiom,((! [A:option_element_ptr_a,B:(option_element_ptr_a > (option2026120038on_j_k > $o)),C:option2026120038on_j_k]: (((A = none_element_ptr_a) => (B @ A @ C)) => (((C = none_S1393028981on_j_k) => (B @ A @ C)) => ((! [D:element_ptr_a,E:sum_su1221287958on_j_k]: ((A = (some_element_ptr_a @ D)) => ((C = (some_S1960742641on_j_k @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_combine__options__cases)).
% 228.49/61.56 thf(1177,plain,((! [A:option_element_ptr_a,B:(option_element_ptr_a > (option2026120038on_j_k > $o)),C:option2026120038on_j_k]: (((A = none_element_ptr_a) => (B @ A @ C)) => (((C = none_S1393028981on_j_k) => (B @ A @ C)) => ((! [D:element_ptr_a,E:sum_su1221287958on_j_k]: ((A = (some_element_ptr_a @ D)) => ((C = (some_S1960742641on_j_k @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
% 228.49/61.56 thf(197,axiom,((! [A:list_char,B:list_char]: ((A = (append_char @ B @ A)) = (B = nil_char)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_self__append__conv2)).
% 228.49/61.56 thf(1198,plain,((! [A:list_char,B:list_char]: ((A = (append_char @ B @ A)) = (B = nil_char)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
% 228.49/61.56 thf(279,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: (((append846395565tr_b_c @ A @ B) = (cons_n413985352tr_b_c @ C @ D)) = (((A = nil_no279930520tr_b_c) & (B = (cons_n413985352tr_b_c @ C @ D))) | ? [E:list_n282880152tr_b_c]: ((A = (cons_n413985352tr_b_c @ C @ E)) & ((append846395565tr_b_c @ E @ B) = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_append__eq__Cons__conv)).
% 228.49/61.56 thf(1643,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: (((append846395565tr_b_c @ A @ B) = (cons_n413985352tr_b_c @ C @ D)) = (((A = nil_no279930520tr_b_c) & (B = (cons_n413985352tr_b_c @ C @ D))) | ? [E:list_n282880152tr_b_c]: ((A = (cons_n413985352tr_b_c @ C @ E)) & ((append846395565tr_b_c @ E @ B) = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])).
% 228.49/61.56 thf(233,axiom,((! [A:option2026120038on_j_k]: ((A != none_S1393028981on_j_k) => (~ (! [B:sum_su1221287958on_j_k]: (A != (some_S1960742641on_j_k @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_option_Oexhaust)).
% 228.49/61.56 thf(1364,plain,((! [A:option2026120038on_j_k]: ((~ (A = none_S1393028981on_j_k)) => (~ (! [B:sum_su1221287958on_j_k]: ~ (A = (some_S1960742641on_j_k @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
% 228.49/61.56 thf(86,axiom,((! [A:(nat > $o)]: ((~ (A @ zero_zero_nat)) => ((? [B:nat]: (A @ B)) => (? [B:nat]: (~ (A @ B) & (A @ (suc @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_exists__least__lemma)).
% 228.49/61.56 thf(653,plain,((! [A:(nat > $o)]: ((~ (A @ zero_zero_nat)) => ((? [B:nat]: (A @ B)) => (? [B:nat]: (~ (A @ B) & (A @ (suc @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
% 228.49/61.56 thf(265,axiom,((! [A:option_element_ptr_a]: ((A != none_element_ptr_a) => (~ (! [B:element_ptr_a]: (A != (some_element_ptr_a @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_option_Oexhaust)).
% 228.49/61.56 thf(1562,plain,((! [A:option_element_ptr_a]: ((~ (A = none_element_ptr_a)) => (~ (! [B:element_ptr_a]: ~ (A = (some_element_ptr_a @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])).
% 228.49/61.56 thf(146,axiom,((! [A:list_char,B:list_char]: (((splice_char @ A @ B) = nil_char) = ((A = nil_char) & (B = nil_char))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_split__Nil__iff)).
% 228.49/61.56 thf(912,plain,((! [A:list_char,B:list_char]: (((splice_char @ A @ B) = nil_char) = ((A = nil_char) & (B = nil_char))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
% 228.49/61.56 thf(193,axiom,((! [A:(option_element_ptr_a > $o),B:option_element_ptr_a,C:(element_ptr_a > option_element_ptr_a)]: ((A @ (bind_e22036734_ptr_a @ B @ C)) = (((B = none_element_ptr_a) => (A @ none_element_ptr_a)) & ! [D:element_ptr_a]: ((B = (some_element_ptr_a @ D)) => (A @ (C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_bind__split)).
% 228.49/61.56 thf(1171,plain,((! [A:(option_element_ptr_a > $o),B:option_element_ptr_a,C:(element_ptr_a > option_element_ptr_a)]: ((A @ (bind_e22036734_ptr_a @ B @ (C))) = (((B = none_element_ptr_a) => (A @ none_element_ptr_a)) & ! [D:element_ptr_a]: ((B = (some_element_ptr_a @ D)) => (A @ (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
% 228.49/61.56 thf(260,axiom,((! [A:list_char,B:list_char,C:char,D:list_char]: (((append_char @ A @ B) = (cons_char @ C @ D)) = (((A = nil_char) & (B = (cons_char @ C @ D))) | ? [E:list_char]: ((A = (cons_char @ C @ E)) & ((append_char @ E @ B) = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_append__eq__Cons__conv)).
% 228.49/61.56 thf(1528,plain,((! [A:list_char,B:list_char,C:char,D:list_char]: (((append_char @ A @ B) = (cons_char @ C @ D)) = (((A = nil_char) & (B = (cons_char @ C @ D))) | ? [E:list_char]: ((A = (cons_char @ C @ E)) & ((append_char @ E @ B) = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])).
% 228.49/61.56 thf(986,plain,(((^ [A:(option_element_ptr_a > $o)]: ((A @ none_element_ptr_a) | ? [B:element_ptr_a]: (A @ (some_element_ptr_a @ B)))) = ((?) @ option_element_ptr_a))),inference(lifteq,[status(thm)],[985])).
% 228.49/61.56 thf(51,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_old_Onat_Oinducts)).
% 228.49/61.56 thf(505,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => (A @ (suc @ C)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
% 228.49/61.56 thf(35,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_verit__sum__simplify)).
% 228.49/61.56 thf(438,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 228.49/61.56 thf(276,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((append846395565tr_b_c @ A @ B) = B) = (A = nil_no279930520tr_b_c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_append__self__conv2)).
% 228.49/61.56 thf(1626,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((append846395565tr_b_c @ A @ B) = B) = (A = nil_no279930520tr_b_c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])).
% 228.49/61.56 thf(588,plain,(! [A:(rObjec1617416918on_j_k > nat)] : (((size_o26122489on_j_k @ (A) @ none_R1587534007on_j_k) = (suc @ zero_zero_nat)))),inference(cnf,[status(esa)],[587])).
% 228.49/61.56 thf(589,plain,(! [A:(rObjec1617416918on_j_k > nat)] : (((size_o26122489on_j_k @ (A) @ none_R1587534007on_j_k) = (suc @ zero_zero_nat)))),inference(lifteq,[status(thm)],[588])).
% 228.49/61.56 thf(247,axiom,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((discon866287741on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = E))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_RDocument_Oselect__convs_I4_J)).
% 228.49/61.56 thf(1467,plain,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((discon866287741on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = E))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
% 228.49/61.56 thf(679,plain,(! [A:nat] : (((size_s2106487044tr_b_c @ (sk27 @ A)) = A))),inference(cnf,[status(esa)],[678])).
% 228.49/61.56 thf(680,plain,(! [A:nat] : (((size_s2106487044tr_b_c @ (sk27 @ A)) = A))),inference(lifteq,[status(thm)],[679])).
% 228.49/61.56 thf(2234,plain,(((nat_triangle @ (suc @ zero_zero_nat)) = (suc @ zero_zero_nat))),inference(rewrite,[status(thm)],[2035,355])).
% 228.49/61.56 thf(125,axiom,((size_size_list_char = (gen_length_char @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_length__code)).
% 228.49/61.56 thf(812,plain,(((size_size_list_char) = (gen_length_char @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
% 228.49/61.56 thf(156,axiom,((! [A:(option2026120038on_j_k > option2026120038on_j_k),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((more_u1044474223_c_a_b @ A @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ (A @ G)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_RDocument_Oupdate__convs_I5_J)).
% 228.49/61.56 thf(968,plain,((! [A:(option2026120038on_j_k > option2026120038on_j_k),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((more_u1044474223_c_a_b @ (A) @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ (A @ G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
% 228.49/61.56 thf(422,plain,((! [A:(nat > (nat > $o))]: ((! [B:nat,C:nat]: ((A @ B @ C) = (A @ C @ B))) => ((! [B:nat]: (A @ B @ zero_zero_nat)) => ((! [B:nat,C:nat]: ((A @ B @ C) => (A @ B @ (plus_plus_nat @ B @ C)))) => (! [B:nat,C:nat]: (A @ B @ C))))))),inference(miniscope,[status(thm)],[421])).
% 228.49/61.56 thf(423,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : (((~ ((A @ (sk3 @ (A)) @ (sk4 @ (A))) = (A @ (sk4 @ (A)) @ (sk3 @ (A)))) | ~ (A @ (sk5 @ (A)) @ zero_zero_nat) | (A @ (sk6 @ (A)) @ (sk7 @ (A))) | (A @ B @ C)) & (~ ((A @ (sk3 @ (A)) @ (sk4 @ (A))) = (A @ (sk4 @ (A)) @ (sk3 @ (A)))) | ~ (A @ (sk5 @ (A)) @ zero_zero_nat) | ~ (A @ (sk6 @ (A)) @ (plus_plus_nat @ (sk6 @ (A)) @ (sk7 @ (A)))) | (A @ B @ C))))),inference(cnf,[status(esa)],[422])).
% 228.49/61.56 thf(424,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((~ ((A @ (sk3 @ (A)) @ (sk4 @ (A))) = (A @ (sk4 @ (A)) @ (sk3 @ (A))))) | (~ (A @ (sk5 @ (A)) @ zero_zero_nat)) | (A @ (sk6 @ (A)) @ (sk7 @ (A))) | (A @ B @ C))),inference(cnfConj,[status(thm)],[423])).
% 228.49/61.56 thf(426,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : (((A @ (sk4 @ (A)) @ (sk3 @ (A))) != (A @ (sk3 @ (A)) @ (sk4 @ (A)))) | (~ (A @ (sk5 @ (A)) @ zero_zero_nat)) | (A @ (sk6 @ (A)) @ (sk7 @ (A))) | (A @ B @ C))),inference(lifteq,[status(thm)],[424])).
% 228.49/61.56 thf(191,axiom,(((subseqs_char @ nil_char) = (cons_list_char @ nil_char @ nil_list_char))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_subseqs_Osimps_I1_J)).
% 228.49/61.56 thf(1166,plain,(((subseqs_char @ nil_char) = (cons_list_char @ nil_char @ nil_list_char))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])).
% 228.49/61.56 thf(615,plain,((~ (? [A:docume1935157360tr_d_e]: ((size_s724035844tr_d_e @ A) = zero_zero_nat)))),inference(miniscope,[status(thm)],[614])).
% 228.49/61.56 thf(616,plain,(! [A:docume1935157360tr_d_e] : ((~ ((size_s724035844tr_d_e @ A) = zero_zero_nat)))),inference(cnf,[status(esa)],[615])).
% 228.49/61.56 thf(617,plain,(! [A:docume1935157360tr_d_e] : (((size_s724035844tr_d_e @ A) != zero_zero_nat))),inference(lifteq,[status(thm)],[616])).
