%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX155^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:24 AM UTC 2026
% Result : Theorem 0.45s 0.38s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX155^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n004.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:08:56 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.Nz5wer6szc/E---3.1_1484892.p
% 0.45/0.38 % Version: 3.5.1-ho
% 0.45/0.38 % partial match(1): HSLMSLSMSSSNHFA
% 0.45/0.38 % Preprocessing class: HSLMSLSSSSSNHFA.
% 0.45/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.38 % Starting new_ho_10 with 1200s (4) cores
% 0.45/0.38 % Starting sh5l with 600s (2) cores
% 0.45/0.38 % Starting new_bool_1 with 300s (1) cores
% 0.45/0.38 % Starting new_bool_2 with 300s (1) cores
% 0.45/0.38 % new_bool_2 with pid 1484928 completed with status 9
% 0.45/0.38 % new_bool_1 with pid 1484927 completed with status 9
% 0.45/0.38 % sh5l with pid 1484926 completed with status 0
% 0.45/0.38 % Result found by sh5l
% 0.45/0.38 % partial match(1): HSLMSLSMSSSNHFA
% 0.45/0.38 % Preprocessing class: HSLMSLSSSSSNHFA.
% 0.45/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.38 % Starting new_ho_10 with 1200s (4) cores
% 0.45/0.38 % Starting sh5l with 600s (2) cores
% 0.45/0.38 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.45/0.38 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.45/0.38 % Search class: HGHSM-SMLM31-DHFFFMBN
% 0.45/0.38 % partial match(1): HGHSM-SMLM31-MHFFFMBN
% 0.45/0.38 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.45/0.38 % Starting SubtermCWHack with 55s (1) cores
% 0.45/0.38 % Starting sh5l with 61s (1) cores
% 0.45/0.38 % SubtermCWHack with pid 1484954 completed with status 0
% 0.45/0.38 % Result found by SubtermCWHack
% 0.45/0.38 % partial match(1): HSLMSLSMSSSNHFA
% 0.45/0.38 % Preprocessing class: HSLMSLSSSSSNHFA.
% 0.45/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.38 % Starting new_ho_10 with 1200s (4) cores
% 0.45/0.38 % Starting sh5l with 600s (2) cores
% 0.45/0.38 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.45/0.38 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.45/0.38 % Search class: HGHSM-SMLM31-DHFFFMBN
% 0.45/0.38 % partial match(1): HGHSM-SMLM31-MHFFFMBN
% 0.45/0.38 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.45/0.38 % Starting SubtermCWHack with 55s (1) cores
% 0.45/0.38 % Preprocessing time : 0.013 s
% 0.45/0.38
% 0.45/0.38 % Proof found!
% 0.45/0.38 % SZS status Theorem
% 0.45/0.38 % SZS output start CNFRefutation
% 0.45/0.38 thf(decl_sort1, type, term: $tType).
% 0.45/0.38 thf(decl_sort2, type, subst: $tType).
% 0.45/0.38 thf(decl_sort3, type, d_term: $tType).
% 0.45/0.38 thf(decl_sort4, type, d_subst: $tType).
% 0.45/0.38 thf(decl_23, type, one: term).
% 0.45/0.38 thf(decl_24, type, ap: term > term > term).
% 0.45/0.38 thf(decl_25, type, lam: term > term).
% 0.45/0.38 thf(decl_26, type, sub: term > subst > term).
% 0.45/0.38 thf(decl_27, type, id: subst).
% 0.45/0.38 thf(decl_28, type, sh: subst).
% 0.45/0.38 thf(decl_29, type, push: term > subst > subst).
% 0.45/0.38 thf(decl_30, type, comp: subst > subst > subst).
% 0.45/0.38 thf(decl_31, type, var: term > $o).
% 0.45/0.38 thf(decl_32, type, pushprop_lem1v2: $o).
% 0.45/0.38 thf(decl_33, type, pushprop_lem1_gthm: $o).
% 0.45/0.38 thf(decl_34, type, axmap: $o).
% 0.45/0.38 thf(decl_35, type, pushprop_lem0_gthm: $o).
% 0.45/0.38 thf(decl_36, type, shinj: $o).
% 0.45/0.38 thf(decl_37, type, hoasinduction_lem1v2: $o).
% 0.45/0.38 thf(decl_38, type, hoasinduction_lem1v2_gthm: $o).
