0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.11/0.38 % Computer : n017.cluster.edu 0.11/0.38 % Model : x86_64 x86_64 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.38 % Memory : 8046.5625MB 0.11/0.38 % OS : Linux 6.8.0-71-generic 0.11/0.38 % CPULimit : 1440 0.11/0.38 % WCLimit : 180 0.11/0.38 % DateTime : Mon Jul 27 12:42:07 UTC 2026 0.11/0.38 % CPUTime : 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.11/0.43 Running higher-order theorem proving 0.18/0.47 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.MnTs4411x6/E---3.1_1376801.p 0.62/0.79 % Version: 3.5.1-ho 0.62/0.79 % partial match(1): HSLMSLSMSSSNHSA 0.62/0.79 % Preprocessing class: HSLMSLSSSSSNHSA. 0.62/0.79 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.62/0.79 % Starting new_ho_10 with 360s (2) cores 0.62/0.79 % Starting sh3 with 360s (2) cores 0.62/0.79 % Starting ho_unfolding_3 with 360s (2) cores 0.62/0.79 % Starting new_ho_10_cnf2 with 360s (2) cores 0.62/0.79 % ho_unfolding_3 with pid 1376816 completed with status 0 0.62/0.79 % Result found by ho_unfolding_3 0.62/0.79 % partial match(1): HSLMSLSMSSSNHSA 0.62/0.79 % Preprocessing class: HSLMSLSSSSSNHSA. 0.62/0.79 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.62/0.79 % Starting new_ho_10 with 360s (2) cores 0.62/0.79 % Starting sh3 with 360s (2) cores 0.62/0.79 % Starting ho_unfolding_3 with 360s (2) cores 0.62/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 0.62/0.79 % No SInE strategy applied 0.62/0.79 % Search class: HGHSM-SMLM31-MHSFFMBN 0.62/0.79 % partial match(1): HGHSM-SMLM31-MHSFFSBN 0.62/0.79 % Scheduled 7 strats onto 2 cores with 360 seconds (360 total) 0.62/0.79 % Starting SubtermCWHack with 33s (1) cores 0.62/0.79 % Starting ho_unfolding_3 with 37s (1) cores 0.62/0.79 % ho_unfolding_3 with pid 1376819 completed with status 0 0.62/0.79 % Result found by ho_unfolding_3 0.62/0.79 % partial match(1): HSLMSLSMSSSNHSA 0.62/0.79 % Preprocessing class: HSLMSLSSSSSNHSA. 0.62/0.79 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.62/0.79 % Starting new_ho_10 with 360s (2) cores 0.62/0.79 % Starting sh3 with 360s (2) cores 0.62/0.79 % Starting ho_unfolding_3 with 360s (2) cores 0.62/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 0.62/0.79 % No SInE strategy applied 0.62/0.79 % Search class: HGHSM-SMLM31-MHSFFMBN 0.62/0.79 % partial match(1): HGHSM-SMLM31-MHSFFSBN 0.62/0.79 % Scheduled 7 strats onto 2 cores with 360 seconds (360 total) 0.62/0.79 % Starting SubtermCWHack with 33s (1) cores 0.62/0.79 % Starting ho_unfolding_3 with 37s (1) cores 0.62/0.79 % Preprocessing time : 0.051 s 0.62/0.79 % Presaturation interreduction done 0.62/0.79 0.62/0.79 % Proof found! 0.62/0.79 % SZS status Theorem 0.62/0.79 % SZS output start CNFRefutation 0.62/0.79 thf(decl_sort1, type, term: $tType). 0.62/0.79 thf(decl_sort2, type, subst: $tType). 0.62/0.79 thf(decl_sort3, type, d_term: $tType). 0.62/0.79 thf(decl_sort4, type, d_subst: $tType). 0.62/0.79 thf(decl_23, type, one: term). 0.62/0.79 thf(decl_24, type, ap: term > term > term). 0.62/0.79 thf(decl_25, type, lam: term > term). 0.62/0.79 thf(decl_26, type, sub: term > subst > term). 0.62/0.79 thf(decl_27, type, id: subst). 0.62/0.79 thf(decl_28, type, sh: subst). 0.62/0.79 thf(decl_29, type, push: term > subst > subst). 0.62/0.79 thf(decl_30, type, comp: subst > subst > subst). 0.62/0.79 thf(decl_31, type, var: term > $o). 0.62/0.79 thf(decl_32, type, pushprop_lem1v2: $o). 0.62/0.79 thf(decl_33, type, pushprop_lem1_gthm: $o). 0.62/0.79 thf(decl_34, type, axmap: $o). 0.62/0.79 thf(decl_35, type, pushprop_lem0_gthm: $o). 0.62/0.79 thf(decl_36, type, shinj: $o). 0.62/0.79 thf(decl_37, type, hoasinduction_lem1v2: $o). 0.62/0.79 thf(decl_38, type, hoasinduction_lem1v2_gthm: $o). 0.62/0.79 thf(decl_39, type, hoasap: subst > term > subst > term > term). 0.62/0.79 thf(decl_40, type, induction2lem: $o). 0.62/0.79 thf(decl_41, type, hoasinduction_lem3v2_f: $o). 0.62/0.79 thf(decl_42, type, axvarshift: $o). 0.62/0.79 thf(decl_43, type, hoasapinj2: $o). 0.62/0.79 thf(decl_44, type, hoasapnotvar_gthm: $o). 0.62/0.79 thf(decl_45, type, hoasapinj1: $o). 0.62/0.79 thf(decl_46, type, ulamvar1: $o). 0.62/0.79 thf(decl_47, type, induction2lem_lthm: $o). 0.62/0.79 thf(decl_48, type, hoasinduction_lem3v2_gthm: $o). 0.62/0.79 thf(decl_49, type, apnotvar: $o). 0.62/0.79 thf(decl_50, type, pushprop_lthm_orig: $o). 0.62/0.79 thf(decl_51, type, hoasinduction_lem3v2_f_lthm: $o). 0.62/0.79 thf(decl_52, type, hoasinduction_lthm: $o). 0.62/0.79 thf(decl_53, type, hoasinduction_no_psi_cond_lthm: $o). 0.62/0.79 thf(decl_54, type, hoaslaminj: $o). 0.62/0.79 thf(decl_55, type, hoasinduction_lem3aaa: $o). 0.62/0.79 thf(decl_56, type, induction2lem_gthm: $o). 0.62/0.79 thf(decl_57, type, hoasinduction_lem3aa_lthm: $o). 0.62/0.79 thf(decl_58, type, hoasinduction_lem3: $o). 0.62/0.79 thf(decl_59, type, hoasinduction_lem2: $o). 0.62/0.79 thf(decl_60, type, termmset_lthm: $o). 0.62/0.79 thf(decl_61, type, hoasinduction_lem1: $o). 0.62/0.79 thf(decl_62, type, hoaslamnotap_lthm: $o). 0.62/0.79 thf(decl_63, type, pushprop_lem1v2_lthm: $o). 0.62/0.79 thf(decl_64, type, hoasapnotvar: $o). 0.62/0.79 thf(decl_65, type, hoasinduction_lem0: $o). 0.62/0.79 thf(decl_66, type, hoasinduction: $o). 0.62/0.79 thf(decl_67, type, hoasinduction_gthm: $o). 0.62/0.79 thf(decl_68, type, axapp: $o). 0.62/0.79 thf(decl_69, type, hoaslamnotvar_lthm: $o). 0.62/0.79 thf(decl_70, type, pushprop_lem3v2_lthm: $o). 0.62/0.79 thf(decl_71, type, hoasinduction_lem3b_lthm: $o). 0.62/0.79 thf(decl_72, type, ulamvarind: $o). 0.62/0.79 thf(decl_73, type, induction: $o). 0.62/0.79 thf(decl_74, type, hoasinduction_lem3a_lthm: $o). 0.62/0.79 thf(decl_75, type, termmset_gthm: $o). 0.62/0.79 thf(decl_76, type, hoasinduction_lem3aa: $o). 0.62/0.79 thf(decl_77, type, pushprop_lem1v2_gthm: $o). 0.62/0.79 thf(decl_78, type, hoaslamnotap_gthm: $o). 0.62/0.79 thf(decl_79, type, hoaslamnotvar_gthm: $o). 0.62/0.79 thf(decl_80, type, hoasinduction_lem3b_gthm: $o). 0.62/0.79 thf(decl_81, type, pushprop_lem2v2: $o). 0.62/0.79 thf(decl_82, type, hoasinduction_lem3a_gthm: $o). 0.62/0.79 thf(decl_83, type, axclos: $o). 0.62/0.79 thf(decl_84, type, axassoc: $o). 0.62/0.79 thf(decl_85, type, hoasinduction_lem2v2: $o). 0.62/0.79 thf(decl_86, type, pushprop_lthm: $o). 0.62/0.79 thf(decl_87, type, apinj2: $o). 0.62/0.79 thf(decl_88, type, apinj1: $o). 0.62/0.79 thf(decl_89, type, hoasapinj2_lthm: $o). 0.62/0.79 thf(decl_90, type, hoasinduction_lem3v2a: $o). 0.62/0.79 thf(decl_91, type, hoasapinj1_lthm: $o). 0.62/0.79 thf(decl_92, type, hoaslaminj_lthm: $o). 0.62/0.79 thf(decl_93, type, axvarcons: $o). 0.62/0.79 thf(decl_94, type, hoaslam: subst > (subst > term > term) > term). 0.62/0.79 thf(decl_95, type, axscons: $o). 0.62/0.79 thf(decl_96, type, hoasinduction_lem2v2_gthm: $o). 0.62/0.79 thf(decl_97, type, axidr: $o). 0.62/0.79 thf(decl_98, type, pushprop_lem1: $o). 0.62/0.79 thf(decl_99, type, laminj: $o). 0.62/0.79 thf(decl_100, type, hoasinduction_lem3_lthm: $o). 0.62/0.79 thf(decl_101, type, pushprop_lem0: $o). 0.62/0.79 thf(decl_102, type, pushprop_gthm: $o). 0.62/0.79 thf(decl_103, type, axabs: $o). 0.62/0.79 thf(decl_104, type, hoasinduction_lem3v2a_lthm: $o). 0.62/0.79 thf(decl_105, type, hoasinduction_lem2_lthm: $o). 0.62/0.79 thf(decl_106, type, hoasapinj2_gthm: $o). 0.62/0.79 thf(decl_107, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o). 0.62/0.79 thf(decl_108, type, hoasinduction_lem1_lthm: $o). 0.62/0.79 thf(decl_109, type, lamnotap: $o). 0.62/0.79 thf(decl_110, type, hoasapinj1_gthm: $o). 0.62/0.79 thf(decl_111, type, hoaslamnotvar: $o). 0.62/0.79 thf(decl_112, type, axidl: $o). 0.62/0.79 thf(decl_113, type, hoaslaminj_gthm: $o). 0.62/0.79 thf(decl_114, type, induction2_lthm: $o). 0.62/0.79 thf(decl_115, type, hoasinduction_lem0_lthm: $o). 0.62/0.79 thf(decl_116, type, substmonoid_lthm: $o). 0.62/0.79 thf(decl_117, type, pushprop: $o). 0.62/0.79 thf(decl_118, type, hoasinduction_lem3_gthm: $o). 0.62/0.79 thf(decl_119, type, hoasinduction_lem2_gthm: $o). 0.62/0.79 thf(decl_120, type, hoasinduction_lem3b: $o). 0.62/0.79 thf(decl_121, type, substmonoid: $o). 0.62/0.79 thf(decl_122, type, lamnotvar: $o). 0.62/0.79 thf(decl_123, type, hoasinduction_lem3a: $o). 0.62/0.79 thf(decl_124, type, hoasinduction_lem1_gthm: $o). 0.62/0.79 thf(decl_125, type, hoasinduction_no_psi_cond: $o). 0.62/0.79 thf(decl_126, type, induction2_gthm: $o). 0.62/0.79 thf(decl_127, type, pushprop_lem2v2_lthm: $o). 0.62/0.79 thf(decl_128, type, hoasvar: subst > term > subst > $o). 0.62/0.79 thf(decl_129, type, hoaslamnotap: $o). 0.62/0.79 thf(decl_130, type, substmonoid_gthm: $o). 0.62/0.79 thf(decl_131, type, ulamvarsh: $o). 0.62/0.79 thf(decl_132, type, induction2: $o). 0.62/0.79 thf(decl_133, type, pushprop_lem3v2: $o). 0.62/0.79 thf(decl_134, type, pushprop_lem2v2_gthm: $o). 0.62/0.79 thf(decl_135, type, pushprop_lem1_lthm: $o). 0.62/0.79 thf(decl_136, type, hoasinduction_lem3v2: $o). 0.62/0.79 thf(decl_137, type, axshiftcons: $o). 0.62/0.79 thf(decl_138, type, termmset: $o). 0.62/0.79 thf(decl_139, type, pushprop_lem0_lthm: $o). 0.62/0.79 thf(decl_140, type, hoasapnotvar_lthm: $o). 0.62/0.79 thf(decl_141, type, hoasinduction_lem3v2_lthm: $o). 0.62/0.79 thf(decl_142, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o). 0.62/0.79 thf(decl_143, type, axvarid: $o). 0.62/0.79 thf(decl_144, type, hoasinduction_lthm_3: $o). 0.62/0.79 thf(decl_145, type, d2term: d_term > term). 0.62/0.79 thf(decl_146, type, d2subst: d_subst > subst). 0.62/0.79 thf(decl_147, type, d_one: d_term). 0.62/0.79 thf(decl_148, type, d_id: d_subst). 0.62/0.79 thf(decl_149, type, epred1_0: $o). 0.62/0.79 thf(decl_150, type, epred2_2: (subst > term > subst > $o) > term > $o). 0.62/0.79 thf(decl_151, type, epred3_0: $o). 0.62/0.79 thf(decl_153, type, epred5_0: $o). 0.62/0.79 thf(decl_154, type, epred6_3: term > (subst > term > subst > $o) > (term > $o) > $o). 0.62/0.79 thf(decl_155, type, epred7_0: $o). 0.62/0.79 thf(decl_156, type, epred8_0: $o). 0.62/0.79 thf(decl_159, type, epred11_0: $o). 0.62/0.79 thf(decl_160, type, epred12_0: $o). 0.62/0.79 thf(decl_161, type, esk1_4: (term > $o) > (term > $o) > term > subst > term). 0.62/0.79 thf(decl_162, type, epred13_0: term > $o). 0.62/0.79 thf(decl_163, type, epred14_0: term > $o). 0.62/0.79 thf(decl_164, type, esk2_0: term). 0.62/0.79 thf(decl_165, type, esk3_0: subst). 0.62/0.79 thf(decl_166, type, esk4_3: (term > $o) > term > subst > term). 0.62/0.79 thf(decl_167, type, esk5_3: (term > $o) > term > subst > term). 0.62/0.79 thf(decl_168, type, esk6_3: (term > $o) > term > subst > term). 0.62/0.79 thf(decl_169, type, esk7_1: (term > $o) > term). 0.62/0.79 thf(decl_170, type, epred15_0: term > $o). 0.62/0.79 thf(decl_171, type, esk8_0: term). 0.62/0.79 thf(decl_172, type, esk9_0: subst). 0.62/0.79 thf(decl_173, type, esk10_1: term > term). 0.62/0.79 thf(decl_174, type, esk11_0: term). 0.62/0.79 thf(decl_175, type, esk12_0: term). 0.62/0.79 thf(decl_176, type, esk13_0: term). 0.62/0.79 thf(decl_177, type, esk14_0: term). 0.62/0.79 thf(decl_178, type, esk15_0: term). 0.62/0.79 thf(decl_179, type, esk16_0: term). 0.62/0.79 thf(decl_180, type, esk17_0: term). 0.62/0.79 thf(decl_181, type, esk18_0: term). 0.62/0.79 thf(decl_182, type, esk19_1: term > subst > term > term). 0.62/0.79 thf(decl_183, type, esk20_0: term). 0.62/0.79 thf(decl_184, type, esk21_1: (subst > term > term) > term). 0.62/0.79 thf(decl_185, type, esk22_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_186, type, epred16_0: subst > term > subst > $o). 0.62/0.79 thf(decl_187, type, esk23_1: (term > $o) > term). 0.62/0.79 thf(decl_188, type, epred17_0: term > $o). 0.62/0.79 thf(decl_189, type, esk24_0: term). 0.62/0.79 thf(decl_190, type, esk25_1: term > term). 0.62/0.79 thf(decl_191, type, esk26_0: term). 0.62/0.79 thf(decl_192, type, epred18_1: (subst > term > subst > $o) > term > $o). 0.62/0.79 thf(decl_193, type, esk27_1: (term > $o) > term). 0.62/0.79 thf(decl_194, type, esk28_1: (term > $o) > term). 0.62/0.79 thf(decl_195, type, esk29_1: (term > $o) > term). 0.62/0.79 thf(decl_196, type, esk30_1: (term > $o) > term). 0.62/0.79 thf(decl_197, type, epred19_0: subst > term > subst > $o). 0.62/0.79 thf(decl_198, type, esk31_0: term). 0.62/0.79 thf(decl_199, type, esk32_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_200, type, esk33_1: (subst > term > term) > term). 0.62/0.79 thf(decl_201, type, esk34_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_202, type, esk35_1: (subst > term > term) > term). 0.62/0.79 thf(decl_203, type, esk36_2: (subst > term > subst > $o) > term > term). 0.62/0.79 thf(decl_204, type, esk37_1: (subst > term > subst > $o) > subst > term > term). 0.62/0.79 thf(decl_205, type, epred20_1: (subst > term > subst > $o) > term > $o). 0.62/0.79 thf(decl_206, type, epred21_0: subst > term > subst > $o). 0.62/0.79 thf(decl_207, type, esk38_1: (term > $o) > term). 0.62/0.79 thf(decl_208, type, esk39_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_209, type, epred22_0: subst > term > subst > $o). 0.62/0.79 thf(decl_210, type, esk40_0: term). 0.62/0.79 thf(decl_211, type, esk41_1: term > subst > term > term). 0.62/0.79 thf(decl_212, type, esk42_0: term). 0.62/0.79 thf(decl_213, type, epred23_0: subst > term > subst > $o). 0.62/0.79 thf(decl_214, type, epred24_0: term > $o). 0.62/0.79 thf(decl_215, type, esk43_0: term). 0.62/0.79 thf(decl_216, type, esk44_0: term). 