0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.15/0.42 % Computer : n029.cluster.edu 0.15/0.42 % Model : x86_64 x86_64 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.42 % Memory : 8046.5625MB 0.15/0.42 % OS : Linux 6.8.0-71-generic 0.15/0.42 % CPULimit : 1440 0.15/0.42 % WCLimit : 180 0.15/0.42 % DateTime : Mon Jul 27 13:24:16 UTC 2026 0.15/0.42 % CPUTime : 0.15/0.42 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.15/0.49 Running higher-order theorem proving 0.23/0.54 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.rebpBEUsS2/E---3.1_2894887.p 0.31/0.88 % Version: 3.5.1-ho 0.31/0.88 % partial match(1): HSLMSMSSSSMNHSA 0.31/0.88 % Preprocessing class: HSLMSLSSSSMNHSA. 0.31/0.88 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.31/0.88 % Starting new_ho_10 with 900s (5) cores 0.31/0.88 % Starting sh5l with 180s (1) cores 0.31/0.88 % Starting new_bool_1 with 180s (1) cores 0.31/0.88 % Starting new_bool_2 with 180s (1) cores 0.31/0.88 % new_ho_10 with pid 2894900 completed with status 0 0.31/0.88 % Result found by new_ho_10 0.31/0.88 % partial match(1): HSLMSMSSSSMNHSA 0.31/0.88 % Preprocessing class: HSLMSLSSSSMNHSA. 0.31/0.88 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.31/0.88 % Starting new_ho_10 with 900s (5) cores 0.31/0.88 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 0.31/0.88 % No SInE strategy applied 0.31/0.88 % Search class: HGHSM-SMLM31-MHSFFMBN 0.31/0.88 % partial match(1): HGHSM-SMLM31-MHSFFSBN 0.31/0.88 % Scheduled 5 strats onto 5 cores with 900 seconds (900 total) 0.31/0.88 % Starting SubtermCWHack with 91s (1) cores 0.31/0.88 % Starting new_ho_10 with 541s (1) cores 0.31/0.88 % Starting new_bool_1 with 91s (1) cores 0.31/0.88 % Starting new_bool_2 with 91s (1) cores 0.31/0.88 % Starting new_bool_9 with 86s (1) cores 0.31/0.88 % new_ho_10 with pid 2894910 completed with status 0 0.31/0.88 % Result found by new_ho_10 0.31/0.88 % partial match(1): HSLMSMSSSSMNHSA 0.31/0.88 % Preprocessing class: HSLMSLSSSSMNHSA. 0.31/0.88 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.31/0.88 % Starting new_ho_10 with 900s (5) cores 0.31/0.88 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 0.31/0.88 % No SInE strategy applied 0.31/0.88 % Search class: HGHSM-SMLM31-MHSFFMBN 0.31/0.88 % partial match(1): HGHSM-SMLM31-MHSFFSBN 0.31/0.88 % Scheduled 5 strats onto 5 cores with 900 seconds (900 total) 0.31/0.88 % Starting SubtermCWHack with 91s (1) cores 0.31/0.88 % Starting new_ho_10 with 541s (1) cores 0.31/0.88 % Preprocessing time : 0.053 s 0.31/0.88 % Presaturation interreduction done 0.31/0.88 0.31/0.88 % Proof found! 0.31/0.88 % SZS status Theorem 0.31/0.88 % SZS output start CNFRefutation 0.31/0.88 thf(decl_sort1, type, term: $tType). 0.31/0.88 thf(decl_sort2, type, subst: $tType). 0.31/0.88 thf(decl_sort3, type, d_term: $tType). 0.31/0.88 thf(decl_sort4, type, d_subst: $tType). 0.31/0.88 thf(decl_23, type, one: term). 0.31/0.88 thf(decl_24, type, ap: term > term > term). 0.31/0.88 thf(decl_25, type, lam: term > term). 0.31/0.88 thf(decl_26, type, sub: term > subst > term). 0.31/0.88 thf(decl_27, type, id: subst). 0.31/0.88 thf(decl_28, type, sh: subst). 0.31/0.88 thf(decl_29, type, push: term > subst > subst). 0.31/0.88 thf(decl_30, type, comp: subst > subst > subst). 0.31/0.88 thf(decl_31, type, var: term > $o). 0.31/0.88 thf(decl_32, type, pushprop_lem1v2: $o). 0.31/0.88 thf(decl_33, type, pushprop_lem1_gthm: $o). 0.31/0.88 thf(decl_34, type, axmap: $o). 0.31/0.88 thf(decl_35, type, pushprop_lem0_gthm: $o). 0.31/0.88 thf(decl_36, type, shinj: $o). 0.31/0.88 thf(decl_37, type, hoasinduction_lem1v2: $o). 0.31/0.88 thf(decl_38, type, hoasinduction_lem1v2_gthm: $o). 0.31/0.88 thf(decl_39, type, hoasap: subst > term > subst > term > term). 0.31/0.88 thf(decl_40, type, induction2lem: $o). 0.31/0.88 thf(decl_41, type, hoasinduction_lem3v2_f: $o). 0.31/0.88 thf(decl_42, type, axvarshift: $o). 0.31/0.88 thf(decl_43, type, hoasapinj2: $o). 0.31/0.88 thf(decl_44, type, hoasapnotvar_gthm: $o). 0.31/0.88 thf(decl_45, type, hoasapinj1: $o). 0.31/0.88 thf(decl_46, type, ulamvar1: $o). 0.31/0.88 thf(decl_47, type, induction2lem_lthm: $o). 0.31/0.88 thf(decl_48, type, hoasinduction_lem3v2_gthm: $o). 0.31/0.88 thf(decl_49, type, apnotvar: $o). 0.31/0.88 thf(decl_50, type, pushprop_lthm_orig: $o). 0.31/0.88 thf(decl_51, type, hoasinduction_lem3v2_f_lthm: $o). 0.31/0.88 thf(decl_52, type, hoasinduction_lthm: $o). 0.31/0.88 thf(decl_53, type, hoasinduction_no_psi_cond_lthm: $o). 0.31/0.88 thf(decl_54, type, hoaslaminj: $o). 0.31/0.88 thf(decl_55, type, hoasinduction_lem3aaa: $o). 0.31/0.88 thf(decl_56, type, induction2lem_gthm: $o). 0.31/0.88 thf(decl_57, type, hoasinduction_lem3aa_lthm: $o). 0.31/0.88 thf(decl_58, type, hoasinduction_lem3: $o). 0.31/0.88 thf(decl_59, type, hoasinduction_lem2: $o). 0.31/0.88 thf(decl_60, type, termmset_lthm: $o). 0.31/0.88 thf(decl_61, type, hoasinduction_lem1: $o). 0.31/0.88 thf(decl_62, type, hoaslamnotap_lthm: $o). 0.31/0.88 thf(decl_63, type, pushprop_lem1v2_lthm: $o). 0.31/0.88 thf(decl_64, type, hoasapnotvar: $o). 0.31/0.88 thf(decl_65, type, hoasinduction_lem0: $o). 0.31/0.88 thf(decl_66, type, hoasinduction: $o). 0.31/0.88 thf(decl_67, type, hoasinduction_gthm: $o). 0.31/0.88 thf(decl_68, type, axapp: $o). 0.31/0.88 thf(decl_69, type, hoaslamnotvar_lthm: $o). 0.31/0.88 thf(decl_70, type, pushprop_lem3v2_lthm: $o). 0.31/0.88 thf(decl_71, type, hoasinduction_lem3b_lthm: $o). 0.31/0.88 thf(decl_72, type, ulamvarind: $o). 0.31/0.88 thf(decl_73, type, induction: $o). 0.31/0.88 thf(decl_74, type, hoasinduction_lem3a_lthm: $o). 0.31/0.88 thf(decl_75, type, termmset_gthm: $o). 0.31/0.88 thf(decl_76, type, hoasinduction_lem3aa: $o). 0.31/0.88 thf(decl_77, type, pushprop_lem1v2_gthm: $o). 0.31/0.88 thf(decl_78, type, hoaslamnotap_gthm: $o). 0.31/0.88 thf(decl_79, type, hoaslamnotvar_gthm: $o). 0.31/0.88 thf(decl_80, type, hoasinduction_lem3b_gthm: $o). 0.31/0.88 thf(decl_81, type, pushprop_lem2v2: $o). 0.31/0.88 thf(decl_82, type, hoasinduction_lem3a_gthm: $o). 0.31/0.88 thf(decl_83, type, axclos: $o). 0.31/0.88 thf(decl_84, type, axassoc: $o). 0.31/0.88 thf(decl_85, type, hoasinduction_lem2v2: $o). 0.31/0.88 thf(decl_86, type, pushprop_lthm: $o). 0.31/0.88 thf(decl_87, type, apinj2: $o). 0.31/0.88 thf(decl_88, type, apinj1: $o). 0.31/0.88 thf(decl_89, type, hoasapinj2_lthm: $o). 0.31/0.88 thf(decl_90, type, hoasinduction_lem3v2a: $o). 0.31/0.88 thf(decl_91, type, hoasapinj1_lthm: $o). 0.31/0.88 thf(decl_92, type, hoaslaminj_lthm: $o). 0.31/0.88 thf(decl_93, type, axvarcons: $o). 0.31/0.88 thf(decl_94, type, hoaslam: subst > (subst > term > term) > term). 0.31/0.88 thf(decl_95, type, axscons: $o). 0.31/0.88 thf(decl_96, type, hoasinduction_lem2v2_gthm: $o). 0.31/0.88 thf(decl_97, type, axidr: $o). 0.31/0.88 thf(decl_98, type, pushprop_lem1: $o). 0.31/0.88 thf(decl_99, type, laminj: $o). 0.31/0.88 thf(decl_100, type, hoasinduction_lem3_lthm: $o). 0.31/0.88 thf(decl_101, type, pushprop_lem0: $o). 0.31/0.88 thf(decl_102, type, pushprop_gthm: $o). 0.31/0.88 thf(decl_103, type, axabs: $o). 0.31/0.88 thf(decl_104, type, hoasinduction_lem3v2a_lthm: $o). 0.31/0.88 thf(decl_105, type, hoasinduction_lem2_lthm: $o). 0.31/0.88 thf(decl_106, type, hoasapinj2_gthm: $o). 0.31/0.88 thf(decl_107, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o). 0.31/0.88 thf(decl_108, type, hoasinduction_lem1_lthm: $o). 0.31/0.88 thf(decl_109, type, lamnotap: $o). 0.31/0.88 thf(decl_110, type, hoasapinj1_gthm: $o). 0.31/0.88 thf(decl_111, type, hoaslamnotvar: $o). 0.31/0.88 thf(decl_112, type, axidl: $o). 0.31/0.88 thf(decl_113, type, hoaslaminj_gthm: $o). 0.31/0.88 thf(decl_114, type, induction2_lthm: $o). 0.31/0.88 thf(decl_115, type, hoasinduction_lem0_lthm: $o). 0.31/0.88 thf(decl_116, type, substmonoid_lthm: $o). 0.31/0.88 thf(decl_117, type, pushprop: $o). 0.31/0.88 thf(decl_118, type, hoasinduction_lem3_gthm: $o). 0.31/0.88 thf(decl_119, type, hoasinduction_lem2_gthm: $o). 0.31/0.88 thf(decl_120, type, hoasinduction_lem3b: $o). 0.31/0.88 thf(decl_121, type, substmonoid: $o). 0.31/0.88 thf(decl_122, type, lamnotvar: $o). 0.31/0.88 thf(decl_123, type, hoasinduction_lem3a: $o). 0.31/0.88 thf(decl_124, type, hoasinduction_lem1_gthm: $o). 0.31/0.88 thf(decl_125, type, hoasinduction_no_psi_cond: $o). 0.31/0.88 thf(decl_126, type, induction2_gthm: $o). 0.31/0.88 thf(decl_127, type, pushprop_lem2v2_lthm: $o). 0.31/0.88 thf(decl_128, type, hoasvar: subst > term > subst > $o). 0.31/0.88 thf(decl_129, type, hoaslamnotap: $o). 0.31/0.88 thf(decl_130, type, substmonoid_gthm: $o). 0.31/0.88 thf(decl_131, type, ulamvarsh: $o). 0.31/0.88 thf(decl_132, type, induction2: $o). 0.31/0.88 thf(decl_133, type, pushprop_lem3v2: $o). 0.31/0.88 thf(decl_134, type, pushprop_lem2v2_gthm: $o). 0.31/0.88 thf(decl_135, type, pushprop_lem1_lthm: $o). 0.31/0.88 thf(decl_136, type, hoasinduction_lem3v2: $o). 0.31/0.88 thf(decl_137, type, axshiftcons: $o). 0.31/0.88 thf(decl_138, type, termmset: $o). 0.31/0.88 thf(decl_139, type, pushprop_lem0_lthm: $o). 0.31/0.88 thf(decl_140, type, hoasapnotvar_lthm: $o). 0.31/0.88 thf(decl_141, type, hoasinduction_lem3v2_lthm: $o). 0.31/0.88 thf(decl_142, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o). 0.31/0.88 thf(decl_143, type, axvarid: $o). 0.31/0.88 thf(decl_144, type, hoasinduction_lthm_3: $o). 0.31/0.88 thf(decl_145, type, d2term: d_term > term). 0.31/0.88 thf(decl_146, type, d2subst: d_subst > subst). 0.31/0.88 thf(decl_147, type, d_one: d_term). 0.31/0.88 thf(decl_148, type, d_id: d_subst). 0.31/0.88 thf(decl_149, type, epred1_0: $o). 0.31/0.88 thf(decl_152, type, epred4_0: $o). 0.31/0.88 thf(decl_153, type, epred5_0: $o). 0.31/0.88 thf(decl_154, type, epred6_0: $o). 0.31/0.88 thf(decl_155, type, epred7_0: $o). 0.31/0.88 thf(decl_157, type, epred9_0: $o). 0.31/0.88 thf(decl_158, type, epred10_0: $o). 0.31/0.88 thf(decl_159, type, epred11_0: $o). 0.31/0.88 thf(decl_160, type, epred12_2: (subst > term > subst > $o) > term > $o). 0.31/0.88 thf(decl_161, type, esk1_1: term > d_term). 0.31/0.88 thf(decl_162, type, esk2_1: subst > d_subst). 0.31/0.88 thf(decl_163, type, esk3_4: term > subst > (term > $o) > (term > $o) > term). 0.31/0.88 thf(decl_164, type, esk4_0: term). 0.31/0.88 thf(decl_165, type, esk5_0: term). 0.31/0.88 thf(decl_166, type, epred13_0: term > $o). 0.31/0.88 thf(decl_167, type, esk6_0: term). 0.31/0.88 thf(decl_168, type, esk7_0: subst). 0.31/0.88 thf(decl_169, type, esk8_1: term > term). 0.31/0.88 thf(decl_170, type, esk9_3: (term > $o) > term > subst > term). 0.31/0.88 thf(decl_171, type, esk10_3: (term > $o) > term > subst > term). 0.31/0.88 thf(decl_172, type, esk11_1: (term > $o) > term). 0.31/0.88 thf(decl_173, type, esk12_1: (term > $o) > term). 0.31/0.88 thf(decl_174, type, esk13_0: term). 0.31/0.88 thf(decl_175, type, esk14_0: subst). 0.31/0.88 thf(decl_176, type, esk15_0: term). 0.31/0.88 thf(decl_177, type, esk16_0: subst). 0.31/0.88 thf(decl_178, type, esk17_0: subst). 0.31/0.88 thf(decl_179, type, esk18_1: term > subst > term > term). 0.31/0.88 thf(decl_180, type, esk19_0: term). 0.31/0.88 thf(decl_181, type, esk20_1: (subst > term > term) > term). 0.31/0.88 thf(decl_182, type, esk21_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_183, type, epred14_0: subst > term > subst > $o). 0.31/0.88 thf(decl_184, type, esk22_1: (term > $o) > term). 0.31/0.88 thf(decl_185, type, epred15_0: term > $o). 0.31/0.88 thf(decl_186, type, esk23_0: term). 0.31/0.88 thf(decl_187, type, esk24_1: term > term). 0.31/0.88 thf(decl_188, type, esk25_0: term). 0.31/0.88 thf(decl_189, type, epred16_1: (subst > term > subst > $o) > term > $o). 0.31/0.88 thf(decl_190, type, esk26_1: (term > $o) > term). 0.31/0.88 thf(decl_191, type, esk27_1: (term > $o) > term). 0.31/0.88 thf(decl_192, type, esk28_1: (term > $o) > term). 0.31/0.88 thf(decl_193, type, esk29_1: (term > $o) > term). 0.31/0.88 thf(decl_194, type, esk30_0: subst > term > term). 0.31/0.88 thf(decl_195, type, esk31_0: subst > term > term). 0.31/0.88 thf(decl_196, type, esk32_0: subst). 0.31/0.88 thf(decl_197, type, esk33_0: term). 0.31/0.88 thf(decl_198, type, esk34_2: (subst > term > term) > (subst > term > term) > subst). 0.31/0.88 thf(decl_199, type, esk35_2: (subst > term > term) > (subst > term > term) > term). 0.31/0.88 thf(decl_200, type, esk36_2: (subst > term > term) > (subst > term > term) > subst). 0.31/0.88 thf(decl_201, type, esk37_2: (subst > term > term) > (subst > term > term) > subst). 0.31/0.88 thf(decl_202, type, esk38_2: (subst > term > term) > (subst > term > term) > term). 0.31/0.88 thf(decl_203, type, esk39_2: (subst > term > term) > (subst > term > term) > subst). 0.31/0.88 thf(decl_204, type, esk40_2: (subst > term > subst > $o) > term > term). 0.31/0.88 thf(decl_205, type, esk41_1: (subst > term > subst > $o) > subst > term > term). 