% 0.45/0.38 thf(decl_39, type, hoasap: subst > term > subst > term > term).
% 0.45/0.38 thf(decl_40, type, induction2lem: $o).
% 0.45/0.38 thf(decl_41, type, hoasinduction_lem3v2_f: $o).
% 0.45/0.38 thf(decl_42, type, axvarshift: $o).
% 0.45/0.38 thf(decl_43, type, hoasapinj2: $o).
% 0.45/0.38 thf(decl_44, type, hoasapnotvar_gthm: $o).
% 0.45/0.38 thf(decl_45, type, hoasapinj1: $o).
% 0.45/0.38 thf(decl_46, type, ulamvar1: $o).
% 0.45/0.38 thf(decl_47, type, induction2lem_lthm: $o).
% 0.45/0.38 thf(decl_48, type, hoasinduction_lem3v2_gthm: $o).
% 0.45/0.38 thf(decl_49, type, apnotvar: $o).
% 0.45/0.38 thf(decl_50, type, pushprop_lthm_orig: $o).
% 0.45/0.38 thf(decl_51, type, hoasinduction_lem3v2_f_lthm: $o).
% 0.45/0.38 thf(decl_52, type, hoasinduction_lthm: $o).
% 0.45/0.38 thf(decl_53, type, hoasinduction_no_psi_cond_lthm: $o).
% 0.45/0.38 thf(decl_54, type, hoaslaminj: $o).
% 0.45/0.38 thf(decl_55, type, hoasinduction_lem3aaa: $o).
% 0.45/0.38 thf(decl_56, type, induction2lem_gthm: $o).
% 0.45/0.38 thf(decl_57, type, hoasinduction_lem3aa_lthm: $o).
% 0.45/0.38 thf(decl_58, type, hoasinduction_lem3: $o).
% 0.45/0.38 thf(decl_59, type, hoasinduction_lem2: $o).
% 0.45/0.38 thf(decl_60, type, termmset_lthm: $o).
% 0.45/0.38 thf(decl_61, type, hoasinduction_lem1: $o).
% 0.45/0.38 thf(decl_62, type, hoaslamnotap_lthm: $o).
% 0.45/0.38 thf(decl_63, type, pushprop_lem1v2_lthm: $o).
% 0.45/0.38 thf(decl_64, type, hoasapnotvar: $o).
% 0.45/0.38 thf(decl_65, type, hoasinduction_lem0: $o).
% 0.45/0.38 thf(decl_66, type, hoasinduction: $o).
% 0.45/0.38 thf(decl_67, type, hoasinduction_gthm: $o).
% 0.45/0.38 thf(decl_68, type, axapp: $o).
% 0.45/0.38 thf(decl_69, type, hoaslamnotvar_lthm: $o).
% 0.45/0.38 thf(decl_70, type, pushprop_lem3v2_lthm: $o).
% 0.45/0.38 thf(decl_71, type, hoasinduction_lem3b_lthm: $o).
% 0.45/0.38 thf(decl_72, type, ulamvarind: $o).
% 0.45/0.38 thf(decl_73, type, induction: $o).
% 0.45/0.38 thf(decl_74, type, hoasinduction_lem3a_lthm: $o).
% 0.45/0.38 thf(decl_75, type, termmset_gthm: $o).
% 0.45/0.38 thf(decl_76, type, hoasinduction_lem3aa: $o).
% 0.45/0.38 thf(decl_77, type, pushprop_lem1v2_gthm: $o).
% 0.45/0.38 thf(decl_78, type, hoaslamnotap_gthm: $o).
% 0.45/0.38 thf(decl_79, type, hoaslamnotvar_gthm: $o).
% 0.45/0.38 thf(decl_80, type, hoasinduction_lem3b_gthm: $o).
% 0.45/0.38 thf(decl_81, type, pushprop_lem2v2: $o).
% 0.45/0.38 thf(decl_82, type, hoasinduction_lem3a_gthm: $o).
% 0.45/0.38 thf(decl_83, type, axclos: $o).
% 0.45/0.38 thf(decl_84, type, axassoc: $o).
% 0.45/0.38 thf(decl_85, type, hoasinduction_lem2v2: $o).
% 0.45/0.38 thf(decl_86, type, pushprop_lthm: $o).
% 0.45/0.38 thf(decl_87, type, apinj2: $o).