0.62/0.79 thf(decl_217, type, esk45_4: (subst > term > subst > $o) > (term > $o) > term > term > subst). 0.62/0.79 thf(decl_218, type, esk46_4: (subst > term > subst > $o) > (term > $o) > term > term > term). 0.62/0.79 thf(decl_219, type, esk47_4: (subst > term > subst > $o) > (term > $o) > term > term > subst). 0.62/0.79 thf(decl_220, type, esk48_4: (subst > term > subst > $o) > (term > $o) > term > term > subst). 0.62/0.79 thf(decl_221, type, esk49_2: (subst > term > subst > $o) > (term > $o) > term). 0.62/0.79 thf(decl_222, type, esk50_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_223, type, esk51_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_224, type, esk52_1: (subst > term > subst > $o) > subst). 0.62/0.79 thf(decl_225, type, esk53_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_226, type, esk54_1: (subst > term > subst > $o) > subst). 0.62/0.79 thf(decl_227, type, esk55_1: (subst > term > subst > $o) > subst). 0.62/0.79 thf(decl_228, type, esk56_0: term). 0.62/0.79 thf(decl_229, type, esk57_0: term). 0.62/0.79 thf(decl_230, type, esk58_0: term). 0.62/0.79 thf(decl_231, type, esk59_0: term). 0.62/0.79 thf(decl_232, type, esk60_0: term). 0.62/0.79 thf(decl_233, type, esk61_0: term). 0.62/0.79 thf(decl_234, type, esk62_0: term). 0.62/0.79 thf(decl_235, type, esk63_0: term). 0.62/0.79 thf(decl_236, type, esk64_0: term). 0.62/0.79 thf(decl_237, type, esk65_0: term). 0.62/0.79 thf(decl_238, type, esk66_0: term). 0.62/0.79 thf(decl_239, type, esk67_0: term). 0.62/0.79 thf(decl_240, type, esk68_0: term). 0.62/0.79 thf(decl_241, type, esk69_0: term). 0.62/0.79 thf(decl_242, type, epred25_0: term > $o). 0.62/0.79 thf(decl_243, type, esk70_0: term). 0.62/0.79 thf(decl_244, type, esk71_0: subst). 0.62/0.79 thf(decl_245, type, esk72_1: (term > $o) > term). 0.62/0.79 thf(decl_246, type, epred26_3: (term > $o) > term > subst > term > $o). 0.62/0.79 thf(decl_247, type, esk73_0: term). 0.62/0.79 thf(decl_248, type, esk74_1: (subst > term > term) > term). 0.62/0.79 thf(decl_249, type, esk75_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_250, type, esk76_0: term). 0.62/0.79 thf(decl_251, type, esk77_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term). 0.62/0.79 thf(decl_252, type, esk78_3: (subst > term > subst > $o) > (term > $o) > term > term). 0.62/0.79 thf(decl_253, type, esk79_3: (subst > term > subst > $o) > (term > $o) > term > term). 0.62/0.79 thf(decl_254, type, esk80_1: term > subst > term > term). 0.62/0.79 thf(decl_255, type, epred27_0: subst > term > subst > $o). 0.62/0.79 thf(decl_256, type, epred28_0: term > $o). 0.62/0.79 thf(decl_257, type, esk81_0: term). 0.62/0.79 thf(decl_258, type, esk82_1: (subst > term > term) > term). 0.62/0.79 thf(decl_259, type, esk83_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_260, type, esk84_1: (subst > term > term) > term). 0.62/0.79 thf(decl_261, type, esk85_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_262, type, esk86_0: term). 0.62/0.79 thf(decl_263, type, esk87_0: term). 0.62/0.79 thf(decl_264, type, esk88_1: term > subst > term > term). 0.62/0.79 thf(decl_265, type, epred29_0: subst > term > subst > $o). 0.62/0.79 thf(decl_266, type, esk89_0: term). 0.62/0.79 thf(decl_267, type, esk90_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_268, type, esk91_1: (subst > term > term) > term). 0.62/0.79 thf(decl_269, type, esk92_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_270, type, esk93_1: (subst > term > term) > term). 0.62/0.79 thf(decl_271, type, esk94_2: (subst > term > subst > $o) > term > term). 0.62/0.79 thf(decl_272, type, esk95_1: (subst > term > subst > $o) > subst > term > term). 0.62/0.79 thf(decl_273, type, esk96_0: subst > term > term). 0.62/0.79 thf(decl_274, type, esk97_0: term). 0.62/0.79 thf(decl_275, type, esk98_0: term). 0.62/0.79 thf(decl_276, type, esk99_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_277, type, esk100_1: (subst > term > term) > term). 0.62/0.79 thf(decl_278, type, esk101_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_279, type, esk102_1: (term > $o) > term). 0.62/0.79 thf(decl_280, type, esk103_1: (term > $o) > term). 0.62/0.79 thf(decl_281, type, esk104_1: (term > $o) > term). 0.62/0.79 thf(decl_282, type, esk105_1: (term > $o) > term). 0.62/0.79 thf(decl_283, type, epred30_0: term > $o). 0.62/0.79 thf(decl_284, type, esk106_0: term). 0.62/0.79 thf(decl_285, type, esk107_1: term > term). 0.62/0.79 thf(decl_286, type, esk108_0: term). 0.62/0.79 thf(decl_287, type, epred31_0: subst > term > subst > $o). 0.62/0.79 thf(decl_288, type, esk109_1: (term > $o) > term). 0.62/0.79 thf(decl_289, type, epred32_1: (subst > term > subst > $o) > term > $o). 0.62/0.79 thf(decl_290, type, esk110_0: term). 0.62/0.79 thf(decl_291, type, epred33_0: subst > term > subst > $o). 0.62/0.79 thf(decl_292, type, epred34_0: term > $o). 0.62/0.79 thf(decl_293, type, esk111_0: term). 0.62/0.79 thf(decl_294, type, esk112_0: term). 0.62/0.79 thf(decl_295, type, epred35_3: (term > $o) > term > subst > term > $o). 0.62/0.79 thf(decl_296, type, epred36_0: term > $o). 0.62/0.79 thf(decl_297, type, esk113_0: term). 0.62/0.79 thf(decl_298, type, esk114_0: subst). 0.62/0.79 thf(decl_299, type, esk115_1: (term > $o) > term). 0.62/0.79 thf(decl_300, type, esk116_0: term). 0.62/0.79 thf(decl_301, type, esk117_0: subst). 0.62/0.79 thf(decl_302, type, esk118_0: term). 0.62/0.79 thf(decl_303, type, esk119_0: subst). 0.62/0.79 thf(decl_304, type, esk120_0: term). 0.62/0.79 thf(decl_305, type, esk121_0: subst). 0.62/0.79 thf(decl_306, type, epred37_0: term > $o). 0.62/0.79 thf(decl_307, type, epred38_0: term > $o). 0.62/0.79 thf(decl_308, type, esk122_0: term). 0.62/0.79 thf(decl_309, type, esk123_0: subst). 0.62/0.79 thf(decl_310, type, esk124_0: term). 0.62/0.79 thf(decl_311, type, esk125_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_312, type, esk126_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_313, type, esk127_1: (subst > term > subst > $o) > subst > term > term). 0.62/0.79 thf(decl_314, type, epred39_0: subst > term > subst > $o). 0.62/0.79 thf(decl_315, type, esk128_0: term). 0.62/0.79 thf(decl_316, type, esk129_1: (subst > term > term) > term). 0.62/0.79 thf(decl_317, type, esk130_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_318, type, esk131_1: (subst > term > term) > term). 0.62/0.79 thf(decl_319, type, esk132_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_320, type, esk133_0: subst). 0.62/0.79 thf(decl_321, type, esk134_0: subst). 0.62/0.79 thf(decl_322, type, esk135_0: subst). 0.62/0.79 thf(decl_323, type, esk136_0: subst). 0.62/0.79 thf(decl_324, type, esk137_0: subst). 0.62/0.79 thf(decl_325, type, esk138_0: subst). 0.62/0.79 thf(decl_326, type, epred40_1: (subst > term > subst > $o) > term > $o). 0.62/0.79 thf(decl_327, type, epred41_0: subst > term > subst > $o). 0.62/0.79 thf(decl_328, type, esk139_1: (term > $o) > term). 0.62/0.79 thf(decl_329, type, esk140_0: subst). 0.62/0.79 thf(decl_330, type, esk141_0: term). 0.62/0.79 thf(decl_331, type, epred42_0: term > $o). 0.62/0.79 thf(decl_332, type, epred43_0: term > $o). 0.62/0.79 thf(decl_333, type, esk142_0: term). 0.62/0.79 thf(decl_334, type, esk143_0: subst). 0.62/0.79 thf(decl_335, type, esk144_0: term). 0.62/0.79 thf(decl_336, type, esk145_0: subst). 0.62/0.79 thf(decl_337, type, esk146_0: subst). 0.62/0.79 thf(decl_338, type, esk147_0: term). 0.62/0.79 thf(decl_339, type, esk148_0: subst). 0.62/0.79 thf(decl_340, type, esk149_0: term). 0.62/0.79 thf(decl_341, type, esk150_0: subst). 0.62/0.79 thf(decl_342, type, esk151_0: term). 0.62/0.79 thf(decl_343, type, esk152_0: subst). 0.62/0.79 thf(decl_344, type, esk153_0: term). 0.62/0.79 thf(decl_345, type, esk154_0: term). 0.62/0.79 thf(decl_346, type, esk155_2: (subst > term > term) > (subst > term > term) > subst). 0.62/0.79 thf(decl_347, type, esk156_2: (subst > term > term) > (subst > term > term) > term). 0.62/0.79 thf(decl_348, type, esk157_2: (subst > term > term) > (subst > term > term) > subst). 0.62/0.79 thf(decl_349, type, esk158_2: (subst > term > term) > (subst > term > term) > subst). 0.62/0.79 thf(decl_350, type, esk159_2: (subst > term > term) > (subst > term > term) > term). 0.62/0.79 thf(decl_351, type, esk160_2: (subst > term > term) > (subst > term > term) > subst). 0.62/0.79 thf(decl_352, type, esk161_0: subst > term > term). 0.62/0.79 thf(decl_353, type, esk162_0: subst > term > term). 0.62/0.79 thf(decl_354, type, esk163_0: subst). 0.62/0.79 thf(decl_355, type, esk164_0: term). 0.62/0.79 thf(decl_356, type, esk165_0: term). 0.62/0.79 thf(decl_357, type, esk166_0: term). 0.62/0.79 thf(decl_358, type, esk167_0: term). 0.62/0.79 thf(decl_359, type, esk168_0: term). 0.62/0.79 thf(decl_360, type, esk169_0: term). 0.62/0.79 thf(decl_361, type, esk170_0: term). 0.62/0.79 thf(decl_362, type, esk171_0: term). 0.62/0.79 thf(decl_363, type, esk172_0: term). 0.62/0.79 thf(decl_364, type, esk173_0: term). 0.62/0.79 thf(decl_365, type, esk174_3: (subst > term > subst > $o) > (term > $o) > term > term). 0.62/0.79 thf(decl_366, type, esk175_2: (subst > term > subst > $o) > (term > $o) > term). 0.62/0.79 thf(decl_367, type, esk176_1: (subst > term > subst > $o) > subst > term > term). 0.62/0.79 thf(decl_368, type, epred44_0: subst > term > subst > $o). 0.62/0.79 thf(decl_369, type, epred45_0: term > $o). 0.62/0.79 thf(decl_370, type, esk177_0: term). 0.62/0.79 thf(decl_371, type, esk178_1: (subst > term > term) > term). 0.62/0.79 thf(decl_372, type, esk179_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_373, type, esk180_1: (subst > term > term) > term). 0.62/0.79 thf(decl_374, type, esk181_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_375, type, esk182_0: term). 0.62/0.79 thf(decl_376, type, esk183_0: term). 0.62/0.79 thf(decl_377, type, esk184_0: term). 0.62/0.79 thf(decl_378, type, esk185_0: term). 0.62/0.79 thf(decl_379, type, epred46_0: subst > term > subst > $o). 0.62/0.79 thf(decl_380, type, esk186_0: term). 0.62/0.79 thf(decl_381, type, esk187_1: (subst > term > term) > term). 0.62/0.79 thf(decl_382, type, esk188_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_383, type, esk189_1: (subst > term > term) > term). 0.62/0.79 thf(decl_384, type, esk190_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_385, type, esk191_2: (subst > term > subst > $o) > term > subst > term > term). 0.62/0.79 thf(decl_386, type, esk192_2: (subst > term > subst > $o) > term > term). 0.62/0.79 thf(decl_387, type, esk193_0: term). 0.62/0.79 thf(decl_388, type, epred47_0: subst > term > subst > $o). 0.62/0.79 thf(decl_389, type, esk194_0: term). 0.62/0.79 thf(decl_390, type, esk195_1: (subst > term > term) > term). 0.62/0.79 thf(decl_391, type, esk196_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_392, type, esk197_1: (subst > term > term) > term). 0.62/0.79 thf(decl_393, type, esk198_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_394, type, esk199_2: (subst > term > subst > $o) > term > term). 0.62/0.79 thf(decl_395, type, esk200_1: (subst > term > subst > $o) > subst > term > term). 0.62/0.79 thf(decl_396, type, esk201_2: (subst > term > subst > $o) > term > term). 0.62/0.79 thf(decl_397, type, esk202_1: (subst > term > subst > $o) > subst > term > term). 0.62/0.79 thf(decl_398, type, epred48_0: subst > term > subst > $o). 0.62/0.79 thf(decl_399, type, esk203_0: term). 0.62/0.79 thf(decl_400, type, esk204_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_401, type, esk205_1: (subst > term > term) > term). 0.62/0.79 thf(decl_402, type, esk206_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_403, type, esk207_1: (subst > term > term) > term). 0.62/0.79 thf(decl_404, type, epred49_0: term > $o). 0.62/0.79 thf(decl_405, type, esk208_0: term). 0.62/0.79 thf(decl_406, type, esk209_1: (term > $o) > term). 0.62/0.79 thf(decl_407, type, esk210_1: (term > $o) > term). 0.62/0.79 thf(decl_408, type, esk211_1: (term > $o) > term). 0.62/0.79 thf(decl_409, type, esk212_1: (term > $o) > term). 0.62/0.79 thf(decl_410, type, epred50_0: term > $o). 0.62/0.79 thf(decl_411, type, epred51_0: term > $o). 0.62/0.79 thf(decl_412, type, esk213_0: term). 0.62/0.79 thf(decl_413, type, esk214_0: subst). 0.62/0.79 thf(decl_414, type, esk215_0: term). 0.62/0.79 thf(decl_415, type, esk216_0: subst). 0.62/0.79 thf(decl_416, type, esk217_4: (term > $o) > (term > $o) > term > subst > term). 0.62/0.79 thf(decl_417, type, epred52_0: subst > term > subst > $o). 0.62/0.79 thf(decl_418, type, esk218_0: term). 0.62/0.79 thf(decl_419, type, esk219_0: term). 0.62/0.79 thf(decl_420, type, esk220_3: (subst > term > subst > $o) > term > term > subst). 0.62/0.79 thf(decl_421, type, esk221_3: (subst > term > subst > $o) > term > term > term). 0.62/0.79 thf(decl_422, type, esk222_3: (subst > term > subst > $o) > term > term > subst). 0.62/0.79 thf(decl_423, type, esk223_3: (subst > term > subst > $o) > term > term > subst). 0.62/0.79 thf(decl_424, type, esk224_3: (subst > term > subst > $o) > term > term > subst). 0.62/0.79 thf(decl_425, type, esk225_3: (subst > term > subst > $o) > term > term > term). 0.62/0.79 thf(decl_426, type, esk226_3: (subst > term > subst > $o) > term > term > subst). 0.62/0.79 thf(decl_427, type, esk227_3: (subst > term > subst > $o) > term > term > subst). 0.62/0.79 thf(decl_428, type, esk228_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_429, type, esk229_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_430, type, epred53_0: subst > term > subst > $o). 