% 228.49/61.56 thf(52,axiom,((! [A:object945351580_d_e_f,B:object945351580_d_e_f,C:rObjec1413572695_j_k_l,D:heap_S1465075775_j_k_l]: ((A != B) => ((get_O_623850005_j_k_l @ A @ (put_O_834343516_j_k_l @ B @ C @ D)) = (get_O_623850005_j_k_l @ A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_get__object__ptr__simp2)).
% 228.49/61.56 thf(516,plain,((! [A:object945351580_d_e_f,B:object945351580_d_e_f,C:rObjec1413572695_j_k_l,D:heap_S1465075775_j_k_l]: ((~ (A = B)) => ((get_O_623850005_j_k_l @ A @ (put_O_834343516_j_k_l @ B @ C @ D)) = (get_O_623850005_j_k_l @ A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
% 228.49/61.56 thf(130,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:list_char,D:(list_char > list_char),E:(list_char > list_char)]: ((A = B) => (((doctyp814403297on_j_k @ B) = C) => ((! [F:list_char]: ((F = C) => ((D @ F) = (E @ F)))) => ((doctyp68000440on_j_k @ D @ A) = (doctyp68000440on_j_k @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_RDocument_Ounfold__congs_I3_J)).
% 228.49/61.56 thf(836,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:list_char,D:(list_char > list_char),E:(list_char > list_char)]: ((A = B) => (((doctyp814403297on_j_k @ B) = C) => ((! [F:list_char]: ((F = C) => ((D @ F) = (E @ F)))) => ((doctyp68000440on_j_k @ (D) @ A) = (doctyp68000440on_j_k @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])).
% 228.49/61.56 thf(264,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c,D:(list_n282880152tr_b_c > (list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)))]: (((size_s2106487044tr_b_c @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_s2106487044tr_b_c @ C)) => ((D @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c,G:node_p1234578834tr_b_c,H:list_n282880152tr_b_c,I:node_p1234578834tr_b_c,J:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ F) = (size_s2106487044tr_b_c @ H)) => (((size_s2106487044tr_b_c @ H) = (size_s2106487044tr_b_c @ J)) => ((D @ F @ H @ J) => (D @ (cons_n413985352tr_b_c @ E @ F) @ (cons_n413985352tr_b_c @ G @ H) @ (cons_n413985352tr_b_c @ I @ J)))))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_list__induct3)).
% 228.49/61.56 thf(1551,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c,D:(list_n282880152tr_b_c > (list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)))]: (((size_s2106487044tr_b_c @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_s2106487044tr_b_c @ C)) => ((D @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c,G:node_p1234578834tr_b_c,H:list_n282880152tr_b_c,I:node_p1234578834tr_b_c,J:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ F) = (size_s2106487044tr_b_c @ H)) => (((size_s2106487044tr_b_c @ H) = (size_s2106487044tr_b_c @ J)) => ((D @ F @ H @ J) => (D @ (cons_n413985352tr_b_c @ E @ F) @ (cons_n413985352tr_b_c @ G @ H) @ (cons_n413985352tr_b_c @ I @ J)))))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])).
% 228.49/61.56 thf(1797,plain,(! [A:node_p1234578834tr_b_c] : (((count_2128515342tr_b_c @ nil_no279930520tr_b_c @ A) = zero_zero_nat))),inference(cnf,[status(esa)],[1796])).
% 228.49/61.56 thf(1798,plain,(! [A:node_p1234578834tr_b_c] : (((count_2128515342tr_b_c @ nil_no279930520tr_b_c @ A) = zero_zero_nat))),inference(lifteq,[status(thm)],[1797])).
% 228.49/61.56 thf(270,axiom,((! [A:(rObjec1617416918on_j_k > $o),B:rObjec1617416918on_j_k]: ((! [C:product_unit,D:rDocum326988203on_j_k]: (A @ (rObjec1303043984on_j_k @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_RObject_Oinduct__scheme)).
% 228.49/61.56 thf(1598,plain,((! [A:(rObjec1617416918on_j_k > $o),B:rObjec1617416918on_j_k]: ((! [C:product_unit,D:rDocum326988203on_j_k]: (A @ (rObjec1303043984on_j_k @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])).
% 228.49/61.56 thf(266,axiom,((! [A:(list_char > (list_n282880152tr_b_c > $o)),B:list_char,C:list_n282880152tr_b_c]: ((A @ nil_char @ nil_no279930520tr_b_c) => ((! [D:char,E:list_char]: (A @ (cons_char @ D @ E) @ nil_no279930520tr_b_c)) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (A @ nil_char @ (cons_n413985352tr_b_c @ D @ E))) => ((! [D:char,E:list_char,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: ((A @ E @ G) => (A @ (cons_char @ D @ E) @ (cons_n413985352tr_b_c @ F @ G)))) => (A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_list__induct2_H)).
% 228.49/61.56 thf(1566,plain,((! [A:(list_char > (list_n282880152tr_b_c > $o)),B:list_char,C:list_n282880152tr_b_c]: ((A @ nil_char @ nil_no279930520tr_b_c) => ((! [D:char,E:list_char]: (A @ (cons_char @ D @ E) @ nil_no279930520tr_b_c)) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (A @ nil_char @ (cons_n413985352tr_b_c @ D @ E))) => ((! [D:char,E:list_char,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: ((A @ E @ G) => (A @ (cons_char @ D @ E) @ (cons_n413985352tr_b_c @ F @ G)))) => (A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])).
% 228.49/61.56 thf(106,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Zero__neq__Suc)).
% 228.49/61.56 thf(739,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
% 228.49/61.56 thf(234,axiom,((! [A:list_char,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c,D:list_char,E:(list_char > (list_n282880152tr_b_c > (list_n282880152tr_b_c > (list_char > $o))))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_s2106487044tr_b_c @ C)) => (((size_s2106487044tr_b_c @ C) = (size_size_list_char @ D)) => ((E @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char) => ((! [F:char,G:list_char,H:node_p1234578834tr_b_c,I:list_n282880152tr_b_c,J:node_p1234578834tr_b_c,K:list_n282880152tr_b_c,L:char,M:list_char]: (((size_size_list_char @ G) = (size_s2106487044tr_b_c @ I)) => (((size_s2106487044tr_b_c @ I) = (size_s2106487044tr_b_c @ K)) => (((size_s2106487044tr_b_c @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_n413985352tr_b_c @ H @ I) @ (cons_n413985352tr_b_c @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_list__induct4)).
% 228.49/61.56 thf(1368,plain,((! [A:list_char,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c,D:list_char,E:(list_char > (list_n282880152tr_b_c > (list_n282880152tr_b_c > (list_char > $o))))]: (((size_size_list_char @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_s2106487044tr_b_c @ C)) => (((size_s2106487044tr_b_c @ C) = (size_size_list_char @ D)) => ((E @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char) => ((! [F:char,G:list_char,H:node_p1234578834tr_b_c,I:list_n282880152tr_b_c,J:node_p1234578834tr_b_c,K:list_n282880152tr_b_c,L:char,M:list_char]: (((size_size_list_char @ G) = (size_s2106487044tr_b_c @ I)) => (((size_s2106487044tr_b_c @ I) = (size_s2106487044tr_b_c @ K)) => (((size_s2106487044tr_b_c @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_n413985352tr_b_c @ H @ I) @ (cons_n413985352tr_b_c @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])).
% 228.49/61.56 thf(261,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((append846395565tr_b_c @ A @ B) = nil_no279930520tr_b_c) = ((A = nil_no279930520tr_b_c) & (B = nil_no279930520tr_b_c))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_append__is__Nil__conv)).
% 228.49/61.56 thf(1531,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((append846395565tr_b_c @ A @ B) = nil_no279930520tr_b_c) = ((A = nil_no279930520tr_b_c) & (B = nil_no279930520tr_b_c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])).
% 228.49/61.56 thf(27,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_plus__nat_Oadd__0)).
% 228.49/61.56 thf(409,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
% 228.49/61.56 thf(237,axiom,((! [A:node_p1234578834tr_b_c]: ((insert678865070tr_b_c @ A @ nil_no279930520tr_b_c) = (cons_n413985352tr_b_c @ A @ nil_no279930520tr_b_c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_insert__Nil)).
% 228.49/61.56 thf(1400,plain,((! [A:node_p1234578834tr_b_c]: ((insert678865070tr_b_c @ A @ nil_no279930520tr_b_c) = (cons_n413985352tr_b_c @ A @ nil_no279930520tr_b_c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
% 228.49/61.56 thf(413,plain,(! [B:nat,A:nat] : (((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(cnf,[status(esa)],[412])).
% 228.49/61.56 thf(414,plain,(! [B:nat,A:nat] : (((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(lifteq,[status(thm)],[413])).
% 228.49/61.56 thf(157,axiom,((! [A:((node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)) > (list_n282880152tr_b_c > $o)),B:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),C:list_n282880152tr_b_c]: ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o))]: (A @ D @ nil_no279930520tr_b_c)) => ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),E:node_p1234578834tr_b_c]: (A @ D @ (cons_n413985352tr_b_c @ E @ nil_no279930520tr_b_c))) => ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),E:node_p1234578834tr_b_c,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: ((A @ D @ (cons_n413985352tr_b_c @ F @ G)) => (A @ D @ (cons_n413985352tr_b_c @ E @ (cons_n413985352tr_b_c @ F @ G))))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_successively_Oinduct)).
% 228.49/61.56 thf(971,plain,((! [A:((node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)) > (list_n282880152tr_b_c > $o)),B:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),C:list_n282880152tr_b_c]: ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o))]: (A @ (D) @ nil_no279930520tr_b_c)) => ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),E:node_p1234578834tr_b_c]: (A @ (D) @ (cons_n413985352tr_b_c @ E @ nil_no279930520tr_b_c))) => ((! [D:(node_p1234578834tr_b_c > (node_p1234578834tr_b_c > $o)),E:node_p1234578834tr_b_c,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: ((A @ (D) @ (cons_n413985352tr_b_c @ F @ G)) => (A @ (D) @ (cons_n413985352tr_b_c @ E @ (cons_n413985352tr_b_c @ F @ G))))) => (A @ (B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])).
% 228.49/61.56 thf(165,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k]: (((cast_D1252964113_h_i_l @ A) = (cast_D1252964113_h_i_l @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_cast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t__inject)).
% 228.49/61.56 thf(1053,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k]: (((cast_D1252964113_h_i_l @ A) = (cast_D1252964113_h_i_l @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
% 228.49/61.56 thf(36,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_add__eq__0__iff__both__eq__0)).
% 228.49/61.56 thf(441,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
% 228.49/61.56 thf(3449,plain,(! [C:sum_su1576157353tr_d_e,B:(sum_su1576157353tr_d_e > nat),A:nat] : (((suc @ A) = (docume1799427087tr_d_e @ (B) @ (docume1825929374tr_d_e @ C))) | ((plus_plus_nat @ zero_zero_nat @ A) != (plus_plus_nat @ (B @ C) @ zero_zero_nat)))),inference(paramod_ordered,[status(thm)],[355,3403])).
% 228.49/61.56 thf(3483,plain,(! [A:sum_su1576157353tr_d_e] : (((docume1799427087tr_d_e @ (^ [B:sum_su1576157353tr_d_e]: (zero_zero_nat)) @ (docume1825929374tr_d_e @ A)) = (suc @ zero_zero_nat)))),inference(pre_uni,[status(thm)],[3449:[bind(A, $thf(zero_zero_nat)),bind(B, $thf(^ [D:sum_su1576157353tr_d_e]: (zero_zero_nat)))]])).