0.31/0.88 thf(decl_206, type, epred17_0: subst > term > subst > $o). 0.31/0.88 thf(decl_207, type, esk42_0: term). 0.31/0.88 thf(decl_208, type, esk43_1: (subst > term > term) > term). 0.31/0.88 thf(decl_209, type, esk44_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_210, type, esk45_1: (subst > term > term) > term). 0.31/0.88 thf(decl_211, type, esk46_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_212, type, epred18_0: subst > term > subst > $o). 0.31/0.88 thf(decl_213, type, esk47_0: term). 0.31/0.88 thf(decl_214, type, esk48_1: (subst > term > term) > term). 0.31/0.88 thf(decl_215, type, esk49_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_216, type, esk50_1: (subst > term > term) > term). 0.31/0.88 thf(decl_217, type, esk51_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_218, type, esk52_2: (subst > term > subst > $o) > term > term). 0.31/0.88 thf(decl_219, type, esk53_1: (subst > term > subst > $o) > subst > term > term). 0.31/0.88 thf(decl_220, type, esk54_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_221, type, esk55_1: (subst > term > subst > $o) > term). 0.31/0.88 thf(decl_222, type, esk56_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_223, type, esk57_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_224, type, esk58_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_225, type, esk59_1: (subst > term > subst > $o) > term). 0.31/0.88 thf(decl_226, type, esk60_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_227, type, esk61_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_228, type, esk62_3: (subst > term > subst > $o) > term > term > subst). 0.31/0.88 thf(decl_229, type, esk63_3: (subst > term > subst > $o) > term > term > term). 0.31/0.88 thf(decl_230, type, esk64_3: (subst > term > subst > $o) > term > term > subst). 0.31/0.88 thf(decl_231, type, esk65_3: (subst > term > subst > $o) > term > term > subst). 0.31/0.88 thf(decl_232, type, esk66_3: (subst > term > subst > $o) > term > term > term). 0.31/0.88 thf(decl_233, type, esk67_3: (subst > term > subst > $o) > term > term > term). 0.31/0.88 thf(decl_234, type, esk68_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_235, type, esk69_1: (subst > term > subst > $o) > term). 0.31/0.88 thf(decl_236, type, esk70_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_237, type, esk71_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_238, type, epred19_0: subst > term > subst > $o). 0.31/0.88 thf(decl_239, type, esk72_0: term). 0.31/0.88 thf(decl_240, type, esk73_0: term). 0.31/0.88 thf(decl_241, type, epred20_1: (subst > term > subst > $o) > term > $o). 0.31/0.88 thf(decl_242, type, epred21_0: subst > term > subst > $o). 0.31/0.88 thf(decl_243, type, esk74_1: (term > $o) > term). 0.31/0.88 thf(decl_244, type, esk75_2: (subst > term > subst > $o) > term > subst > term > term). 0.31/0.88 thf(decl_245, type, esk76_2: (subst > term > subst > $o) > term > term). 0.31/0.88 thf(decl_246, type, epred22_0: subst > term > subst > $o). 0.31/0.88 thf(decl_247, type, esk77_0: term). 0.31/0.88 thf(decl_248, type, esk78_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_249, type, esk79_1: (subst > term > term) > term). 0.31/0.88 thf(decl_250, type, esk80_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_251, type, esk81_1: (subst > term > term) > term). 0.31/0.88 thf(decl_252, type, esk82_0: term). 0.31/0.88 thf(decl_253, type, epred23_0: subst > term > subst > $o). 0.31/0.88 thf(decl_254, type, esk83_0: term). 0.31/0.88 thf(decl_255, type, esk84_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_256, type, esk85_1: (subst > term > term) > term). 0.31/0.88 thf(decl_257, type, esk86_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_258, type, esk87_1: (subst > term > term) > term). 0.31/0.88 thf(decl_259, type, esk88_2: (subst > term > subst > $o) > term > subst > term > term). 0.31/0.88 thf(decl_260, type, esk89_2: (subst > term > subst > $o) > term > term). 0.31/0.88 thf(decl_261, type, esk90_0: term). 0.31/0.88 thf(decl_262, type, esk91_0: term). 0.31/0.88 thf(decl_263, type, esk92_0: term). 0.31/0.88 thf(decl_264, type, esk93_0: term). 0.31/0.88 thf(decl_265, type, esk94_0: term). 0.31/0.88 thf(decl_266, type, esk95_0: term). 0.31/0.88 thf(decl_267, type, esk96_0: term). 0.31/0.88 thf(decl_268, type, esk97_0: term). 0.31/0.88 thf(decl_269, type, esk98_0: term). 0.31/0.88 thf(decl_270, type, esk99_0: term). 0.31/0.88 thf(decl_271, type, esk100_0: term). 0.31/0.88 thf(decl_272, type, esk101_0: term). 0.31/0.88 thf(decl_273, type, esk102_3: (subst > term > subst > $o) > (term > $o) > term > term). 0.31/0.88 thf(decl_274, type, esk103_3: (subst > term > subst > $o) > (term > $o) > term > term). 0.31/0.88 thf(decl_275, type, esk104_1: (subst > term > subst > $o) > subst > term > term). 0.31/0.88 thf(decl_276, type, epred24_0: subst > term > subst > $o). 0.31/0.88 thf(decl_277, type, epred25_0: term > $o). 0.31/0.88 thf(decl_278, type, esk105_0: term). 0.31/0.88 thf(decl_279, type, esk106_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_280, type, esk107_1: (subst > term > term) > term). 0.31/0.88 thf(decl_281, type, esk108_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_282, type, esk109_1: (subst > term > term) > term). 0.31/0.88 thf(decl_283, type, esk110_0: subst). 0.31/0.88 thf(decl_284, type, epred26_0: term > $o). 0.31/0.88 thf(decl_285, type, epred27_0: term > $o). 0.31/0.88 thf(decl_286, type, esk111_0: term). 0.31/0.88 thf(decl_287, type, esk112_0: subst). 0.31/0.88 thf(decl_288, type, esk113_0: term). 0.31/0.88 thf(decl_289, type, esk114_0: term). 0.31/0.88 thf(decl_290, type, esk115_0: term). 0.31/0.88 thf(decl_291, type, epred28_3: (term > $o) > term > subst > term > $o). 0.31/0.88 thf(decl_292, type, epred29_0: term > $o). 0.31/0.88 thf(decl_293, type, esk116_0: term). 0.31/0.88 thf(decl_294, type, esk117_0: subst). 0.31/0.88 thf(decl_295, type, esk118_1: (term > $o) > term). 0.31/0.88 thf(decl_296, type, esk119_0: term). 0.31/0.88 thf(decl_297, type, esk120_0: subst). 0.31/0.88 thf(decl_298, type, esk121_0: subst). 0.31/0.88 thf(decl_299, type, esk122_0: subst). 0.31/0.88 thf(decl_300, type, esk123_0: subst). 0.31/0.88 thf(decl_301, type, esk124_0: term). 0.31/0.88 thf(decl_302, type, esk125_1: term > subst > term > term). 0.31/0.88 thf(decl_303, type, esk126_0: subst). 0.31/0.88 thf(decl_304, type, esk127_0: subst). 0.31/0.88 thf(decl_305, type, esk128_0: subst > term > term). 0.31/0.88 thf(decl_306, type, esk129_0: term). 0.31/0.88 thf(decl_307, type, esk130_0: term). 0.31/0.88 thf(decl_308, type, esk131_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_309, type, esk132_1: (subst > term > term) > term). 0.31/0.88 thf(decl_310, type, esk133_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_311, type, esk134_0: term). 0.31/0.88 thf(decl_312, type, esk135_0: subst). 0.31/0.88 thf(decl_313, type, esk136_0: term). 0.31/0.88 thf(decl_314, type, esk137_0: subst). 0.31/0.88 thf(decl_315, type, epred30_0: term > $o). 0.31/0.88 thf(decl_316, type, epred31_0: term > $o). 0.31/0.88 thf(decl_317, type, esk138_0: term). 0.31/0.88 thf(decl_318, type, esk139_0: subst). 0.31/0.88 thf(decl_319, type, esk140_0: term). 0.31/0.88 thf(decl_320, type, esk141_0: term). 0.31/0.88 thf(decl_321, type, esk142_0: subst). 0.31/0.88 thf(decl_322, type, esk143_0: term). 0.31/0.88 thf(decl_323, type, esk144_0: term). 0.31/0.88 thf(decl_324, type, epred32_0: subst > term > subst > $o). 0.31/0.88 thf(decl_325, type, esk145_1: (term > $o) > term). 0.31/0.88 thf(decl_326, type, epred33_1: (subst > term > subst > $o) > term > $o). 0.31/0.88 thf(decl_327, type, esk146_0: term). 0.31/0.88 thf(decl_328, type, epred34_3: (term > $o) > term > subst > term > $o). 0.31/0.88 thf(decl_329, type, epred35_0: term > $o). 0.31/0.88 thf(decl_330, type, esk147_0: term). 0.31/0.88 thf(decl_331, type, esk148_0: subst). 0.31/0.88 thf(decl_332, type, esk149_1: (term > $o) > term). 0.31/0.88 thf(decl_333, type, esk150_1: (term > $o) > term). 0.31/0.88 thf(decl_334, type, esk151_1: (term > $o) > term). 0.31/0.88 thf(decl_335, type, esk152_1: (term > $o) > term). 0.31/0.88 thf(decl_336, type, esk153_1: (term > $o) > term). 0.31/0.88 thf(decl_337, type, epred36_0: term > $o). 0.31/0.88 thf(decl_338, type, esk154_0: term). 0.31/0.88 thf(decl_339, type, esk155_1: term > term). 0.31/0.88 thf(decl_340, type, esk156_1: (subst > term > subst > $o) > subst > term > term). 0.31/0.88 thf(decl_341, type, esk157_1: (subst > term > subst > $o) > term). 0.31/0.88 thf(decl_342, type, esk158_1: (subst > term > subst > $o) > term). 0.31/0.88 thf(decl_343, type, epred37_0: subst > term > subst > $o). 0.31/0.88 thf(decl_344, type, esk159_0: term). 0.31/0.88 thf(decl_345, type, esk160_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_346, type, esk161_1: (subst > term > term) > term). 0.31/0.88 thf(decl_347, type, esk162_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_348, type, esk163_1: (subst > term > term) > term). 0.31/0.88 thf(decl_349, type, epred38_0: subst > term > subst > $o). 0.31/0.88 thf(decl_350, type, esk164_0: term). 0.31/0.88 thf(decl_351, type, esk165_1: (subst > term > term) > term). 0.31/0.88 thf(decl_352, type, esk166_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_353, type, esk167_1: (subst > term > term) > term). 0.31/0.88 thf(decl_354, type, esk168_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_355, type, esk169_2: (subst > term > subst > $o) > term > subst > term > term). 0.31/0.88 thf(decl_356, type, esk170_2: (subst > term > subst > $o) > term > term). 0.31/0.88 thf(decl_357, type, epred39_1: (subst > term > subst > $o) > term > $o). 0.31/0.88 thf(decl_358, type, epred40_0: subst > term > subst > $o). 0.31/0.88 thf(decl_359, type, esk171_1: (term > $o) > term). 0.31/0.88 thf(decl_360, type, esk172_0: subst). 0.31/0.88 thf(decl_361, type, esk173_1: term > subst > term > term). 0.31/0.88 thf(decl_362, type, epred41_0: subst > term > subst > $o). 0.31/0.88 thf(decl_363, type, epred42_0: term > $o). 0.31/0.88 thf(decl_364, type, esk174_0: term). 0.31/0.88 thf(decl_365, type, esk175_1: (subst > term > term) > term). 0.31/0.88 thf(decl_366, type, esk176_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_367, type, esk177_1: (subst > term > term) > term). 0.31/0.88 thf(decl_368, type, esk178_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_369, type, esk179_0: term). 0.31/0.88 thf(decl_370, type, esk180_1: (subst > term > term) > term). 0.31/0.88 thf(decl_371, type, esk181_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_372, type, esk182_0: term). 0.31/0.88 thf(decl_373, type, esk183_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term). 0.31/0.88 thf(decl_374, type, esk184_3: (subst > term > subst > $o) > (term > $o) > term > term). 0.31/0.88 thf(decl_375, type, esk185_2: (subst > term > subst > $o) > (term > $o) > term). 0.31/0.88 thf(decl_376, type, esk186_0: term). 0.31/0.88 thf(decl_377, type, esk187_0: subst). 0.31/0.88 thf(decl_378, type, esk188_0: term). 0.31/0.88 thf(decl_379, type, esk189_0: subst). 0.31/0.88 thf(decl_380, type, esk190_0: term). 0.31/0.88 thf(decl_381, type, esk191_0: subst). 0.31/0.88 thf(decl_382, type, esk192_0: term). 0.31/0.88 thf(decl_383, type, esk193_0: subst). 0.31/0.88 thf(decl_384, type, esk194_0: term). 0.31/0.88 thf(decl_385, type, esk195_0: term). 0.31/0.88 thf(decl_386, type, esk196_2: (subst > term > term) > (subst > term > term) > subst). 0.31/0.88 thf(decl_387, type, esk197_2: (subst > term > term) > (subst > term > term) > term). 0.31/0.88 thf(decl_388, type, esk198_2: (subst > term > term) > (subst > term > term) > subst). 0.31/0.88 thf(decl_389, type, esk199_2: (subst > term > term) > (subst > term > term) > subst). 0.31/0.88 thf(decl_390, type, esk200_2: (subst > term > term) > (subst > term > term) > term). 0.31/0.88 thf(decl_391, type, esk201_2: (subst > term > term) > (subst > term > term) > subst). 0.31/0.88 thf(decl_392, type, esk202_0: subst > term > term). 0.31/0.88 thf(decl_393, type, esk203_0: subst > term > term). 0.31/0.88 thf(decl_394, type, esk204_0: subst). 0.31/0.88 thf(decl_395, type, esk205_0: term). 0.31/0.88 thf(decl_396, type, esk206_0: term). 0.31/0.88 thf(decl_397, type, esk207_0: term). 0.31/0.88 thf(decl_398, type, esk208_0: term). 0.31/0.88 thf(decl_399, type, esk209_0: term). 0.31/0.88 thf(decl_400, type, esk210_0: term). 0.31/0.88 thf(decl_401, type, esk211_0: term). 0.31/0.88 thf(decl_402, type, esk212_0: term). 0.31/0.88 thf(decl_403, type, esk213_0: term). 0.31/0.88 thf(decl_404, type, esk214_0: term). 0.31/0.88 thf(decl_405, type, esk215_0: term). 0.31/0.88 thf(decl_406, type, esk216_0: term). 0.31/0.88 thf(decl_407, type, esk217_0: term). 0.31/0.88 thf(decl_408, type, esk218_0: term). 0.31/0.88 thf(decl_409, type, epred43_0: subst > term > subst > $o). 