0.62/0.79 thf(decl_431, type, esk230_0: term). 0.62/0.79 thf(decl_432, type, esk231_1: (subst > term > term) > term). 0.62/0.79 thf(decl_433, type, esk232_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_434, type, esk233_1: (subst > term > term) > term). 0.62/0.79 thf(decl_435, type, esk234_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_436, type, esk235_2: (subst > term > subst > $o) > term > subst). 0.62/0.79 thf(decl_437, type, esk236_2: (subst > term > subst > $o) > term > term). 0.62/0.79 thf(decl_438, type, esk237_2: (subst > term > subst > $o) > term > subst). 0.62/0.79 thf(decl_439, type, esk238_2: (subst > term > subst > $o) > term > subst). 0.62/0.79 thf(decl_440, type, esk239_2: (subst > term > subst > $o) > term > term). 0.62/0.79 thf(decl_441, type, esk240_1: (subst > term > subst > $o) > subst > term > term). 0.62/0.79 thf(decl_442, type, esk241_1: (subst > term > subst > $o) > subst). 0.62/0.79 thf(decl_443, type, esk242_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_444, type, esk243_1: (subst > term > subst > $o) > subst). 0.62/0.79 thf(decl_445, type, esk244_1: (subst > term > subst > $o) > subst). 0.62/0.79 thf(decl_446, type, epred54_0: subst > term > subst > $o). 0.62/0.79 thf(decl_447, type, esk245_0: term). 0.62/0.79 thf(decl_448, type, esk246_2: (subst > term > term) > term > subst). 0.62/0.79 thf(decl_449, type, esk247_2: (subst > term > term) > term > term). 0.62/0.79 thf(decl_450, type, esk248_2: (subst > term > term) > term > subst). 0.62/0.79 thf(decl_451, type, esk249_2: (subst > term > term) > term > subst). 0.62/0.79 thf(decl_452, type, esk250_2: (subst > term > term) > term > term). 0.62/0.79 thf(decl_453, type, esk251_2: (subst > term > term) > term > subst). 0.62/0.79 thf(decl_454, type, esk252_2: (subst > term > term) > term > term). 0.62/0.79 thf(decl_455, type, esk253_2: (subst > term > subst > $o) > term > term). 0.62/0.79 thf(decl_456, type, esk254_1: (subst > term > subst > $o) > subst > term > term). 0.62/0.79 thf(decl_457, type, esk255_1: (subst > term > subst > $o) > term). 0.62/0.79 thf(decl_458, type, esk256_0: subst > term > term). 0.62/0.79 thf(decl_459, type, esk257_0: subst > term > term). 0.62/0.79 thf(decl_460, type, esk258_0: subst). 0.62/0.79 thf(decl_461, type, esk259_0: term). 0.62/0.79 thf(decl_462, type, esk260_2: (subst > term > term) > (subst > term > term) > subst). 0.62/0.79 thf(decl_463, type, esk261_2: (subst > term > term) > (subst > term > term) > term). 0.62/0.79 thf(decl_464, type, esk262_2: (subst > term > term) > (subst > term > term) > subst). 0.62/0.79 thf(decl_465, type, esk263_2: (subst > term > term) > (subst > term > term) > subst). 0.62/0.79 thf(decl_466, type, esk264_2: (subst > term > term) > (subst > term > term) > term). 0.62/0.79 thf(decl_467, type, esk265_2: (subst > term > term) > (subst > term > term) > subst). 0.62/0.79 thf(decl_468, type, esk266_0: term). 0.62/0.79 thf(decl_469, type, esk267_0: subst). 0.62/0.79 thf(decl_470, type, esk268_0: term). 0.62/0.79 thf(decl_471, type, esk269_0: subst). 0.62/0.79 thf(decl_472, type, esk270_0: subst). 0.62/0.79 thf(decl_473, type, esk271_1: term > subst > term > term). 0.62/0.79 thf(decl_474, type, esk272_0: term). 0.62/0.79 thf(decl_475, type, esk273_1: (subst > term > term) > term). 0.62/0.79 thf(decl_476, type, esk274_1: (subst > term > term) > subst). 0.62/0.79 thf(decl_477, type, esk275_0: term). 0.62/0.79 thf(decl_478, type, esk276_0: term). 0.62/0.79 thf(decl_479, type, esk277_4: term > subst > (term > $o) > (term > $o) > term). 0.62/0.79 thf(decl_480, type, esk278_2: (subst > term > subst > $o) > (term > $o) > term). 0.62/0.79 thf(decl_481, type, esk279_1: subst > d_subst). 0.62/0.79 thf(decl_482, type, esk280_1: term > d_term). 0.62/0.79 thf(decl_483, type, epred55_0: term > $o). 0.62/0.79 thf(decl_484, type, epred56_0: term > $o). 0.62/0.79 thf(decl_485, type, esk281_0: term). 0.62/0.79 thf(decl_486, type, esk282_0: subst). 0.62/0.79 thf(alg444_1, axiom, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X1:d_term]:(((X1)=(d_one)))&![X2:d_term, X3:d_term]:((((d2term @ X2)=(d2term @ X3))=>((X2)=(X3)))))&![X4:d_subst, X5:d_subst]:((((X4)=(X5))<=((d2subst @ X4)=(d2subst @ X5)))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&((hoaslam)=(^[X6:subst, X7:subst > term > term]:(d2term @ d_one))))&((pushprop_lem1v2)<=>![X8:term > $o, X9:term > $o, X10:term, X11:subst]:(((X9 @ one)|~(![X12:term]:(((X9 @ X12)<=>(X8 @ (sub @ X12 @ (push @ X10 @ X11))))))|~((X8 @ X10))))))&(axmap))&(hoasinduction_lem1v2))&((induction2lem)<=>![X8:term > $o, X13:term, X14:subst]:((~(![X10:term, X15:term]:(((X8 @ (ap @ X10 @ X15))|~((X8 @ X15))|~((X8 @ X10)))))|(X8 @ (sub @ X13 @ X14))|~(![X15:term]:(((X8 @ (sub @ X15 @ X14))|~((var @ X15)))))|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:(((X8 @ (sub @ X10 @ (push @ X15 @ id)))|~((X8 @ X15))))))))))))&(![X10:term, X15:term, X16:term, X17:term]:((((ap @ (sub @ X10 @ id) @ X16)!=(ap @ (sub @ X15 @ id) @ X17))|((X16)=(X17))))<=>(hoasapinj2)))&(hoasapnotvar_gthm))&((hoasapinj1)<=>![X10:term, X15:term, X16:term, X17:term]:((((X10)=(X15))|((ap @ (sub @ X10 @ id) @ X16)!=(ap @ (sub @ X15 @ id) @ X17))))))&(apnotvar))&(pushprop_lthm_orig))&((hoasinduction_lem3v2_f_lthm)<=>![X15:term]:(~(![X18:subst > term > term]:(~(![X10:term, X11:subst]:(((sub @ X15 @ (push @ X10 @ X11))=(X18 @ X11 @ X10)))))))))&((hoasinduction_no_psi_cond_lthm)<=>(![X19:subst > term > subst > $o]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X19 @ id @ X12 @ id)))))))=>(![X8:term > $o, X20:term]:((~(![X10:term]:((~((var @ X10))|(X8 @ X10))))|(X8 @ X20)|~(![X10:term]:((~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id))))))|(X8 @ (lam @ X10)))))|~(![X10:term, X15:term]:((~((X8 @ X10))|(X8 @ (ap @ X10 @ X15))|~((X8 @ X15)))))))=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(![X21:subst > term > subst > $o, X22:term]:(((X21 @ id @ X22 @ id)|~(![X18:subst > term > term]:(((X21 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X21 @ id @ (X18 @ id @ X10) @ id)|~((X21 @ id @ X10 @ id)))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X10:term, X15:term]:(((X21 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X21 @ id @ X15 @ id))|~((X21 @ id @ X10 @ id)))))))<=![X24:subst > term > subst > $o, X9:term > $o, X25:term]:((~(![X18:subst > term > term]:((~(![X10:term]:((~((X24 @ id @ X10 @ id))|(X24 @ id @ (X18 @ id @ X10) @ id))))|(X24 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X12:term]:(((X9 @ X12)<=>(X24 @ id @ X12 @ id))))|(X9 @ (lam @ X25))|~(![X15:term]:(((X9 @ (sub @ X25 @ (push @ X15 @ id)))|~((X9 @ X15)))))))))))))&(induction2lem_gthm))&(![X26:subst > term > subst > $o, X27:term]:((~(![X15:term]:(((X26 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)|~((X26 @ id @ X15 @ id)))))|(X26 @ id @ (lam @ (sub @ X27 @ (push @ one @ sh))) @ id)|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X26 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X26 @ id @ X10 @ id))|(X26 @ id @ (X18 @ id @ X10) @ id)))))))))<=>(hoasinduction_lem3aa_lthm)))&((![X10:term]:(((X10)=(sub @ X10 @ id)))=>![X10:term]:(((X10)=(sub @ X10 @ id))))<=>(termmset_lthm)))&(hoasinduction_lem1))&((hoasinduction_lem0)<=>![X28:subst > term > subst > $o]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X28 @ id @ X12 @ id)))))))))&((hoasinduction)<=>![X29:subst > term > subst > $o, X30:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X29 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X29 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X29 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X29 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|~(![X10:term]:((~((X29 @ id @ X10 @ id))|(X29 @ id @ (X18 @ id @ X10) @ id))))|(X29 @ id @ (lam @ (X18 @ sh @ one)) @ id))))|(X29 @ id @ X30 @ id)|~(![X10:term, X15:term]:((~((X29 @ id @ X10 @ id))|(X29 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X29 @ id @ X15 @ id)))))|~(![X10:term]:(((X29 @ id @ X10 @ id)|~((var @ (sub @ X10 @ id))))))))))&(hoasinduction_gthm))&(pushprop_lem3v2_lthm))&((hoasinduction_lem3b_lthm)<=>![X15:term]:(~(![X18:subst > term > term]:(((X18 @ sh @ one)!=(sub @ X15 @ (push @ one @ sh))))))))&(termmset_gthm))&(pushprop_lem1v2_gthm))&(hoaslamnotvar_gthm))&(pushprop_lem2v2))&(![X32:subst > term > subst > $o, X9:term > $o, X33:term, X34:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X32 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X32 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~((X9 @ X33))|~((X9 @ X34))|(X9 @ (ap @ X33 @ X34))|~(![X12:term]:(((X9 @ X12)<=>(X32 @ id @ X12 @ id))))|~(![X10:term, X15:term]:(((X32 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X32 @ id @ X15 @ id))|~((X32 @ id @ X10 @ id)))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X32 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X32 @ X11 @ X10 @ (comp @ X31 @ X23))))))))<=>(hoasinduction_lem2v2)))&(pushprop_lthm))&((apinj1)<=>![X10:term, X15:term, X16:term, X17:term]:((((X10)=(X15))|((ap @ X10 @ X16)!=(ap @ X15 @ X17))))))&((hoasapinj2_lthm)<=>(![X10:term, X15:term, X16:term, X17:term]:((((X16)=(X17))|((ap @ (sub @ X10 @ id) @ X16)!=(ap @ (sub @ X15 @ id) @ X17))))<=![X10:term, X15:term, X16:term, X17:term]:((((ap @ X10 @ X16)!=(ap @ X15 @ X17))|((X16)=(X17)))))))&(![X10:term, X15:term]:((((lam @ X10)!=(lam @ X15))|((X10)=(X15))))<=>(laminj)))&(![X8:term > $o, X10:term, X11:subst]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X8 @ (sub @ X12 @ (push @ X10 @ X11)))))))))<=>(pushprop_lem0)))&(axabs))&((hoasinduction_lem3v2a_lthm)<=>(![X15:term]:(~(![X18:subst > term > term]:(~(![X10:term, X11:subst]:(((sub @ X15 @ (push @ X10 @ X11))=(X18 @ X11 @ X10)))))))=>(![X35:subst > term > subst > $o, X9:term > $o, X25:term]:((~(![X18:subst > term > term]:(((X35 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X35 @ id @ X10 @ id))|(X35 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X12:term]:(((X9 @ X12)<=>(X35 @ id @ X12 @ id))))|~(![X15:term]:(((X9 @ (sub @ X25 @ (push @ X15 @ id)))|~((X9 @ X15)))))|(X9 @ (lam @ X25))))<=![X10:term]:(((X10)=(sub @ X10 @ id)))))))&(hoasinduction_lem2_lthm))&~((lamnotap)))&(hoaslaminj_gthm))&((induction2_lthm)<=>((![X8:term > $o, X20:term]:(((X8 @ X20)|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:(((X8 @ (sub @ X10 @ (push @ X15 @ id)))|~((X8 @ X15))))))))|~(![X10:term, X15:term]:(((X8 @ (ap @ X10 @ X15))|~((X8 @ X15))|~((X8 @ X10)))))|~(![X10:term]:((~((var @ X10))|(X8 @ X10))))))<=![X8:term > $o, X13:term, X14:subst]:((~(![X10:term]:((~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id))))))|(X8 @ (lam @ X10)))))|(X8 @ (sub @ X13 @ X14))|~(![X15:term]:(((X8 @ (sub @ X15 @ X14))|~((var @ X15)))))|~(![X10:term, X15:term]:(((X8 @ (ap @ X10 @ X15))|~((X8 @ X15))|~((X8 @ X10))))))))<=![X10:term]:(((X10)=(sub @ X10 @ id))))))&(pushprop))&(hoasinduction_lem3_gthm))&(hoasinduction_lem2_gthm))&(![X15:term]:(~(![X18:subst > term > term]:(((X18 @ sh @ one)!=(sub @ X15 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b)))&(![X36:subst > term > subst > $o, X37:term]:((~(![X15:term]:(((X36 @ id @ (sub @ X37 @ (push @ X15 @ id)) @ id)|~((X36 @ id @ X15 @ id)))))|(X36 @ id @ (lam @ X37) @ id)|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X36 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X36 @ id @ X10 @ id))|(X36 @ id @ (X18 @ id @ X10) @ id)))))))))<=>(hoasinduction_lem3a)))&(induction2_gthm))&(pushprop_lem2v2_lthm))&(![X18:subst > term > term, X38:term, X39:term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|((lam @ (X18 @ sh @ one))!