% 228.49/61.56 thf(3554,plain,(! [A:sum_su1576157353tr_d_e] : (((docume1799427087tr_d_e @ (^ [B:sum_su1576157353tr_d_e]: (zero_zero_nat)) @ (docume1825929374tr_d_e @ A)) = (suc @ zero_zero_nat)))),inference(simp,[status(thm)],[3483])).
% 228.49/61.56 thf(212,axiom,((! [A:(list_char > (list_char > $o)),B:list_char,C:list_char]: ((! [D:list_char]: (A @ nil_char @ D)) => ((! [D:list_char]: (A @ D @ nil_char)) => ((! [D:char,E:list_char,F:char,G:list_char]: ((A @ E @ (cons_char @ F @ G)) => ((A @ (cons_char @ D @ E) @ G) => (A @ (cons_char @ D @ E) @ (cons_char @ F @ G))))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_shuffles_Oinduct)).
% 228.49/61.56 thf(1262,plain,((! [A:(list_char > (list_char > $o)),B:list_char,C:list_char]: ((! [D:list_char]: (A @ nil_char @ D)) => ((! [D:list_char]: (A @ D @ nil_char)) => ((! [D:char,E:list_char,F:char,G:list_char]: ((A @ E @ (cons_char @ F @ G)) => ((A @ (cons_char @ D @ E) @ G) => (A @ (cons_char @ D @ E) @ (cons_char @ F @ G))))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])).
% 228.49/61.56 thf(42,axiom,(((size_s2008079621t_char @ nil_list_char) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_list_Osize_I3_J)).
% 228.49/61.56 thf(463,plain,(((size_s2008079621t_char @ nil_list_char) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
% 228.49/61.56 thf(1333,plain,((! [A:option2026120038on_j_k]: ((? [B:sum_su1221287958on_j_k]: (A = (some_S1960742641on_j_k @ B))) => (~ (A = none_S1393028981on_j_k))))),inference(miniscope,[status(thm)],[1332])).
% 228.49/61.56 thf(1334,plain,(! [B:sum_su1221287958on_j_k,A:option2026120038on_j_k] : ((~ (A = (some_S1960742641on_j_k @ B))) | (~ (A = none_S1393028981on_j_k)))),inference(cnf,[status(esa)],[1333])).
% 228.49/61.56 thf(1335,plain,(! [B:sum_su1221287958on_j_k,A:option2026120038on_j_k] : ((A != (some_S1960742641on_j_k @ B)) | (A != none_S1393028981on_j_k))),inference(lifteq,[status(thm)],[1334])).
% 228.49/61.56 thf(1336,plain,(! [A:sum_su1221287958on_j_k] : (((some_S1960742641on_j_k @ A) != none_S1393028981on_j_k))),inference(simp,[status(thm)],[1335])).
% 228.49/61.56 thf(202,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((nil_no279930520tr_b_c = (append846395565tr_b_c @ A @ B)) = ((A = nil_no279930520tr_b_c) & (B = nil_no279930520tr_b_c))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_Nil__is__append__conv)).
% 228.49/61.56 thf(1220,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: ((nil_no279930520tr_b_c = (append846395565tr_b_c @ A @ B)) = ((A = nil_no279930520tr_b_c) & (B = nil_no279930520tr_b_c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
% 228.49/61.56 thf(301,axiom,((! [A:(list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)),B:list_n282880152tr_b_c,C:list_n282880152tr_b_c]: ((! [D:list_n282880152tr_b_c]: (A @ nil_no279930520tr_b_c @ D)) => ((! [D:list_n282880152tr_b_c]: (A @ D @ nil_no279930520tr_b_c)) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: ((A @ E @ (cons_n413985352tr_b_c @ F @ G)) => ((A @ (cons_n413985352tr_b_c @ D @ E) @ G) => (A @ (cons_n413985352tr_b_c @ D @ E) @ (cons_n413985352tr_b_c @ F @ G))))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_shuffles_Oinduct)).
% 228.49/61.56 thf(1790,plain,((! [A:(list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)),B:list_n282880152tr_b_c,C:list_n282880152tr_b_c]: ((! [D:list_n282880152tr_b_c]: (A @ nil_no279930520tr_b_c @ D)) => ((! [D:list_n282880152tr_b_c]: (A @ D @ nil_no279930520tr_b_c)) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: ((A @ E @ (cons_n413985352tr_b_c @ F @ G)) => ((A @ (cons_n413985352tr_b_c @ D @ E) @ G) => (A @ (cons_n413985352tr_b_c @ D @ E) @ (cons_n413985352tr_b_c @ F @ G))))) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])).
% 228.49/61.56 thf(3409,plain,(! [B:sum_su1576157353tr_d_e,A:(sum_su1576157353tr_d_e > nat)] : (((nat_triangle @ (docume1799427087tr_d_e @ (A) @ (docume1825929374tr_d_e @ B))) != zero_zero_nat) | ((suc @ (plus_plus_nat @ (A @ B) @ zero_zero_nat)) != (suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat))))),inference(paramod_ordered,[status(thm)],[3403,3313])).
% 228.49/61.56 thf(3475,plain,(! [A:sum_su1576157353tr_d_e] : (((nat_triangle @ (docume1799427087tr_d_e @ (^ [B:sum_su1576157353tr_d_e]: (nat_triangle @ zero_zero_nat)) @ (docume1825929374tr_d_e @ A))) != zero_zero_nat))),inference(pre_uni,[status(thm)],[3409:[bind(A, $thf(^ [C:sum_su1576157353tr_d_e]: (nat_triangle @ zero_zero_nat))),bind(B, $thf(B))]])).
% 228.49/61.56 thf(3548,plain,(! [A:sum_su1576157353tr_d_e] : (((nat_triangle @ (docume1799427087tr_d_e @ (^ [B:sum_su1576157353tr_d_e]: (nat_triangle @ zero_zero_nat)) @ (docume1825929374tr_d_e @ A))) != zero_zero_nat))),inference(simp,[status(thm)],[3475])).
% 228.49/61.56 thf(5418,plain,(! [A:sum_su1576157353tr_d_e] : (((nat_triangle @ (docume1799427087tr_d_e @ (^ [B:sum_su1576157353tr_d_e]: (zero_zero_nat)) @ (docume1825929374tr_d_e @ A))) != zero_zero_nat))),inference(rewrite,[status(thm)],[3548,803])).
% 228.49/61.56 thf(15,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_add_Ocommute)).
% 228.49/61.56 thf(369,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 228.49/61.56 thf(370,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(lifteq,[status(thm)],[369])).
% 228.49/61.56 thf(220,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((n_list1807568544tr_b_c @ A @ nil_no279930520tr_b_c) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c))) & ((A != zero_zero_nat) => ((n_list1807568544tr_b_c @ A @ nil_no279930520tr_b_c) = nil_li198338206tr_b_c))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_n__lists__Nil)).
% 228.49/61.56 thf(1317,plain,((! [A:nat]: (((A = zero_zero_nat) => ((n_list1807568544tr_b_c @ A @ nil_no279930520tr_b_c) = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c))) & ((~ (A = zero_zero_nat)) => ((n_list1807568544tr_b_c @ A @ nil_no279930520tr_b_c) = nil_li198338206tr_b_c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])).
% 228.49/61.56 thf(1829,plain,((~ (? [A:(node_p1234578834tr_b_c > $o)]: (list_e469495899tr_b_c @ (A) @ nil_no279930520tr_b_c)))),inference(miniscope,[status(thm)],[1828])).
% 228.49/61.56 thf(1830,plain,(! [A:(node_p1234578834tr_b_c > $o)] : ((~ (list_e469495899tr_b_c @ (A) @ nil_no279930520tr_b_c)))),inference(cnf,[status(esa)],[1829])).
% 228.49/61.56 thf(322,axiom,((! [A:(product_unit > product_unit),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((nothin1105341917on_j_k @ A @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ (A @ C) @ D @ E @ F @ G))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_RDocument_Oupdate__convs_I1_J)).
% 228.49/61.56 thf(1901,plain,((! [A:(product_unit > product_unit),B:product_unit,C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: ((nothin1105341917on_j_k @ (A) @ (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) = (rObjec1303043984on_j_k @ B @ (rDocum427676485on_j_k @ (A @ C) @ D @ E @ F @ G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])).
% 228.49/61.56 thf(1357,plain,(! [A:list_n282880152tr_b_c] : (((nths_n1256675478tr_b_c @ A @ bot_bot_set_nat) = nil_no279930520tr_b_c))),inference(cnf,[status(esa)],[1356])).
% 228.49/61.56 thf(1358,plain,(! [A:list_n282880152tr_b_c] : (((nths_n1256675478tr_b_c @ A @ bot_bot_set_nat) = nil_no279930520tr_b_c))),inference(lifteq,[status(thm)],[1357])).
% 228.49/61.56 thf(328,axiom,((! [A:(list_char > (list_char > $o)),B:list_char,C:list_char]: ((A @ nil_char @ nil_char) => ((! [D:char,E:list_char]: (A @ (cons_char @ D @ E) @ nil_char)) => ((! [D:char,E:list_char]: (A @ nil_char @ (cons_char @ D @ E))) => ((! [D:char,E:list_char,F:char,G:list_char]: ((A @ E @ G) => (A @ (cons_char @ D @ E) @ (cons_char @ F @ G)))) => (A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_list__induct2_H)).
% 228.49/61.56 thf(1934,plain,((! [A:(list_char > (list_char > $o)),B:list_char,C:list_char]: ((A @ nil_char @ nil_char) => ((! [D:char,E:list_char]: (A @ (cons_char @ D @ E) @ nil_char)) => ((! [D:char,E:list_char]: (A @ nil_char @ (cons_char @ D @ E))) => ((! [D:char,E:list_char,F:char,G:list_char]: ((A @ E @ G) => (A @ (cons_char @ D @ E) @ (cons_char @ F @ G)))) => (A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])).
% 228.49/61.56 thf(304,axiom,((! [A:sum_su1221287958on_j_k]: (none_S1393028981on_j_k != (some_S1960742641on_j_k @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_option_Odistinct_I1_J)).
% 228.49/61.56 thf(1802,plain,((! [A:sum_su1221287958on_j_k]: ~ (none_S1393028981on_j_k = (some_S1960742641on_j_k @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])).
% 228.49/61.56 thf(104,axiom,((! [A:product_unit,B:product_unit]: ((nothing_Product_unit @ (rObjec730108904t_unit @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_RObject_Oselect__convs_I1_J)).
% 228.49/61.56 thf(727,plain,((! [A:product_unit,B:product_unit]: ((nothing_Product_unit @ (rObjec730108904t_unit @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
% 228.49/61.56 thf(269,axiom,((! [A:list_char,B:list_char,C:list_n282880152tr_b_c,D:list_char,E:(list_char > (list_char > (list_n282880152tr_b_c > (list_char > $o))))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => (((size_s2106487044tr_b_c @ C) = (size_size_list_char @ D)) => ((E @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_char) => ((! [F:char,G:list_char,H:char,I:list_char,J:node_p1234578834tr_b_c,K:list_n282880152tr_b_c,L:char,M:list_char]: (((size_size_list_char @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_s2106487044tr_b_c @ K)) => (((size_s2106487044tr_b_c @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_char @ H @ I) @ (cons_n413985352tr_b_c @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_list__induct4)).
% 228.49/61.56 thf(1585,plain,((! [A:list_char,B:list_char,C:list_n282880152tr_b_c,D:list_char,E:(list_char > (list_char > (list_n282880152tr_b_c > (list_char > $o))))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => (((size_s2106487044tr_b_c @ C) = (size_size_list_char @ D)) => ((E @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_char) => ((! [F:char,G:list_char,H:char,I:list_char,J:node_p1234578834tr_b_c,K:list_n282880152tr_b_c,L:char,M:list_char]: (((size_size_list_char @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_s2106487044tr_b_c @ K)) => (((size_s2106487044tr_b_c @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_char @ H @ I) @ (cons_n413985352tr_b_c @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])).