0.31/0.88 thf(decl_410, type, epred44_0: term > $o). 0.31/0.88 thf(decl_411, type, esk219_0: term). 0.31/0.88 thf(decl_412, type, esk220_0: term). 0.31/0.88 thf(decl_413, type, esk221_4: (subst > term > subst > $o) > (term > $o) > term > term > term). 0.31/0.88 thf(decl_414, type, esk222_4: (subst > term > subst > $o) > (term > $o) > term > term > term). 0.31/0.88 thf(decl_415, type, esk223_4: (subst > term > subst > $o) > (term > $o) > term > term > term). 0.31/0.88 thf(decl_416, type, esk224_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_417, type, esk225_1: (subst > term > subst > $o) > term). 0.31/0.88 thf(decl_418, type, esk226_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_419, type, esk227_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_420, type, esk228_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_421, type, esk229_1: (subst > term > subst > $o) > term). 0.31/0.88 thf(decl_422, type, esk230_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_423, type, esk231_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_424, type, esk232_2: (subst > term > subst > $o) > term > term). 0.31/0.88 thf(decl_425, type, esk233_1: (subst > term > subst > $o) > subst > term > term). 0.31/0.88 thf(decl_426, type, epred45_0: subst > term > subst > $o). 0.31/0.88 thf(decl_427, type, esk234_0: term). 0.31/0.88 thf(decl_428, type, esk235_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_429, type, esk236_1: (subst > term > term) > term). 0.31/0.88 thf(decl_430, type, esk237_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_431, type, esk238_1: (subst > term > term) > term). 0.31/0.88 thf(decl_432, type, esk239_1: (term > $o) > term). 0.31/0.88 thf(decl_433, type, esk240_1: (term > $o) > term). 0.31/0.88 thf(decl_434, type, esk241_1: (term > $o) > term). 0.31/0.88 thf(decl_435, type, esk242_1: (term > $o) > term). 0.31/0.88 thf(decl_436, type, epred46_0: term > $o). 0.31/0.88 thf(decl_437, type, esk243_0: term). 0.31/0.88 thf(decl_438, type, esk244_1: term > subst > term > term). 0.31/0.88 thf(decl_439, type, esk245_0: term). 0.31/0.88 thf(decl_440, type, esk246_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_441, type, esk247_1: (subst > term > subst > $o) > term). 0.31/0.88 thf(decl_442, type, esk248_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_443, type, esk249_1: (subst > term > subst > $o) > subst). 0.31/0.88 thf(decl_444, type, epred47_0: subst > term > subst > $o). 0.31/0.88 thf(decl_445, type, esk250_0: term). 0.31/0.88 thf(decl_446, type, esk251_0: term). 0.31/0.88 thf(decl_447, type, esk252_0: subst). 0.31/0.88 thf(decl_448, type, esk253_4: (term > $o) > (term > $o) > term > subst > term). 0.31/0.88 thf(decl_449, type, epred48_0: term > $o). 0.31/0.88 thf(decl_450, type, epred49_0: term > $o). 0.31/0.88 thf(decl_451, type, esk254_0: term). 0.31/0.88 thf(decl_452, type, esk255_0: subst). 0.31/0.88 thf(decl_453, type, epred50_0: subst > term > subst > $o). 0.31/0.88 thf(decl_454, type, esk256_0: term). 0.31/0.88 thf(decl_455, type, esk257_2: (subst > term > term) > term > term). 0.31/0.88 thf(decl_456, type, esk258_2: (subst > term > term) > term > subst). 0.31/0.88 thf(decl_457, type, esk259_2: (subst > term > term) > term > term). 0.31/0.88 thf(decl_458, type, esk260_2: (subst > term > term) > term > subst). 0.31/0.88 thf(decl_459, type, esk261_2: (subst > term > term) > term > subst). 0.31/0.88 thf(decl_460, type, esk262_2: (subst > term > term) > term > term). 0.31/0.88 thf(decl_461, type, esk263_2: (subst > term > term) > term > subst). 0.31/0.88 thf(decl_462, type, esk264_2: (subst > term > subst > $o) > term > subst > term > term). 0.31/0.88 thf(decl_463, type, esk265_2: (subst > term > subst > $o) > term > term). 0.31/0.88 thf(decl_464, type, esk266_2: (subst > term > subst > $o) > term > term). 0.31/0.88 thf(decl_465, type, esk267_0: term). 0.31/0.88 thf(decl_466, type, esk268_0: term). 0.31/0.88 thf(decl_467, type, esk269_0: term). 0.31/0.88 thf(decl_468, type, esk270_0: term). 0.31/0.88 thf(decl_469, type, esk271_0: term). 0.31/0.88 thf(decl_470, type, esk272_0: term). 0.31/0.88 thf(decl_471, type, esk273_0: term). 0.31/0.88 thf(decl_472, type, esk274_0: term). 0.31/0.88 thf(decl_473, type, esk275_0: term). 0.31/0.88 thf(decl_474, type, esk276_1: (subst > term > term) > term). 0.31/0.88 thf(decl_475, type, esk277_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_476, type, esk278_1: term > subst > term > term). 0.31/0.88 thf(decl_477, type, epred51_0: term > $o). 0.31/0.88 thf(decl_478, type, epred52_0: term > $o). 0.31/0.88 thf(decl_479, type, esk279_0: term). 0.31/0.88 thf(decl_480, type, esk280_0: subst). 0.31/0.88 thf(decl_481, type, esk281_4: (term > $o) > (term > $o) > term > subst > term). 0.31/0.88 thf(decl_482, type, esk282_2: (subst > term > subst > $o) > (term > $o) > term). 0.31/0.88 thf(decl_483, type, epred53_0: subst > term > subst > $o). 0.31/0.88 thf(decl_484, type, esk283_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_485, type, esk284_1: (subst > term > term) > term). 0.31/0.88 thf(decl_486, type, esk285_1: (subst > term > term) > subst). 0.31/0.88 thf(decl_487, type, esk286_1: (subst > term > term) > term). 0.31/0.88 thf(decl_488, type, esk287_0: term). 0.31/0.88 thf(decl_489, type, esk288_1: (subst > term > subst > $o) > subst > term > term). 0.31/0.88 thf(decl_490, type, esk289_2: (subst > term > subst > $o) > term > term). 0.31/0.88 thf(alg444_1, axiom, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X1:term]:(?[X2:d_term]:(((X1)=(d2term @ X2))))&![X2:d_term]:(((X2)=(d_one))))&![X3:d_term, X4:d_term]:((((X3)=(X4))<=((d2term @ X3)=(d2term @ X4)))))&![X5:subst]:(?[X6:d_subst]:(((X5)=(d2subst @ X6)))))&((one)=(d2term @ d_one)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&((pushprop_p_and_p_prime)=(^[X7:term, X8:subst, X9:term > $o, X10:term > $o]:(![X11:term]:((((X10 @ X11))<=>((X9 @ (sub @ X11 @ (push @ X7 @ X8))))))))))&~((var @ (d2term @ d_one))))&(pushprop_lem1_gthm))&((shinj)<=>![X7:term, X12:term]:((((X7)=(X12))|((sub @ X7 @ sh)!=(sub @ X12 @ sh))))))&(hoasinduction_lem1v2))&(![X9:term > $o, X13:term, X14:subst]:((~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:((~((X9 @ X12))|(X9 @ (sub @ X7 @ (push @ X12 @ id)))))))))|(X9 @ (sub @ X13 @ X14))|~(![X12:term]:((~((var @ X12))|(X9 @ (sub @ X12 @ X14)))))|~(![X7:term, X12:term]:((~((X9 @ X7))|~((X9 @ X12))|(X9 @ (ap @ X7 @ X12)))))))<=>(induction2lem)))&~((ulamvar1)))&((induction2lem_lthm)<=>(![X7:term, X8:subst]:(((X7)=(sub @ one @ (push @ X7 @ X8))))=>((![X8:subst]:(((X8)=(comp @ X8 @ id)))=>(![X9:term > $o, X15:term]:((~(![X7:term, X12:term]:((~((X9 @ X7))|~((X9 @ X12))|(X9 @ (ap @ X7 @ X12)))))|~(![X7:term]:((~((X9 @ X7))|(X9 @ (lam @ X7)))))|(X9 @ X15)|~(![X7:term]:(((X9 @ X7)|~((var @ X7)))))))=>![X9:term > $o, X13:term, X14:subst]:((~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:((~((X9 @ X12))|(X9 @ (sub @ X7 @ (push @ X12 @ id)))))))))|~(![X12:term]:(((X9 @ (sub @ X12 @ X14))|~((var @ X12)))))|(X9 @ (sub @ X13 @ X14))|~(![X7:term, X12:term]:((~((X9 @ X12))|(X9 @ (ap @ X7 @ X12))|~((X9 @ X7)))))))))<=![X7:term, X8:subst]:(((X8)=(comp @ sh @ (push @ X7 @ X8))))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((hoasinduction_lem3v2_f_lthm)<=>![X12:term]:(~(![X16:subst > term > term]:(~(![X7:term, X8:subst]:(((sub @ X12 @ (push @ X7 @ X8))=(X16 @ X8 @ X7)))))))))&((hoasinduction_lthm)<=>(![X9:term > $o, X17:term]:((~(![X7:term, X12:term]:(((X9 @ (ap @ X7 @ X12))|~((X9 @ X12))|~((X9 @ X7)))))|~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:((~((X9 @ X12))|(X9 @ (sub @ X7 @ (push @ X12 @ id)))))))))|(X9 @ X17)|~(![X7:term]:((~((var @ X7))|(X9 @ X7))))))=>(![X18:subst > term > subst > $o, X19:term, X20:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X18 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X18 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X18 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))|(X18 @ X8 @ X7 @ (comp @ X22 @ X21)))))|~((X18 @ id @ X19 @ id))|~((X18 @ id @ X20 @ id))|(X18 @ id @ (ap @ X19 @ X20) @ id)|~(![X7:term, X12:term]:((~((X18 @ id @ X7 @ id))|~((X18 @ id @ X12 @ id))|(X18 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id))))))=>(![X23:subst > term > subst > $o, X24:term]:((~(![X16:subst > term > term]:(((X23 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:((~((X23 @ id @ X7 @ id))|(X23 @ id @ (X16 @ id @ X7) @ id))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|(X23 @ id @ (lam @ X24) @ id)|~(![X12:term]:(((X23 @ id @ (sub @ X24 @ (push @ X12 @ id)) @ id)|~((X23 @ id @ X12 @ id)))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X23 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X23 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X23 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)|~((X23 @ X8 @ X7 @ (comp @ X22 @ X21))))))))=>![X25:subst > term > subst > $o, X26:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X25 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X25 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)))))|~(![X7:term]:((~((var @ (sub @ X7 @ id)))|(X25 @ id @ X7 @ id))))|~(![X16:subst > term > term]:(((X25 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:(((X25 @ id @ (X16 @ id @ X7) @ id)|~((X25 @ id @ X7 @ id)))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|(X25 @ id @ X26 @ id)|~(![X7:term, X12:term]:((~((X25 @ id @ X12 @ id))|(X25 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id)|~((X25 @ id @ X7 @ id)))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X25 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)|~((X25 @ X8 @ X7 @ (comp @ X22 @ X21)))))))))))))&((hoasinduction_no_psi_cond_lthm)<=>(![X27:subst > term > subst > $o]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X27 @ id @ X11 @ id)))))))=>((![X7:term]:(((X7)=(sub @ X7 @ id)))=>(![X28:subst > term > subst > $o, X10:term > $o, X29:term]:((~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X7:term]:((~((X28 @ id @ X7 @ id))|(X28 @ id @ (X16 @ id @ X7) @ id))))|(X28 @ id @ (lam @ (X16 @ sh @ one)) @ id))))|~(![X11:term]:(((X10 @ X11)<=>(X28 @ id @ X11 @ id))))|(X10 @ (lam @ X29))|~(![X12:term]:((~((X10 @ X12))|(X10 @ (sub @ X29 @ (push @ X12 @ id))))))))=>![X30:subst > term > subst > $o, X31:term]:(((X30 @ id @ X31 @ id)|~(![X16:subst > term > term]:((~(![X7:term]:((~((X30 @ id @ X7 @ id))|(X30 @ id @ (X16 @ id @ X7) @ id))))|(X30 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|~(![X7:term, X12:term]:((~((X30 @ id @ X7 @ id))|~((X30 @ id @ X12 @ id))|(X30 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id))))))))<=![X9:term > $o, X17:term]:(((X9 @ X17)|~(![X7:term]:((~(![X12:term]:(((X9 @ (sub @ X7 @ (push @ X12 @ id)))|~((X9 @ X12)))))|(X9 @ (lam @ X7)))))|~(![X7:term, X12:term]:((~((X9 @ X7))|(X9 @ (ap @ X7 @ X12))|~((X9 @ X12)))))|~(![X7:term]:(((X9 @ X7)|~((var @ X7)))))))))))&(![X16:subst > term > term, X32:subst > term > term, X33:subst, X34:term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X32 @ X8 @ X7) @ X21)=(X32 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|((X16 @ X33 @ X34)=(X32 @ X33 @ X34))|((lam @ (X16 @ sh @ one))!=(lam @ (X32 @ sh @ one)))))<=>(hoaslaminj)))&(induction2lem_gthm))&((hoasinduction_lem3aa_lthm)<=>![X35:subst > term > subst > $o, X36:term]:((~(![X12:term]:((~((X35 @ id @ X12 @ id))|(X35 @ id @ (sub @ X36 @ (push @ X12 @ id)) @ id))))|(X35 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X16:subst > term > term]:((~(![X7:term]:(((X35 @ id @ (X16 @ id @ X7) @ id)|~((X35 @ id @ X7 @ id)))))|(X35 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))))))&(![X37:subst > term > subst > $o, X24:term]:((~(![X12:term]:(((X37 @ id @ (sub @ X24 @ (push @ X12 @ id)) @ id)|~((X37 @ id @ X12 @ id)))))|(X37 @ id @ (lam @ X24) @ id)|~(![X16:subst > term > term]:((~(![X7:term]:((~((X37 @ id @ X7 @ id))|(X37 @ id @ (X16 @ id @ X7) @ id))))|(X37 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X37 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X37 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X37 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X37 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))))<=>(hoasinduction_lem3)))&((hoasinduction_lem2)<=>![X38:subst > term > subst > $o, X19:term, X20:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X38 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X38 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)))))|~(![X7:term, X12:term]:(((X38 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id)|~((X38 @ id @ X12 @ id))|~((X38 @ id @ X7 @ id)))))|~((X38 @ id @ X20 @ id))|(X38 @ id @ (ap @ X19 @ X20) @ id)|~((X38 @ id @ X19 @ id))|~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X38 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)|~((X38 @ X8 @ X7 @ (comp @ X22 @ X21))))))))))&(hoasinduction_lem1))&(hoasapnotvar))&((hoasinduction_lem0)<=>![X39:subst > term > subst > $o]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X39 @ id @ X11 @ id)))))))))&(hoasinduction_gthm))&(axapp))&(hoaslamnotvar_lthm))&(pushprop_lem3v2_lthm))&(ulamvarind))&(((![X40:subst > term > subst > $o, X41:term]:((~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X7:term]:((~((X40 @ id @ X7 @ id))|(X40 @ id @ (X16 @ id @ X7) @ id))))|(X40 @ id @ (lam @ (X16 @ sh @ one)) @ id))))|~(![X12:term]:((~((X40 @ id @ X12 @ id))|(X40 @ id @ (sub @ X41 @ (push @ X12 @ id)) @ id))))|(X40 @ id @ (lam @ X41) @ id)))<=![X42:subst > term > subst > $o, X36:term]:((~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|(X42 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:((~((X42 @ id @ X7 @ id))|(X42 @ id @ (X16 @ id @ X7) @ id)))))))|(X42 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X12:term]:(((X42 @ id @ (sub @ X36 @ (push @ X12 @ id)) @ id)|~((X42 @ id @ X12 @ id))))))))<=![X7:term]:(((X7)=(sub @ X7 @ id))))<=>(hoasinduction_lem3a_lthm)))&(pushprop_lem1v2_gthm))&(hoaslamnotap_gthm))&(hoasinduction_lem3b_gthm))&(pushprop_lem2v2))&(hoasinduction_lem3a_gthm))&(axassoc))&((apinj2)<=>![X7:term, X12:term, X43:term, X44:term]:((((X43)=(X44))|((ap @ X7 @ X43)!