% 0.45/0.38 thf(decl_88, type, apinj1: $o).
% 0.45/0.38 thf(decl_89, type, hoasapinj2_lthm: $o).
% 0.45/0.38 thf(decl_90, type, hoasinduction_lem3v2a: $o).
% 0.45/0.38 thf(decl_91, type, hoasapinj1_lthm: $o).
% 0.45/0.38 thf(decl_92, type, hoaslaminj_lthm: $o).
% 0.45/0.38 thf(decl_93, type, axvarcons: $o).
% 0.45/0.38 thf(decl_94, type, hoaslam: subst > (subst > term > term) > term).
% 0.45/0.38 thf(decl_95, type, axscons: $o).
% 0.45/0.38 thf(decl_96, type, hoasinduction_lem2v2_gthm: $o).
% 0.45/0.38 thf(decl_97, type, axidr: $o).
% 0.45/0.38 thf(decl_98, type, pushprop_lem1: $o).
% 0.45/0.38 thf(decl_99, type, laminj: $o).
% 0.45/0.38 thf(decl_100, type, hoasinduction_lem3_lthm: $o).
% 0.45/0.38 thf(decl_101, type, pushprop_lem0: $o).
% 0.45/0.38 thf(decl_102, type, pushprop_gthm: $o).
% 0.45/0.38 thf(decl_103, type, axabs: $o).
% 0.45/0.38 thf(decl_104, type, hoasinduction_lem3v2a_lthm: $o).
% 0.45/0.38 thf(decl_105, type, hoasinduction_lem2_lthm: $o).
% 0.45/0.38 thf(decl_106, type, hoasapinj2_gthm: $o).
% 0.45/0.38 thf(decl_107, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 0.45/0.38 thf(decl_108, type, hoasinduction_lem1_lthm: $o).
% 0.45/0.38 thf(decl_109, type, lamnotap: $o).
% 0.45/0.38 thf(decl_110, type, hoasapinj1_gthm: $o).
% 0.45/0.38 thf(decl_111, type, hoaslamnotvar: $o).
% 0.45/0.38 thf(decl_112, type, axidl: $o).
% 0.45/0.38 thf(decl_113, type, hoaslaminj_gthm: $o).
% 0.45/0.38 thf(decl_114, type, induction2_lthm: $o).
% 0.45/0.38 thf(decl_115, type, hoasinduction_lem0_lthm: $o).
% 0.45/0.38 thf(decl_116, type, substmonoid_lthm: $o).
% 0.45/0.38 thf(decl_117, type, pushprop: $o).
% 0.45/0.38 thf(decl_118, type, hoasinduction_lem3_gthm: $o).
% 0.45/0.38 thf(decl_119, type, hoasinduction_lem2_gthm: $o).
% 0.45/0.38 thf(decl_120, type, hoasinduction_lem3b: $o).
% 0.45/0.38 thf(decl_121, type, substmonoid: $o).
% 0.45/0.38 thf(decl_122, type, lamnotvar: $o).
% 0.45/0.38 thf(decl_123, type, hoasinduction_lem3a: $o).
% 0.45/0.38 thf(decl_124, type, hoasinduction_lem1_gthm: $o).
% 0.45/0.38 thf(decl_125, type, hoasinduction_no_psi_cond: $o).
% 0.45/0.38 thf(decl_126, type, induction2_gthm: $o).
% 0.45/0.38 thf(decl_127, type, pushprop_lem2v2_lthm: $o).
% 0.45/0.38 thf(decl_128, type, hoasvar: subst > term > subst > $o).
% 0.45/0.38 thf(decl_129, type, hoaslamnotap: $o).
% 0.45/0.38 thf(decl_130, type, substmonoid_gthm: $o).
% 0.45/0.38 thf(decl_131, type, ulamvarsh: $o).
% 0.45/0.38 thf(decl_132, type, induction2: $o).
% 0.45/0.38 thf(decl_133, type, pushprop_lem3v2: $o).
% 0.45/0.38 thf(decl_134, type, pushprop_lem2v2_gthm: $o).
% 0.45/0.38 thf(decl_135, type, pushprop_lem1_lthm: $o).
% 0.45/0.38 thf(decl_136, type, hoasinduction_lem3v2: $o).
% 0.45/0.38 thf(decl_137, type, axshiftcons: $o).