=(ap @ (sub @ X38 @ id) @ X39))))<=>(hoaslamnotap)))&((induction2)<=>![X8:term > $o, X20:term]:((~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:(((X8 @ (sub @ X10 @ (push @ X15 @ id)))|~((X8 @ X15))))))))|(X8 @ X20)|~(![X10:term, X15:term]:((~((X8 @ X10))|~((X8 @ X15))|(X8 @ (ap @ X10 @ X15)))))|~(![X10:term]:(((X8 @ X10)|~((var @ X10)))))))))&((termmset)<=>![X10:term]:(((X10)=(sub @ X10 @ id)))))&((hoasinduction_lthm_3)<=>((![X8:term > $o, X20:term]:((~(![X10:term]:((~((var @ X10))|(X8 @ X10))))|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id)))))))))|(X8 @ X20)|~(![X10:term, X15:term]:((~((X8 @ X10))|(X8 @ (ap @ X10 @ X15))|~((X8 @ X15)))))))=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(![X40:subst > term > subst > $o, X30:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X40 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X40 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X10:term]:(((X40 @ id @ X10 @ id)|~((var @ (sub @ X10 @ id))))))|~(![X10:term, X15:term]:((~((X40 @ id @ X10 @ id))|~((X40 @ id @ X15 @ id))|(X40 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id))))|(X40 @ id @ X30 @ id)|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X40 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X40 @ id @ (X18 @ id @ X10) @ id)|~((X40 @ id @ X10 @ id))))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X40 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X40 @ X11 @ X10 @ (comp @ X31 @ X23)))))))<=![X41:subst > term > subst > $o, X9:term > $o, X25:term]:((~(![X12:term]:(((X9 @ X12)<=>(X41 @ id @ X12 @ id))))|(X9 @ (lam @ X25))|~(![X15:term]:((~((X9 @ X15))|(X9 @ (sub @ X25 @ (push @ X15 @ id))))))|~(![X18:subst > term > term]:(((X41 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X41 @ id @ X10 @ id))|(X41 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))))))))))<=![X42:subst > term > subst > $o]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X42 @ id @ X12 @ id))))))))))&((axvarid)<=>![X10:term]:(((X10)=(sub @ X10 @ id)))))&((![X10:term]:(((X10)=(sub @ X10 @ id)))=>![X43:subst > term > subst > $o, X9:term > $o, X44:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X43 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X43 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X43 @ X11 @ X10 @ (comp @ X31 @ X23))|~((X43 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)))))|~(![X18:subst > term > term]:(((X43 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X43 @ id @ (X18 @ id @ X10) @ id)|~((X43 @ id @ X10 @ id)))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X12:term]:(((X9 @ X12)<=>(X43 @ id @ X12 @ id))))|~(![X15:term]:((~((X9 @ X15))|(X9 @ (sub @ X44 @ (push @ X15 @ id))))))|(X9 @ (lam @ X44)))))<=>(hoasinduction_lem3v2_lthm)))&(hoasapnotvar_lthm))&((pushprop_lem0_lthm)<=>![X8:term > $o, X10:term, X11:subst]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X8 @ (sub @ X12 @ (push @ X10 @ X11)))))))))))&(![X10:term, X11:subst]:(((X11)=(comp @ sh @ (push @ X10 @ X11))))<=>(axshiftcons)))&((hoasinduction_lem3v2)<=>![X45:subst > term > subst > $o, X9:term > $o, X44:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X45 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X45 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~(![X12:term]:(((X9 @ X12)<=>(X45 @ id @ X12 @ id))))|(X9 @ (lam @ X44))|~(![X15:term]:((~((X9 @ X15))|(X9 @ (sub @ X44 @ (push @ X15 @ id))))))|~(![X18:subst > term > term]:((~(![X10:term]:((~((X45 @ id @ X10 @ id))|(X45 @ id @ (X18 @ id @ X10) @ id))))|(X45 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X45 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X45 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))))))))&((pushprop_lem1_lthm)<=>((![X10:term, X11:subst]:(((X11)=(comp @ sh @ (push @ X10 @ X11))))=>![X8:term > $o, X46:term > $o, X10:term, X11:subst, X15:term]:(((X46 @ (sub @ X10 @ (push @ X15 @ X11)))|~((X8 @ X10)))))<=![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11)))))))&(pushprop_lem2v2_gthm))&(pushprop_lem3v2))&(ulamvarsh))&(substmonoid_gthm))&~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))&((hoasinduction_no_psi_cond)<=>![X47:subst > term > subst > $o, X22:term]:((~(![X10:term, X15:term]:((~((X47 @ id @ X10 @ id))|(X47 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X47 @ id @ X15 @ id)))))|(X47 @ id @ X22 @ id)|~(![X18:subst > term > term]:(((X47 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X47 @ id @ (X18 @ id @ X10) @ id)|~((X47 @ id @ X10 @ id)))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))))))&(hoasinduction_lem1_gthm))&(lamnotvar))&((![X11:subst]:(((X11)=(comp @ X11 @ id)))&![X11:subst]:(((X11)=(comp @ id @ X11))))<=>(substmonoid)))&((((![X11:subst]:(((X11)=(comp @ id @ X11)))&![X11:subst]:(((X11)=(comp @ X11 @ id))))<=![X11:subst]:(((X11)=(comp @ X11 @ id))))<=![X11:subst]:(((X11)=(comp @ id @ X11))))<=>(substmonoid_lthm)))&((hoasinduction_lem0_lthm)<=>![X48:subst > term > subst > $o]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X48 @ id @ X12 @ id)))))))))&((axidl)<=>![X11:subst]:(((X11)=(comp @ id @ X11)))))&(hoaslamnotvar))&(hoasapinj1_gthm))&(hoasinduction_lem1_lthm))&(hoasapinj2_gthm))&(pushprop_gthm))&((hoasinduction_lem3_lthm)<=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(![X49:subst > term > subst > $o, X27:term]:(((X49 @ id @ (lam @ (sub @ X27 @ (push @ one @ sh))) @ id)|~(![X15:term]:(((X49 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)|~((X49 @ id @ X15 @ id)))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X49 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X49 @ id @ (X18 @ id @ X10) @ id)|~((X49 @ id @ X10 @ id))))))))))=>![X50:subst > term > subst > $o, X51:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X50 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X50 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X50 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X50 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X50 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X50 @ id @ X10 @ id))|(X50 @ id @ (X18 @ id @ X10) @ id)))))))|~(![X15:term]:(((X50 @ id @ (sub @ X51 @ (push @ X15 @ id)) @ id)|~((X50 @ id @ X15 @ id)))))|(X50 @ id @ (lam @ X51) @ id)))))))&((pushprop_lem1)<=>![X8:term > $o, X52:term > $o, X10:term, X11:subst, X15:term]:(((X52 @ (sub @ X10 @ (push @ X15 @ X11)))|~((X8 @ X10))))))&(![X11:subst]:(((X11)=(comp @ X11 @ id)))<=>(axidr)))&(hoasinduction_lem2v2_gthm))&(![X11:subst]:(((X11)=(push @ (sub @ one @ X11) @ (comp @ sh @ X11))))<=>(axscons)))&((axvarcons)<=>![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11))))))&((hoaslaminj_lthm)<=>(![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11))))=>((![X10:term, X15:term]:((((lam @ X10)!=(lam @ X15))|((X10)=(X15))))=>![X18:subst > term > term, X53:subst > term > term, X54:subst, X55:term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X53 @ X11 @ X10) @ X23)=(X53 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|((lam @ (X18 @ sh @ one))!=(lam @ (X53 @ sh @ one)))|((X18 @ X54 @ X55)=(X53 @ X54 @ X55)))))<=![X10:term, X11:subst]:(((X11)=(comp @ sh @ (push @ X10 @ X11))))))))&((hoasapinj1_lthm)<=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(![X10:term, X15:term, X16:term, X17:term]:((((X10)=(X15))|((ap @ X10 @ X16)!=(ap @ X15 @ X17))))=>![X10:term, X15:term, X16:term, X17:term]:((((X10)=(X15))|((ap @ (sub @ X10 @ id) @ X16)!=(ap @ (sub @ X15 @ id) @ X17))))))))&((hoasinduction_lem3v2a)<=>![X56:subst > term > subst > $o, X9:term > $o, X25:term]:((~(![X15:term]:((~((X9 @ X15))|(X9 @ (sub @ X25 @ (push @ X15 @ id))))))|(X9 @ (lam @ X25))|~(![X12:term]:(((X9 @ X12)<=>(X56 @ id @ X12 @ id))))|~(![X18:subst > term > term]:((~(![X10:term]:((~((X56 @ id @ X10 @ id))|(X56 @ id @ (X18 @ id @ X10) @ id))))|(X56 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))))))&((apinj2)<=>![X10:term, X15:term, X16:term, X17:term]:((((X16)=(X17))|((ap @ X10 @ X16)!=(ap @ X15 @ X17))))))&(axassoc))&(axclos))&(hoasinduction_lem3a_gthm))&(hoasinduction_lem3b_gthm))&(hoaslamnotap_gthm))&(![X57:subst > term > subst > $o, X27:term]:((~(![X18:subst > term > term]:(((X57 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X57 @ id @ X10 @ id))|(X57 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|(X57 @ id @ (lam @ (sub @ X27 @ (push @ one @ sh))) @ id)|~(![X15:term]:(((X57 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)|~((X57 @ id @ X15 @ id)))))))<=>(hoasinduction_lem3aa)))&((hoasinduction_lem3a_lthm)<=>((![X58:subst > term > subst > $o, X27:term]:((~(![X15:term]:(((X58 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)|~((X58 @ id @ X15 @ id)))))|(X58 @ id @ (lam @ (sub @ X27 @ (push @ one @ sh))) @ id)|~(![X18:subst > term > term]:(((X58 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X58 @ id @ X10 @ id))|(X58 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))))=>![X59:subst > term > subst > $o, X37:term]:(((X59 @ id @ (lam @ X37) @ id)|~(![X15:term]:((~((X59 @ id @ X15 @ id))|(X59 @ id @ (sub @ X37 @ (push @ X15 @ id)) @ id))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|~(![X10:term]:((~((X59 @ id @ X10 @ id))|(X59 @ id @ (X18 @ id @ X10) @ id))))|(X59 @ id @ (lam @ (X18 @ sh @ one)) @ id)))))))<=![X10:term]:(((X10)=(sub @ X10 @ id))))))&(![X8:term > $o, X60:term]:(((X8 @ X60)|~(![X10:term]:(((X8 @ (lam @ X10))|~((X8 @ X10)))))|~(![X10:term, X15:term]:((~((X8 @ X10))|~((X8 @ X15))|(X8 @ (ap @ X10 @ X15)))))|~(![X10:term]:((~((var @ X10))|(X8 @ X10))))))<=>(induction)))&(ulamvarind))&(hoaslamnotvar_lthm))&(axapp))&(hoasapnotvar))&((![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11))))=>![X8:term > $o, X9:term > $o, X10:term, X11:subst]:((~((X8 @ X10))|~(![X12:term]:(((X9 @ X12)<=>(X8 @ (sub @ X12 @ (push @ X10 @ X11))))))|(X9 @ one))))<=>(pushprop_lem1v2_lthm)))&(hoaslamnotap_lthm))&(![X61:subst > term > subst > $o, X62:term, X63:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X61 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X61 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X61 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X61 @ X11 @ X10 @ (comp @ X31 @ X23)))))|(X61 @ id @ (ap @ X62 @ X63) @ id)|~((X61 @ id @ X63 @ id))|~((X61 @ id @ X62 @ id))|~(![X10:term, X15:term]:((~((X61 @ id @ X10 @ id))|~((X61 @ id @ X15 @ id))|(X61 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id))))))<=>(hoasinduction_lem2)))&(![X64:subst > term > subst > $o, X51:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X64 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X64 @ X11 @ X10 @ (comp @ X31 @ X23)))))|(X64 @ id @ (lam @ X51) @ id)|~(![X15:term]:((~((X64 @ id @ X15 @ id))|(X64 @ id @ (sub @ X51 @ (push @ X15 @ id)) @ id))))|~(![X18:subst > term > term]:(((X64 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X64 @ id @ X10 @ id))|(X64 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X64 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X64 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))))))<=>(hoasinduction_lem3)))&(![X65:subst > term > subst > $o, X66:term]:((~(![X15:term]:(((X65 @ id @ (sub @ X66 @ (push @ X15 @ id)) @ id)|~((X65 @ id @ X15 @ id)))))|(X65 @ id @ (lam @ (sub @ X66 @ (push @ one @ sh))) @ id)|~(![X18:subst > term > term, X67:term]:((~(![X68:subst, X69:term, X70:subst]:(((X18 @ (comp @ X68 @ X70) @ (sub @ X69 @ X70))=(sub @ X67 @ (push @ (sub @ X69 @ X70) @ (comp @ X68 @ X70))))))|~(![X71:subst, X72:term, X73:subst]:(((sub @ (X18 @ X71 @ X72) @ X73)=(sub @ (sub @ X67 @ (push @ X72 @ X71)) @ X73))))|(X65 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X65 @ id @ (X18 @ id @ X10) @ id)|~((X65 @ id @ X10 @ id))))))))))<=>(hoasinduction_lem3aaa)))&(![X18:subst > term > term, X53:subst > term > term, X54:subst, X55:term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|((X18 @ X54 @ X55)=(X53 @ X54 @ X55))|((lam @ (X18 @ sh @ one))!=(lam @ (X53 @ sh @ one)))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X53 @ X11 @ X10) @ X23)=(X53 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))))<=>(hoaslaminj)))&((hoasinduction_lthm)<=>(![X8:term > $o, X20:term]:((~(![X10:term]:((~((var @ X10))|(X8 @ X10))))|~(![X10:term, X15:term]:((~((X8 @ X15))|(X8 @ (ap @ X10 @ X15))|~((X8 @ X10)))))|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id)))))))))|(X8 @ X20)))=>((![X74:subst > term > subst > $o, X30:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X74 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X74 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X74 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X74 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~(![X10:term]:(((X74 @ id @ X10 @ id)|~((var @ (sub @ X10 @ id))))))|~(![X10:term, X15:term]:((~((X74 @ id @ X10 @ id))|(X74 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X74 @ id @ X15 @ id)))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|~(![X10:term]:(((X74 @ id @ (X18 @ id @ X10) @ id)|~((X74 @ id @ X10 @ id)))))|(X74 @ id @ (lam @ (X18 @ sh @ one)) @ id))))|(X74 @ id @ X30 @ id)))<=![X75:subst > term > subst > $o, X51:term]:((~(![X18:subst > term > term]:((~(![X10:term]:(((X75 @ id @ (X18 @ id @ X10) @ id)|~((X75 @ id @ X10 @ id)))))|(X75 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|(X75 @ id @ (lam @ X51) @ id)|~(![X15:term]:((~((X75 @ id @ X15 @ id))|(X75 @ id @ (sub @ X51 @ (push @ X15 @ id)) @ id))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X75 @ X11 @ X10 @ (comp @ X31 @ X23))|~((X75 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X75 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X75 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)))))))<=![X76:subst > term > subst > $o, X62:term, X63:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X76 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X76 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X76 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X76 @ X11 @ X10 @ (comp @ X31 @ X23)))))|(X76 @ id @ (ap @ X62 @ X63) @ id)|~((X76 @ id @ X63 @ id))|~((X76 @ id @ X62 @ id))|~(![X10:term, X15:term]:((~((X76 @ id @ X10 @ id))|~((X76 @ id @ X15 @ id))|(X76 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id))))))))))&(hoasinduction_lem3v2_gthm))&((![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11))))=>(![X10:term, X11:subst]:(((X11)=(comp @ sh @ (push @ X10 @ X11))))=>(![X11:subst]:(((X11)=(comp @ X11 @ id)))=>(![X8:term > $o, X13:term, X14:subst]:(((X8 @ (sub @ X13 @ X14))|~(![X15:term]:((~((var @ X15))|(X8 @ (sub @ X15 @ X14)))))|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id)))))))))|~(![X10:term, X15:term]:(((X8 @ (ap @ X10 @ X15))|~((X8 @ X15))|~((X8 @ X10)))))))<=![X8:term > $o, X60:term]:(((X8 @ X60)|~(![X10:term]:((~((X8 @ X10))|(X8 @ (lam @ X10)))))|~(![X10:term, X15:term]:((~((X8 @ X10))|~((X8 @ X15))|(X8 @ (ap @ X10 @ X15)))))|~(![X10:term]:((~((var @ X10))|(X8 @ X10))))))))))<=>(induction2lem_lthm)))&~((ulamvar1)))&(axvarshift))&((hoasinduction_lem3v2_f)<=>![X15:term]:(~(![X18:subst > term > term]:(~(![X10:term, X11:subst]:(((sub @ X15 @ (push @ X10 @ X11))=(X18 @ X11 @ X10)))))))))&(hoasinduction_lem1v2_gthm))&(![X10:term, X15:term]:((((X10)=(X15))|((sub @ X10 @ sh)!