=(ap @ X12 @ X44))))))&((hoasapinj2_lthm)<=>(![X7:term, X12:term, X43:term, X44:term]:((((X43)=(X44))|((ap @ (sub @ X7 @ id) @ X43)!=(ap @ (sub @ X12 @ id) @ X44))))<=![X7:term, X12:term, X43:term, X44:term]:((((ap @ X7 @ X43)!=(ap @ X12 @ X44))|((X43)=(X44)))))))&((hoasinduction_lem3v2a)<=>![X45:subst > term > subst > $o, X10:term > $o, X29:term]:((~(![X11:term]:(((X10 @ X11)<=>(X45 @ id @ X11 @ id))))|(X10 @ (lam @ X29))|~(![X12:term]:((~((X10 @ X12))|(X10 @ (sub @ X29 @ (push @ X12 @ id))))))|~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X7:term]:(((X45 @ id @ (X16 @ id @ X7) @ id)|~((X45 @ id @ X7 @ id)))))|(X45 @ id @ (lam @ (X16 @ sh @ one)) @ id))))))))&((axscons)<=>![X8:subst]:(((X8)=(push @ (sub @ one @ X8) @ (comp @ sh @ X8))))))&(hoasinduction_lem2v2_gthm))&(![X9:term > $o, X46:term > $o, X7:term, X8:subst, X12:term]:((~((X9 @ X7))|(X46 @ (sub @ X7 @ (push @ X12 @ X8)))))<=>(pushprop_lem1)))&(![X7:term, X12:term]:((((X7)=(X12))|((lam @ X7)!=(lam @ X12))))<=>(laminj)))&((pushprop_lem0)<=>![X9:term > $o, X7:term, X8:subst]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X9 @ (sub @ X11 @ (push @ X7 @ X8)))))))))))&(pushprop_gthm))&(axabs))&(hoasinduction_lem2_lthm))&(hoasapinj2_gthm))&~((lamnotap)))&(hoasapinj1_gthm))&(hoaslamnotvar))&(hoaslaminj_gthm))&((induction2_lthm)<=>((![X9:term > $o, X17:term]:((~(![X7:term]:(((X9 @ X7)|~((var @ X7)))))|(X9 @ X17)|~(![X7:term]:((~(![X12:term]:((~((X9 @ X12))|(X9 @ (sub @ X7 @ (push @ X12 @ id))))))|(X9 @ (lam @ X7)))))|~(![X7:term, X12:term]:((~((X9 @ X7))|~((X9 @ X12))|(X9 @ (ap @ X7 @ X12)))))))<=![X9:term > $o, X13:term, X14:subst]:((~(![X7:term, X12:term]:((~((X9 @ X12))|(X9 @ (ap @ X7 @ X12))|~((X9 @ X7)))))|~(![X12:term]:((~((var @ X12))|(X9 @ (sub @ X12 @ X14)))))|(X9 @ (sub @ X13 @ X14))|~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:((~((X9 @ X12))|(X9 @ (sub @ X7 @ (push @ X12 @ id))))))))))))<=![X7:term]:(((X7)=(sub @ X7 @ id))))))&((substmonoid_lthm)<=>((![X8:subst]:(((X8)=(comp @ X8 @ id)))=>(![X8:subst]:(((X8)=(comp @ X8 @ id)))&![X8:subst]:(((X8)=(comp @ id @ X8)))))<=![X8:subst]:(((X8)=(comp @ id @ X8))))))&(hoasinduction_lem3_gthm))&(![X12:term]:(~(![X16:subst > term > term]:(((X16 @ sh @ one)!=(sub @ X12 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b)))&((substmonoid)<=>(![X8:subst]:(((X8)=(comp @ id @ X8)))&![X8:subst]:(((X8)=(comp @ X8 @ id))))))&(lamnotvar))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))&(![X16:subst > term > term, X47:term, X48:term]:((((lam @ (X16 @ sh @ one))!=(ap @ (sub @ X47 @ id) @ X48))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))))<=>(hoaslamnotap)))&(substmonoid_gthm))&(pushprop_lem2v2_gthm))&((pushprop_lem1_lthm)<=>((![X7:term, X8:subst]:(((X8)=(comp @ sh @ (push @ X7 @ X8))))=>![X9:term > $o, X49:term > $o, X7:term, X8:subst, X12:term]:((~((X9 @ X7))|(X49 @ (sub @ X7 @ (push @ X12 @ X8))))))<=![X7:term, X8:subst]:(((X7)=(sub @ one @ (push @ X7 @ X8)))))))&((hoasinduction_lem3v2)<=>![X50:subst > term > subst > $o, X10:term > $o, X51:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X50 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X50 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)))))|~(![X11:term]:(((X10 @ X11)<=>(X50 @ id @ X11 @ id))))|~(![X12:term]:((~((X10 @ X12))|(X10 @ (sub @ X51 @ (push @ X12 @ id))))))|(X10 @ (lam @ X51))|~(![X16:subst > term > term]:(((X50 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:((~((X50 @ id @ X7 @ id))|(X50 @ id @ (X16 @ id @ X7) @ id))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X50 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X50 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))))))&(![X7:term, X8:subst]:(((X8)=(comp @ sh @ (push @ X7 @ X8))))<=>(axshiftcons)))&((termmset)<=>![X7:term]:(((X7)=(sub @ X7 @ id)))))&(![X7:term]:(((X7)=(sub @ X7 @ id)))<=>(axvarid)))&((hoasinduction_lthm_3)<=>(![X52:subst > term > subst > $o]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X52 @ id @ X11 @ id)))))))=>(![X9:term > $o, X17:term]:(((X9 @ X17)|~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:(((X9 @ (sub @ X7 @ (push @ X12 @ id)))|~((X9 @ X12))))))))|~(![X7:term, X12:term]:(((X9 @ (ap @ X7 @ X12))|~((X9 @ X12))|~((X9 @ X7)))))|~(![X7:term]:((~((var @ X7))|(X9 @ X7))))))=>((![X53:subst > term > subst > $o, X26:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X53 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X53 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)))))|~(![X7:term]:((~((var @ (sub @ X7 @ id)))|(X53 @ id @ X7 @ id))))|(X53 @ id @ X26 @ id)|~(![X16:subst > term > term]:(((X53 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:(((X53 @ id @ (X16 @ id @ X7) @ id)|~((X53 @ id @ X7 @ id)))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|~(![X7:term, X12:term]:((~((X53 @ id @ X7 @ id))|~((X53 @ id @ X12 @ id))|(X53 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X53 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)|~((X53 @ X8 @ X7 @ (comp @ X22 @ X21))))))))<=![X54:subst > term > subst > $o, X10:term > $o, X29:term]:((~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|(X54 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:(((X54 @ id @ (X16 @ id @ X7) @ id)|~((X54 @ id @ X7 @ id))))))))|(X10 @ (lam @ X29))|~(![X12:term]:(((X10 @ (sub @ X29 @ (push @ X12 @ id)))|~((X10 @ X12)))))|~(![X11:term]:(((X10 @ X11)<=>(X54 @ id @ X11 @ id)))))))<=![X7:term]:(((X7)=(sub @ X7 @ id))))))))&((![X55:subst > term > subst > $o, X10:term > $o, X51:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X55 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)|~((X55 @ X8 @ X7 @ (comp @ X22 @ X21))))))|~(![X11:term]:(((X10 @ X11)<=>(X55 @ id @ X11 @ id))))|~(![X12:term]:(((X10 @ (sub @ X51 @ (push @ X12 @ id)))|~((X10 @ X12)))))|(X10 @ (lam @ X51))|~(![X16:subst > term > term]:(((X55 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:(((X55 @ id @ (X16 @ id @ X7) @ id)|~((X55 @ id @ X7 @ id)))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X55 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X55 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)))))))<=![X7:term]:(((X7)=(sub @ X7 @ id))))<=>(hoasinduction_lem3v2_lthm)))&(hoasapnotvar_lthm))&((pushprop_lem0_lthm)<=>![X9:term > $o, X7:term, X8:subst]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X9 @ (sub @ X11 @ (push @ X7 @ X8)))))))))))&(pushprop_lem3v2))&((induction2)<=>![X9:term > $o, X17:term]:((~(![X7:term]:(((X9 @ X7)|~((var @ X7)))))|~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:(((X9 @ (sub @ X7 @ (push @ X12 @ id)))|~((X9 @ X12))))))))|(X9 @ X17)|~(![X7:term, X12:term]:((~((X9 @ X12))|(X9 @ (ap @ X7 @ X12))|~((X9 @ X7)))))))))&(ulamvarsh))&((hoasinduction_no_psi_cond)<=>![X56:subst > term > subst > $o, X31:term]:((~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|(X56 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:(((X56 @ id @ (X16 @ id @ X7) @ id)|~((X56 @ id @ X7 @ id))))))))|(X56 @ id @ X31 @ id)|~(![X7:term, X12:term]:((~((X56 @ id @ X7 @ id))|(X56 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id)|~((X56 @ id @ X12 @ id)))))))))&(hoasinduction_lem1_gthm))&(![X57:subst > term > subst > $o, X41:term]:((~(![X16:subst > term > term]:((~(![X7:term]:(((X57 @ id @ (X16 @ id @ X7) @ id)|~((X57 @ id @ X7 @ id)))))|(X57 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|~(![X12:term]:((~((X57 @ id @ X12 @ id))|(X57 @ id @ (sub @ X41 @ (push @ X12 @ id)) @ id))))|(X57 @ id @ (lam @ X41) @ id)))<=>(hoasinduction_lem3a)))&(hoasinduction_lem2_gthm))&(pushprop))&((hoasinduction_lem0_lthm)<=>![X58:subst > term > subst > $o]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X58 @ id @ X11 @ id)))))))))&(![X8:subst]:(((X8)=(comp @ id @ X8)))<=>(axidl)))&(hoasinduction_lem1_lthm))&((![X12:term]:(~(![X16:subst > term > term]:(~(![X7:term, X8:subst]:(((sub @ X12 @ (push @ X7 @ X8))=(X16 @ X8 @ X7)))))))=>(![X7:term]:(((X7)=(sub @ X7 @ id)))=>![X59:subst > term > subst > $o, X10:term > $o, X29:term]:((~(![X16:subst > term > term]:(((X59 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:((~((X59 @ id @ X7 @ id))|(X59 @ id @ (X16 @ id @ X7) @ id))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|(X10 @ (lam @ X29))|~(![X12:term]:((~((X10 @ X12))|(X10 @ (sub @ X29 @ (push @ X12 @ id))))))|~(![X11:term]:(((X10 @ X11)<=>(X59 @ id @ X11 @ id))))))))<=>(hoasinduction_lem3v2a_lthm)))&((hoasinduction_lem3_lthm)<=>(![X7:term]:(((X7)=(sub @ X7 @ id)))=>(![X60:subst > term > subst > $o, X36:term]:((~(![X12:term]:(((X60 @ id @ (sub @ X36 @ (push @ X12 @ id)) @ id)|~((X60 @ id @ X12 @ id)))))|(X60 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X16:subst > term > term]:((~(![X7:term]:((~((X60 @ id @ X7 @ id))|(X60 @ id @ (X16 @ id @ X7) @ id))))|(X60 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))))=>![X61:subst > term > subst > $o, X24:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X61 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X61 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X61 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))|(X61 @ X8 @ X7 @ (comp @ X22 @ X21)))))|(X61 @ id @ (lam @ X24) @ id)|~(![X12:term]:(((X61 @ id @ (sub @ X24 @ (push @ X12 @ id)) @ id)|~((X61 @ id @ X12 @ id)))))|~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|(X61 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:(((X61 @ id @ (X16 @ id @ X7) @ id)|~((X61 @ id @ X7 @ id))))))))))))))&(![X8:subst]:(((X8)=(comp @ X8 @ id)))<=>(axidr)))&((axvarcons)<=>![X7:term, X8:subst]:(((X7)=(sub @ one @ (push @ X7 @ X8))))))&((hoaslaminj_lthm)<=>(![X7:term, X8:subst]:(((X7)=(sub @ one @ (push @ X7 @ X8))))=>((![X7:term, X12:term]:((((X7)=(X12))|((lam @ X7)!=(lam @ X12))))=>![X16:subst > term > term, X32:subst > term > term, X33:subst, X34:term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X32 @ X8 @ X7) @ X21)=(X32 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|((X16 @ X33 @ X34)=(X32 @ X33 @ X34))|((lam @ (X16 @ sh @ one))!=(lam @ (X32 @ sh @ one))))))<=![X7:term, X8:subst]:(((X8)=(comp @ sh @ (push @ X7 @ X8))))))))&((hoasapinj1_lthm)<=>((![X7:term, X12:term, X43:term, X44:term]:((((ap @ (sub @ X7 @ id) @ X43)!=(ap @ (sub @ X12 @ id) @ X44))|((X7)=(X12))))<=![X7:term, X12:term, X43:term, X44:term]:((((X7)=(X12))|((ap @ X7 @ X43)!=(ap @ X12 @ X44)))))<=![X7:term]:(((X7)=(sub @ X7 @ id))))))&(![X7:term, X12:term, X43:term, X44:term]:((((X7)=(X12))|((ap @ X7 @ X43)!=(ap @ X12 @ X44))))<=>(apinj1)))&(pushprop_lthm))&(![X62:subst > term > subst > $o, X10:term > $o, X63:term, X64:term]:((~(![X7:term, X12:term]:((~((X62 @ id @ X7 @ id))|~((X62 @ id @ X12 @ id))|(X62 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id))))|~(![X11:term]:(((X10 @ X11)<=>(X62 @ id @ X11 @ id))))|~((X10 @ X64))|(X10 @ (ap @ X63 @ X64))|~((X10 @ X63))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X62 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))|(X62 @ X8 @ X7 @ (comp @ X22 @ X21)))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X62 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X62 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))))<=>(hoasinduction_lem2v2)))&(axclos))&(hoaslamnotvar_gthm))&((hoasinduction_lem3aa)<=>![X65:subst > term > subst > $o, X36:term]:(((X65 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X12:term]:(((X65 @ id @ (sub @ X36 @ (push @ X12 @ id)) @ id)|~((X65 @ id @ X12 @ id)))))|~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X7:term]:((~((X65 @ id @ X7 @ id))|(X65 @ id @ (X16 @ id @ X7) @ id))))|(X65 @ id @ (lam @ (X16 @ sh @ one)) @ id))))))))&(termmset_gthm))&((induction)<=>![X9:term > $o, X15:term]:((~(![X7:term]:(((X9 @ X7)|~((var @ X7)))))|~(![X7:term, X12:term]:((~((X9 @ X7))|~((X9 @ X12))|(X9 @ (ap @ X7 @ X12)))))|(X9 @ X15)|~(![X7:term]:((~((X9 @ X7))|(X9 @ (lam @ X7)))))))))&((hoasinduction_lem3b_lthm)<=>![X12:term]:(~(![X16:subst > term > term]:(((X16 @ sh @ one)!