% 228.49/61.56 thf(291,axiom,((! [A:list_char,B:list_char,C:list_n282880152tr_b_c,D:list_n282880152tr_b_c,E:(list_char > (list_char > (list_n282880152tr_b_c > (list_n282880152tr_b_c > $o))))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => (((size_s2106487044tr_b_c @ C) = (size_s2106487044tr_b_c @ D)) => ((E @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [F:char,G:list_char,H:char,I:list_char,J:node_p1234578834tr_b_c,K:list_n282880152tr_b_c,L:node_p1234578834tr_b_c,M:list_n282880152tr_b_c]: (((size_size_list_char @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_s2106487044tr_b_c @ K)) => (((size_s2106487044tr_b_c @ K) = (size_s2106487044tr_b_c @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_char @ H @ I) @ (cons_n413985352tr_b_c @ J @ K) @ (cons_n413985352tr_b_c @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_list__induct4)).
% 228.49/61.56 thf(1717,plain,((! [A:list_char,B:list_char,C:list_n282880152tr_b_c,D:list_n282880152tr_b_c,E:(list_char > (list_char > (list_n282880152tr_b_c > (list_n282880152tr_b_c > $o))))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => (((size_s2106487044tr_b_c @ C) = (size_s2106487044tr_b_c @ D)) => ((E @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [F:char,G:list_char,H:char,I:list_char,J:node_p1234578834tr_b_c,K:list_n282880152tr_b_c,L:node_p1234578834tr_b_c,M:list_n282880152tr_b_c]: (((size_size_list_char @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_s2106487044tr_b_c @ K)) => (((size_s2106487044tr_b_c @ K) = (size_s2106487044tr_b_c @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_char @ H @ I) @ (cons_n413985352tr_b_c @ J @ K) @ (cons_n413985352tr_b_c @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])).
% 228.49/61.56 thf(214,axiom,((! [A:list_char,B:list_char,C:list_n282880152tr_b_c,D:(list_char > (list_char > (list_n282880152tr_b_c > $o)))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => ((D @ nil_char @ nil_char @ nil_no279930520tr_b_c) => ((! [E:char,F:list_char,G:char,H:list_char,I:node_p1234578834tr_b_c,J:list_n282880152tr_b_c]: (((size_size_list_char @ F) = (size_size_list_char @ H)) => (((size_size_list_char @ H) = (size_s2106487044tr_b_c @ J)) => ((D @ F @ H @ J) => (D @ (cons_char @ E @ F) @ (cons_char @ G @ H) @ (cons_n413985352tr_b_c @ I @ J)))))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_list__induct3)).
% 228.49/61.56 thf(1272,plain,((! [A:list_char,B:list_char,C:list_n282880152tr_b_c,D:(list_char > (list_char > (list_n282880152tr_b_c > $o)))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => ((D @ nil_char @ nil_char @ nil_no279930520tr_b_c) => ((! [E:char,F:list_char,G:char,H:list_char,I:node_p1234578834tr_b_c,J:list_n282880152tr_b_c]: (((size_size_list_char @ F) = (size_size_list_char @ H)) => (((size_size_list_char @ H) = (size_s2106487044tr_b_c @ J)) => ((D @ F @ H @ J) => (D @ (cons_char @ E @ F) @ (cons_char @ G @ H) @ (cons_n413985352tr_b_c @ I @ J)))))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
% 228.49/61.56 thf(3365,plain,(! [C:nat,B:nat,A:nat] : (((sk2 @ C @ A) = B) | ((plus_plus_nat @ A @ zero_zero_nat) != (plus_plus_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[394,3358])).
% 228.49/61.56 thf(3366,plain,(! [A:nat] : (((sk2 @ zero_zero_nat @ A) = A))),inference(pattern_uni,[status(thm)],[3365:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(zero_zero_nat))]])).
% 228.49/61.56 thf(141,axiom,((! [A:(list_n282880152tr_b_c > $o),B:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: ((A @ D) => (A @ (cons_n413985352tr_b_c @ C @ D)))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_list_Oinducts)).
% 228.49/61.56 thf(876,plain,((! [A:(list_n282880152tr_b_c > $o),B:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: ((A @ D) => (A @ (cons_n413985352tr_b_c @ C @ D)))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
% 228.49/61.56 thf(273,axiom,((! [A:option2026120038on_j_k]: ((A != none_S1393028981on_j_k) = (? [B:sum_su1221287958on_j_k]: (A = (some_S1960742641on_j_k @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_not__None__eq)).
% 228.49/61.56 thf(1617,plain,((! [A:option2026120038on_j_k]: ((~ (A = none_S1393028981on_j_k)) = (? [B:sum_su1221287958on_j_k]: (A = (some_S1960742641on_j_k @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])).
% 228.49/61.56 thf(297,axiom,((! [A:list_n282880152tr_b_c]: ((append846395565tr_b_c @ nil_no279930520tr_b_c @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_append_Oleft__neutral)).
% 228.49/61.56 thf(1766,plain,((! [A:list_n282880152tr_b_c]: ((append846395565tr_b_c @ nil_no279930520tr_b_c @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])).
% 228.49/61.56 thf(253,axiom,((! [A:(rDocum326988203on_j_k > $o),B:rDocum326988203on_j_k]: ((! [C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: (A @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_RDocument_Oext__induct)).
% 228.49/61.56 thf(1485,plain,((! [A:(rDocum326988203on_j_k > $o),B:rDocum326988203on_j_k]: ((! [C:product_unit,D:list_char,E:option_element_ptr_a,F:list_n282880152tr_b_c,G:option2026120038on_j_k]: (A @ (rDocum427676485on_j_k @ C @ D @ E @ F @ G))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])).
% 228.49/61.56 thf(2059,plain,(! [B:nat,A:nat] : (((nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ A)))) != zero_zero_nat) | ((suc @ (plus_plus_nat @ (nat_triangle @ A) @ A)) != (suc @ B)))),inference(paramod_ordered,[status(thm)],[2020,2058])).
% 228.49/61.56 thf(2060,plain,(! [A:nat] : (((nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ A)))) != zero_zero_nat))),inference(pattern_uni,[status(thm)],[2059:[bind(A, $thf(D)),bind(B, $thf(plus_plus_nat @ (nat_triangle @ D) @ D))]])).
% 228.49/61.56 thf(2070,plain,(! [A:nat] : (((nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ A)))) != zero_zero_nat))),inference(simp,[status(thm)],[2060])).
% 228.49/61.56 thf(2688,plain,(! [B:nat,A:nat] : (((nat_triangle @ (nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ A))))) != zero_zero_nat) | ((suc @ (plus_plus_nat @ (nat_triangle @ A) @ A)) != (suc @ B)))),inference(paramod_ordered,[status(thm)],[2020,2070])).
% 228.49/61.56 thf(2689,plain,(! [A:nat] : (((nat_triangle @ (nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ A))))) != zero_zero_nat))),inference(pattern_uni,[status(thm)],[2688:[bind(A, $thf(D)),bind(B, $thf(plus_plus_nat @ (nat_triangle @ D) @ D))]])).
% 228.49/61.56 thf(2711,plain,(! [A:nat] : (((nat_triangle @ (nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ A))))) != zero_zero_nat))),inference(simp,[status(thm)],[2689])).
% 228.49/61.56 thf(43,axiom,((! [A:option841825948on_j_k,B:rObjec1617416918on_j_k]: ((A = (some_R67702331on_j_k @ B)) => (A != none_R1587534007on_j_k)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_option_OdiscI)).
% 228.49/61.56 thf(465,plain,((! [A:option841825948on_j_k,B:rObjec1617416918on_j_k]: ((A = (some_R67702331on_j_k @ B)) => (~ (A = none_R1587534007on_j_k))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
% 228.49/61.56 thf(506,plain,((! [A:(nat > $o)]: ((A @ zero_zero_nat) => ((! [B:nat]: ((A @ B) => (A @ (suc @ B)))) => (! [B:nat]: (A @ B)))))),inference(miniscope,[status(thm)],[505])).
% 228.49/61.56 thf(507,plain,(! [B:nat,A:(nat > $o)] : (((~ (A @ zero_zero_nat) | (A @ (sk11 @ (A))) | (A @ B)) & (~ (A @ zero_zero_nat) | ~ (A @ (suc @ (sk11 @ (A)))) | (A @ B))))),inference(cnf,[status(esa)],[506])).
% 228.49/61.56 thf(508,plain,(! [B:nat,A:(nat > $o)] : ((~ (A @ zero_zero_nat)) | (A @ (sk11 @ (A))) | (A @ B))),inference(cnfConj,[status(thm)],[507])).
% 228.49/61.56 thf(510,plain,(! [A:nat] : ((~ (zero_zero_nat = zero_zero_nat)) | (zero_zero_nat = (sk11 @ ((=) @ nat @ zero_zero_nat))) | (zero_zero_nat = A))),inference(replace_leibeq,[status(thm)],[508:[bind(A, $thf((=) @ nat @ zero_zero_nat))]])).
% 228.49/61.56 thf(512,plain,(! [A:nat] : ((zero_zero_nat != zero_zero_nat) | ((sk11 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat) | (zero_zero_nat = A))),inference(lifteq,[status(thm)],[510])).
% 228.49/61.56 thf(513,plain,(! [A:nat] : (((sk11 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat) | (zero_zero_nat = A))),inference(simp,[status(thm)],[512])).
% 228.49/61.56 thf(3618,plain,(! [B:nat,A:nat] : (((sk11 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat) | (zero_zero_nat != zero_zero_nat) | (A != (nat_triangle @ (suc @ B))))),inference(paramod_ordered,[status(thm)],[513,2049])).
% 228.49/61.56 thf(3619,plain,(! [B:nat,A:nat] : (((sk11 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat) | (A != (nat_triangle @ (suc @ B))))),inference(simp,[status(thm)],[3618])).
% 228.49/61.56 thf(3620,plain,(((sk11 @ ((=) @ nat @ zero_zero_nat)) = zero_zero_nat)),inference(pattern_uni,[status(thm)],[3619:[bind(A, $thf(nat_triangle @ (suc @ D))),bind(B, $thf(D))]])).
% 228.49/61.56 thf(2274,plain,(! [A:nat] : (((suc @ (plus_plus_nat @ (nat_triangle @ A) @ A)) = (suc @ zero_zero_nat)) | ((nat_triangle @ (suc @ A)) != (nat_triangle @ (suc @ zero_zero_nat))))),inference(paramod_ordered,[status(thm)],[2020,2234])).
% 228.49/61.56 thf(2275,plain,(((suc @ (plus_plus_nat @ (nat_triangle @ zero_zero_nat) @ zero_zero_nat)) = (suc @ zero_zero_nat))),inference(pattern_uni,[status(thm)],[2274:[bind(A, $thf(zero_zero_nat))]])).
% 228.49/61.56 thf(2458,plain,(((suc @ (nat_triangle @ zero_zero_nat)) = (suc @ zero_zero_nat))),inference(rewrite,[status(thm)],[2275,394])).
% 228.49/61.56 thf(4831,plain,(! [A:nat] : (((nat_triangle @ (nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ zero_zero_nat))))) != zero_zero_nat) | ((suc @ (nat_triangle @ zero_zero_nat)) != (suc @ A)))),inference(paramod_ordered,[status(thm)],[2458,2711])).
% 228.49/61.56 thf(4832,plain,(((nat_triangle @ (nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ zero_zero_nat))))) != zero_zero_nat)),inference(pattern_uni,[status(thm)],[4831:[bind(A, $thf(nat_triangle @ zero_zero_nat))]])).