=(sub @ X15 @ sh))))<=>(shinj)))&(pushprop_lem0_gthm))&(pushprop_lem1_gthm))&~((var @ (d2term @ d_one))))&((pushprop_p_and_p_prime)=(^[X10:term, X11:subst, X8:term > $o, X9:term > $o]:(![X12:term]:((((X9 @ X12))<=>((X8 @ (sub @ X12 @ (push @ X10 @ X11))))))))))&((hoasinduction_p_and_p_prime)=(^[X77:subst > term > subst > $o, X9:term > $o]:(![X12:term]:((((X9 @ X12))<=>((X77 @ id @ X12 @ id))))))))&((id)=(d2subst @ d_id)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&![X78:d_subst]:(((X78)=(d_id))))&![X79:subst]:(?[X78:d_subst]:(((X79)=(d2subst @ X78)))))&![X80:term]:(?[X1:d_term]:(((X80)=(d2term @ X1))))), file('/export/starexec/sandbox/tmp/tmp.MnTs4411x6/E---3.1_1376801.p', alg444_1)). 0.62/0.79 thf(pushprop_lem1v2, conjecture, ((pushprop_lem1v2)<=>![X8:term > $o, X9:term > $o, X10:term, X11:subst]:(((X8 @ X10)=>((pushprop_p_and_p_prime @ X10 @ X11 @ X8 @ X9)=>(X9 @ one))))), file('/export/starexec/sandbox/tmp/tmp.MnTs4411x6/E---3.1_1376801.p', pushprop_lem1v2)). 0.62/0.79 thf(c_0_2, plain, ((epred1_0)<=>(![X24:subst > term > subst > $o, X9:term > $o, X25:term]:((~(![X18:subst > term > term]:((~(![X10:term]:((~((X24 @ id @ X10 @ id))|(X24 @ id @ (X18 @ id @ X10) @ id))))|(X24 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X12:term]:(((X9 @ X12)<=>(X24 @ id @ X12 @ id))))|(X9 @ (lam @ X25))|~(![X15:term]:(((X9 @ (sub @ X25 @ (push @ X15 @ id)))|~((X9 @ X15)))))))=>![X21:subst > term > subst > $o, X22:term]:(((X21 @ id @ X22 @ id)|~(![X18:subst > term > term]:(((X21 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X21 @ id @ (X18 @ id @ X10) @ id)|~((X21 @ id @ X10 @ id)))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X10:term, X15:term]:(((X21 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X21 @ id @ X15 @ id))|~((X21 @ id @ X10 @ id))))))))), introduced(definition)). 0.62/0.79 thf(c_0_3, plain, ![X30:term, X29:subst > term > subst > $o]:(((epred2_2 @ X29 @ X30)<=>(~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X29 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X29 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X29 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X29 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|~(![X10:term]:((~((X29 @ id @ X10 @ id))|(X29 @ id @ (X18 @ id @ X10) @ id))))|(X29 @ id @ (lam @ (X18 @ sh @ one)) @ id))))|(X29 @ id @ X30 @ id)|~(![X10:term, X15:term]:((~((X29 @ id @ X10 @ id))|(X29 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X29 @ id @ X15 @ id)))))))), introduced(definition)). 0.62/0.79 thf(c_0_4, plain, ((epred3_0)<=>(![X8:term > $o, X13:term, X14:subst]:((~(![X10:term]:((~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id))))))|(X8 @ (lam @ X10)))))|(X8 @ (sub @ X13 @ X14))|~(![X15:term]:(((X8 @ (sub @ X15 @ X14))|~(var @ X15))))|~(![X10:term, X15:term]:(((X8 @ (ap @ X10 @ X15))|~((X8 @ X15))|~((X8 @ X10)))))))=>![X8:term > $o, X20:term]:(((X8 @ X20)|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:(((X8 @ (sub @ X10 @ (push @ X15 @ id)))|~((X8 @ X15))))))))|~(![X10:term, X15:term]:(((X8 @ (ap @ X10 @ X15))|~((X8 @ X15))|~((X8 @ X10)))))|~(![X10:term]:((~(var @ X10)|(X8 @ X10)))))))), introduced(definition)). 0.62/0.79 thf(c_0_5, plain, ((epred5_0)<=>(![X8:term > $o, X20:term]:((~(![X10:term]:((~(var @ X10)|(X8 @ X10))))|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id)))))))))|(X8 @ X20)|~(![X10:term, X15:term]:((~((X8 @ X10))|(X8 @ (ap @ X10 @ X15))|~((X8 @ X15)))))))=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(![X41:subst > term > subst > $o, X9:term > $o, X25:term]:((~(![X12:term]:(((X9 @ X12)<=>(X41 @ id @ X12 @ id))))|(X9 @ (lam @ X25))|~(![X15:term]:((~((X9 @ X15))|(X9 @ (sub @ X25 @ (push @ X15 @ id))))))|~(![X18:subst > term > term]:(((X41 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X41 @ id @ X10 @ id))|(X41 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))))=>![X40:subst > term > subst > $o, X30:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X40 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X40 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X10:term]:(((X40 @ id @ X10 @ id)|~(var @ (sub @ X10 @ id)))))|~(![X10:term, X15:term]:((~((X40 @ id @ X10 @ id))|~((X40 @ id @ X15 @ id))|(X40 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id))))|(X40 @ id @ X30 @ id)|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X40 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X40 @ id @ (X18 @ id @ X10) @ id)|~((X40 @ id @ X10 @ id))))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X40 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X40 @ X11 @ X10 @ (comp @ X31 @ X23))))))))))), introduced(definition)). 0.62/0.79 thf(c_0_6, plain, ![X9:term > $o, X43:subst > term > subst > $o, X44:term]:(((epred6_3 @ X44 @ X43 @ X9)<=>(~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X43 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X43 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X43 @ X11 @ X10 @ (comp @ X31 @ X23))|~((X43 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)))))|~(![X18:subst > term > term]:(((X43 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X43 @ id @ (X18 @ id @ X10) @ id)|~((X43 @ id @ X10 @ id)))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X12:term]:(((X9 @ X12)<=>(X43 @ id @ X12 @ id))))|~(![X15:term]:((~((X9 @ X15))|(X9 @ (sub @ X44 @ (push @ X15 @ id))))))))), introduced(definition)). 0.62/0.79 thf(c_0_7, plain, ((epred7_0)<=>![X45:subst > term > subst > $o, X9:term > $o, X44:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X45 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X45 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~(![X12:term]:(((X9 @ X12)<=>(X45 @ id @ X12 @ id))))|(X9 @ (lam @ X44))|~(![X15:term]:((~((X9 @ X15))|(X9 @ (sub @ X44 @ (push @ X15 @ id))))))|~(![X18:subst > term > term]:((~(![X10:term]:((~((X45 @ id @ X10 @ id))|(X45 @ id @ (X18 @ id @ X10) @ id))))|(X45 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X45 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X45 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))))))), introduced(definition)). 0.62/0.79 thf(c_0_8, plain, ((epred8_0)<=>(![X49:subst > term > subst > $o, X27:term]:(((X49 @ id @ (lam @ (sub @ X27 @ (push @ one @ sh))) @ id)|~(![X15:term]:(((X49 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)|~((X49 @ id @ X15 @ id)))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X49 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X49 @ id @ (X18 @ id @ X10) @ id)|~((X49 @ id @ X10 @ id))))))))))=>![X50:subst > term > subst > $o, X51:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X50 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X50 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X50 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X50 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X50 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X50 @ id @ X10 @ id))|(X50 @ id @ (X18 @ id @ X10) @ id)))))))|~(![X15:term]:(((X50 @ id @ (sub @ X51 @ (push @ X15 @ id)) @ id)|~((X50 @ id @ X15 @ id)))))|(X50 @ id @ (lam @ X51) @ id))))), introduced(definition)). 0.62/0.79 thf(c_0_9, plain, ((epred11_0)<=>(![X8:term > $o, X20:term]:((~(![X10:term]:((~(var @ X10)|(X8 @ X10))))|~(![X10:term, X15:term]:((~((X8 @ X15))|(X8 @ (ap @ X10 @ X15))|~((X8 @ X10)))))|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id)))))))))|(X8 @ X20)))=>(![X76:subst > term > subst > $o, X62:term, X63:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X76 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X76 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X76 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X76 @ X11 @ X10 @ (comp @ X31 @ X23)))))|(X76 @ id @ (ap @ X62 @ X63) @ id)|~((X76 @ id @ X63 @ id))|~((X76 @ id @ X62 @ id))|~(![X10:term, X15:term]:((~((X76 @ id @ X10 @ id))|~((X76 @ id @ X15 @ id))|(X76 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id))))))=>(![X75:subst > term > subst > $o, X51:term]:((~(![X18:subst > term > term]:((~(![X10:term]:(((X75 @ id @ (X18 @ id @ X10) @ id)|~((X75 @ id @ X10 @ id)))))|(X75 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|(X75 @ id @ (lam @ X51) @ id)|~(![X15:term]:((~((X75 @ id @ X15 @ id))|(X75 @ id @ (sub @ X51 @ (push @ X15 @ id)) @ id))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X75 @ X11 @ X10 @ (comp @ X31 @ X23))|~((X75 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X75 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X75 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))))))=>![X74:subst > term > subst > $o, X30:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X74 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X74 @ X11 @ X10 @ (comp @ X31 @ X23))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X74 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X74 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~(![X10:term]:(((X74 @ id @ X10 @ id)|~(var @ (sub @ X10 @ id)))))|~(![X10:term, X15:term]:((~((X74 @ id @ X10 @ id))|(X74 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X74 @ id @ X15 @ id)))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|~(![X10:term]:(((X74 @ id @ (X18 @ id @ X10) @ id)|~((X74 @ id @ X10 @ id)))))|(X74 @ id @ (lam @ (X18 @ sh @ one)) @ id))))|(X74 @ id @ X30 @ id))))))), introduced(definition)). 0.62/0.79 thf(c_0_10, plain, ((epred12_0)<=>(![X8:term > $o, X60:term]:(((X8 @ X60)|~(![X10:term]:((~((X8 @ X10))|(X8 @ (lam @ X10)))))|~(![X10:term, X15:term]:((~((X8 @ X10))|~((X8 @ X15))|(X8 @ (ap @ X10 @ X15)))))|~(![X10:term]:((~(var @ X10)|(X8 @ X10))))))=>![X8:term > $o, X13:term, X14:subst]:(((X8 @ (sub @ X13 @ X14))|~(![X15:term]:((~(var @ X15)|(X8 @ (sub @ X15 @ X14)))))|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id)))))))))|~(![X10:term, X15:term]:(((X8 @ (ap @ X10 @ X15))|~((X8 @ X15))|~((X8 @ X10))))))))), introduced(definition)). 0.62/0.79 thf(c_0_11, plain, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X1:d_term]:(((X1)=(d_one)))&![X2:d_term, X3:d_term]:((((d2term @ X2)=(d2term @ X3))=>((X2)=(X3)))))&![X4:d_subst, X5:d_subst]:((((d2subst @ X4)=(d2subst @ X5))=>((X4)=(X5)))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&![X625:subst, X626:subst > term > term]:(((hoaslam @ X625 @ X626)=(d2term @ d_one))))&((pushprop_lem1v2)<=>![X8:term > $o, X9:term > $o, X10:term, X11:subst]:(((X9 @ one)|~(![X12:term]:(((X9 @ X12)<=>(X8 @ (sub @ X12 @ (push @ X10 @ X11))))))|~((X8 @ X10))))))&(axmap))&(hoasinduction_lem1v2))&((induction2lem)<=>![X8:term > $o, X13:term, X14:subst]:((~(![X10:term, X15:term]:(((X8 @ (ap @ X10 @ X15))|~((X8 @ X15))|~((X8 @ X10)))))|(X8 @ (sub @ X13 @ X14))|~(![X15:term]:(((X8 @ (sub @ X15 @ X14))|~(var @ X15))))|~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:(((X8 @ (sub @ X10 @ (push @ X15 @ id)))|~((X8 @ X15))))))))))))&(![X10:term, X15:term, X16:term, X17:term]:((((ap @ (sub @ X10 @ id) @ X16)!=(ap @ (sub @ X15 @ id) @ X17))|((X16)=(X17))))<=>(hoasapinj2)))&(hoasapnotvar_gthm))&((hoasapinj1)<=>![X10:term, X15:term, X16:term, X17:term]:((((X10)=(X15))|((ap @ (sub @ X10 @ id) @ X16)!=(ap @ (sub @ X15 @ id) @ X17))))))&(apnotvar))&(pushprop_lthm_orig))&((hoasinduction_lem3v2_f_lthm)<=>![X15:term]:(~(![X18:subst > term > term]:(~(![X10:term, X11:subst]:(((sub @ X15 @ (push @ X10 @ X11))=(X18 @ X11 @ X10)))))))))&((hoasinduction_no_psi_cond_lthm)<=>(![X19:subst > term > subst > $o]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X19 @ id @ X12 @ id)))))))=>(![X8:term > $o, X20:term]:((~(![X10:term]:((~(var @ X10)|(X8 @ X10))))|(X8 @ X20)|~(![X10:term]:((~(![X15:term]:((~((X8 @ X15))|(X8 @ (sub @ X10 @ (push @ X15 @ id))))))|(X8 @ (lam @ X10)))))|~(![X10:term, X15:term]:((~((X8 @ X10))|(X8 @ (ap @ X10 @ X15))|~((X8 @ X15)))))))=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(epred1_0))))))&(induction2lem_gthm))&(![X26:subst > term > subst > $o, X27:term]:((~(![X15:term]:(((X26 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)|~((X26 @ id @ X15 @ id)))))|(X26 @ id @ (lam @ (sub @ X27 @ (push @ one @ sh))) @ id)|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X26 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X26 @ id @ X10 @ id))|(X26 @ id @ (X18 @ id @ X10) @ id)))))))))<=>(hoasinduction_lem3aa_lthm)))&(termmset_lthm))&(hoasinduction_lem1))&((hoasinduction_lem0)<=>![X28:subst > term > subst > $o]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X28 @ id @ X12 @ id)))))))))&((hoasinduction)<=>![X29:subst > term > subst > $o, X30:term]:(((epred2_2 @ X29 @ X30)|~(![X10:term]:(((X29 @ id @ X10 @ id)|~(var @ (sub @ X10 @ id)))))))))&(hoasinduction_gthm))&(pushprop_lem3v2_lthm))&((hoasinduction_lem3b_lthm)<=>![X15:term]:(~(![X18:subst > term > term]:(((X18 @ sh @ one)!=(sub @ X15 @ (push @ one @ sh))))))))&(termmset_gthm))&(pushprop_lem1v2_gthm))&(hoaslamnotvar_gthm))&(pushprop_lem2v2))&(![X32:subst > term > subst > $o, X9:term > $o, X33:term, X34:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X32 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X32 @ X11 @ X10 @ (comp @ X31 @ X23)))))|~((X9 @ X33))|~((X9 @ X34))|(X9 @ (ap @ X33 @ X34))|~(![X12:term]:(((X9 @ X12)<=>(X32 @ id @ X12 @ id))))|~(![X10:term, X15:term]:(((X32 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X32 @ id @ X15 @ id))|~((X32 @ id @ X10 @ id)))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:(((X32 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23)|~((X32 @ X11 @ X10 @ (comp @ X31 @ X23))))))))<=>(hoasinduction_lem2v2)))&(pushprop_lthm))&((apinj1)<=>![X10:term, X15:term, X16:term, X17:term]:((((X10)=(X15))|((ap @ X10 @ X16)!