=(sub @ X12 @ (push @ one @ sh))))))))&((hoasinduction)<=>![X66:subst > term > subst > $o, X26:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X66 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X66 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))|(X66 @ id @ X26 @ id)|~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|(X66 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:((~((X66 @ id @ X7 @ id))|(X66 @ id @ (X16 @ id @ X7) @ id)))))))|~(![X7:term, X12:term]:((~((X66 @ id @ X12 @ id))|(X66 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id)|~((X66 @ id @ X7 @ id)))))|~(![X7:term]:((~((var @ (sub @ X7 @ id)))|(X66 @ id @ X7 @ id))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X66 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))|(X66 @ X8 @ X7 @ (comp @ X22 @ X21)))))))))&((pushprop_lem1v2_lthm)<=>(![X7:term, X8:subst]:(((X7)=(sub @ one @ (push @ X7 @ X8))))=>![X9:term > $o, X10:term > $o, X7:term, X8:subst]:((~((X9 @ X7))|(X10 @ one)|~(![X11:term]:(((X10 @ X11)<=>(X9 @ (sub @ X11 @ (push @ X7 @ X8)))))))))))&(hoaslamnotap_lthm))&((![X7:term]:(((X7)=(sub @ X7 @ id)))<=![X7:term]:(((X7)=(sub @ X7 @ id))))<=>(termmset_lthm)))&(![X67:subst > term > subst > $o, X68:term]:((~(![X16:subst > term > term, X69:term]:((~(![X7:term]:(((X67 @ id @ (X16 @ id @ X7) @ id)|~((X67 @ id @ X7 @ id)))))|~(![X70:subst, X71:term, X72:subst]:(((X16 @ (comp @ X70 @ X72) @ (sub @ X71 @ X72))=(sub @ X69 @ (push @ (sub @ X71 @ X72) @ (comp @ X70 @ X72))))))|~(![X73:subst, X74:term, X75:subst]:(((sub @ (X16 @ X73 @ X74) @ X75)=(sub @ (sub @ X69 @ (push @ X74 @ X73)) @ X75))))|(X67 @ id @ (lam @ (X16 @ sh @ one)) @ id))))|(X67 @ id @ (lam @ (sub @ X68 @ (push @ one @ sh))) @ id)|~(![X12:term]:(((X67 @ id @ (sub @ X68 @ (push @ X12 @ id)) @ id)|~((X67 @ id @ X12 @ id)))))))<=>(hoasinduction_lem3aaa)))&(![X7:term, X12:term, X43:term, X44:term]:((((X7)=(X12))|((ap @ (sub @ X7 @ id) @ X43)!=(ap @ (sub @ X12 @ id) @ X44))))<=>(hoasapinj1)))&(hoasapnotvar_gthm))&((hoasapinj2)<=>![X7:term, X12:term, X43:term, X44:term]:((((ap @ (sub @ X7 @ id) @ X43)!=(ap @ (sub @ X12 @ id) @ X44))|((X43)=(X44))))))&(axvarshift))&(![X12:term]:(~(![X16:subst > term > term]:(~(![X7:term, X8:subst]:(((sub @ X12 @ (push @ X7 @ X8))=(X16 @ X8 @ X7)))))))<=>(hoasinduction_lem3v2_f)))&(hoasinduction_lem1v2_gthm))&(pushprop_lem0_gthm))&(axmap))&(![X9:term > $o, X10:term > $o, X7:term, X8:subst]:((~((X9 @ X7))|~(![X11:term]:(((X10 @ X11)<=>(X9 @ (sub @ X11 @ (push @ X7 @ X8))))))|(X10 @ one)))<=>(pushprop_lem1v2)))&((hoasinduction_p_and_p_prime)=(^[X76:subst > term > subst > $o, X10:term > $o]:(![X11:term]:((((X10 @ X11))<=>((X76 @ id @ X11 @ id))))))))&((hoaslam)=(^[X77:subst, X78:subst > term > term]:(d2term @ d_one))))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&![X79:d_subst, X80:d_subst]:((((d2subst @ X79)=(d2subst @ X80))=>((X79)=(X80)))))&![X6:d_subst]:(((X6)=(d_id)))), file('/export/starexec/sandbox2/tmp/tmp.rebpBEUsS2/E---3.1_2894887.p', alg444_1)). 0.31/0.88 thf(hoasinduction_lem3a, conjecture, ((hoasinduction_lem3a)<=>![X81:subst > term > subst > $o]:((![X16:subst > term > term]:((((X81 @ id @ (hoaslam @ id @ (^[X8:subst, X7:term]:(X16 @ X8 @ X7))) @ id)<=![X7:term]:(((X81 @ id @ (X16 @ id @ X7) @ id)<=(X81 @ id @ X7 @ id))))<=![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))=>![X7:term]:(((X81 @ id @ (lam @ X7) @ id)<=![X12:term]:(((X81 @ id @ (sub @ X7 @ (push @ X12 @ id)) @ id)<=(X81 @ id @ X12 @ id)))))))), file('/export/starexec/sandbox2/tmp/tmp.rebpBEUsS2/E---3.1_2894887.p', hoasinduction_lem3a)). 0.31/0.88 thf(c_0_2, plain, ((epred1_0)<=>(![X9:term > $o, X15:term]:((~(![X7:term, X12:term]:((~((X9 @ X7))|~((X9 @ X12))|(X9 @ (ap @ X7 @ X12)))))|~(![X7:term]:((~((X9 @ X7))|(X9 @ (lam @ X7)))))|(X9 @ X15)|~(![X7:term]:(((X9 @ X7)|~(var @ X7))))))=>![X9:term > $o, X13:term, X14:subst]:((~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:((~((X9 @ X12))|(X9 @ (sub @ X7 @ (push @ X12 @ id)))))))))|~(![X12:term]:(((X9 @ (sub @ X12 @ X14))|~(var @ X12))))|(X9 @ (sub @ X13 @ X14))|~(![X7:term, X12:term]:((~((X9 @ X12))|(X9 @ (ap @ X7 @ X12))|~((X9 @ X7))))))))), introduced(definition)). 0.31/0.88 thf(c_0_3, plain, ((epred4_0)<=>(![X9:term > $o, X17:term]:((~(![X7:term, X12:term]:(((X9 @ (ap @ X7 @ X12))|~((X9 @ X12))|~((X9 @ X7)))))|~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:((~((X9 @ X12))|(X9 @ (sub @ X7 @ (push @ X12 @ id)))))))))|(X9 @ X17)|~(![X7:term]:((~(var @ X7)|(X9 @ X7))))))=>(![X18:subst > term > subst > $o, X19:term, X20:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X18 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X18 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X18 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))|(X18 @ X8 @ X7 @ (comp @ X22 @ X21)))))|~((X18 @ id @ X19 @ id))|~((X18 @ id @ X20 @ id))|(X18 @ id @ (ap @ X19 @ X20) @ id)|~(![X7:term, X12:term]:((~((X18 @ id @ X7 @ id))|~((X18 @ id @ X12 @ id))|(X18 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id))))))=>(![X23:subst > term > subst > $o, X24:term]:((~(![X16:subst > 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introduced(definition)). 0.31/0.88 thf(c_0_7, plain, ((epred9_0)<=>(![X9:term > $o, X17:term]:(((X9 @ X17)|~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:(((X9 @ (sub @ X7 @ (push @ X12 @ id)))|~((X9 @ X12))))))))|~(![X7:term, X12:term]:(((X9 @ (ap @ X7 @ X12))|~((X9 @ X12))|~((X9 @ X7)))))|~(![X7:term]:((~(var @ X7)|(X9 @ X7))))))=>(![X7:term]:(((X7)=(sub @ X7 @ id)))=>(![X54:subst > term > subst > $o, X10:term > $o, X29:term]:((~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|(X54 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:(((X54 @ id @ (X16 @ id @ X7) @ id)|~((X54 @ id @ X7 @ id))))))))|(X10 @ (lam @ X29))|~(![X12:term]:(((X10 @ (sub @ X29 @ (push @ X12 @ id)))|~((X10 @ X12)))))|~(![X11:term]:(((X10 @ X11)<=>(X54 @ id @ X11 @ id))))))=>![X53:subst > term > subst > $o, X26:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X53 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X53 @ (comp @ 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@ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))))=>![X61:subst > term > subst > $o, X24:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X61 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X61 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X61 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))|(X61 @ X8 @ X7 @ (comp @ X22 @ X21)))))|(X61 @ id @ (lam @ X24) @ id)|~(![X12:term]:(((X61 @ id @ (sub @ X24 @ (push @ X12 @ id)) @ id)|~((X61 @ id @ X12 @ id)))))|~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|(X61 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:(((X61 @ id @ (X16 @ id @ X7) @ id)|~((X61 @ id @ X7 @ id)))))))))))), introduced(definition)). 0.31/0.88 thf(c_0_10, plain, ![X26:term, X66:subst > term > subst > $o]:(((epred12_2 @ X66 @ X26)<=>(~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X66 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X66 @ (comp @ 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@ X8))))=>(![X7:term, X8:subst]:(((X8)=(comp @ sh @ (push @ X7 @ X8))))=>(![X8:subst]:(((X8)=(comp @ X8 @ id)))=>(epred1_0))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((hoasinduction_lem3v2_f_lthm)<=>![X12:term]:(~(![X16:subst > term > term]:(~(![X7:term, X8:subst]:(((sub @ X12 @ (push @ X7 @ X8))=(X16 @ X8 @ X7)))))))))&((hoasinduction_lthm)<=>(epred4_0)))&((hoasinduction_no_psi_cond_lthm)<=>(![X27:subst > term > subst > $o]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X27 @ id @ X11 @ id)))))))=>(![X9:term > $o, X17:term]:(((X9 @ X17)|~(![X7:term]:((~(![X12:term]:(((X9 @ (sub @ X7 @ (push @ X12 @ id)))|~((X9 @ X12)))))|(X9 @ (lam @ X7)))))|~(![X7:term, X12:term]:((~((X9 @ X7))|(X9 @ (ap @ X7 @ X12))|~((X9 @ X12)))))|~(![X7:term]:(((X9 @ X7)|~(var @ X7))))))=>(![X7:term]:(((X7)=(sub @ X7 @ id)))=>(epred5_0))))))&(![X16:subst > term > term, X32:subst > term > term, X33:subst, X34:term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X32 @ X8 @ X7) @ X21)=(X32 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|((X16 @ X33 @ X34)=(X32 @ X33 @ X34))|((lam @ (X16 @ sh @ one))!=(lam @ (X32 @ sh @ one)))))<=>(hoaslaminj)))&(induction2lem_gthm))&((hoasinduction_lem3aa_lthm)<=>![X35:subst > term > subst > $o, X36:term]:((~(![X12:term]:((~((X35 @ id @ X12 @ id))|(X35 @ id @ (sub @ X36 @ (push @ X12 @ id)) @ id))))|(X35 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X16:subst > term > term]:((~(![X7:term]:(((X35 @ id @ (X16 @ id @ X7) @ id)|~((X35 @ id @ X7 @ id)))))|(X35 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))))))&(![X37:subst > term > subst > $o, X24:term]:((~(![X12:term]:(((X37 @ id @ (sub @ X24 @ (push @ X12 @ id)) @ id)|~((X37 @ id @ X12 @ id)))))|(X37 @ id @ (lam @ X24) @ id)|~(![X16:subst > term > term]:((~(![X7:term]:((~((X37 @ id @ X7 @ id))|(X37 @ id @ (X16 @ id @ X7) @ id))))|(X37 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X37 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X37 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X37 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X37 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))))<=>(hoasinduction_lem3)))&((hoasinduction_lem2)<=>![X38:subst > term > subst > $o, X19:term, X20:term]:((~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X38 @ X8 @ X7 @ (comp @ X22 @ X21))|~((X38 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)))))|~(![X7:term, X12:term]:(((X38 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id)|~((X38 @ id @ X12 @ id))|~((X38 @ id @ X7 @ id)))))|~((X38 @ id @ X20 @ id))|(X38 @ id @ (ap @ X19 @ X20) @ id)|~((X38 @ id @ X19 @ id))|~(![X8:subst, X7:term, X21:subst, X22:subst]:(((X38 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21)|~((X38 @ X8 @ X7 @ (comp @ X22 @ X21))))))))))&(hoasinduction_lem1))&(hoasapnotvar))&((hoasinduction_lem0)<=>![X39:subst > term > subst > $o]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X39 @ id @ X11 @ id)))))))))&(hoasinduction_gthm))&(axapp))&(hoaslamnotvar_lthm))&(pushprop_lem3v2_lthm))&(ulamvarind))&((![X7:term]:(((X7)=(sub @ X7 @ id)))=>(![X42:subst > term > subst > $o, X36:term]:((~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|(X42 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:((~((X42 @ id @ X7 @ id))|(X42 @ id @ (X16 @ id @ X7) @ id)))))))|(X42 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X12:term]:(((X42 @ id @ (sub @ X36 @ (push @ X12 @ id)) @ id)|~((X42 @ id @ X12 @ id)))))))=>![X40:subst > term > subst > $o, X41:term]:((~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X7:term]:((~((X40 @ id @ X7 @ id))|(X40 @ id @ (X16 @ id @ X7) @ id))))|(X40 @ id @ (lam @ (X16 @ sh @ one)) @ id))))|~(![X12:term]:((~((X40 @ id @ X12 @ id))|(X40 @ id @ (sub @ X41 @ (push @ X12 @ id)) @ id))))|(X40 @ id @ (lam @ X41) @ id)))))<=>(hoasinduction_lem3a_lthm)))&(pushprop_lem1v2_gthm))&(hoaslamnotap_gthm))&(hoasinduction_lem3b_gthm))&(pushprop_lem2v2))&(hoasinduction_lem3a_gthm))&(axassoc))&((apinj2)<=>![X7:term, X12:term, X43:term, X44:term]:((((X43)=(X44))|((ap @ X7 @ X43)!=(ap @ X12 @ X44))))))&((hoasapinj2_lthm)<=>(![X7:term, X12:term, X43:term, X44:term]:((((ap @ X7 @ X43)!=(ap @ X12 @ X44))|((X43)=(X44))))=>![X7:term, X12:term, X43:term, X44:term]:((((X43)=(X44))|((ap @ (sub @ X7 @ id) @ X43)!=(ap @ (sub @ X12 @ id) @ X44)))))))&((hoasinduction_lem3v2a)<=>![X45:subst > term > subst > $o, X10:term > $o, X29:term]:((~(![X11:term]:(((X10 @ X11)<=>(X45 @ id @ X11 @ id))))|(X10 @ (lam @ X29))|~(![X12:term]:((~((X10 @ X12))|(X10 @ (sub @ X29 @ (push @ X12 @ id))))))|~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X7:term]:(((X45 @ id @ (X16 @ id @ X7) @ id)|~((X45 @ id @ X7 @ id)))))|(X45 @ id @ (lam @ (X16 @ sh @ one)) @ id))))))))&((axscons)<=>![X8:subst]:(((X8)=(push @ (sub @ one @ X8) @ (comp @ sh @ X8))))))&(hoasinduction_lem2v2_gthm))&(![X9:term > $o, X46:term > $o, X7:term, X8:subst, X12:term]:((~((X9 @ X7))|(X46 @ (sub @ X7 @ (push @ X12 @ X8)))))<=>(pushprop_lem1)))&(![X7:term, X12:term]:((((X7)=(X12))|((lam @ X7)!=(lam @ X12))))<=>(laminj)))&((pushprop_lem0)<=>![X9:term > $o, X7:term, X8:subst]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X9 @ (sub @ X11 @ (push @ X7 @ X8)))))))))))&(pushprop_gthm))&(axabs))&(hoasinduction_lem2_lthm))&(hoasapinj2_gthm))&~(lamnotap))&(hoasapinj1_gthm))&(hoaslamnotvar))&(hoaslaminj_gthm))&((induction2_lthm)<=>(![X7:term]:(((X7)=(sub @ X7 @ id)))=>(epred6_0))))&((substmonoid_lthm)<=>(![X8:subst]:(((X8)=(comp @ id @ X8)))=>(![X8:subst]:(((X8)=(comp @ X8 @ id)))=>(![X8:subst]:(((X8)=(comp @ X8 @ id)))&![X8:subst]:(((X8)=(comp @ id @ X8))))))))&(hoasinduction_lem3_gthm))&(![X12:term]:(~(![X16:subst > term > term]:(((X16 @ sh @ one)!