% 228.49/61.56 thf(4851,plain,(((nat_triangle @ (nat_triangle @ (nat_triangle @ (suc @ zero_zero_nat)))) != zero_zero_nat)),inference(rewrite,[status(thm)],[4832,2234])).
% 228.49/61.56 thf(56,axiom,((! [A:nat,B:sum_su1576157353tr_d_e]: ((docume1511108976tr_d_e @ A) != (docume1825929374tr_d_e @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_document__ptr_Odistinct_I1_J)).
% 228.49/61.56 thf(536,plain,((! [A:nat,B:sum_su1576157353tr_d_e]: ~ ((docume1511108976tr_d_e @ A) = (docume1825929374tr_d_e @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
% 228.49/61.56 thf(537,plain,((~ (? [A:nat,B:sum_su1576157353tr_d_e]: ((docume1511108976tr_d_e @ A) = (docume1825929374tr_d_e @ B))))),inference(miniscope,[status(thm)],[536])).
% 228.49/61.56 thf(538,plain,(! [B:sum_su1576157353tr_d_e,A:nat] : ((~ ((docume1511108976tr_d_e @ A) = (docume1825929374tr_d_e @ B))))),inference(cnf,[status(esa)],[537])).
% 228.49/61.56 thf(539,plain,(! [B:sum_su1576157353tr_d_e,A:nat] : (((docume1511108976tr_d_e @ A) != (docume1825929374tr_d_e @ B)))),inference(lifteq,[status(thm)],[538])).
% 228.49/61.56 thf(482,plain,(((size_s7667464on_j_k @ none_R1587534007on_j_k) = (suc @ zero_zero_nat))),inference(lifteq,[status(thm)],[481])).
% 228.49/61.56 thf(293,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((append846395565tr_b_c @ A @ B) = A) = (B = nil_no279930520tr_b_c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_append__self__conv)).
% 228.49/61.56 thf(1734,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((append846395565tr_b_c @ A @ B) = A) = (B = nil_no279930520tr_b_c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])).
% 228.49/61.56 thf(1167,plain,(((cons_list_char @ nil_char @ nil_list_char) = (subseqs_char @ nil_char))),inference(lifteq,[status(thm)],[1166])).
% 228.49/61.56 thf(1998,plain,(((subseqs_char @ nil_char) = (product_lists_char @ nil_list_char))),inference(rewrite,[status(thm)],[1167,1062])).
% 228.49/61.56 thf(78,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Suc__neq__Zero)).
% 228.49/61.56 thf(627,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
% 228.49/61.56 thf(326,axiom,(((size_size_list_char @ nil_char) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_list_Osize_I3_J)).
% 228.49/61.56 thf(1917,plain,(((size_size_list_char @ nil_char) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])).
% 228.49/61.56 thf(1918,plain,(((size_size_list_char @ nil_char) = zero_zero_nat)),inference(lifteq,[status(thm)],[1917])).
% 228.49/61.56 thf(281,axiom,((! [A:char]: ((insert_char @ A @ nil_char) = (cons_char @ A @ nil_char)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_insert__Nil)).
% 228.49/61.56 thf(1649,plain,((! [A:char]: ((insert_char @ A @ nil_char) = (cons_char @ A @ nil_char)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])).
% 228.49/61.56 thf(158,axiom,((! [A:list_n282880152tr_b_c,B:list_char,C:(list_n282880152tr_b_c > (list_char > $o))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => ((C @ nil_no279930520tr_b_c @ nil_char) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:char,G:list_char]: (((size_s2106487044tr_b_c @ E) = (size_size_list_char @ G)) => ((C @ E @ G) => (C @ (cons_n413985352tr_b_c @ D @ E) @ (cons_char @ F @ G))))) => (C @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_list__induct2)).
% 228.49/61.56 thf(976,plain,((! [A:list_n282880152tr_b_c,B:list_char,C:(list_n282880152tr_b_c > (list_char > $o))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => ((C @ nil_no279930520tr_b_c @ nil_char) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:char,G:list_char]: (((size_s2106487044tr_b_c @ E) = (size_size_list_char @ G)) => ((C @ E @ G) => (C @ (cons_n413985352tr_b_c @ D @ E) @ (cons_char @ F @ G))))) => (C @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
% 228.49/61.56 thf(95,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:option2026120038on_j_k,D:(option2026120038on_j_k > option2026120038on_j_k),E:(option2026120038on_j_k > option2026120038on_j_k)]: ((A = B) => (((more_c1453068134on_j_k @ B) = C) => ((! [F:option2026120038on_j_k]: ((F = C) => ((D @ F) = (E @ F)))) => ((more_u1044474223_c_a_b @ D @ A) = (more_u1044474223_c_a_b @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_RDocument_Ounfold__congs_I6_J)).
% 228.49/61.56 thf(688,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:option2026120038on_j_k,D:(option2026120038on_j_k > option2026120038on_j_k),E:(option2026120038on_j_k > option2026120038on_j_k)]: ((A = B) => (((more_c1453068134on_j_k @ B) = C) => ((! [F:option2026120038on_j_k]: ((F = C) => ((D @ F) = (E @ F)))) => ((more_u1044474223_c_a_b @ (D) @ A) = (more_u1044474223_c_a_b @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])).
% 228.49/61.56 thf(280,axiom,((! [A:(option_element_ptr_a > $o),B:option2026120038on_j_k,C:(sum_su1221287958on_j_k > option_element_ptr_a)]: ((A @ (bind_S287509021_ptr_a @ B @ C)) = (~ (((B = none_S1393028981on_j_k) & ~ (A @ none_element_ptr_a)) | ? [D:sum_su1221287958on_j_k]: ((B = (some_S1960742641on_j_k @ D)) & ~ (A @ (C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_bind__split__asm)).
% 228.49/61.56 thf(1646,plain,((! [A:(option_element_ptr_a > $o),B:option2026120038on_j_k,C:(sum_su1221287958on_j_k > option_element_ptr_a)]: ((A @ (bind_S287509021_ptr_a @ B @ (C))) = (~ (((B = none_S1393028981on_j_k) & ~ (A @ none_element_ptr_a)) | ? [D:sum_su1221287958on_j_k]: ((B = (some_S1960742641on_j_k @ D)) & ~ (A @ (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])).
% 228.49/61.56 thf(221,axiom,((! [A:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ A) = zero_zero_nat) = (A = nil_no279930520tr_b_c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_length__0__conv)).
% 228.49/61.56 thf(1326,plain,((! [A:list_n282880152tr_b_c]: (((size_s2106487044tr_b_c @ A) = zero_zero_nat) = (A = nil_no279930520tr_b_c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
% 228.49/61.56 thf(813,plain,(((gen_length_char @ zero_zero_nat) = (size_size_list_char))),inference(lifteq,[status(thm)],[812])).
% 228.49/61.56 thf(155,axiom,((! [A:((char > (char > $o)) > (list_char > $o)),B:(char > (char > $o)),C:list_char]: ((! [D:(char > (char > $o))]: (A @ D @ nil_char)) => ((! [D:(char > (char > $o)),E:char,F:list_char]: ((A @ D @ F) => (A @ D @ (cons_char @ E @ F)))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_sorted__wrt_Oinduct)).
% 228.49/61.56 thf(963,plain,((! [A:((char > (char > $o)) > (list_char > $o)),B:(char > (char > $o)),C:list_char]: ((! [D:(char > (char > $o))]: (A @ (D) @ nil_char)) => ((! [D:(char > (char > $o)),E:char,F:list_char]: ((A @ (D) @ F) => (A @ (D) @ (cons_char @ E @ F)))) => (A @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
% 228.49/61.56 thf(250,axiom,((! [A:list_char,B:list_char]: ((nil_char = (append_char @ A @ B)) = ((A = nil_char) & (B = nil_char))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_Nil__is__append__conv)).
% 228.49/61.56 thf(1476,plain,((! [A:list_char,B:list_char]: ((nil_char = (append_char @ A @ B)) = ((A = nil_char) & (B = nil_char))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])).
% 228.49/61.56 thf(252,axiom,((! [A:list_l118626078tr_b_c]: ((A != nil_li198338206tr_b_c) => ((! [B:list_l118626078tr_b_c]: (A != (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ B))) => (~ (! [B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c,D:list_l118626078tr_b_c]: (A != (cons_l1809994318tr_b_c @ (cons_n413985352tr_b_c @ B @ C) @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_transpose_Ocases)).
% 228.49/61.56 thf(1481,plain,((! [A:list_l118626078tr_b_c]: ((~ (A = nil_li198338206tr_b_c)) => ((! [B:list_l118626078tr_b_c]: ~ (A = (cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ B))) => (~ (! [B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c,D:list_l118626078tr_b_c]: ~ (A = (cons_l1809994318tr_b_c @ (cons_n413985352tr_b_c @ B @ C) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])).
% 228.49/61.56 thf(652,plain,(((gen_le955068453tr_b_c @ zero_zero_nat) = (size_s2106487044tr_b_c))),inference(lifteq,[status(thm)],[651])).
% 228.49/61.56 thf(277,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:list_char,D:(list_n282880152tr_b_c > (list_n282880152tr_b_c > (list_char > $o)))]: (((size_s2106487044tr_b_c @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_size_list_char @ C)) => ((D @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char) => ((! [E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c,G:node_p1234578834tr_b_c,H:list_n282880152tr_b_c,I:char,J:list_char]: (((size_s2106487044tr_b_c @ F) = (size_s2106487044tr_b_c @ H)) => (((size_s2106487044tr_b_c @ H) = (size_size_list_char @ J)) => ((D @ F @ H @ J) => (D @ (cons_n413985352tr_b_c @ E @ F) @ (cons_n413985352tr_b_c @ G @ H) @ (cons_char @ I @ J)))))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_list__induct3)).
% 228.49/61.56 thf(1629,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:list_char,D:(list_n282880152tr_b_c > (list_n282880152tr_b_c > (list_char > $o)))]: (((size_s2106487044tr_b_c @ A) = (size_s2106487044tr_b_c @ B)) => (((size_s2106487044tr_b_c @ B) = (size_size_list_char @ C)) => ((D @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char) => ((! [E:node_p1234578834tr_b_c,F:list_n282880152tr_b_c,G:node_p1234578834tr_b_c,H:list_n282880152tr_b_c,I:char,J:list_char]: (((size_s2106487044tr_b_c @ F) = (size_s2106487044tr_b_c @ H)) => (((size_s2106487044tr_b_c @ H) = (size_size_list_char @ J)) => ((D @ F @ H @ J) => (D @ (cons_n413985352tr_b_c @ E @ F) @ (cons_n413985352tr_b_c @ G @ H) @ (cons_char @ I @ J)))))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])).
% 228.49/61.56 thf(310,axiom,((! [A:list_char]: ((append_char @ A @ nil_char) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_append_Oright__neutral)).
% 228.49/61.56 thf(1822,plain,((! [A:list_char]: ((append_char @ A @ nil_char) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])).
% 228.49/61.56 thf(785,plain,((~ (? [A:(list_n282880152tr_b_c > $o)]: (list_e529904353tr_b_c @ (A) @ nil_li198338206tr_b_c)))),inference(miniscope,[status(thm)],[784])).
% 228.49/61.56 thf(786,plain,(! [A:(list_n282880152tr_b_c > $o)] : ((~ (list_e529904353tr_b_c @ (A) @ nil_li198338206tr_b_c)))),inference(cnf,[status(esa)],[785])).
% 228.49/61.56 thf(3367,plain,(! [C:nat,B:nat,A:nat] : (((sk2 @ C @ A) = B) | ((plus_plus_nat @ zero_zero_nat @ A) != (plus_plus_nat @ B @ C)))),inference(paramod_ordered,[status(thm)],[355,3358])).