=(ap @ X15 @ X17))))))&((hoasapinj2_lthm)<=>(![X10:term, X15:term, X16:term, X17:term]:((((ap @ X10 @ X16)!=(ap @ X15 @ X17))|((X16)=(X17))))=>![X10:term, X15:term, X16:term, X17:term]:((((X16)=(X17))|((ap @ (sub @ X10 @ id) @ X16)!=(ap @ (sub @ X15 @ id) @ X17)))))))&(![X10:term, X15:term]:((((lam @ X10)!=(lam @ X15))|((X10)=(X15))))<=>(laminj)))&(![X8:term > $o, X10:term, X11:subst]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X8 @ (sub @ X12 @ (push @ X10 @ X11)))))))))<=>(pushprop_lem0)))&(axabs))&((hoasinduction_lem3v2a_lthm)<=>(![X15:term]:(~(![X18:subst > term > term]:(~(![X10:term, X11:subst]:(((sub @ X15 @ (push @ X10 @ X11))=(X18 @ X11 @ X10)))))))=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>![X35:subst > term > subst > $o, X9:term > $o, X25:term]:((~(![X18:subst > term > term]:(((X35 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X35 @ id @ X10 @ id))|(X35 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X12:term]:(((X9 @ X12)<=>(X35 @ id @ X12 @ id))))|~(![X15:term]:(((X9 @ (sub @ X25 @ (push @ X15 @ id)))|~((X9 @ X15)))))|(X9 @ (lam @ X25))))))))&(hoasinduction_lem2_lthm))&~(lamnotap))&(hoaslaminj_gthm))&((induction2_lthm)<=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(epred3_0))))&(pushprop))&(hoasinduction_lem3_gthm))&(hoasinduction_lem2_gthm))&(![X15:term]:(~(![X18:subst > term > term]:(((X18 @ sh @ one)!=(sub @ X15 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b)))&(![X36:subst > term > subst > $o, X37:term]:((~(![X15:term]:(((X36 @ id @ (sub @ X37 @ (push @ X15 @ id)) @ id)|~((X36 @ id @ X15 @ id)))))|(X36 @ id @ (lam @ X37) @ id)|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|(X36 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X36 @ id @ X10 @ id))|(X36 @ id @ (X18 @ id @ X10) @ id)))))))))<=>(hoasinduction_lem3a)))&(induction2_gthm))&(pushprop_lem2v2_lthm))&(![X18:subst > term > term, X38:term, X39:term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|((lam @ (X18 @ sh @ one))!=(ap @ (sub @ X38 @ id) @ X39))))<=>(hoaslamnotap)))&((induction2)<=>![X8:term > $o, X20:term]:((~(![X10:term]:(((X8 @ (lam @ X10))|~(![X15:term]:(((X8 @ (sub @ X10 @ (push @ X15 @ id)))|~((X8 @ X15))))))))|(X8 @ X20)|~(![X10:term, X15:term]:((~((X8 @ X10))|~((X8 @ X15))|(X8 @ (ap @ X10 @ X15)))))|~(![X10:term]:(((X8 @ X10)|~(var @ X10))))))))&((termmset)<=>![X10:term]:(((X10)=(sub @ X10 @ id)))))&((hoasinduction_lthm_3)<=>(![X42:subst > term > subst > $o]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X42 @ id @ X12 @ id)))))))=>(epred5_0))))&((axvarid)<=>![X10:term]:(((X10)=(sub @ X10 @ id)))))&((![X10:term]:(((X10)=(sub @ X10 @ id)))=>![X43:subst > term > subst > $o, X9:term > $o, X44:term]:(((epred6_3 @ X44 @ X43 @ X9)|(X9 @ (lam @ X44)))))<=>(hoasinduction_lem3v2_lthm)))&(hoasapnotvar_lthm))&((pushprop_lem0_lthm)<=>![X8:term > $o, X10:term, X11:subst]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X8 @ (sub @ X12 @ (push @ X10 @ X11)))))))))))&(![X10:term, X11:subst]:(((X11)=(comp @ sh @ (push @ X10 @ X11))))<=>(axshiftcons)))&((hoasinduction_lem3v2)<=>(epred7_0)))&((pushprop_lem1_lthm)<=>(![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11))))=>(![X10:term, X11:subst]:(((X11)=(comp @ sh @ (push @ X10 @ X11))))=>![X8:term > $o, X46:term > $o, X10:term, X11:subst, X15:term]:(((X46 @ (sub @ X10 @ (push @ X15 @ X11)))|~((X8 @ X10))))))))&(pushprop_lem2v2_gthm))&(pushprop_lem3v2))&(ulamvarsh))&(substmonoid_gthm))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&((hoasinduction_no_psi_cond)<=>![X47:subst > term > subst > $o, X22:term]:((~(![X10:term, X15:term]:((~((X47 @ id @ X10 @ id))|(X47 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id)|~((X47 @ id @ X15 @ id)))))|(X47 @ id @ X22 @ id)|~(![X18:subst > term > term]:(((X47 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X47 @ id @ (X18 @ id @ X10) @ id)|~((X47 @ id @ X10 @ id)))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))))))&(hoasinduction_lem1_gthm))&(lamnotvar))&((![X11:subst]:(((X11)=(comp @ X11 @ id)))&![X11:subst]:(((X11)=(comp @ id @ X11))))<=>(substmonoid)))&((![X11:subst]:(((X11)=(comp @ id @ X11)))=>(![X11:subst]:(((X11)=(comp @ X11 @ id)))=>(![X11:subst]:(((X11)=(comp @ id @ X11)))&![X11:subst]:(((X11)=(comp @ X11 @ id))))))<=>(substmonoid_lthm)))&((hoasinduction_lem0_lthm)<=>![X48:subst > term > subst > $o]:(~(![X9:term > $o]:(~(![X12:term]:(((X9 @ X12)<=>(X48 @ id @ X12 @ id)))))))))&((axidl)<=>![X11:subst]:(((X11)=(comp @ id @ X11)))))&(hoaslamnotvar))&(hoasapinj1_gthm))&(hoasinduction_lem1_lthm))&(hoasapinj2_gthm))&(pushprop_gthm))&((hoasinduction_lem3_lthm)<=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(epred8_0))))&((pushprop_lem1)<=>![X8:term > $o, X52:term > $o, X10:term, X11:subst, X15:term]:(((X52 @ (sub @ X10 @ (push @ X15 @ X11)))|~((X8 @ X10))))))&(![X11:subst]:(((X11)=(comp @ X11 @ id)))<=>(axidr)))&(hoasinduction_lem2v2_gthm))&(![X11:subst]:(((X11)=(push @ (sub @ one @ X11) @ (comp @ sh @ X11))))<=>(axscons)))&((axvarcons)<=>![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11))))))&((hoaslaminj_lthm)<=>(![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11))))=>(![X10:term, X11:subst]:(((X11)=(comp @ sh @ (push @ X10 @ X11))))=>(![X10:term, X15:term]:((((lam @ X10)!=(lam @ X15))|((X10)=(X15))))=>![X18:subst > term > term, X53:subst > term > term, X54:subst, X55:term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X53 @ X11 @ X10) @ X23)=(X53 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|((lam @ (X18 @ sh @ one))!=(lam @ (X53 @ sh @ one)))|((X18 @ X54 @ X55)=(X53 @ X54 @ X55)))))))))&((hoasapinj1_lthm)<=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(![X10:term, X15:term, X16:term, X17:term]:((((X10)=(X15))|((ap @ X10 @ X16)!=(ap @ X15 @ X17))))=>![X10:term, X15:term, X16:term, X17:term]:((((X10)=(X15))|((ap @ (sub @ X10 @ id) @ X16)!=(ap @ (sub @ X15 @ id) @ X17))))))))&((hoasinduction_lem3v2a)<=>![X56:subst > term > subst > $o, X9:term > $o, X25:term]:((~(![X15:term]:((~((X9 @ X15))|(X9 @ (sub @ X25 @ (push @ X15 @ id))))))|(X9 @ (lam @ X25))|~(![X12:term]:(((X9 @ X12)<=>(X56 @ id @ X12 @ id))))|~(![X18:subst > term > term]:((~(![X10:term]:((~((X56 @ id @ X10 @ id))|(X56 @ id @ (X18 @ id @ X10) @ id))))|(X56 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))))))&((apinj2)<=>![X10:term, X15:term, X16:term, X17:term]:((((X16)=(X17))|((ap @ X10 @ X16)!=(ap @ X15 @ X17))))))&(axassoc))&(axclos))&(hoasinduction_lem3a_gthm))&(hoasinduction_lem3b_gthm))&(hoaslamnotap_gthm))&(![X57:subst > term > subst > $o, X27:term]:((~(![X18:subst > term > term]:(((X57 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X57 @ id @ X10 @ id))|(X57 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|(X57 @ id @ (lam @ (sub @ X27 @ (push @ one @ sh))) @ id)|~(![X15:term]:(((X57 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)|~((X57 @ id @ X15 @ id)))))))<=>(hoasinduction_lem3aa)))&((hoasinduction_lem3a_lthm)<=>(![X10:term]:(((X10)=(sub @ X10 @ id)))=>(![X58:subst > term > subst > $o, X27:term]:((~(![X15:term]:(((X58 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)|~((X58 @ id @ X15 @ id)))))|(X58 @ id @ (lam @ (sub @ X27 @ (push @ one @ sh))) @ id)|~(![X18:subst > term > term]:(((X58 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X58 @ id @ X10 @ id))|(X58 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))))=>![X59:subst > term > subst > $o, X37:term]:(((X59 @ id @ (lam @ X37) @ id)|~(![X15:term]:((~((X59 @ id @ X15 @ id))|(X59 @ id @ (sub @ X37 @ (push @ X15 @ id)) @ id))))|~(![X18:subst > term > term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|~(![X10:term]:((~((X59 @ id @ X10 @ id))|(X59 @ id @ (X18 @ id @ X10) @ id))))|(X59 @ id @ (lam @ (X18 @ sh @ one)) @ id))))))))))&(![X8:term > $o, X60:term]:(((X8 @ X60)|~(![X10:term]:(((X8 @ (lam @ X10))|~((X8 @ X10)))))|~(![X10:term, X15:term]:((~((X8 @ X10))|~((X8 @ X15))|(X8 @ (ap @ X10 @ X15)))))|~(![X10:term]:((~(var @ X10)|(X8 @ X10))))))<=>(induction)))&(ulamvarind))&(hoaslamnotvar_lthm))&(axapp))&(hoasapnotvar))&((![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11))))=>![X8:term > $o, X9:term > $o, X10:term, X11:subst]:((~((X8 @ X10))|~(![X12:term]:(((X9 @ X12)<=>(X8 @ (sub @ X12 @ (push @ X10 @ X11))))))|(X9 @ one))))<=>(pushprop_lem1v2_lthm)))&(hoaslamnotap_lthm))&(![X61:subst > term > subst > $o, X62:term, X63:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X61 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X61 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X61 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X61 @ X11 @ X10 @ (comp @ X31 @ X23)))))|(X61 @ id @ (ap @ X62 @ X63) @ id)|~((X61 @ id @ X63 @ id))|~((X61 @ id @ X62 @ id))|~(![X10:term, X15:term]:((~((X61 @ id @ X10 @ id))|~((X61 @ id @ X15 @ id))|(X61 @ id @ (ap @ (sub @ X10 @ id) @ X15) @ id))))))<=>(hoasinduction_lem2)))&(![X64:subst > term > subst > $o, X51:term]:((~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X64 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))|(X64 @ X11 @ X10 @ (comp @ X31 @ X23)))))|(X64 @ id @ (lam @ X51) @ id)|~(![X15:term]:((~((X64 @ id @ X15 @ id))|(X64 @ id @ (sub @ X51 @ (push @ X15 @ id)) @ id))))|~(![X18:subst > term > term]:(((X64 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:((~((X64 @ id @ X10 @ id))|(X64 @ id @ (X18 @ id @ X10) @ id))))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23))))))))|~(![X11:subst, X10:term, X23:subst, X31:subst]:((~((X64 @ X11 @ X10 @ (comp @ X31 @ X23)))|(X64 @ (comp @ X11 @ X31) @ (sub @ X10 @ X31) @ X23))))))<=>(hoasinduction_lem3)))&(![X65:subst > term > subst > $o, X66:term]:((~(![X15:term]:(((X65 @ id @ (sub @ X66 @ (push @ X15 @ id)) @ id)|~((X65 @ id @ X15 @ id)))))|(X65 @ id @ (lam @ (sub @ X66 @ (push @ one @ sh))) @ id)|~(![X18:subst > term > term, X67:term]:((~(![X68:subst, X69:term, X70:subst]:(((X18 @ (comp @ X68 @ X70) @ (sub @ X69 @ X70))=(sub @ X67 @ (push @ (sub @ X69 @ X70) @ (comp @ X68 @ X70))))))|~(![X71:subst, X72:term, X73:subst]:(((sub @ (X18 @ X71 @ X72) @ X73)=(sub @ (sub @ X67 @ (push @ X72 @ X71)) @ X73))))|(X65 @ id @ (lam @ (X18 @ sh @ one)) @ id)|~(![X10:term]:(((X65 @ id @ (X18 @ id @ X10) @ id)|~((X65 @ id @ X10 @ id))))))))))<=>(hoasinduction_lem3aaa)))&(![X18:subst > term > term, X53:subst > term > term, X54:subst, X55:term]:((~(![X11:subst, X10:term, X23:subst]:(((sub @ (X18 @ X11 @ X10) @ X23)=(X18 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))|((X18 @ X54 @ X55)=(X53 @ X54 @ X55))|((lam @ (X18 @ sh @ one))!=(lam @ (X53 @ sh @ one)))|~(![X11:subst, X10:term, X23:subst]:(((sub @ (X53 @ X11 @ X10) @ X23)=(X53 @ (comp @ X11 @ X23) @ (sub @ X10 @ X23)))))))<=>(hoaslaminj)))&((hoasinduction_lthm)<=>(epred11_0)))&(hoasinduction_lem3v2_gthm))&((![X10:term, X11:subst]:(((X10)=(sub @ one @ (push @ X10 @ X11))))=>(![X10:term, X11:subst]:(((X11)=(comp @ sh @ (push @ X10 @ X11))))=>(![X11:subst]:(((X11)=(comp @ X11 @ id)))=>(epred12_0))))<=>(induction2lem_lthm)))&~(ulamvar1))&(axvarshift))&((hoasinduction_lem3v2_f)<=>![X15:term]:(~(![X18:subst > term > term]:(~(![X10:term, X11:subst]:(((sub @ X15 @ (push @ X10 @ X11))=(X18 @ X11 @ X10)))))))))&(hoasinduction_lem1v2_gthm))&(![X10:term, X15:term]:((((X10)=(X15))|((sub @ X10 @ sh)!=(sub @ X15 @ sh))))<=>(shinj)))&(pushprop_lem0_gthm))&(pushprop_lem1_gthm))&~(var @ (d2term @ d_one)))&![X627:term, X628:subst, X629:term > $o, X630:term > $o]:(((pushprop_p_and_p_prime @ X627 @ X628 @ X629 @ X630)<=>![X12:term]:(((X630 @ X12)<=>(X629 @ (sub @ X12 @ (push @ X627 @ X628))))))))&![X631:subst > term > subst > $o, X632:term > $o]:(((hoasinduction_p_and_p_prime @ X631 @ X632)<=>![X12:term]:(((X632 @ X12)<=>(X631 @ id @ X12 @ id))))))&((id)=(d2subst @ d_id)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&![X78:d_subst]:(((X78)=(d_id))))&![X79:subst]:(?[X78:d_subst]:(((X79)=(d2subst @ X78)))))&![X80:term]:(?[X1:d_term]:(((X80)=(d2term @ X1))))), 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])). 0.62/0.79 thf(c_0_12, negated_conjecture, ~(((pushprop_lem1v2)<=>![X8:term > $o, X9:term > $o, X10:term, X11:subst]:(((X8 @ X10)=>((pushprop_p_and_p_prime @ X10 @ X11 @ X8 @ X9)=>(X9 @ one)))))), inference(assume_negation,[status(cth)],[pushprop_lem1v2])). 