=(sub @ X12 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b)))&((substmonoid)<=>(![X8:subst]:(((X8)=(comp @ id @ X8)))&![X8:subst]:(((X8)=(comp @ X8 @ id))))))&(lamnotvar))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&(![X16:subst > term > term, X47:term, X48:term]:((((lam @ (X16 @ sh @ one))!=(ap @ (sub @ X47 @ id) @ X48))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))))<=>(hoaslamnotap)))&(substmonoid_gthm))&(pushprop_lem2v2_gthm))&((pushprop_lem1_lthm)<=>(![X7:term, X8:subst]:(((X7)=(sub @ one @ (push @ X7 @ X8))))=>(![X7:term, X8:subst]:(((X8)=(comp @ sh @ (push @ X7 @ X8))))=>![X9:term > $o, X49:term > $o, X7:term, X8:subst, X12:term]:((~((X9 @ X7))|(X49 @ (sub @ X7 @ (push @ X12 @ X8)))))))))&((hoasinduction_lem3v2)<=>(epred7_0)))&(![X7:term, X8:subst]:(((X8)=(comp @ sh @ (push @ X7 @ X8))))<=>(axshiftcons)))&((termmset)<=>![X7:term]:(((X7)=(sub @ X7 @ id)))))&(![X7:term]:(((X7)=(sub @ X7 @ id)))<=>(axvarid)))&((hoasinduction_lthm_3)<=>(![X52:subst > term > subst > $o]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X52 @ id @ X11 @ id)))))))=>(epred9_0))))&((![X7:term]:(((X7)=(sub @ X7 @ id)))=>(epred10_0))<=>(hoasinduction_lem3v2_lthm)))&(hoasapnotvar_lthm))&((pushprop_lem0_lthm)<=>![X9:term > $o, X7:term, X8:subst]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X9 @ (sub @ X11 @ (push @ X7 @ X8)))))))))))&(pushprop_lem3v2))&((induction2)<=>![X9:term > $o, X17:term]:((~(![X7:term]:(((X9 @ X7)|~(var @ X7))))|~(![X7:term]:(((X9 @ (lam @ X7))|~(![X12:term]:(((X9 @ (sub @ X7 @ (push @ X12 @ id)))|~((X9 @ X12))))))))|(X9 @ X17)|~(![X7:term, X12:term]:((~((X9 @ X12))|(X9 @ (ap @ X7 @ X12))|~((X9 @ X7)))))))))&(ulamvarsh))&((hoasinduction_no_psi_cond)<=>![X56:subst > term > subst > $o, X31:term]:((~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|(X56 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:(((X56 @ id @ (X16 @ id @ X7) @ id)|~((X56 @ id @ X7 @ id))))))))|(X56 @ id @ X31 @ id)|~(![X7:term, X12:term]:((~((X56 @ id @ X7 @ id))|(X56 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id)|~((X56 @ id @ X12 @ id)))))))))&(hoasinduction_lem1_gthm))&(![X57:subst > term > subst > $o, X41:term]:((~(![X16:subst > term > term]:((~(![X7:term]:(((X57 @ id @ (X16 @ id @ X7) @ id)|~((X57 @ id @ X7 @ id)))))|(X57 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|~(![X12:term]:((~((X57 @ id @ X12 @ id))|(X57 @ id @ (sub @ X41 @ (push @ X12 @ id)) @ id))))|(X57 @ id @ (lam @ X41) @ id)))<=>(hoasinduction_lem3a)))&(hoasinduction_lem2_gthm))&(pushprop))&((hoasinduction_lem0_lthm)<=>![X58:subst > term > subst > $o]:(~(![X10:term > $o]:(~(![X11:term]:(((X10 @ X11)<=>(X58 @ id @ X11 @ id)))))))))&(![X8:subst]:(((X8)=(comp @ id @ X8)))<=>(axidl)))&(hoasinduction_lem1_lthm))&((![X12:term]:(~(![X16:subst > term > term]:(~(![X7:term, X8:subst]:(((sub @ X12 @ (push @ X7 @ X8))=(X16 @ X8 @ X7)))))))=>(![X7:term]:(((X7)=(sub @ X7 @ id)))=>![X59:subst > term > subst > $o, X10:term > $o, X29:term]:((~(![X16:subst > term > term]:(((X59 @ id @ (lam @ (X16 @ sh @ one)) @ id)|~(![X7:term]:((~((X59 @ id @ X7 @ id))|(X59 @ id @ (X16 @ id @ X7) @ id))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))))|(X10 @ (lam @ X29))|~(![X12:term]:((~((X10 @ X12))|(X10 @ (sub @ X29 @ (push @ X12 @ id))))))|~(![X11:term]:(((X10 @ X11)<=>(X59 @ id @ X11 @ id))))))))<=>(hoasinduction_lem3v2a_lthm)))&((hoasinduction_lem3_lthm)<=>(![X7:term]:(((X7)=(sub @ X7 @ id)))=>(epred11_0))))&(![X8:subst]:(((X8)=(comp @ X8 @ id)))<=>(axidr)))&((axvarcons)<=>![X7:term, X8:subst]:(((X7)=(sub @ one @ (push @ X7 @ X8))))))&((hoaslaminj_lthm)<=>(![X7:term, X8:subst]:(((X7)=(sub @ one @ (push @ X7 @ X8))))=>(![X7:term, X8:subst]:(((X8)=(comp @ sh @ (push @ X7 @ X8))))=>(![X7:term, X12:term]:((((X7)=(X12))|((lam @ X7)!=(lam @ X12))))=>![X16:subst > term > term, X32:subst > term > term, X33:subst, X34:term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X8:subst, X7:term, X21:subst]:(((sub @ (X32 @ X8 @ X7) @ X21)=(X32 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|((X16 @ X33 @ X34)=(X32 @ X33 @ X34))|((lam @ (X16 @ sh @ one))!=(lam @ (X32 @ sh @ one))))))))))&((hoasapinj1_lthm)<=>(![X7:term]:(((X7)=(sub @ X7 @ id)))=>(![X7:term, X12:term, X43:term, X44:term]:((((X7)=(X12))|((ap @ X7 @ X43)!=(ap @ X12 @ X44))))=>![X7:term, X12:term, X43:term, X44:term]:((((ap @ (sub @ X7 @ id) @ X43)!=(ap @ (sub @ X12 @ id) @ X44))|((X7)=(X12))))))))&(![X7:term, X12:term, X43:term, X44:term]:((((X7)=(X12))|((ap @ X7 @ X43)!=(ap @ X12 @ X44))))<=>(apinj1)))&(pushprop_lthm))&(![X62:subst > term > subst > $o, X10:term > $o, X63:term, X64:term]:((~(![X7:term, X12:term]:((~((X62 @ id @ X7 @ id))|~((X62 @ id @ X12 @ id))|(X62 @ id @ (ap @ (sub @ X7 @ id) @ X12) @ id))))|~(![X11:term]:(((X10 @ X11)<=>(X62 @ id @ X11 @ id))))|~((X10 @ X64))|(X10 @ (ap @ X63 @ X64))|~((X10 @ X63))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X62 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))|(X62 @ X8 @ X7 @ (comp @ X22 @ X21)))))|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X62 @ X8 @ X7 @ (comp @ X22 @ X21)))|(X62 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))))))<=>(hoasinduction_lem2v2)))&(axclos))&(hoaslamnotvar_gthm))&((hoasinduction_lem3aa)<=>![X65:subst > term > subst > $o, X36:term]:(((X65 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X12:term]:(((X65 @ id @ (sub @ X36 @ (push @ X12 @ id)) @ id)|~((X65 @ id @ X12 @ id)))))|~(![X16:subst > term > term]:((~(![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21)))))|~(![X7:term]:((~((X65 @ id @ X7 @ id))|(X65 @ id @ (X16 @ id @ X7) @ id))))|(X65 @ id @ (lam @ (X16 @ sh @ one)) @ id))))))))&(termmset_gthm))&((induction)<=>![X9:term > $o, X15:term]:((~(![X7:term]:(((X9 @ X7)|~(var @ X7))))|~(![X7:term, X12:term]:((~((X9 @ X7))|~((X9 @ X12))|(X9 @ (ap @ X7 @ X12)))))|(X9 @ X15)|~(![X7:term]:((~((X9 @ X7))|(X9 @ (lam @ X7)))))))))&((hoasinduction_lem3b_lthm)<=>![X12:term]:(~(![X16:subst > term > term]:(((X16 @ sh @ one)!=(sub @ X12 @ (push @ one @ sh))))))))&((hoasinduction)<=>![X66:subst > term > subst > $o, X26:term]:(((epred12_2 @ X66 @ X26)|~(![X8:subst, X7:term, X21:subst, X22:subst]:((~((X66 @ (comp @ X8 @ X22) @ (sub @ X7 @ X22) @ X21))|(X66 @ X8 @ X7 @ (comp @ X22 @ X21)))))))))&((pushprop_lem1v2_lthm)<=>(![X7:term, X8:subst]:(((X7)=(sub @ one @ (push @ X7 @ X8))))=>![X9:term > $o, X10:term > $o, X7:term, X8:subst]:((~((X9 @ X7))|(X10 @ one)|~(![X11:term]:(((X10 @ X11)<=>(X9 @ (sub @ X11 @ (push @ X7 @ X8)))))))))))&(hoaslamnotap_lthm))&(termmset_lthm))&(![X67:subst > term > subst > $o, X68:term]:((~(![X16:subst > term > term, X69:term]:((~(![X7:term]:(((X67 @ id @ (X16 @ id @ X7) @ id)|~((X67 @ id @ X7 @ id)))))|~(![X70:subst, X71:term, X72:subst]:(((X16 @ (comp @ X70 @ X72) @ (sub @ X71 @ X72))=(sub @ X69 @ (push @ (sub @ X71 @ X72) @ (comp @ X70 @ X72))))))|~(![X73:subst, X74:term, X75:subst]:(((sub @ (X16 @ X73 @ X74) @ X75)=(sub @ (sub @ X69 @ (push @ X74 @ X73)) @ X75))))|(X67 @ id @ (lam @ (X16 @ sh @ one)) @ id))))|(X67 @ id @ (lam @ (sub @ X68 @ (push @ one @ sh))) @ id)|~(![X12:term]:(((X67 @ id @ (sub @ X68 @ (push @ X12 @ id)) @ id)|~((X67 @ id @ X12 @ id)))))))<=>(hoasinduction_lem3aaa)))&(![X7:term, X12:term, X43:term, X44:term]:((((X7)=(X12))|((ap @ (sub @ X7 @ id) @ X43)!=(ap @ (sub @ X12 @ id) @ X44))))<=>(hoasapinj1)))&(hoasapnotvar_gthm))&((hoasapinj2)<=>![X7:term, X12:term, X43:term, X44:term]:((((ap @ (sub @ X7 @ id) @ X43)!=(ap @ (sub @ X12 @ id) @ X44))|((X43)=(X44))))))&(axvarshift))&(![X12:term]:(~(![X16:subst > term > term]:(~(![X7:term, X8:subst]:(((sub @ X12 @ (push @ X7 @ X8))=(X16 @ X8 @ X7)))))))<=>(hoasinduction_lem3v2_f)))&(hoasinduction_lem1v2_gthm))&(pushprop_lem0_gthm))&(axmap))&(![X9:term > $o, X10:term > $o, X7:term, X8:subst]:((~((X9 @ X7))|~(![X11:term]:(((X10 @ X11)<=>(X9 @ (sub @ X11 @ (push @ X7 @ X8))))))|(X10 @ one)))<=>(pushprop_lem1v2)))&![X634:subst > term > subst > $o, X635:term > $o]:(((hoasinduction_p_and_p_prime @ X634 @ X635)<=>![X11:term]:(((X635 @ X11)<=>(X634 @ id @ X11 @ id))))))&![X636:subst, X637:subst > term > term]:(((hoaslam @ X636 @ X637)=(d2term @ d_one))))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&![X79:d_subst, X80:d_subst]:((((d2subst @ X79)=(d2subst @ X80))=>((X79)=(X80)))))&![X6:d_subst]:(((X6)=(d_id)))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[alg444_1])])]), c_0_2]), c_0_3]), c_0_4]), c_0_5]), c_0_6]), c_0_7]), c_0_8]), c_0_9]), c_0_10])). 0.31/0.88 thf(c_0_12, negated_conjecture, ~(((hoasinduction_lem3a)<=>![X81:subst > term > subst > $o]:((![X16:subst > term > term]:((((X81 @ id @ (hoaslam @ id @ (^[X8:subst, X7:term]:(X16 @ X8 @ X7))) @ id)<=![X7:term]:(((X81 @ id @ (X16 @ id @ X7) @ id)<=(X81 @ id @ X7 @ id))))<=![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))))=>![X7:term]:(((X81 @ id @ (lam @ X7) @ id)<=![X12:term]:(((X81 @ id @ (sub @ X7 @ (push @ X12 @ id)) @ id)<=(X81 @ id @ X12 @ id))))))))), inference(assume_negation,[status(cth)],[hoasinduction_lem3a])). 0.31/0.88 thf(c_0_13, plain, ![X638:term, X640:d_term, X641:d_term, X642:d_term, X643:subst, X645:term, X646:subst, X647:term > $o, X648:term > $o, X649:term, X650:term, X651:term, X652:subst, X653:term > $o, X654:term > $o, X656:term, X657:term, X663:term, X665:term, X666:term, X667:term, X668:term > $o, X669:term, X670:subst, X672:term, X681:term, X682:subst, X683:term, X684:subst, X685:subst, X686:term, X688:term, X689:subst, X691:subst > term > term, X695:term > $o, X699:term, X701:term, X702:term, X703:term, X705:subst > term > subst > $o, X707:term, X708:term, X709:term > $o, X710:term, X712:term, X716:term, X721:subst, X722:term, X723:subst, X724:subst, X725:term, X726:subst, X727:subst > term > term, X728:subst > term > term, X735:subst, X736:term, X737:subst > term > subst > $o, X738:term, X741:term, X742:subst, X743:term, X744:subst, X747:term, X748:subst > term > term, X755:term, X756:subst > term > term, X761:subst, X762:term, X763:subst, X764:subst, X765:subst, X766:term, X767:subst, X768:subst, X769:subst > term > subst > $o, X770:term, X773:term, X774:subst, X775:term, X776:subst, X785:subst > term > subst > $o, X786:term, X787:term, X801:subst, X802:term, X803:subst, X804:subst, X805:term, X806:term, X807:subst, X808:term, X809:subst, X810:subst, X811:subst > term > subst > $o, X813:term, X814:term, X816:term > $o, X818:term, X819:subst > term > subst > $o, X820:term, X822:subst, X823:term, X824:subst, X825:term, X829:subst > term > term, X834:term, X838:subst > term > term, X843:term, X844:subst > term > subst > $o, X845:term, X847:subst, X848:term, X849:subst, X850:term, X852:term, X853:term, X854:term, X855:term, X864:term, X865:term, X866:term, X867:term, X868:term, X869:term, X870:term, X871:term, X876:subst > term > subst > $o, X877:term > $o, X878:term, X882:subst, X883:term, X884:subst, X885:term, X889:term, X890:term, X891:subst > term > term, X896:subst, X903:term > $o, X904:term > $o, X905:term, X906:subst, X907:term, X910:term, X911:term, X912:term > $o, X913:term, X914:subst, X916:term, X917:term, X921:term > $o, X924:term, X927:subst, X928:subst, X929:subst, X930:subst, X934:subst > term > term, X935:term, X937:subst, X938:subst, X944:subst, X945:term, X946:subst, X947:subst > term > term, X948:term, X949:term, X957:term > $o, X958:term > $o, X959:term, X960:subst, X961:term, X962:term, X963:subst, X964:term, X965:subst, X973:term, X974:subst, X975:term, X978:term, X980:term > $o, X982:subst > term > subst > $o, X984:term, X985:term, X986:term, X988:term > $o, X989:term, X990:subst, X992:term, X993:term, X997:term > $o, X999:term > $o, X1002:term, X1003:term, X1008:term, X1009:term, X1011:term, X1012:term, X1013:subst > term > subst > $o, X1015:subst, X1016:term, X1017:subst, X1018:term, X1019:term, X1024:subst > term > term, X1029:term, X1030:term, X1033:subst > term > term, X1038:term, X1039:subst > term > subst > $o, X1040:term, X1042:term, X1043:subst, X1044:term, X1045:subst, X1047:subst > term > subst > $o, X1049:term, X1050:term, X1052:term > $o, X1055:subst, X1056:term, X1058:term, X1059:subst, X1060:term, X1064:subst > term > term, X1069:term, X1070:term, X1072:subst > term > term, X1076:subst > term > subst > $o, X1077:term > $o, X1078:term, X1080:term, X1081:subst, X1082:term, X1083:subst, X1087:term, X1089:subst, X1090:term, X1091:subst, X1100:subst > term > term, X1101:subst > term > term, X1108:subst, X1109:term, X1110:term, X1111:subst, X1112:term, X1113:subst, X1114:term, X1115:term, X1120:subst, X1121:term, X1122:subst, X1123:subst, X1124:term, X1125:subst, X1131:term, X1132:term, X1133:term, X1134:term, X1135:term, X1136:term, X1137:term, X1138:term, X1139:term, X1148:term, X1149:term, X1150:term, X1151:term, X1156:term, X1157:term, X1158:term, X1159:subst, X1160:term, X1161:subst, X1162:subst, X1163:subst, X1164:term, X1165:subst, X1166:subst, X1167:subst > term > subst > $o, X1168:term > $o, X1169:term, X1170:term, X1182:subst > term > subst > $o, X1183:term, X1186:subst, X1187:term, X1188:subst, X1189:term, X1192:term, X1193:subst > term > term, X1198:term > $o, X1202:term, X1206:term, X1207:term, X1208:term, X1209:term, X1210:term, X1213:subst > term > term, X1214:subst > term > subst > $o, X1215:term, X1222:subst, X1223:term, X1224:subst, X1225:subst, X1228:term > $o, X1229:term > $o, X1230:term, X1231:subst, X1233:term, X1234:subst, X1239:term, X1242:subst > term > term, X1243:term, X1251:term, X1252:subst > term > subst > $o, X1253:term, X1256:term, X1257:subst, X1258:term, X1259:subst, X1260:subst, X1261:term, X1262:subst, X1268:term, X1269:term, X1270:term, X1271:term, X1272:term, X1273:term, X1274:term, X1275:term, X1281:subst > term > term, X1284:term, X1286:term, X1287:subst, X1292:term, X1293:term > $o, X1294:term > $o, X1295:term, X1296:subst, X1298:subst > term > subst > $o, X1299:term > $o, X1300:term, X1301:term, X1302:subst > term > subst > $o, X1303:term > $o, X1305:subst, X1306:subst > term > term, X1307:d_subst, X1308:d_subst, X1309:d_subst]:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((X638)=(d2term @ (esk1_1 @ X638)))&((X640)=(d_one)))&(((d2term @ X641)!