% 228.49/61.56 thf(3368,plain,(! [A:nat] : (((sk2 @ A @ A) = zero_zero_nat))),inference(pattern_uni,[status(thm)],[3367:[bind(A, $thf(A)),bind(B, $thf(zero_zero_nat)),bind(C, $thf(A))]])).
% 228.49/61.56 thf(218,axiom,((! [A:((char > (char > $o)) > (list_char > $o)),B:(char > (char > $o)),C:list_char]: ((! [D:(char > (char > $o))]: (A @ D @ nil_char)) => ((! [D:(char > (char > $o)),E:char]: (A @ D @ (cons_char @ E @ nil_char))) => ((! [D:(char > (char > $o)),E:char,F:char,G:list_char]: ((A @ D @ (cons_char @ F @ G)) => (A @ D @ (cons_char @ E @ (cons_char @ F @ G))))) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_successively_Oinduct)).
% 228.49/61.56 thf(1294,plain,((! [A:((char > (char > $o)) > (list_char > $o)),B:(char > (char > $o)),C:list_char]: ((! [D:(char > (char > $o))]: (A @ (D) @ nil_char)) => ((! [D:(char > (char > $o)),E:char]: (A @ (D) @ (cons_char @ E @ nil_char))) => ((! [D:(char > (char > $o)),E:char,F:char,G:list_char]: ((A @ (D) @ (cons_char @ F @ G)) => (A @ (D) @ (cons_char @ E @ (cons_char @ F @ G))))) => (A @ (B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
% 228.49/61.56 thf(2268,plain,(((nat_triangle @ (nat_triangle @ (suc @ zero_zero_nat))) != zero_zero_nat)),inference(rewrite,[status(thm)],[2088,2234])).
% 228.49/61.56 thf(2330,plain,(((nat_triangle @ (suc @ zero_zero_nat)) != zero_zero_nat)),inference(rewrite,[status(thm)],[2268,2234])).
% 228.49/61.56 thf(1075,plain,(! [B:list_n282880152tr_b_c,A:list_n282880152tr_b_c] : ((~ (A = B)) | (A = (append846395565tr_b_c @ nil_no279930520tr_b_c @ B)))),inference(cnf,[status(esa)],[1074])).
% 228.49/61.56 thf(1076,plain,(! [B:list_n282880152tr_b_c,A:list_n282880152tr_b_c] : ((A != B) | (A = (append846395565tr_b_c @ nil_no279930520tr_b_c @ B)))),inference(lifteq,[status(thm)],[1075])).
% 228.49/61.56 thf(1077,plain,(! [A:list_n282880152tr_b_c] : (((append846395565tr_b_c @ nil_no279930520tr_b_c @ A) = A))),inference(simp,[status(thm)],[1076])).
% 228.49/61.56 thf(283,axiom,((! [A:(list_n282880152tr_b_c > $o),B:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: ((A @ D) => (A @ (append846395565tr_b_c @ D @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_rev__induct)).
% 228.49/61.56 thf(1661,plain,((! [A:(list_n282880152tr_b_c > $o),B:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: ((A @ D) => (A @ (append846395565tr_b_c @ D @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])).
% 228.49/61.56 thf(94,axiom,((! [A:rObjec1617416918on_j_k]: (none_R1587534007on_j_k != (some_R67702331on_j_k @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_option_Odistinct_I1_J)).
% 228.49/61.56 thf(684,plain,((! [A:rObjec1617416918on_j_k]: ~ (none_R1587534007on_j_k = (some_R67702331on_j_k @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
% 228.49/61.56 thf(243,axiom,((! [A:list_char,B:list_char]: (((append_char @ A @ B) = nil_char) = ((A = nil_char) & (B = nil_char))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_append__is__Nil__conv)).
% 228.49/61.56 thf(1444,plain,((! [A:list_char,B:list_char]: (((append_char @ A @ B) = nil_char) = ((A = nil_char) & (B = nil_char))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])).
% 228.49/61.56 thf(164,axiom,((! [A:set_nat,B:node_p1234578834tr_b_c]: (((member_nat @ zero_zero_nat @ A) => ((nths_n1256675478tr_b_c @ (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c) @ A) = (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c))) & ((~ (member_nat @ zero_zero_nat @ A)) => ((nths_n1256675478tr_b_c @ (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c) @ A) = nil_no279930520tr_b_c))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_nths__singleton)).
% 228.49/61.56 thf(1045,plain,((! [A:set_nat,B:node_p1234578834tr_b_c]: (((member_nat @ zero_zero_nat @ A) => ((nths_n1256675478tr_b_c @ (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c) @ A) = (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c))) & ((~ (member_nat @ zero_zero_nat @ A)) => ((nths_n1256675478tr_b_c @ (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c) @ A) = nil_no279930520tr_b_c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
% 228.49/61.56 thf(272,axiom,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((doctyp814403297on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_RDocument_Oselect__convs_I2_J)).
% 228.49/61.56 thf(1614,plain,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((doctyp814403297on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])).
% 228.49/61.56 thf(163,axiom,((! [A:list_n282880152tr_b_c,B:(list_n282880152tr_b_c > $o)]: ((A != nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c]: (B @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))) => ((! [C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: ((D != nil_no279930520tr_b_c) => ((B @ D) => (B @ (append846395565tr_b_c @ D @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c)))))) => (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_rev__nonempty__induct)).
% 228.49/61.56 thf(1030,plain,((! [A:list_n282880152tr_b_c,B:(list_n282880152tr_b_c > $o)]: ((~ (A = nil_no279930520tr_b_c)) => ((! [C:node_p1234578834tr_b_c]: (B @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))) => ((! [C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: ((~ (D = nil_no279930520tr_b_c)) => ((B @ D) => (B @ (append846395565tr_b_c @ D @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c)))))) => (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
% 228.49/61.56 thf(254,axiom,(((size_s2106487044tr_b_c @ nil_no279930520tr_b_c) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_list_Osize_I3_J)).
% 228.49/61.56 thf(1490,plain,(((size_s2106487044tr_b_c @ nil_no279930520tr_b_c) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])).
% 228.49/61.56 thf(1491,plain,(((size_s2106487044tr_b_c @ nil_no279930520tr_b_c) = zero_zero_nat)),inference(lifteq,[status(thm)],[1490])).
% 228.49/61.56 thf(108,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_n__not__Suc__n)).
% 228.49/61.56 thf(752,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
% 228.49/61.56 thf(257,axiom,((! [A:(list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)),B:list_n282880152tr_b_c,C:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (A @ (cons_n413985352tr_b_c @ D @ E) @ nil_no279930520tr_b_c)) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (A @ nil_no279930520tr_b_c @ (cons_n413985352tr_b_c @ D @ E))) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: ((A @ E @ G) => (A @ (cons_n413985352tr_b_c @ D @ E) @ (cons_n413985352tr_b_c @ F @ G)))) => (A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_list__induct2_H)).
% 228.49/61.56 thf(1512,plain,((! [A:(list_n282880152tr_b_c > (list_n282880152tr_b_c > $o)),B:list_n282880152tr_b_c,C:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (A @ (cons_n413985352tr_b_c @ D @ E) @ nil_no279930520tr_b_c)) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: (A @ nil_no279930520tr_b_c @ (cons_n413985352tr_b_c @ D @ E))) => ((! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c,F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c]: ((A @ E @ G) => (A @ (cons_n413985352tr_b_c @ D @ E) @ (cons_n413985352tr_b_c @ F @ G)))) => (A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])).
% 228.49/61.56 thf(38,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_group__cancel_Oadd1)).
% 228.49/61.56 thf(447,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
% 228.49/61.56 thf(33,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_add__eq__self__zero)).
% 228.49/61.56 thf(432,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) => (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 228.49/61.56 thf(177,axiom,((! [A:list_char,B:list_char,C:(list_char > (list_char > $o))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => ((C @ nil_char @ nil_char) => ((! [D:char,E:list_char,F:char,G:list_char]: (((size_size_list_char @ E) = (size_size_list_char @ G)) => ((C @ E @ G) => (C @ (cons_char @ D @ E) @ (cons_char @ F @ G))))) => (C @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_list__induct2)).
% 228.49/61.56 thf(1097,plain,((! [A:list_char,B:list_char,C:(list_char > (list_char > $o))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => ((C @ nil_char @ nil_char) => ((! [D:char,E:list_char,F:char,G:list_char]: (((size_size_list_char @ E) = (size_size_list_char @ G)) => ((C @ E @ G) => (C @ (cons_char @ D @ E) @ (cons_char @ F @ G))))) => (C @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])).
% 228.49/61.56 thf(205,axiom,((! [A:list_char]: ((A != nil_char) => (~ (! [B:list_char,C:char]: (A != (append_char @ B @ (cons_char @ C @ nil_char)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_rev__exhaust)).
% 228.49/61.56 thf(1229,plain,((! [A:list_char]: ((~ (A = nil_char)) => (~ (! [B:list_char,C:char]: ~ (A = (append_char @ B @ (cons_char @ C @ nil_char)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
% 228.49/61.56 thf(1624,plain,(! [A:(sum_su1221287958on_j_k > nat)] : (((size_o1777465779on_j_k @ (A) @ none_S1393028981on_j_k) = (suc @ zero_zero_nat)))),inference(cnf,[status(esa)],[1623])).
% 228.49/61.56 thf(1625,plain,(! [A:(sum_su1221287958on_j_k > nat)] : (((size_o1777465779on_j_k @ (A) @ none_S1393028981on_j_k) = (suc @ zero_zero_nat)))),inference(lifteq,[status(thm)],[1624])).
% 228.49/61.56 thf(118,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_old_Onat_Oexhaust)).
% 228.49/61.56 thf(790,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
% 228.49/61.56 thf(1480,plain,(((^ [A:(option_element_ptr_a > $o)]: ((A @ none_element_ptr_a) & ! [B:element_ptr_a]: (A @ (some_element_ptr_a @ B)))) = ((!) @ option_element_ptr_a))),inference(lifteq,[status(thm)],[1479])).
% 228.49/61.56 thf(372,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),inference(cnf,[status(esa)],[371])).
% 228.49/61.56 thf(373,plain,(! [B:nat,A:nat] : (((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),inference(lifteq,[status(thm)],[372])).
% 228.49/61.56 thf(148,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((splice1294941035tr_b_c @ A @ B) = nil_no279930520tr_b_c) = ((A = nil_no279930520tr_b_c) & (B = nil_no279930520tr_b_c))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_split__Nil__iff)).
% 228.49/61.56 thf(918,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c]: (((splice1294941035tr_b_c @ A @ B) = nil_no279930520tr_b_c) = ((A = nil_no279930520tr_b_c) & (B = nil_no279930520tr_b_c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
% 228.49/61.56 thf(1363,plain,(((size_s1129069050on_j_k @ none_S1393028981on_j_k) = (suc @ zero_zero_nat))),inference(lifteq,[status(thm)],[1362])).
% 228.49/61.56 thf(357,plain,(! [B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(cnf,[status(esa)],[356])).
% 228.49/61.56 thf(358,plain,(! [B:nat,A:nat] : ((((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(lifteq,[status(thm)],[357])).
% 228.49/61.56 thf(145,axiom,((! [A:list_char,B:(list_char > $o)]: ((A != nil_char) => ((! [C:char]: (B @ (cons_char @ C @ nil_char))) => ((! [C:char,D:list_char]: ((D != nil_char) => ((B @ D) => (B @ (append_char @ D @ (cons_char @ C @ nil_char)))))) => (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_rev__nonempty__induct)).