0.62/0.79 thf(c_0_13, plain, ![X633:d_term, X634:d_term, X635:d_term, X636:d_subst, X637:d_subst, X638:subst, X639:subst > term > term, X640:term > $o, X641:term > $o, X642:term, X643:subst, X649:term, X650:term > $o, X651:term, X652:subst, X657:term, X661:term, X662:term, X663:term, X664:term, X670:term, X671:term, X672:term, X673:term, X674:term, X675:term, X676:term, X677:term, X682:term, X684:term, X685:subst, X687:subst > term > term, X691:term > $o, X695:term, X696:term, X698:term, X699:term, X701:subst > term > subst > $o, X703:term, X704:term, X705:term > $o, X707:term, X709:term, X712:term, X715:term, X716:subst > term > term, X721:subst > term > subst > $o, X722:term, X725:subst, X726:term, X727:subst, X728:term, X729:subst > term > subst > $o, X731:term, X732:term, X734:term > $o, X736:subst > term > subst > $o, X737:term, X741:term, X742:term, X745:subst > term > term, X750:subst, X751:term, X752:subst, X753:subst, X754:term, X755:term, X756:term, X757:subst, X758:term, X759:subst, X760:subst, X761:subst > term > subst > $o, X762:term > $o, X763:term, X764:term, X776:term, X777:term, X778:term, X779:term, X788:term, X789:term, X790:term, X791:term, X792:term, X793:term, X794:term, X795:term, X802:term, X803:term, X807:term > $o, X809:term > $o, X810:term, X811:subst, X813:term, X814:term, X816:subst > term > term, X820:subst > term > subst > $o, X821:term > $o, X822:term, X824:term, X825:subst, X826:term, X827:subst, X830:term, X832:term, X833:subst, X834:term, X838:subst > term > term, X843:term, X844:term, X846:term, X848:subst > term > term, X849:term, X853:term, X854:subst > term > term, X859:subst > term > subst > $o, X860:term, X863:subst, X864:term, X865:subst, X866:term, X870:subst, X871:term, X872:subst, X873:subst > term > term, X877:term, X878:term, X879:term > $o, X881:term, X882:term, X888:term, X890:term, X891:term, X892:term, X893:term, X896:term > $o, X898:subst > term > subst > $o, X900:term, X901:term, X902:term, X904:term, X909:subst > term > subst > $o, X910:term > $o, X911:term, X912:term > $o, X913:term, X914:subst, X916:term, X917:term, X921:term > $o, X925:term, X926:subst, X931:term > $o, X932:term > $o, X933:term, X934:subst, X935:term, X936:term, X937:subst, X938:term, X939:subst, X945:subst > term > subst > $o, X948:term, X950:term, X951:subst, X952:term, X953:subst, X956:term, X957:term, X958:subst > term > term, X965:subst, X966:subst, X967:subst, X968:subst, X973:subst, X974:subst, X975:subst > term > subst > $o, X977:term, X978:term, X980:term > $o, X982:subst, X985:term, X986:term > $o, X987:term > $o, X988:term, X989:subst, X990:term, X997:subst, X999:subst, X1000:term, X1001:subst, X1010:subst > term > term, X1011:subst > term > term, X1018:subst, X1019:term, X1020:term, X1021:subst, X1022:term, X1023:subst, X1024:term, X1025:term, X1030:subst, X1031:term, X1032:subst, X1033:subst, X1034:term, X1035:subst, X1041:term, X1042:term, X1043:term, X1044:term, X1045:term, X1046:term, X1047:term, X1048:term, X1049:term, X1054:subst > term > subst > $o, X1055:term > $o, X1056:term, X1060:term, X1061:subst, X1062:term, X1063:subst, X1067:term, X1068:term, X1069:subst > term > term, X1074:term, X1075:term, X1076:term, X1077:term, X1084:subst > term > term, X1089:term, X1090:subst > term > subst > $o, X1091:term, X1093:term, X1094:subst, X1095:term, X1096:subst, X1101:term, X1102:subst > term > term, X1107:subst > term > subst > $o, X1108:term, X1111:subst, X1112:term, X1113:subst, X1114:term, X1115:term, X1116:subst > term > subst > $o, X1117:term, X1120:term, X1121:subst, X1122:term, X1123:subst, X1126:term, X1127:subst > term > term, X1134:term, X1135:term, X1136:term, X1137:term, X1138:term > $o, X1139:term, X1144:term, X1145:subst, X1150:term, X1153:term > $o, X1154:term > $o, X1155:term, X1156:subst, X1161:subst, X1162:term, X1163:subst, X1164:subst, X1165:subst, X1166:term, X1167:subst, X1168:subst, X1169:term, X1170:term, X1171:subst > term > subst > $o, X1172:term, X1173:term, X1186:subst, X1187:term, X1188:subst, X1189:subst, X1190:term, X1191:subst > term > term, X1196:subst, X1197:term, X1198:subst, X1199:subst, X1200:subst > term > subst > $o, X1201:term, X1208:term, X1209:subst, X1210:term, X1211:subst, X1218:term, X1219:subst > term > term, X1220:term, X1228:subst > term > subst > $o, X1229:term, X1233:subst, X1234:term, X1235:subst, X1236:subst, X1237:term, X1238:subst, X1239:term, X1244:subst, X1245:term, X1246:subst, X1247:subst, X1248:term, X1249:subst, X1250:subst > term > term, X1251:subst > term > term, X1255:subst, X1256:term, X1260:term, X1261:subst, X1262:term, X1263:subst, X1264:subst, X1270:term, X1272:term, X1273:subst, X1275:subst > term > term, X1280:term, X1281:term, X1282:term, X1283:subst, X1284:term > $o, X1285:term > $o, X1286:term, X1287:term, X1288:term, X1289:subst, X1290:term > $o, X1291:term > $o, X1293:subst > term > subst > $o, X1294:term > $o, X1295:term, X1296:term, X1297:subst > term > subst > $o, X1298:term > $o, X1300:d_subst, X1301:subst, X1303:term]:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((X633)=(d_one))&(((d2term @ X634)!=(d2term @ X635))|((X634)=(X635))))&(((d2subst @ X636)!=(d2subst @ X637))|((X636)=(X637))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&((hoaslam @ X638 @ X639)=(d2term @ d_one)))&(((~(X641 @ (esk1_4 @ X640 @ X641 @ X642 @ X643))|~(X640 @ (sub @ (esk1_4 @ X640 @ X641 @ X642 @ X643) @ (push @ X642 @ X643)))|(X641 @ one)|~(X640 @ X642)|~(pushprop_lem1v2))&((X641 @ (esk1_4 @ X640 @ X641 @ X642 @ X643))|(X640 @ (sub @ (esk1_4 @ X640 @ X641 @ X642 @ X643) @ (push @ X642 @ X643)))|(X641 @ one)|~(X640 @ X642)|~(pushprop_lem1v2)))&(((~(epred14_0 @ one)|(pushprop_lem1v2))&((~(epred14_0 @ X649)|(epred13_0 @ (sub @ X649 @ (push @ esk2_0 @ esk3_0)))|(pushprop_lem1v2))&(~(epred13_0 @ (sub @ X649 @ (push @ esk2_0 @ esk3_0)))|(epred14_0 @ X649)|(pushprop_lem1v2))))&((epred13_0 @ esk2_0)|(pushprop_lem1v2)))))&(axmap))&(hoasinduction_lem1v2))&((((((~(X650 @ (lam @ (esk7_1 @ X650)))|(~(X650 @ (sub @ (esk6_3 @ X650 @ X651 @ X652) @ X652))|(~(X650 @ (ap @ (esk4_3 @ X650 @ X651 @ X652) @ (esk5_3 @ X650 @ X651 @ X652)))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem))&((X650 @ (sub @ (esk7_1 @ X650) @ (push @ X657 @ id)))|~(X650 @ X657)|(~(X650 @ (sub @ (esk6_3 @ X650 @ X651 @ X652) @ X652))|(~(X650 @ (ap @ (esk4_3 @ X650 @ X651 @ X652) @ (esk5_3 @ X650 @ X651 @ X652)))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem)))&((~(X650 @ (lam @ (esk7_1 @ X650)))|((var @ (esk6_3 @ X650 @ X651 @ X652))|(~(X650 @ (ap @ (esk4_3 @ X650 @ X651 @ X652) @ (esk5_3 @ X650 @ X651 @ X652)))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem))&((X650 @ (sub @ (esk7_1 @ X650) @ (push @ X657 @ id)))|~(X650 @ X657)|((var @ (esk6_3 @ X650 @ X651 @ X652))|(~(X650 @ (ap @ (esk4_3 @ X650 @ X651 @ X652) @ (esk5_3 @ X650 @ X651 @ X652)))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem))))&(((~(X650 @ (lam @ (esk7_1 @ X650)))|(~(X650 @ (sub @ (esk6_3 @ X650 @ X651 @ X652) @ X652))|((X650 @ (esk5_3 @ X650 @ X651 @ X652))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem))&((X650 @ (sub @ (esk7_1 @ X650) @ (push @ X657 @ id)))|~(X650 @ X657)|(~(X650 @ (sub @ (esk6_3 @ X650 @ X651 @ X652) @ X652))|((X650 @ (esk5_3 @ X650 @ X651 @ X652))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem)))&((~(X650 @ (lam @ (esk7_1 @ X650)))|((var @ (esk6_3 @ X650 @ X651 @ X652))|((X650 @ (esk5_3 @ X650 @ X651 @ X652))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem))&((X650 @ (sub @ (esk7_1 @ X650) @ (push @ X657 @ id)))|~(X650 @ X657)|((var @ (esk6_3 @ X650 @ X651 @ X652))|((X650 @ (esk5_3 @ X650 @ X651 @ X652))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem)))))&(((~(X650 @ (lam @ (esk7_1 @ X650)))|(~(X650 @ (sub @ (esk6_3 @ X650 @ X651 @ X652) @ X652))|((X650 @ (esk4_3 @ X650 @ X651 @ X652))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem))&((X650 @ (sub @ (esk7_1 @ X650) @ (push @ X657 @ id)))|~(X650 @ X657)|(~(X650 @ (sub @ (esk6_3 @ X650 @ X651 @ X652) @ X652))|((X650 @ (esk4_3 @ X650 @ X651 @ X652))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem)))&((~(X650 @ (lam @ (esk7_1 @ X650)))|((var @ (esk6_3 @ X650 @ X651 @ X652))|((X650 @ (esk4_3 @ X650 @ X651 @ X652))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem))&((X650 @ (sub @ (esk7_1 @ X650) @ (push @ X657 @ id)))|~(X650 @ X657)|((var @ (esk6_3 @ X650 @ X651 @ X652))|((X650 @ (esk4_3 @ X650 @ X651 @ X652))|(X650 @ (sub @ X651 @ X652))))|~(induction2lem)))))&(((((epred15_0 @ (ap @ X661 @ X662))|~(epred15_0 @ X662)|~(epred15_0 @ X661)|(induction2lem))&(~(epred15_0 @ (sub @ esk8_0 @ esk9_0))|(induction2lem)))&((epred15_0 @ (sub @ X663 @ esk9_0))|~(var @ X663)|(induction2lem)))&((~(epred15_0 @ (sub @ X664 @ (push @ (esk10_1 @ X664) @ id)))|(epred15_0 @ (lam @ X664))|(induction2lem))&((epred15_0 @ (esk10_1 @ X664))|(epred15_0 @ (lam @ X664))|(induction2lem))))))&(((((ap @ (sub @ esk11_0 @ id) @ esk13_0)=(ap @ (sub @ esk12_0 @ id) @ esk14_0))|(hoasapinj2))&(((esk13_0)!=(esk14_0))|(hoasapinj2)))&(~(hoasapinj2)|(((ap @ (sub @ X670 @ id) @ X672)!=(ap @ (sub @ X671 @ id) @ X673))|((X672)=(X673))))))&(hoasapnotvar_gthm))&((~(hoasapinj1)|(((X674)=(X675))|((ap @ (sub @ X674 @ id) @ X676)!=(ap @ (sub @ X675 @ id) @ X677))))&((((esk15_0)!=(esk16_0))|(hoasapinj1))&(((ap @ (sub @ esk15_0 @ id) @ esk17_0)=(ap @ (sub @ esk16_0 @ id) @ esk18_0))|(hoasapinj1)))))&(apnotvar))&(pushprop_lthm_orig))&((~(hoasinduction_lem3v2_f_lthm)|((sub @ X682 @ (push @ X684 @ X685))=(esk19_1 @ X682 @ X685 @ X684)))&(((sub @ esk20_0 @ (push @ (esk21_1 @ X687) @ (esk22_1 @ X687)))!=(X687 @ (esk22_1 @ X687) @ (esk21_1 @ X687)))|(hoasinduction_lem3v2_f_lthm))))&((((((~(var @ X695)|(epred17_0 @ X695)|(((esk26_0)!=(sub @ esk26_0 @ id))|(epred1_0))|(~(X691 @ (esk23_1 @ X691))|~(epred16_0 @ id @ (esk23_1 @ X691) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred17_0 @ esk24_0)|(((esk26_0)!=(sub @ esk26_0 @ id))|(epred1_0))|(~(X691 @ (esk23_1 @ X691))|~(epred16_0 @ id @ (esk23_1 @ X691) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred17_0 @ (esk25_1 @ X696))|(epred17_0 @ (lam @ X696))|(((esk26_0)!=(sub @ esk26_0 @ id))|(epred1_0))|(~(X691 @ (esk23_1 @ X691))|~(epred16_0 @ id @ (esk23_1 @ X691) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred17_0 @ (sub @ X696 @ (push @ (esk25_1 @ X696) @ id)))|(epred17_0 @ (lam @ X696))|(((esk26_0)!=(sub @ esk26_0 @ id))|(epred1_0))|(~(X691 @ (esk23_1 @ X691))|~(epred16_0 @ id @ (esk23_1 @ X691) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred17_0 @ X698)|(epred17_0 @ (ap @ X698 @ X699))|~(epred17_0 @ X699)|(((esk26_0)!=(sub @ esk26_0 @ id))|(epred1_0))|(~(X691 @ (esk23_1 @ X691))|~(epred16_0 @ id @ (esk23_1 @ X691) @ id))|~(hoasinduction_no_psi_cond_lthm)))&((((~(var @ X695)|(epred17_0 @ X695)|(((esk26_0)!=(sub @ esk26_0 @ id))|(epred1_0))|((X691 @ (esk23_1 @ X691))|(epred16_0 @ id @ (esk23_1 @ X691) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred17_0 @ esk24_0)|(((esk26_0)!=(sub @ esk26_0 @ id))|(epred1_0))|((X691 @ (esk23_1 @ X691))|(epred16_0 @ id @ (esk23_1 @ X691) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred17_0 @ (esk25_1 @ X696))|(epred17_0 @ (lam @ X696))|(((esk26_0)!=(sub @ esk26_0 @ id))|(epred1_0))|((X691 @ (esk23_1 @ X691))|(epred16_0 @ id @ (esk23_1 @ X691) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred17_0 @ (sub @ X696 @ (push @ (esk25_1 @ X696) @ id)))|(epred17_0 @ (lam @ X696))|(((esk26_0)!=(sub @ esk26_0 @ id))|(epred1_0))|((X691 @ (esk23_1 @ X691))|(epred16_0 @ id @ (esk23_1 @ X691) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred17_0 @ X698)|(epred17_0 @ (ap @ X698 @ X699))|~(epred17_0 @ 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X1201)))|(X1200 @ id @ (lam @ X1201) @ id))))|~(hoasinduction_lem3))))))))&(((((epred54_0 @ id @ (sub @ esk245_0 @ (push @ X1218 @ id)) @ id)|~(epred54_0 @ id @ X1218 @ id)|(hoasinduction_lem3aaa))&(~(epred54_0 @ id @ (lam @ (sub @ esk245_0 @ (push @ one @ sh))) @ id)|(hoasinduction_lem3aaa)))&((~(epred54_0 @ id @ (X1219 @ id @ (esk252_2 @ X1219 @ X1220)) @ id)|(((X1219 @ (comp @ (esk246_2 @ X1219 @ X1220) @ (esk248_2 @ X1219 @ X1220)) @ (sub @ (esk247_2 @ X1219 @ X1220) @ (esk248_2 @ X1219 @ X1220)))!=(sub @ X1220 @ (push @ (sub @ (esk247_2 @ X1219 @ X1220) @ (esk248_2 @ X1219 @ X1220)) @ (comp @ (esk246_2 @ X1219 @ X1220) @ (esk248_2 @ X1219 @ X1220)))))|((sub @ (X1219 @ (esk249_2 @ X1219 @ X1220) @ (esk250_2 @ X1219 @ X1220)) @ (esk251_2 @ X1219 @ X1220))!=(sub @ (sub @ X1220 @ (push @ (esk250_2 @ X1219 @ X1220) @ (esk249_2 @ X1219 @ X1220))) @ (esk251_2 @ X1219 @ X1220)))|(epred54_0 @ id @ (lam @ (X1219 @ sh @ one)) @ id))|(hoasinduction_lem3aaa))&((epred54_0 @ id @ (esk252_2 @ X1219 @ X1220) @ id)|(((X1219 @ (comp @ (esk246_2 @ X1219 @ X1220) @ (esk248_2 @ X1219 @ X1220)) @ (sub @ (esk247_2 @ X1219 @ X1220) @ (esk248_2 @ X1219 @ X1220)))!=(sub @ X1220 @ (push @ (sub @ (esk247_2 @ X1219 @ X1220) @ (esk248_2 @ X1219 @ X1220)) @ (comp @ (esk246_2 @ X1219 @ X1220) @ (esk248_2 @ X1219 @ X1220)))))|((sub @ (X1219 @ (esk249_2 @ X1219 @ X1220) @ (esk250_2 @ X1219 @ X1220)) @ (esk251_2 @ X1219 @ X1220))!=(sub @ (sub @ X1220 @ (push @ (esk250_2 @ X1219 @ X1220) @ (esk249_2 @ X1219 @ X1220))) @ (esk251_2 @ X1219 @ X1220)))|(epred54_0 @ id @ (lam @ (X1219 @ sh @ one)) @ id))|(hoasinduction_lem3aaa))))&(((((((esk254_1 @ X1228 @ (comp @ X1233 @ X1235) @ (sub @ X1234 @ X1235))=(sub @ (esk255_1 @ X1228) @ (push @ (sub @ X1234 @ X1235) @ (comp @ X1233 @ X1235))))|(~(X1228 @ id @ (sub @ X1229 @ (push @ (esk253_2 @ X1228 @ X1229) @ id)) @ id)|(X1228 @ id @ (lam @ (sub @ X1229 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&(((sub @ (esk254_1 @ X1228 @ X1236 @ X1237) @ X1238)=(sub @ (sub @ (esk255_1 @ X1228) @ (push @ X1237 @ X1236)) @ X1238))|(~(X1228 @ id @ (sub @ X1229 @ (push @ (esk253_2 @ X1228 @ X1229) @ id)) @ id)|(X1228 @ id @ (lam @ (sub @ X1229 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&(~(X1228 @ id @ (lam @ (esk254_1 @ X1228 @ sh @ one)) @ id)|(~(X1228 @ id @ (sub @ X1229 @ (push @ (esk253_2 @ X1228 @ X1229) @ id)) @ id)|(X1228 @ id @ (lam @ (sub @ X1229 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&((X1228 @ id @ (esk254_1 @ X1228 @ id @ X1239) @ id)|~(X1228 @ id @ X1239 @ id)|(~(X1228 @ id @ (sub @ X1229 @ (push @ (esk253_2 @ X1228 @ X1229) @ id)) @ id)|(X1228 @ id @ (lam @ (sub @ X1229 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&((((((esk254_1 @ X1228 @ (comp @ X1233 @ X1235) @ (sub @ X1234 @ X1235))=(sub @ (esk255_1 @ X1228) @ (push @ (sub @ X1234 @ X1235) @ (comp @ X1233 @ X1235))))|((X1228 @ id @ (esk253_2 @ X1228 @ X1229) @ id)|(X1228 @ id @ (lam @ (sub @ X1229 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&(((sub @ (esk254_1 @ X1228 @ X1236 @ X1237) @ X1238)=(sub @ (sub @ (esk255_1 @ X1228) @ (push @ X1237 @ X1236)) @ X1238))|((X1228 @ id @ (esk253_2 @ X1228 @ X1229) @ id)|(X1228 @ id @ (lam @ (sub @ X1229 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&(~(X1228 @ id @ (lam @ (esk254_1 @ X1228 @ sh @ one)) @ id)|((X1228 @ id @ (esk253_2 @ X1228 @ X1229) @ id)|(X1228 @ id @ (lam @ (sub @ X1229 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&((X1228 @ id @ (esk254_1 @ X1228 @ id @ X1239) @ id)|~(X1228 @ id @ X1239 @ id)|((X1228 @ id @ (esk253_2 @ X1228 @ X1229) @ id)|(X1228 @ id @ (lam @ (sub @ X1229 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))))))&(((((((sub @ (esk256_0 @ X1244 @ X1245) @ X1246)=(esk256_0 @ (comp @ X1244 @ X1246) @ (sub @ X1245 @ X1246)))|(hoaslaminj))&(((esk256_0 @ esk258_0 @ esk259_0)!