=(d2term @ X642))|((X641)=(X642))))&((X643)=(d2subst @ (esk2_1 @ X643))))&((one)=(d2term @ d_one)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&(((~(X648 @ X649)|(X647 @ (sub @ X649 @ (push @ X645 @ X646)))|~(pushprop_p_and_p_prime @ X645 @ X646 @ X647 @ X648))&(~(X647 @ (sub @ X650 @ (push @ X645 @ X646)))|(X648 @ X650)|~(pushprop_p_and_p_prime @ X645 @ X646 @ X647 @ X648)))&((~(X654 @ (esk3_4 @ X651 @ X652 @ X653 @ X654))|~(X653 @ (sub @ (esk3_4 @ X651 @ X652 @ X653 @ X654) @ (push @ X651 @ X652)))|(pushprop_p_and_p_prime @ X651 @ X652 @ X653 @ X654))&((X654 @ (esk3_4 @ X651 @ X652 @ X653 @ X654))|(X653 @ (sub @ (esk3_4 @ X651 @ X652 @ X653 @ X654) @ (push @ X651 @ X652)))|(pushprop_p_and_p_prime @ X651 @ X652 @ X653 @ X654)))))&~(var @ (d2term @ d_one)))&(pushprop_lem1_gthm))&((~(shinj)|(((X656)=(X657))|((sub @ X656 @ sh)!=(sub @ X657 @ sh))))&((((esk4_0)!=(esk5_0))|(shinj))&(((sub @ esk4_0 @ sh)=(sub @ esk5_0 @ sh))|(shinj)))))&(hoasinduction_lem1v2))&(((((((epred13_0 @ (esk8_1 @ X663))|(epred13_0 @ (lam @ X663))|(induction2lem))&(~(epred13_0 @ (sub @ X663 @ (push @ (esk8_1 @ X663) @ id)))|(epred13_0 @ (lam @ X663))|(induction2lem)))&(~(epred13_0 @ (sub @ esk6_0 @ esk7_0))|(induction2lem)))&(~(var @ X665)|(epred13_0 @ (sub @ X665 @ esk7_0))|(induction2lem)))&(~(epred13_0 @ X666)|~(epred13_0 @ X667)|(epred13_0 @ (ap @ X666 @ X667))|(induction2lem)))&((((((X668 @ (esk11_1 @ X668))|((var @ (esk10_3 @ X668 @ X669 @ X670))|(~(X668 @ (lam @ (esk9_3 @ X668 @ X669 @ X670)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem))&((X668 @ (esk12_1 @ X668))|((var @ (esk10_3 @ X668 @ X669 @ X670))|(~(X668 @ (lam @ (esk9_3 @ X668 @ X669 @ X670)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem)))&(~(X668 @ (ap @ (esk11_1 @ X668) @ (esk12_1 @ X668)))|((var @ (esk10_3 @ X668 @ X669 @ X670))|(~(X668 @ (lam @ (esk9_3 @ X668 @ X669 @ X670)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem)))&((((X668 @ (esk11_1 @ X668))|(~(X668 @ (sub @ (esk10_3 @ X668 @ X669 @ X670) @ X670))|(~(X668 @ (lam @ (esk9_3 @ X668 @ X669 @ X670)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem))&((X668 @ (esk12_1 @ X668))|(~(X668 @ (sub @ (esk10_3 @ X668 @ X669 @ X670) @ X670))|(~(X668 @ (lam @ (esk9_3 @ X668 @ X669 @ X670)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem)))&(~(X668 @ (ap @ (esk11_1 @ X668) @ (esk12_1 @ X668)))|(~(X668 @ (sub @ (esk10_3 @ X668 @ X669 @ X670) @ X670))|(~(X668 @ (lam @ (esk9_3 @ X668 @ X669 @ X670)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem))))&(((((X668 @ (esk11_1 @ X668))|((var @ (esk10_3 @ X668 @ X669 @ X670))|(~(X668 @ X672)|(X668 @ (sub @ (esk9_3 @ X668 @ X669 @ X670) @ (push @ X672 @ id)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem))&((X668 @ (esk12_1 @ X668))|((var @ (esk10_3 @ X668 @ X669 @ X670))|(~(X668 @ X672)|(X668 @ (sub @ (esk9_3 @ X668 @ X669 @ X670) @ (push @ X672 @ id)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem)))&(~(X668 @ (ap @ (esk11_1 @ X668) @ (esk12_1 @ X668)))|((var @ (esk10_3 @ X668 @ X669 @ X670))|(~(X668 @ X672)|(X668 @ (sub @ (esk9_3 @ X668 @ X669 @ X670) @ (push @ X672 @ id)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem)))&((((X668 @ (esk11_1 @ X668))|(~(X668 @ (sub @ (esk10_3 @ X668 @ X669 @ X670) @ X670))|(~(X668 @ X672)|(X668 @ (sub @ (esk9_3 @ X668 @ X669 @ X670) @ (push @ X672 @ id)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem))&((X668 @ (esk12_1 @ X668))|(~(X668 @ (sub @ (esk10_3 @ X668 @ X669 @ X670) @ X670))|(~(X668 @ X672)|(X668 @ (sub @ (esk9_3 @ X668 @ X669 @ X670) @ (push @ X672 @ id)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem)))&(~(X668 @ (ap @ (esk11_1 @ X668) @ (esk12_1 @ X668)))|(~(X668 @ (sub @ (esk10_3 @ X668 @ X669 @ X670) @ X670))|(~(X668 @ X672)|(X668 @ (sub @ (esk9_3 @ X668 @ X669 @ X670) @ (push @ X672 @ id)))|(X668 @ (sub @ X669 @ X670))))|~(induction2lem)))))))&~(ulamvar1))&((~(induction2lem_lthm)|(((esk13_0)!=(sub @ one @ (push @ esk13_0 @ esk14_0)))|(((esk16_0)!=(comp @ sh @ (push @ esk15_0 @ esk16_0)))|(((esk17_0)!=(comp @ esk17_0 @ id))|(epred1_0)))))&((((X681)=(sub @ one @ (push @ X681 @ X682)))|(induction2lem_lthm))&((((X684)=(comp @ sh @ (push @ X683 @ X684)))|(induction2lem_lthm))&((((X685)=(comp @ X685 @ id))|(induction2lem_lthm))&(~(epred1_0)|(induction2lem_lthm)))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((~(hoasinduction_lem3v2_f_lthm)|((sub @ X686 @ (push @ X688 @ X689))=(esk18_1 @ X686 @ X689 @ X688)))&(((sub @ esk19_0 @ (push @ (esk20_1 @ X691) @ (esk21_1 @ X691)))!=(X691 @ (esk21_1 @ X691) @ (esk20_1 @ X691)))|(hoasinduction_lem3v2_f_lthm))))&((~(hoasinduction_lthm)|(epred4_0))&(~(epred4_0)|(hoasinduction_lthm))))&((((((~(epred15_0 @ esk23_0)|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|(~(X695 @ (esk22_1 @ X695))|~(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))&((~(epred15_0 @ (sub @ X699 @ (push @ (esk24_1 @ X699) @ id)))|(epred15_0 @ (lam @ X699))|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|(~(X695 @ (esk22_1 @ X695))|~(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))&((epred15_0 @ (esk24_1 @ X699))|(epred15_0 @ (lam @ X699))|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|(~(X695 @ (esk22_1 @ X695))|~(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred15_0 @ X701)|(epred15_0 @ (ap @ X701 @ X702))|~(epred15_0 @ X702)|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|(~(X695 @ (esk22_1 @ X695))|~(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm)))&((epred15_0 @ X703)|~(var @ X703)|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|(~(X695 @ (esk22_1 @ X695))|~(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm)))&((((~(epred15_0 @ esk23_0)|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|((X695 @ (esk22_1 @ X695))|(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))&((~(epred15_0 @ (sub @ X699 @ (push @ (esk24_1 @ X699) @ id)))|(epred15_0 @ (lam @ X699))|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|((X695 @ (esk22_1 @ X695))|(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))&((epred15_0 @ (esk24_1 @ X699))|(epred15_0 @ (lam @ X699))|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|((X695 @ (esk22_1 @ X695))|(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred15_0 @ X701)|(epred15_0 @ (ap @ X701 @ X702))|~(epred15_0 @ X702)|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|((X695 @ (esk22_1 @ X695))|(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm)))&((epred15_0 @ X703)|~(var @ X703)|(((esk25_0)!=(sub @ esk25_0 @ id))|(epred5_0))|((X695 @ (esk22_1 @ X695))|(epred14_0 @ id @ (esk22_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(((~(epred16_1 @ X705 @ X707)|(X705 @ id @ X707 @ id)|(hoasinduction_no_psi_cond_lthm))&(~(X705 @ id @ X708 @ id)|(epred16_1 @ X705 @ X708)|(hoasinduction_no_psi_cond_lthm)))&((((((~(X709 @ (esk29_1 @ X709))|((X709 @ (esk27_1 @ X709))|((X709 @ (sub @ (esk26_1 @ X709) @ (push @ X712 @ id)))|~(X709 @ X712)|(X709 @ X710)))|(hoasinduction_no_psi_cond_lthm))&((var @ (esk29_1 @ X709))|((X709 @ (esk27_1 @ X709))|((X709 @ (sub @ (esk26_1 @ X709) @ (push @ X712 @ id)))|~(X709 @ X712)|(X709 @ X710)))|(hoasinduction_no_psi_cond_lthm)))&((~(X709 @ (esk29_1 @ X709))|(~(X709 @ (ap @ (esk27_1 @ X709) @ (esk28_1 @ X709)))|((X709 @ (sub @ (esk26_1 @ X709) @ (push @ X712 @ id)))|~(X709 @ X712)|(X709 @ X710)))|(hoasinduction_no_psi_cond_lthm))&((var @ (esk29_1 @ X709))|(~(X709 @ (ap @ (esk27_1 @ X709) @ (esk28_1 @ X709)))|((X709 @ (sub @ (esk26_1 @ X709) @ (push @ X712 @ id)))|~(X709 @ X712)|(X709 @ X710)))|(hoasinduction_no_psi_cond_lthm))))&((~(X709 @ (esk29_1 @ X709))|((X709 @ (esk28_1 @ X709))|((X709 @ (sub @ (esk26_1 @ X709) @ (push @ X712 @ id)))|~(X709 @ X712)|(X709 @ X710)))|(hoasinduction_no_psi_cond_lthm))&((var @ (esk29_1 @ X709))|((X709 @ (esk28_1 @ X709))|((X709 @ (sub @ 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esk254_0 @ esk255_0)))|(epred49_0 @ X1239)|(pushprop_lem1v2_lthm)))))))&(hoaslamnotap_lthm))&(termmset_lthm))&(((((~(epred50_0 @ id @ (X1242 @ id @ (esk257_2 @ X1242 @ X1243)) @ id)|((X1242 @ (comp @ (esk258_2 @ X1242 @ X1243) @ (esk260_2 @ X1242 @ X1243)) @ (sub @ (esk259_2 @ X1242 @ X1243) @ (esk260_2 @ X1242 @ X1243)))!=(sub @ X1243 @ (push @ (sub @ (esk259_2 @ X1242 @ X1243) @ (esk260_2 @ X1242 @ X1243)) @ (comp @ (esk258_2 @ X1242 @ X1243) @ (esk260_2 @ X1242 @ X1243)))))|((sub @ (X1242 @ (esk261_2 @ X1242 @ X1243) @ (esk262_2 @ X1242 @ X1243)) @ (esk263_2 @ X1242 @ X1243))!=(sub @ (sub @ X1243 @ (push @ (esk262_2 @ X1242 @ X1243) @ (esk261_2 @ X1242 @ X1243))) @ (esk263_2 @ X1242 @ X1243)))|(epred50_0 @ id @ (lam @ (X1242 @ sh @ one)) @ id)|(hoasinduction_lem3aaa))&((epred50_0 @ id @ (esk257_2 @ X1242 @ X1243) @ id)|((X1242 @ (comp @ (esk258_2 @ X1242 @ X1243) @ (esk260_2 @ X1242 @ X1243)) @ (sub @ (esk259_2 @ X1242 @ X1243) @ (esk260_2 @ X1242 @ X1243)))!=(sub @ X1243 @ (push @ (sub @ (esk259_2 @ X1242 @ X1243) @ (esk260_2 @ X1242 @ X1243)) @ (comp @ (esk258_2 @ X1242 @ X1243) @ (esk260_2 @ X1242 @ X1243)))))|((sub @ (X1242 @ (esk261_2 @ X1242 @ X1243) @ (esk262_2 @ X1242 @ X1243)) @ (esk263_2 @ X1242 @ X1243))!=(sub @ (sub @ X1243 @ (push @ (esk262_2 @ X1242 @ X1243) @ (esk261_2 @ X1242 @ X1243))) @ (esk263_2 @ X1242 @ X1243)))|(epred50_0 @ id @ (lam @ (X1242 @ sh @ one)) @ id)|(hoasinduction_lem3aaa)))&(~(epred50_0 @ id @ (lam @ (sub @ esk256_0 @ (push @ one @ sh))) @ id)|(hoasinduction_lem3aaa)))&((epred50_0 @ id @ (sub @ esk256_0 @ (push @ X1251 @ id)) @ id)|~(epred50_0 @ id @ X1251 @ id)|(hoasinduction_lem3aaa)))&(((((~(X1252 @ id @ (sub @ X1253 @ (push @ (esk266_2 @ X1252 @ X1253) @ id)) @ id)|((X1252 @ id @ (esk264_2 @ X1252 @ X1253 @ id @ X1256) @ id)|~(X1252 @ id @ X1256 @ id)|(X1252 @ id @ (lam @ (sub @ X1253 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&((X1252 @ id @ (esk266_2 @ X1252 @ X1253) @ id)|((X1252 @ id @ (esk264_2 @ X1252 @ X1253 @ id @ X1256) @ id)|~(X1252 @ id @ X1256 @ id)|(X1252 @ id @ (lam @ (sub @ X1253 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&((~(X1252 @ id @ (sub @ X1253 @ (push @ (esk266_2 @ X1252 @ X1253) @ id)) @ id)|(((esk264_2 @ X1252 @ X1253 @ (comp @ X1257 @ X1259) @ (sub @ X1258 @ X1259))=(sub @ (esk265_2 @ X1252 @ X1253) @ (push @ (sub @ X1258 @ X1259) @ (comp @ X1257 @ X1259))))|(X1252 @ id @ (lam @ (sub @ X1253 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&((X1252 @ id @ (esk266_2 @ X1252 @ X1253) @ id)|(((esk264_2 @ X1252 @ X1253 @ (comp @ X1257 @ X1259) @ (sub @ X1258 @ X1259))=(sub @ (esk265_2 @ X1252 @ X1253) @ (push @ (sub @ X1258 @ X1259) @ (comp @ X1257 @ X1259))))|(X1252 @ id @ (lam @ (sub @ X1253 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))))&((~(X1252 @ id @ (sub @ X1253 @ (push @ (esk266_2 @ X1252 @ X1253) @ id)) @ id)|(((sub @ (esk264_2 @ X1252 @ X1253 @ X1260 @ X1261) @ X1262)=(sub @ (sub @ (esk265_2 @ X1252 @ X1253) @ (push @ X1261 @ X1260)) @ X1262))|(X1252 @ id @ (lam @ (sub @ X1253 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&((X1252 @ id @ (esk266_2 @ X1252 @ X1253) @ id)|(((sub @ (esk264_2 @ X1252 @ X1253 @ X1260 @ X1261) @ X1262)=(sub @ (sub @ (esk265_2 @ X1252 @ X1253) @ (push @ X1261 @ X1260)) @ X1262))|(X1252 @ id @ (lam @ (sub @ X1253 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))))&((~(X1252 @ id @ (sub @ X1253 @ (push @ (esk266_2 @ X1252 @ X1253) @ id)) @ id)|(~(X1252 @ id @ (lam @ (esk264_2 @ X1252 @ X1253 @ sh @ one)) @ id)|(X1252 @ id @ (lam @ (sub @ X1253 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&((X1252 @ id @ (esk266_2 @ X1252 @ X1253) @ id)|(~(X1252 @ id @ (lam @ (esk264_2 @ X1252 @ X1253 @ sh @ one)) @ id)|(X1252 @ id @ (lam @ (sub @ X1253 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))))))&(((((esk267_0)!