% 228.49/61.56 thf(897,plain,((! [A:list_char,B:(list_char > $o)]: ((~ (A = nil_char)) => ((! [C:char]: (B @ (cons_char @ C @ nil_char))) => ((! [C:char,D:list_char]: ((~ (D = nil_char)) => ((B @ D) => (B @ (append_char @ D @ (cons_char @ C @ nil_char)))))) => (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
% 228.49/61.56 thf(102,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_old_Onat_Odistinct_I1_J)).
% 228.49/61.56 thf(720,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])).
% 228.49/61.56 thf(795,plain,(! [A:set_nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(cnf,[status(esa)],[794])).
% 228.49/61.56 thf(796,plain,(! [A:set_nat] : (((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(lifteq,[status(thm)],[795])).
% 228.49/61.56 thf(29,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_comm__monoid__add__class_Oadd__0)).
% 228.49/61.56 thf(415,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 228.49/61.56 thf(308,axiom,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((docume1175131570on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = D))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_RDocument_Oselect__convs_I3_J)).
% 228.49/61.56 thf(1816,plain,((! [A:product_unit,B:product_unit,C:list_char,D:option_element_ptr_a,E:list_n282880152tr_b_c,F:option2026120038on_j_k]: ((docume1175131570on_j_k @ (rObjec1303043984on_j_k @ A @ (rDocum427676485on_j_k @ B @ C @ D @ E @ F))) = D))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])).
% 228.49/61.56 thf(1196,plain,((~ (? [A:(char > $o)]: (list_ex1_char @ (A) @ nil_char)))),inference(miniscope,[status(thm)],[1195])).
% 228.49/61.56 thf(1197,plain,(! [A:(char > $o)] : ((~ (list_ex1_char @ (A) @ nil_char)))),inference(cnf,[status(esa)],[1196])).
% 228.49/61.56 thf(154,axiom,((! [A:list_char]: ((append_char @ nil_char @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_append_Oleft__neutral)).
% 228.49/61.56 thf(960,plain,((! [A:list_char]: ((append_char @ nil_char @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
% 228.49/61.56 thf(80,axiom,((! [A:rObjec103300152t_unit,B:rDocum326988203on_j_k]: ((more_R1625109589on_j_k @ (extend1066431834on_j_k @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_object__more__extend__id)).
% 228.49/61.56 thf(635,plain,((! [A:rObjec103300152t_unit,B:rDocum326988203on_j_k]: ((more_R1625109589on_j_k @ (extend1066431834on_j_k @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
% 228.49/61.56 thf(249,axiom,((! [A:rObjec1617416918on_j_k]: ((rObjec1303043984on_j_k @ product_Unity @ (more_R1625109589on_j_k @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_object__empty)).
% 228.49/61.56 thf(1473,plain,((! [A:rObjec1617416918on_j_k]: ((rObjec1303043984on_j_k @ product_Unity @ (more_R1625109589on_j_k @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])).
% 228.49/61.56 thf(213,axiom,((! [A:list_n282880152tr_b_c]: ((A != nil_no279930520tr_b_c) => (~ (! [B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c]: (A != (cons_n413985352tr_b_c @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_list_Oexhaust)).
% 228.49/61.56 thf(1268,plain,((! [A:list_n282880152tr_b_c]: ((~ (A = nil_no279930520tr_b_c)) => (~ (! [B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c]: ~ (A = (cons_n413985352tr_b_c @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
% 228.49/61.56 thf(425,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : ((~ ((A @ (sk3 @ (A)) @ (sk4 @ (A))) = (A @ (sk4 @ (A)) @ (sk3 @ (A))))) | (~ (A @ (sk5 @ (A)) @ zero_zero_nat)) | (~ (A @ (sk6 @ (A)) @ (plus_plus_nat @ (sk6 @ (A)) @ (sk7 @ (A))))) | (A @ B @ C))),inference(cnfConj,[status(thm)],[423])).
% 228.49/61.56 thf(427,plain,(! [C:nat,B:nat,A:(nat > (nat > $o))] : (((A @ (sk4 @ (A)) @ (sk3 @ (A))) != (A @ (sk3 @ (A)) @ (sk4 @ (A)))) | (~ (A @ (sk5 @ (A)) @ zero_zero_nat)) | (~ (A @ (sk6 @ (A)) @ (plus_plus_nat @ (sk6 @ (A)) @ (sk7 @ (A))))) | (A @ B @ C))),inference(lifteq,[status(thm)],[425])).
% 228.49/61.56 thf(136,axiom,((! [A:list_l118626078tr_b_c]: (((size_s9369994tr_b_c @ A) = zero_zero_nat) = (A = nil_li198338206tr_b_c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_length__0__conv)).
% 228.49/61.56 thf(860,plain,((! [A:list_l118626078tr_b_c]: (((size_s9369994tr_b_c @ A) = zero_zero_nat) = (A = nil_li198338206tr_b_c)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])).
% 228.49/61.56 thf(263,axiom,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c]: (((splice1294941035tr_b_c @ A @ B) = C) => (((A = nil_no279930520tr_b_c) => (C != B)) => (~ (! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: ((A = (cons_n413985352tr_b_c @ D @ E)) => (C != (cons_n413985352tr_b_c @ D @ (splice1294941035tr_b_c @ B @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_splice_Oelims)).
% 228.49/61.56 thf(1537,plain,((! [A:list_n282880152tr_b_c,B:list_n282880152tr_b_c,C:list_n282880152tr_b_c]: (((splice1294941035tr_b_c @ A @ B) = C) => (((A = nil_no279930520tr_b_c) => (~ (C = B))) => (~ (! [D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: ((A = (cons_n413985352tr_b_c @ D @ E)) => (~ (C = (cons_n413985352tr_b_c @ D @ (splice1294941035tr_b_c @ B @ E))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])).
% 228.49/61.56 thf(595,plain,(! [A:nat] : (((size_size_list_char @ (sk23 @ A)) = A))),inference(cnf,[status(esa)],[594])).
% 228.49/61.56 thf(596,plain,(! [A:nat] : (((size_size_list_char @ (sk23 @ A)) = A))),inference(lifteq,[status(thm)],[595])).
% 228.49/61.56 thf(268,axiom,((! [A:list_n282880152tr_b_c]: ((append846395565tr_b_c @ A @ nil_no279930520tr_b_c) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_append__Nil2)).
% 228.49/61.56 thf(1582,plain,((! [A:list_n282880152tr_b_c]: ((append846395565tr_b_c @ A @ nil_no279930520tr_b_c) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])).
% 228.49/61.56 thf(133,axiom,((! [A:docume1935157360tr_d_e,B:docume1935157360tr_d_e]: (((cast_d1608273229_b_c_f @ A) = (cast_d1608273229_b_c_f @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_cast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r__inject)).
% 228.49/61.56 thf(850,plain,((! [A:docume1935157360tr_d_e,B:docume1935157360tr_d_e]: (((cast_d1608273229_b_c_f @ A) = (cast_d1608273229_b_c_f @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
% 228.49/61.56 thf(242,axiom,((! [A:list_n282880152tr_b_c,B:list_char,C:list_n282880152tr_b_c,D:list_char,E:(list_n282880152tr_b_c > (list_char > (list_n282880152tr_b_c > (list_char > $o))))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => (((size_s2106487044tr_b_c @ C) = (size_size_list_char @ D)) => ((E @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c @ nil_char) => ((! [F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c,H:char,I:list_char,J:node_p1234578834tr_b_c,K:list_n282880152tr_b_c,L:char,M:list_char]: (((size_s2106487044tr_b_c @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_s2106487044tr_b_c @ K)) => (((size_s2106487044tr_b_c @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_n413985352tr_b_c @ F @ G) @ (cons_char @ H @ I) @ (cons_n413985352tr_b_c @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_list__induct4)).
% 228.49/61.56 thf(1431,plain,((! [A:list_n282880152tr_b_c,B:list_char,C:list_n282880152tr_b_c,D:list_char,E:(list_n282880152tr_b_c > (list_char > (list_n282880152tr_b_c > (list_char > $o))))]: (((size_s2106487044tr_b_c @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_s2106487044tr_b_c @ C)) => (((size_s2106487044tr_b_c @ C) = (size_size_list_char @ D)) => ((E @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c @ nil_char) => ((! [F:node_p1234578834tr_b_c,G:list_n282880152tr_b_c,H:char,I:list_char,J:node_p1234578834tr_b_c,K:list_n282880152tr_b_c,L:char,M:list_char]: (((size_s2106487044tr_b_c @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_s2106487044tr_b_c @ K)) => (((size_s2106487044tr_b_c @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_n413985352tr_b_c @ F @ G) @ (cons_char @ H @ I) @ (cons_n413985352tr_b_c @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
% 228.49/61.56 thf(219,axiom,((! [A:option_element_ptr_a,B:(option_element_ptr_a > (option_element_ptr_a > $o)),C:option_element_ptr_a]: (((A = none_element_ptr_a) => (B @ A @ C)) => (((C = none_element_ptr_a) => (B @ A @ C)) => ((! [D:element_ptr_a,E:element_ptr_a]: ((A = (some_element_ptr_a @ D)) => ((C = (some_element_ptr_a @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_combine__options__cases)).
% 228.49/61.56 thf(1299,plain,((! [A:option_element_ptr_a,B:(option_element_ptr_a > (option_element_ptr_a > $o)),C:option_element_ptr_a]: (((A = none_element_ptr_a) => (B @ A @ C)) => (((C = none_element_ptr_a) => (B @ A @ C)) => ((! [D:element_ptr_a,E:element_ptr_a]: ((A = (some_element_ptr_a @ D)) => ((C = (some_element_ptr_a @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
% 228.49/61.56 thf(207,axiom,((! [A:list_char]: ((append_char @ nil_char @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_append__Nil)).
% 228.49/61.56 thf(1236,plain,((! [A:list_char]: ((append_char @ nil_char @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
% 228.49/61.56 thf(160,axiom,((! [A:(list_n282880152tr_b_c > $o),B:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c]: (A @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))) => ((! [C:node_p1234578834tr_b_c,D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: ((A @ E) => ((A @ (cons_n413985352tr_b_c @ D @ E)) => (A @ (cons_n413985352tr_b_c @ C @ (cons_n413985352tr_b_c @ D @ E)))))) => (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_induct__list012)).
% 228.49/61.56 thf(987,plain,((! [A:(list_n282880152tr_b_c > $o),B:list_n282880152tr_b_c]: ((A @ nil_no279930520tr_b_c) => ((! [C:node_p1234578834tr_b_c]: (A @ (cons_n413985352tr_b_c @ C @ nil_no279930520tr_b_c))) => ((! [C:node_p1234578834tr_b_c,D:node_p1234578834tr_b_c,E:list_n282880152tr_b_c]: ((A @ E) => ((A @ (cons_n413985352tr_b_c @ D @ E)) => (A @ (cons_n413985352tr_b_c @ C @ (cons_n413985352tr_b_c @ D @ E)))))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
% 228.49/61.56 thf(1350,plain,((~ (~ (! [A:rObjec103300152t_unit]: ? [B:product_unit]: (A = (rObjec730108904t_unit @ B @ product_Unity)))))),inference(miniscope,[status(thm)],[1349])).
% 228.49/61.56 thf(1351,plain,(! [A:rObjec103300152t_unit] : ((A = (rObjec730108904t_unit @ (sk164 @ A) @ product_Unity)))),inference(cnf,[status(esa)],[1350])).
% 228.49/61.56 thf(1352,plain,(! [A:rObjec103300152t_unit] : (((rObjec730108904t_unit @ (sk164 @ A) @ product_Unity) = A))),inference(lifteq,[status(thm)],[1351])).
% 228.49/61.56 thf(464,plain,(((size_s2008079621t_char @ nil_list_char) = zero_zero_nat)),inference(lifteq,[status(thm)],[463])).
% 228.49/61.56 thf(331,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(cnf,[status(esa)],[330])).