=(esk257_0 @ esk258_0 @ esk259_0))|(hoaslaminj)))&(((lam @ (esk256_0 @ sh @ one))=(lam @ (esk257_0 @ sh @ one)))|(hoaslaminj)))&(((sub @ (esk257_0 @ X1247 @ X1248) @ X1249)=(esk257_0 @ (comp @ X1247 @ X1249) @ (sub @ X1248 @ X1249)))|(hoaslaminj)))&(~(hoaslaminj)|(((sub @ (X1250 @ (esk260_2 @ X1250 @ X1251) @ (esk261_2 @ X1250 @ X1251)) @ (esk262_2 @ X1250 @ X1251))!=(X1250 @ (comp @ (esk260_2 @ X1250 @ X1251) @ (esk262_2 @ X1250 @ X1251)) @ (sub @ (esk261_2 @ X1250 @ X1251) @ (esk262_2 @ X1250 @ X1251))))|((X1250 @ X1255 @ X1256)=(X1251 @ X1255 @ X1256))|((lam @ (X1250 @ sh @ one))!=(lam @ (X1251 @ sh @ one)))|((sub @ (X1251 @ (esk263_2 @ X1250 @ X1251) @ (esk264_2 @ X1250 @ X1251)) @ (esk265_2 @ X1250 @ X1251))!=(X1251 @ (comp @ (esk263_2 @ X1250 @ X1251) @ (esk265_2 @ X1250 @ X1251)) @ (sub @ (esk264_2 @ X1250 @ X1251) @ (esk265_2 @ X1250 @ X1251))))))))&((~(hoasinduction_lthm)|(epred11_0))&(~(epred11_0)|(hoasinduction_lthm))))&(hoasinduction_lem3v2_gthm))&(((((X1260)=(sub @ one @ (push @ X1260 @ X1261)))|(induction2lem_lthm))&((((X1263)=(comp @ sh @ (push @ X1262 @ X1263)))|(induction2lem_lthm))&((((X1264)=(comp @ X1264 @ id))|(induction2lem_lthm))&(~(epred12_0)|(induction2lem_lthm)))))&(~(induction2lem_lthm)|(((esk266_0)!=(sub @ one @ (push @ esk266_0 @ esk267_0)))|(((esk269_0)!=(comp @ sh @ (push @ esk268_0 @ esk269_0)))|(((esk270_0)!=(comp @ esk270_0 @ id))|(epred12_0)))))))&~(ulamvar1))&(axvarshift))&((~(hoasinduction_lem3v2_f)|((sub @ X1270 @ (push @ X1272 @ X1273))=(esk271_1 @ X1270 @ X1273 @ X1272)))&(((sub @ esk272_0 @ (push @ (esk273_1 @ X1275) @ (esk274_1 @ X1275)))!=(X1275 @ (esk274_1 @ X1275) @ (esk273_1 @ X1275)))|(hoasinduction_lem3v2_f))))&(hoasinduction_lem1v2_gthm))&(((((esk275_0)!=(esk276_0))|(shinj))&(((sub @ esk275_0 @ sh)=(sub @ esk276_0 @ sh))|(shinj)))&(~(shinj)|(((X1280)=(X1281))|((sub @ X1280 @ sh)!=(sub @ X1281 @ sh))))))&(pushprop_lem0_gthm))&(pushprop_lem1_gthm))&~(var @ (d2term @ d_one)))&(((~(X1285 @ X1286)|(X1284 @ (sub @ X1286 @ (push @ X1282 @ X1283)))|~(pushprop_p_and_p_prime @ X1282 @ X1283 @ X1284 @ X1285))&(~(X1284 @ (sub @ X1287 @ (push @ X1282 @ X1283)))|(X1285 @ X1287)|~(pushprop_p_and_p_prime @ X1282 @ X1283 @ X1284 @ X1285)))&((~(X1291 @ (esk277_4 @ X1288 @ X1289 @ X1290 @ X1291))|~(X1290 @ (sub @ (esk277_4 @ X1288 @ X1289 @ X1290 @ X1291) @ (push @ X1288 @ X1289)))|(pushprop_p_and_p_prime @ X1288 @ X1289 @ X1290 @ X1291))&((X1291 @ (esk277_4 @ X1288 @ X1289 @ X1290 @ X1291))|(X1290 @ (sub @ (esk277_4 @ X1288 @ X1289 @ X1290 @ X1291) @ (push @ X1288 @ X1289)))|(pushprop_p_and_p_prime @ X1288 @ X1289 @ X1290 @ X1291)))))&(((~(X1294 @ X1295)|(X1293 @ id @ X1295 @ id)|~(hoasinduction_p_and_p_prime @ X1293 @ X1294))&(~(X1293 @ id @ X1296 @ id)|(X1294 @ X1296)|~(hoasinduction_p_and_p_prime @ X1293 @ X1294)))&((~(X1298 @ (esk278_2 @ X1297 @ X1298))|~(X1297 @ id @ (esk278_2 @ X1297 @ X1298) @ id)|(hoasinduction_p_and_p_prime @ X1297 @ X1298))&((X1298 @ (esk278_2 @ X1297 @ X1298))|(X1297 @ id @ (esk278_2 @ X1297 @ X1298) @ id)|(hoasinduction_p_and_p_prime @ X1297 @ X1298)))))&((id)=(d2subst @ d_id)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((X1300)=(d_id)))&((X1301)=(d2subst @ (esk279_1 @ X1301))))&((X1303)=(d2term @ (esk280_1 @ X1303))))), 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])])])])])])])). 0.62/0.79 thf(c_0_14, negated_conjecture, ![X1309:term > $o, X1310:term > $o, X1311:term, X1312:subst]:(((((epred55_0 @ esk281_0)|~(pushprop_lem1v2))&(((pushprop_p_and_p_prime @ esk281_0 @ esk282_0 @ epred55_0 @ epred56_0)|~(pushprop_lem1v2))&(~(epred56_0 @ one)|~(pushprop_lem1v2))))&((pushprop_lem1v2)|(~(X1309 @ X1311)|(~(pushprop_p_and_p_prime @ X1311 @ X1312 @ X1309 @ X1310)|(X1310 @ one)))))), 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_12])])])])])])). 0.62/0.79 thf(c_0_15, plain, ![X10:term]:(((X10)=(d2term @ (esk280_1 @ X10)))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_16, plain, ![X1:d_term]:(((X1)=(d_one))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_17, plain, ((one)=(d2term @ d_one)), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_18, negated_conjecture, ((pushprop_p_and_p_prime @ esk281_0 @ esk282_0 @ epred55_0 @ epred56_0)|~((pushprop_lem1v2))), inference(split_conjunct,[status(thm)],[c_0_14])). 0.62/0.79 thf(c_0_19, plain, ![X10:term]:(((one)=(X10))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16]), c_0_17])). 0.62/0.79 thf(c_0_20, plain, ![X6:subst]:(((X6)=(d2subst @ (esk279_1 @ X6)))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_21, plain, ![X4:d_subst]:(((X4)=(d_id))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_22, plain, ((id)=(d2subst @ d_id)), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_23, plain, ((termmset)|((esk108_0)!=(sub @ esk108_0 @ id))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_24, plain, ((apinj2)|((esk184_0)!=(esk185_0))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_25, negated_conjecture, ((pushprop_p_and_p_prime @ one @ esk282_0 @ epred55_0 @ epred56_0)|~((pushprop_lem1v2))), inference(rw,[status(thm)],[c_0_18, c_0_19])). 0.62/0.79 thf(c_0_26, plain, ![X6:subst]:(((id)=(X6))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21]), c_0_22])). 0.62/0.79 thf(c_0_27, plain, ![X10:term]:((((X10)=(sub @ X10 @ id))|~((termmset)))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_28, plain, (termmset), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_19]), c_0_19]), c_0_19])])). 0.62/0.79 thf(c_0_29, plain, ((epred13_0 @ esk2_0)|(pushprop_lem1v2)), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_30, plain, ![X10:term, X15:term, X13:term, X12:term]:((((X10)=(X12))|~((apinj2))|((ap @ X13 @ X10)!=(ap @ X15 @ X12)))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_31, plain, (apinj2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_19]), c_0_19])])). 0.62/0.79 thf(c_0_32, negated_conjecture, ((pushprop_p_and_p_prime @ one @ id @ epred55_0 @ epred56_0)|~((pushprop_lem1v2))), inference(rw,[status(thm)],[c_0_25, c_0_26])). 0.62/0.79 thf(c_0_33, plain, ![X10:term]:(((epred14_0 @ X10)|(pushprop_lem1v2)|~((epred13_0 @ (sub @ X10 @ (push @ esk2_0 @ esk3_0)))))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_34, plain, ![X10:term]:(((sub @ X10 @ id)=(X10))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_28])])). 0.62/0.79 thf(c_0_35, plain, ((epred13_0 @ one)|(pushprop_lem1v2)), inference(rw,[status(thm)],[c_0_29, c_0_19])). 0.62/0.79 thf(c_0_36, plain, ![X10:term, X12:term]:(((X10)=(X12))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_19]), c_0_19]), c_0_31])])). 0.62/0.79 thf(c_0_37, plain, ((pushprop_lem1v2)|~((epred14_0 @ one))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_38, negated_conjecture, ((epred55_0 @ esk281_0)|~((pushprop_lem1v2))), inference(split_conjunct,[status(thm)],[c_0_14])). 0.62/0.79 thf(c_0_39, negated_conjecture, ![X6:subst]:(((pushprop_p_and_p_prime @ one @ X6 @ epred55_0 @ epred56_0)|~((pushprop_lem1v2)))), inference(spm,[status(thm)],[c_0_32, c_0_26])). 0.62/0.79 thf(c_0_40, plain, ![X10:term]:(((epred14_0 @ X10)|(pushprop_lem1v2)|~((epred13_0 @ X10)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_19]), c_0_26]), c_0_26]), c_0_34])). 0.62/0.79 thf(c_0_41, plain, ![X10:term]:(((epred13_0 @ X10)|(pushprop_lem1v2))), inference(spm,[status(thm)],[c_0_35, c_0_36])). 0.62/0.79 thf(c_0_42, plain, ![X10:term]:(((pushprop_lem1v2)|~((epred14_0 @ X10)))), inference(spm,[status(thm)],[c_0_37, c_0_36])). 0.62/0.79 thf(c_0_43, negated_conjecture, ((epred55_0 @ one)|~((pushprop_lem1v2))), inference(rw,[status(thm)],[c_0_38, c_0_19])). 0.62/0.79 thf(c_0_44, negated_conjecture, (~((epred56_0 @ one))|~((pushprop_lem1v2))), inference(split_conjunct,[status(thm)],[c_0_14])). 0.62/0.79 thf(c_0_45, plain, ![X6:subst, X8:term > $o, X12:term, X10:term, X9:term > $o]:(((X9 @ X10)|~((X8 @ (sub @ X10 @ (push @ X12 @ X6))))|~((pushprop_p_and_p_prime @ X12 @ X6 @ X8 @ X9)))), inference(split_conjunct,[status(thm)],[c_0_13])). 0.62/0.79 thf(c_0_46, negated_conjecture, ![X10:term, X6:subst]:(((pushprop_p_and_p_prime @ X10 @ X6 @ epred55_0 @ epred56_0)|~((pushprop_lem1v2)))), inference(spm,[status(thm)],[c_0_39, c_0_36])). 0.62/0.79 thf(c_0_47, plain, (pushprop_lem1v2), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_40, c_0_41]), c_0_42])). 0.62/0.79 thf(c_0_48, negated_conjecture, ![X10:term]:(((epred55_0 @ X10)|~((pushprop_lem1v2)))), inference(spm,[status(thm)],[c_0_43, c_0_36])). 0.62/0.79 thf(c_0_49, negated_conjecture, ![X10:term]:((~((epred56_0 @ X10))|~((pushprop_lem1v2)))), inference(spm,[status(thm)],[c_0_44, c_0_36])). 0.62/0.79 thf(c_0_50, plain, ![X6:subst, X8:term > $o, X9:term > $o, X12:term, X10:term]:(((X8 @ X10)|~((pushprop_p_and_p_prime @ X12 @ X6 @ X9 @ X8))|~((X9 @ X10)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_26]), c_0_34])). 0.62/0.79 thf(c_0_51, negated_conjecture, ![X10:term, X6:subst]:((pushprop_p_and_p_prime @ X10 @ X6 @ epred55_0 @ epred56_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46, c_0_47])])). 0.62/0.79 thf(c_0_52, negated_conjecture, ![X10:term]:((epred55_0 @ X10)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_47])])). 0.62/0.79 thf(c_0_53, negated_conjecture, ![X10:term]:(~((epred56_0 @ X10))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_47])])). 0.62/0.79 thf(c_0_54, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_52])]), c_0_53]), ['proof']). 0.62/0.79 % SZS output end CNFRefutation 0.62/0.79 % Parsed axioms : 132 0.62/0.79 % Removed by relevancy pruning/SinE : 0 0.62/0.79 % Initial clauses : 1405 0.62/0.79 % Removed in clause preprocessing : 131 0.62/0.79 % Initial clauses in saturation : 1274 0.62/0.79 % Processed clauses : 1612 0.62/0.79 % ...of these trivial : 691 0.62/0.79 % ...subsumed : 254 0.62/0.79 % ...remaining for further processing : 667 0.62/0.79 % Other redundant clauses eliminated : 0 0.62/0.79 % Clauses deleted for lack of memory : 0 0.62/0.79 % Backward-subsumed : 170 0.62/0.79 % Backward-rewritten : 99 0.62/0.79 % Generated clauses : 286 0.62/0.79 % ...of the previous two non-redundant : 324 0.62/0.79 % ...aggressively subsumed : 0 0.62/0.79 % Contextual simplify-reflections : 157 0.62/0.79 % Paramodulations : 272 0.62/0.79 % Factorizations : 0 0.62/0.79 % NegExts : 0 0.62/0.79 % Equation resolutions : 0 0.62/0.79 % Disequality decompositions : 0 0.62/0.79 % Total rewrite steps : 13377 0.62/0.79 % ...of those cached : 12710 0.62/0.79 % Propositional unsat checks : 0 0.62/0.79 % Propositional check models : 0 0.62/0.79 % Propositional check unsatisfiable : 0 0.62/0.79 % Propositional clauses : 0 0.62/0.79 % Propositional clauses after purity: 0 0.62/0.79 % Propositional unsat core size : 0 0.62/0.79 % Propositional preprocessing time : 0.000 0.62/0.79 % Propositional encoding time : 0.000 0.62/0.79 % Propositional solver time : 0.000 0.62/0.79 % Success case prop preproc time : 0.000 0.62/0.79 % Success case prop encoding time : 0.000 0.62/0.79 % Success case prop solver time : 0.000 0.62/0.79 % Current number of processed clauses : 155 0.62/0.79 % Positive orientable unit clauses : 101 0.62/0.79 % Positive unorientable unit clauses: 4 0.62/0.79 % Negative unit clauses : 8 0.62/0.79 % Non-unit-clauses : 42 0.62/0.79 % Current number of unprocessed clauses: 88 0.62/0.79 % ...number of literals in the above : 298 0.62/0.79 % Current number of archived formulas : 0 0.62/0.79 % Current number of archived clauses : 513 0.62/0.79 % Clause-clause subsumption calls (NU) : 41259 0.62/0.79 % Rec. Clause-clause subsumption calls : 14932 0.62/0.79 % Non-unit clause-clause subsumptions : 587 0.62/0.79 % Unit Clause-clause subsumption calls : 3891 0.62/0.79 % Rewrite failures with RHS unbound : 0 0.62/0.79 % BW rewrite match attempts : 2567 0.62/0.79 % BW rewrite match successes : 85 0.62/0.79 % Condensation attempts : 1615 0.62/0.79 % Condensation successes : 77 0.62/0.79 % Termbank termtop insertions : 252258 0.62/0.79 % Search garbage collected termcells : 24909 0.62/0.79 0.62/0.79 % ------------------------------------------------- 0.62/0.79 % User time : 0.210 s 0.62/0.79 % System time : 0.021 s 0.62/0.79 % Total time : 0.231 s 0.62/0.79 % Maximum resident set size: 8080 pages 0.62/0.79 0.62/0.79 % ------------------------------------------------- 0.62/0.79 % User time : 0.308 s 0.62/0.79 % System time : 0.038 s 0.62/0.79 % Total time : 0.346 s 0.62/0.79 % Maximum resident set size: 5120 pages 0.62/0.79 % E exiting 0.62/0.79 EOF