=(esk268_0))|(hoasapinj1))&(((ap @ (sub @ esk267_0 @ id) @ esk269_0)=(ap @ (sub @ esk268_0 @ id) @ esk270_0))|(hoasapinj1)))&(~(hoasapinj1)|(((X1268)=(X1269))|((ap @ (sub @ X1268 @ id) @ X1270)!=(ap @ (sub @ X1269 @ id) @ X1271))))))&(hoasapnotvar_gthm))&((~(hoasapinj2)|(((ap @ (sub @ X1272 @ id) @ X1274)!=(ap @ (sub @ X1273 @ id) @ X1275))|((X1274)=(X1275))))&((((ap @ (sub @ esk271_0 @ id) @ esk273_0)=(ap @ (sub @ esk272_0 @ id) @ esk274_0))|(hoasapinj2))&(((esk273_0)!=(esk274_0))|(hoasapinj2)))))&(axvarshift))&((((sub @ esk275_0 @ (push @ (esk276_1 @ X1281) @ (esk277_1 @ X1281)))!=(X1281 @ (esk277_1 @ X1281) @ (esk276_1 @ X1281)))|(hoasinduction_lem3v2_f))&(~(hoasinduction_lem3v2_f)|((sub @ X1284 @ (push @ X1286 @ X1287))=(esk278_1 @ X1284 @ X1287 @ X1286)))))&(hoasinduction_lem1v2_gthm))&(pushprop_lem0_gthm))&(axmap))&(((((epred51_0 @ esk279_0)|(pushprop_lem1v2))&((~(epred52_0 @ X1292)|(epred51_0 @ (sub @ X1292 @ (push @ esk279_0 @ esk280_0)))|(pushprop_lem1v2))&(~(epred51_0 @ (sub @ X1292 @ (push @ esk279_0 @ esk280_0)))|(epred52_0 @ X1292)|(pushprop_lem1v2))))&(~(epred52_0 @ one)|(pushprop_lem1v2)))&((~(X1294 @ (esk281_4 @ X1293 @ X1294 @ X1295 @ X1296))|~(X1293 @ (sub @ (esk281_4 @ X1293 @ X1294 @ X1295 @ X1296) @ (push @ X1295 @ X1296)))|~(X1293 @ X1295)|(X1294 @ one)|~(pushprop_lem1v2))&((X1294 @ (esk281_4 @ X1293 @ X1294 @ X1295 @ X1296))|(X1293 @ (sub @ (esk281_4 @ X1293 @ X1294 @ X1295 @ X1296) @ (push @ X1295 @ X1296)))|~(X1293 @ X1295)|(X1294 @ one)|~(pushprop_lem1v2)))))&(((~(X1299 @ X1300)|(X1298 @ id @ X1300 @ id)|~(hoasinduction_p_and_p_prime @ X1298 @ X1299))&(~(X1298 @ id @ X1301 @ id)|(X1299 @ X1301)|~(hoasinduction_p_and_p_prime @ X1298 @ X1299)))&((~(X1303 @ (esk282_2 @ X1302 @ X1303))|~(X1302 @ id @ (esk282_2 @ X1302 @ X1303) @ id)|(hoasinduction_p_and_p_prime @ X1302 @ X1303))&((X1303 @ (esk282_2 @ X1302 @ X1303))|(X1302 @ id @ (esk282_2 @ X1302 @ X1303) @ id)|(hoasinduction_p_and_p_prime @ X1302 @ X1303)))))&((hoaslam @ X1305 @ X1306)=(d2term @ d_one)))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&(((d2subst @ X1307)!=(d2subst @ X1308))|((X1307)=(X1308))))&((X1309)=(d_id)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])])])). 0.31/0.88 thf(c_0_14, negated_conjecture, ~(((hoasinduction_lem3a)<=>![X81:subst > term > subst > $o]:((![X16:subst > term > term]:((![X8:subst, X7:term, X21:subst]:(((sub @ (X16 @ X8 @ X7) @ X21)=(X16 @ (comp @ X8 @ X21) @ (sub @ X7 @ X21))))=>(![X7:term]:(((X81 @ id @ X7 @ id)=>(X81 @ id @ (X16 @ id @ X7) @ id)))=>(X81 @ id @ (hoaslam @ id @ (^[Z0:subst, Z1:term]:(X16 @ Z0 @ Z1))) @ id))))=>![X7:term]:((![X12:term]:(((X81 @ id @ X12 @ id)=>(X81 @ id @ (sub @ X7 @ (push @ X12 @ id)) @ id)))=>(X81 @ id @ (lam @ X7) @ id))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_12])])). 0.31/0.88 thf(c_0_15, plain, ![X1:term]:(((X1)=(d2term @ (esk1_1 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_16, plain, ![X2:d_term]:(((X2)=(d_one))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_17, plain, ((one)=(d2term @ d_one)), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_18, negated_conjecture, ![X1311:subst > term > term, X1317:term, X1318:subst > term > subst > $o, X1320:subst, X1321:term, X1322:subst, X1323:term, X1324:term]:((((((epred53_0 @ id @ (esk286_1 @ X1311) @ id)|(epred53_0 @ id @ (hoaslam @ id @ X1311) @ id)|((sub @ (X1311 @ (esk283_1 @ X1311) @ (esk284_1 @ X1311)) @ (esk285_1 @ X1311))!=(X1311 @ (comp @ (esk283_1 @ X1311) @ (esk285_1 @ X1311)) @ (sub @ (esk284_1 @ X1311) @ (esk285_1 @ X1311))))|~(hoasinduction_lem3a))&(~(epred53_0 @ id @ (X1311 @ id @ (esk286_1 @ X1311)) @ id)|(epred53_0 @ id @ (hoaslam @ id @ X1311) @ id)|((sub @ (X1311 @ (esk283_1 @ X1311) @ (esk284_1 @ X1311)) @ (esk285_1 @ X1311))!=(X1311 @ (comp @ (esk283_1 @ X1311) @ (esk285_1 @ X1311)) @ (sub @ (esk284_1 @ X1311) @ (esk285_1 @ X1311))))|~(hoasinduction_lem3a)))&((~(epred53_0 @ id @ X1317 @ id)|(epred53_0 @ id @ (sub @ esk287_0 @ (push @ X1317 @ id)) @ id)|~(hoasinduction_lem3a))&(~(epred53_0 @ id @ (lam @ esk287_0) @ id)|~(hoasinduction_lem3a))))&((((X1318 @ id @ (esk289_2 @ X1318 @ X1324) @ id)|(X1318 @ id @ (lam @ X1324) @ id)|((sub @ (esk288_1 @ X1318 @ X1320 @ X1321) @ X1322)=(esk288_1 @ X1318 @ (comp @ X1320 @ X1322) @ (sub @ X1321 @ X1322)))|(hoasinduction_lem3a))&(~(X1318 @ id @ (sub @ X1324 @ (push @ (esk289_2 @ X1318 @ X1324) @ id)) @ id)|(X1318 @ id @ (lam @ X1324) @ id)|((sub @ (esk288_1 @ X1318 @ X1320 @ X1321) @ X1322)=(esk288_1 @ X1318 @ (comp @ X1320 @ X1322) @ (sub @ X1321 @ X1322)))|(hoasinduction_lem3a)))&((((X1318 @ id @ (esk289_2 @ X1318 @ X1324) @ id)|(X1318 @ id @ (lam @ X1324) @ id)|(~(X1318 @ id @ X1323 @ id)|(X1318 @ id @ (esk288_1 @ X1318 @ id @ X1323) @ id))|(hoasinduction_lem3a))&(~(X1318 @ id @ (sub @ X1324 @ (push @ (esk289_2 @ X1318 @ X1324) @ id)) @ id)|(X1318 @ id @ (lam @ X1324) @ id)|(~(X1318 @ id @ X1323 @ id)|(X1318 @ id @ (esk288_1 @ X1318 @ id @ X1323) @ id))|(hoasinduction_lem3a)))&(((X1318 @ id @ (esk289_2 @ X1318 @ X1324) @ id)|(X1318 @ id @ (lam @ X1324) @ id)|~(X1318 @ id @ (hoaslam @ id @ (esk288_1 @ X1318)) @ id)|(hoasinduction_lem3a))&(~(X1318 @ id @ (sub @ X1324 @ (push @ (esk289_2 @ X1318 @ X1324) @ id)) @ id)|(X1318 @ id @ (lam @ X1324) @ id)|~(X1318 @ id @ (hoaslam @ id @ (esk288_1 @ X1318)) @ id)|(hoasinduction_lem3a))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])])])). 0.31/0.88 thf(c_0_19, plain, ((laminj)|((esk114_0)!=(esk115_0))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_20, plain, ![X1:term]:(((one)=(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16]), c_0_17])). 0.31/0.88 thf(c_0_21, negated_conjecture, (~((epred53_0 @ id @ (lam @ esk287_0) @ id))|~((hoasinduction_lem3a))), inference(split_conjunct,[status(thm)],[c_0_18])). 0.31/0.88 thf(c_0_22, plain, ![X1:term, X7:term]:((((X1)=(X7))|~((laminj))|((lam @ X1)!=(lam @ X7)))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_23, plain, (laminj), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20]), c_0_20])])). 0.31/0.88 thf(c_0_24, plain, ![X5:subst]:(((X5)=(d2subst @ (esk2_1 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_25, plain, ![X6:d_subst]:(((X6)=(d_id))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_26, plain, ((id)=(d2subst @ d_id)), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_27, negated_conjecture, ![X1:term]:(((epred53_0 @ id @ (sub @ esk287_0 @ (push @ X1 @ id)) @ id)|~((epred53_0 @ id @ X1 @ id))|~((hoasinduction_lem3a)))), inference(split_conjunct,[status(thm)],[c_0_18])). 0.31/0.88 thf(c_0_28, negated_conjecture, (~((epred53_0 @ id @ one @ id))|~((hoasinduction_lem3a))), inference(rw,[status(thm)],[c_0_21, c_0_20])). 0.31/0.88 thf(c_0_29, plain, ((hoasinduction_lem3a)|~((epred38_0 @ id @ (lam @ esk164_0) @ id))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_30, negated_conjecture, ![X16:subst > term > term]:(((epred53_0 @ id @ (esk286_1 @ X16) @ id)|(epred53_0 @ id @ (hoaslam @ id @ X16) @ id)|((sub @ (X16 @ (esk283_1 @ X16) @ (esk284_1 @ X16)) @ (esk285_1 @ X16))!=(X16 @ (comp @ (esk283_1 @ X16) @ (esk285_1 @ X16)) @ (sub @ (esk284_1 @ X16) @ (esk285_1 @ X16))))|~((hoasinduction_lem3a)))), inference(split_conjunct,[status(thm)],[c_0_18])). 0.31/0.88 thf(c_0_31, plain, ![X1:term, X7:term]:(((X1)=(X7))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_20]), c_0_20]), c_0_23])])). 0.31/0.88 thf(c_0_32, plain, ![X5:subst]:(((id)=(X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25]), c_0_26])). 0.31/0.88 thf(c_0_33, negated_conjecture, ![X1:term]:((~((epred53_0 @ id @ X1 @ id))|~((hoasinduction_lem3a)))), inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_20]), c_0_20]), c_0_28])). 0.31/0.88 thf(c_0_34, plain, ![X1:term]:(((epred38_0 @ id @ (sub @ esk164_0 @ (push @ X1 @ id)) @ id)|(hoasinduction_lem3a)|~((epred38_0 @ id @ X1 @ id)))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_35, plain, ((hoasinduction_lem3a)|~((epred38_0 @ id @ one @ id))), inference(rw,[status(thm)],[c_0_29, c_0_20])). 0.31/0.88 thf(c_0_36, plain, ![X16:subst > term > term]:(((epred38_0 @ id @ (esk165_1 @ X16) @ id)|(epred38_0 @ id @ (lam @ (X16 @ sh @ one)) @ id)|(hoasinduction_lem3a)|((sub @ (X16 @ (esk166_1 @ X16) @ (esk167_1 @ X16)) @ (esk168_1 @ X16))!=(X16 @ (comp @ (esk166_1 @ X16) @ (esk168_1 @ X16)) @ (sub @ (esk167_1 @ X16) @ (esk168_1 @ X16)))))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.31/0.88 thf(c_0_37, negated_conjecture, ~((hoasinduction_lem3a)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31]), c_0_31]), c_0_32]), c_0_32]), c_0_32]), c_0_31]), c_0_32]), c_0_20]), c_0_31]), c_0_32]), c_0_31]), c_0_31]), c_0_32]), c_0_20])]), c_0_33])). 0.31/0.88 thf(c_0_38, plain, ![X1:term]:(((hoasinduction_lem3a)|~((epred38_0 @ id @ X1 @ id)))), inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_31]), c_0_32]), c_0_20]), c_0_35])). 0.31/0.88 thf(c_0_39, plain, (epred38_0 @ id @ one @ id), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_31]), c_0_20]), c_0_32]), c_0_32]), c_0_32]), c_0_31]), c_0_32]), c_0_20]), c_0_31]), c_0_32]), c_0_31]), c_0_31]), c_0_32]), c_0_20])]), c_0_37])). 0.31/0.88 thf(c_0_40, plain, ![X1:term]:(~((epred38_0 @ id @ X1 @ id))), inference(sr,[status(thm)],[c_0_38, c_0_37])). 0.31/0.88 thf(c_0_41, plain, ($false), inference(sr,[status(thm)],[c_0_39, c_0_40]), ['proof']). 0.31/0.88 % SZS output end CNFRefutation 0.31/0.88 % Parsed axioms : 132 0.31/0.88 % Removed by relevancy pruning/SinE : 0 0.31/0.88 % Initial clauses : 1381 0.31/0.88 % Removed in clause preprocessing : 130 0.31/0.88 % Initial clauses in saturation : 1251 0.31/0.88 % Processed clauses : 1421 0.31/0.88 % ...of these trivial : 784 0.31/0.88 % ...subsumed : 176 0.31/0.88 % ...remaining for further processing : 461 0.31/0.88 % Other redundant clauses eliminated : 0 0.31/0.88 % Clauses deleted for lack of memory : 0 0.31/0.88 % Backward-subsumed : 61 0.31/0.88 % Backward-rewritten : 91 0.31/0.88 % Generated clauses : 15 0.31/0.88 % ...of the previous two non-redundant : 59 0.31/0.88 % ...aggressively subsumed : 0 0.31/0.88 % Contextual simplify-reflections : 71 0.31/0.88 % Paramodulations : 14 0.31/0.88 % Factorizations : 0 0.31/0.88 % NegExts : 0 0.31/0.88 % Equation resolutions : 0 0.31/0.88 % Disequality decompositions : 0 0.31/0.88 % Total rewrite steps : 13927 0.31/0.88 % ...of those cached : 13248 0.31/0.88 % Propositional unsat checks : 0 0.31/0.88 % Propositional check models : 0 0.31/0.88 % Propositional check unsatisfiable : 0 0.31/0.88 % Propositional clauses : 0 0.31/0.88 % Propositional clauses after purity: 0 0.31/0.88 % Propositional unsat core size : 0 0.31/0.88 % Propositional preprocessing time : 0.000 0.31/0.88 % Propositional encoding time : 0.000 0.31/0.88 % Propositional solver time : 0.000 0.31/0.88 % Success case prop preproc time : 0.000 0.31/0.88 % Success case prop encoding time : 0.000 0.31/0.88 % Success case prop solver time : 0.000 0.31/0.88 % Current number of processed clauses : 113 0.31/0.88 % Positive orientable unit clauses : 94 0.31/0.88 % Positive unorientable unit clauses: 2 0.31/0.88 % Negative unit clauses : 8 0.31/0.88 % Non-unit-clauses : 9 0.31/0.88 % Current number of unprocessed clauses: 83 0.31/0.88 % ...number of literals in the above : 207 0.31/0.88 % Current number of archived formulas : 0 0.31/0.88 % Current number of archived clauses : 348 0.31/0.88 % Clause-clause subsumption calls (NU) : 18078 0.31/0.88 % Rec. Clause-clause subsumption calls : 9199 0.31/0.88 % Non-unit clause-clause subsumptions : 395 0.31/0.88 % Unit Clause-clause subsumption calls : 2148 0.31/0.88 % Rewrite failures with RHS unbound : 0 0.31/0.88 % BW rewrite match attempts : 1689 0.31/0.88 % BW rewrite match successes : 94 0.31/0.88 % Condensation attempts : 1422 0.31/0.88 % Condensation successes : 129 0.31/0.88 % Termbank termtop insertions : 148185 0.31/0.88 % Search garbage collected termcells : 25120 0.31/0.88 0.31/0.88 % ------------------------------------------------- 0.31/0.88 % User time : 0.273 s 0.31/0.88 % System time : 0.023 s 0.31/0.88 % Total time : 0.296 s 0.31/0.88 % Maximum resident set size: 8088 pages 0.31/0.88 0.31/0.88 % ------------------------------------------------- 0.31/0.88 % User time : 0.829 s 0.31/0.88 % System time : 0.075 s 0.31/0.88 % Total time : 0.904 s 0.31/0.88 % Maximum resident set size: 5120 pages 0.31/0.88 % E exiting 0.31/0.88 EOF