% 228.49/61.56 thf(332,plain,(! [C:nat,B:nat,A:nat] : (((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(lifteq,[status(thm)],[331])).
% 228.49/61.56 thf(183,axiom,((! [A:(option2026120038on_j_k > $o),B:option2026120038on_j_k,C:(sum_su1221287958on_j_k > option2026120038on_j_k)]: ((A @ (bind_S607117548on_j_k @ B @ C)) = (~ (((B = none_S1393028981on_j_k) & ~ (A @ none_S1393028981on_j_k)) | ? [D:sum_su1221287958on_j_k]: ((B = (some_S1960742641on_j_k @ D)) & ~ (A @ (C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_bind__split__asm)).
% 228.49/61.56 thf(1129,plain,((! [A:(option2026120038on_j_k > $o),B:option2026120038on_j_k,C:(sum_su1221287958on_j_k > option2026120038on_j_k)]: ((A @ (bind_S607117548on_j_k @ B @ (C))) = (~ (((B = none_S1393028981on_j_k) & ~ (A @ none_S1393028981on_j_k)) | ? [D:sum_su1221287958on_j_k]: ((B = (some_S1960742641on_j_k @ D)) & ~ (A @ (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
% 228.49/61.56 thf(74,axiom,((! [A:list_char,B:list_char]: (((size_size_list_char @ A) != (size_size_list_char @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_size__neq__size__imp__neq)).
% 228.49/61.56 thf(607,plain,((! [A:list_char,B:list_char]: ((~ ((size_size_list_char @ A) = (size_size_list_char @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])).
% 228.49/61.56 thf(47,axiom,((! [A:option841825948on_j_k]: ((A != none_R1587534007on_j_k) = (? [B:rObjec1617416918on_j_k]: (A = (some_R67702331on_j_k @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_not__None__eq)).
% 228.49/61.56 thf(486,plain,((! [A:option841825948on_j_k]: ((~ (A = none_R1587534007on_j_k)) = (? [B:rObjec1617416918on_j_k]: (A = (some_R67702331on_j_k @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
% 228.49/61.56 thf(1945,plain,(! [A:nat] : (((plus_plus_nat @ A) = (^ [B:nat]: (plus_plus_nat @ B @ A))))),inference(func_ext,[status(esa)],[370])).
% 228.49/61.56 thf(294,axiom,((! [A:list_char,B:list_char,C:list_char,D:list_char,E:(list_char > (list_char > (list_char > (list_char > $o))))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_size_list_char @ D)) => ((E @ nil_char @ nil_char @ nil_char @ nil_char) => ((! [F:char,G:list_char,H:char,I:list_char,J:char,K:list_char,L:char,M:list_char]: (((size_size_list_char @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_char @ H @ I) @ (cons_char @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_list__induct4)).
% 228.49/61.56 thf(1737,plain,((! [A:list_char,B:list_char,C:list_char,D:list_char,E:(list_char > (list_char > (list_char > (list_char > $o))))]: (((size_size_list_char @ A) = (size_size_list_char @ B)) => (((size_size_list_char @ B) = (size_size_list_char @ C)) => (((size_size_list_char @ C) = (size_size_list_char @ D)) => ((E @ nil_char @ nil_char @ nil_char @ nil_char) => ((! [F:char,G:list_char,H:char,I:list_char,J:char,K:list_char,L:char,M:list_char]: (((size_size_list_char @ G) = (size_size_list_char @ I)) => (((size_size_list_char @ I) = (size_size_list_char @ K)) => (((size_size_list_char @ K) = (size_size_list_char @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_char @ F @ G) @ (cons_char @ H @ I) @ (cons_char @ J @ K) @ (cons_char @ L @ M))))))) => (E @ A @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])).
% 228.49/61.56 thf(58,axiom,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:product_unit,D:(product_unit > product_unit),E:(product_unit > product_unit)]: ((A = B) => (((nothin757132294on_j_k @ B) = C) => ((! [F:product_unit]: ((F = C) => ((D @ F) = (E @ F)))) => ((nothin1105341917on_j_k @ D @ A) = (nothin1105341917on_j_k @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_RDocument_Ounfold__congs_I2_J)).
% 228.49/61.56 thf(543,plain,((! [A:rObjec1617416918on_j_k,B:rObjec1617416918on_j_k,C:product_unit,D:(product_unit > product_unit),E:(product_unit > product_unit)]: ((A = B) => (((nothin757132294on_j_k @ B) = C) => ((! [F:product_unit]: ((F = C) => ((D @ F) = (E @ F)))) => ((nothin1105341917on_j_k @ (D) @ A) = (nothin1105341917on_j_k @ (E) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
% 228.49/61.56 thf(316,axiom,((! [A:list_n282880152tr_b_c]: ((append846395565tr_b_c @ nil_no279930520tr_b_c @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_append__Nil)).
% 228.49/61.56 thf(1848,plain,((! [A:list_n282880152tr_b_c]: ((append846395565tr_b_c @ nil_no279930520tr_b_c @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])).
% 228.49/61.56 thf(307,axiom,((! [A:list_n282880152tr_b_c]: ((A != nil_no279930520tr_b_c) => ((! [B:node_p1234578834tr_b_c]: (A != (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c))) => (~ (! [B:node_p1234578834tr_b_c,C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: (A != (cons_n413985352tr_b_c @ B @ (cons_n413985352tr_b_c @ C @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_remdups__adj_Ocases)).
% 228.49/61.56 thf(1812,plain,((! [A:list_n282880152tr_b_c]: ((~ (A = nil_no279930520tr_b_c)) => ((! [B:node_p1234578834tr_b_c]: ~ (A = (cons_n413985352tr_b_c @ B @ nil_no279930520tr_b_c))) => (~ (! [B:node_p1234578834tr_b_c,C:node_p1234578834tr_b_c,D:list_n282880152tr_b_c]: ~ (A = (cons_n413985352tr_b_c @ B @ (cons_n413985352tr_b_c @ C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])).
% 228.49/61.56 thf(325,axiom,((! [A:list_n282880152tr_b_c,B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c]: ((A = (cons_n413985352tr_b_c @ B @ C)) => (A != nil_no279930520tr_b_c)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_list_OdiscI)).
% 228.49/61.56 thf(1912,plain,((! [A:list_n282880152tr_b_c,B:node_p1234578834tr_b_c,C:list_n282880152tr_b_c]: ((A = (cons_n413985352tr_b_c @ B @ C)) => (~ (A = nil_no279930520tr_b_c))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])).
% 228.49/61.56 thf(466,plain,((! [A:option841825948on_j_k]: ((? [B:rObjec1617416918on_j_k]: (A = (some_R67702331on_j_k @ B))) => (~ (A = none_R1587534007on_j_k))))),inference(miniscope,[status(thm)],[465])).
% 228.49/61.56 thf(467,plain,(! [B:rObjec1617416918on_j_k,A:option841825948on_j_k] : ((~ (A = (some_R67702331on_j_k @ B))) | (~ (A = none_R1587534007on_j_k)))),inference(cnf,[status(esa)],[466])).
% 228.49/61.56 thf(468,plain,(! [B:rObjec1617416918on_j_k,A:option841825948on_j_k] : ((A != (some_R67702331on_j_k @ B)) | (A != none_R1587534007on_j_k))),inference(lifteq,[status(thm)],[467])).
% 228.49/61.56 thf(469,plain,(! [A:rObjec1617416918on_j_k] : (((some_R67702331on_j_k @ A) != none_R1587534007on_j_k))),inference(simp,[status(thm)],[468])).
% 228.49/61.56 thf(298,axiom,((! [A:(list_char > $o),B:list_char]: ((A @ nil_char) => ((! [C:char]: (A @ (cons_char @ C @ nil_char))) => ((! [C:char,D:char,E:list_char]: ((A @ E) => ((A @ (cons_char @ D @ E)) => (A @ (cons_char @ C @ (cons_char @ D @ E)))))) => (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_induct__list012)).
% 228.49/61.56 thf(1769,plain,((! [A:(list_char > $o),B:list_char]: ((A @ nil_char) => ((! [C:char]: (A @ (cons_char @ C @ nil_char))) => ((! [C:char,D:char,E:list_char]: ((A @ E) => ((A @ (cons_char @ D @ E)) => (A @ (cons_char @ C @ (cons_char @ D @ E)))))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])).
% 228.49/61.56 thf(753,plain,((~ (? [A:nat]: (A = (suc @ A))))),inference(miniscope,[status(thm)],[752])).
% 228.49/61.56 thf(754,plain,(! [A:nat] : ((~ (A = (suc @ A))))),inference(cnf,[status(esa)],[753])).
% 228.49/61.56 thf(755,plain,(! [A:nat] : (((suc @ A) != A))),inference(lifteq,[status(thm)],[754])).
% 228.49/61.56 thf(76743,plain,(($false)),inference(e,[status(thm)],[645,809,1337,1168,1454,1995,347,846,333,893,941,555,666,481,352,1750,1406,683,730,1068,1073,1205,379,597,523,582,614,677,1078,384,1137,2607,4884,797,1233,814,698,1919,1342,1640,3313,1063,670,2491,2020,1359,1887,651,1904,1703,1228,1623,724,504,1132,460,587,3612,802,344,2049,1479,1115,1362,638,853,1704,421,756,1714,1811,1911,376,646,1828,937,353,1283,821,1383,574,2058,397,1215,1447,866,1796,1622,1345,527,428,1201,1697,1242,1074,452,380,942,678,761,366,1067,1470,1708,1730,798,1057,1163,1900,1091,1355,1174,820,392,1223,894,825,1343,1123,349,847,1837,361,3403,435,329,665,1819,889,1787,757,1195,1128,1291,710,1983,1121,1856,403,869,857,697,1089,874,1143,1851,1259,1534,1017,2685,1096,1672,1138,356,783,420,1118,1329,1424,642,590,1700,489,1825,647,985,701,1150,1451,1382,1831,1060,1799,1002,1874,371,503,1525,2634,343,921,765,1286,674,926,558,1071,794,586,618,1146,1680,3358,856,573,444,2524,601,1135,412,819,562,1833,2727,1784,1125,772,1620,1652,743,579,1403,875,711,1256,1226,1428,1707,498,1058,1239,1332,1092,1765,804,1356,350,540,391,1503,611,787,1258,704,604,1209,406,681,2415,784,1806,1524,1349,377,362,1571,863,2246,1492,1603,890,387,631,552,594,483,520,915,769,330,1061,758,1339,799,1909,1177,1381,1198,1643,455,1364,653,1562,912,1171,1066,1528,394,986,505,438,1626,675,1809,589,1467,680,663,374,2234,812,1340,355,968,426,1166,617,516,836,1551,1798,1598,887,1566,739,1368,1531,409,1400,707,414,971,1053,673,441,3554,502,1262,463,470,359,1336,1220,1790,1987,5418,585,370,1317,1830,1763,338,1901,1358,1934,1898,1802,1353,727,1585,1717,571,1272,3366,876,1617,1766,336,1485,2711,845,465,3620,4851,539,482,1834,1126,1734,1998,2458,627,1918,1649,976,688,1646,1326,813,963,1476,1062,1481,652,1629,1822,1523,781,418,786,3368,1294,2330,1077,1661,684,1444,536,1045,1614,1030,1491,752,1512,447,432,1097,1229,1625,790,1480,373,918,1363,358,2070,897,1056,720,796,415,341,1816,400,1197,960,635,1473,395,1268,427,860,1537,596,1582,850,1431,1299,1236,987,1352,464,332,1129,369,607,486,803,1945,1737,543,1848,1490,2351,1812,1912,469,940,1769,1917,755])).
% 228.49/61.56 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 228.49/61.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------