% 0.45/0.38 thf(decl_138, type, termmset: $o).
% 0.45/0.38 thf(decl_139, type, pushprop_lem0_lthm: $o).
% 0.45/0.38 thf(decl_140, type, hoasapnotvar_lthm: $o).
% 0.45/0.38 thf(decl_141, type, hoasinduction_lem3v2_lthm: $o).
% 0.45/0.38 thf(decl_142, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 0.45/0.38 thf(decl_143, type, axvarid: $o).
% 0.45/0.38 thf(decl_144, type, hoasinduction_lthm_3: $o).
% 0.45/0.38 thf(decl_145, type, d2term: d_term > term).
% 0.45/0.38 thf(decl_146, type, d2subst: d_subst > subst).
% 0.45/0.38 thf(decl_147, type, d_one: d_term).
% 0.45/0.38 thf(decl_148, type, d_id: d_subst).
% 0.45/0.38 thf(decl_149, type, epred1_0: $o).
% 0.45/0.38 thf(decl_150, type, epred2_1: (subst > term > subst > $o) > $o).
% 0.45/0.38 thf(decl_152, type, epred4_0: $o).
% 0.45/0.38 thf(decl_153, type, epred5_0: $o).
% 0.45/0.38 thf(decl_154, type, epred6_0: $o).
% 0.45/0.38 thf(decl_155, type, epred7_0: $o).
% 0.45/0.38 thf(decl_156, type, epred8_3: term > (term > $o) > (subst > term > subst > $o) > $o).
% 0.45/0.38 thf(decl_157, type, epred9_0: $o).
% 0.45/0.38 thf(decl_158, type, esk1_0: term).
% 0.45/0.38 thf(decl_159, type, esk2_1: term > d_term).
% 0.45/0.38 thf(decl_160, type, esk3_1: subst > d_subst).
% 0.45/0.38 thf(decl_161, type, esk4_4: (term > $o) > (term > $o) > term > subst > term).
% 0.45/0.38 thf(decl_162, type, epred10_0: term > $o).
% 0.45/0.38 thf(decl_163, type, epred11_0: term > $o).
% 0.45/0.38 thf(decl_164, type, esk5_0: term).
% 0.45/0.38 thf(decl_165, type, esk6_0: subst).
% 0.45/0.38 thf(decl_166, type, esk7_0: term).
% 0.45/0.38 thf(decl_167, type, esk8_0: term).
% 0.45/0.38 thf(decl_168, type, esk9_3: (term > $o) > term > subst > term).
% 0.45/0.38 thf(decl_169, type, esk10_3: (term > $o) > term > subst > term).
% 0.45/0.38 thf(decl_170, type, esk11_3: (term > $o) > term > subst > term).
% 0.45/0.38 thf(decl_171, type, esk12_3: (term > $o) > term > subst > term).
% 0.45/0.38 thf(decl_172, type, epred12_0: term > $o).
% 0.45/0.38 thf(decl_173, type, esk13_0: term).
% 0.45/0.38 thf(decl_174, type, esk14_0: subst).
% 0.45/0.38 thf(decl_175, type, esk15_1: term > term).
% 0.45/0.38 thf(decl_176, type, esk16_1: term > subst > term > term).
% 0.45/0.38 thf(decl_177, type, esk17_0: term).
% 0.45/0.38 thf(decl_178, type, esk18_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_179, type, esk19_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_180, type, esk20_0: term).
% 0.45/0.38 thf(decl_181, type, esk21_0: term).
% 0.45/0.38 thf(decl_182, type, esk22_0: term).
% 0.45/0.38 thf(decl_183, type, esk23_0: term).
% 0.45/0.38 thf(decl_184, type, esk24_0: term).
% 0.45/0.38 thf(decl_185, type, esk25_0: term).
% 0.45/0.38 thf(decl_186, type, esk26_0: term).
% 0.45/0.38 thf(decl_187, type, esk27_0: term).
% 0.45/0.38 thf(decl_188, type, esk28_0: term).
% 0.45/0.38 thf(decl_189, type, esk29_0: subst).
% 0.45/0.38 thf(decl_190, type, esk30_0: term).
% 0.45/0.38 thf(decl_191, type, esk31_0: subst).
% 0.45/0.38 thf(decl_192, type, esk32_0: subst).
% 0.45/0.38 thf(decl_193, type, esk33_1: term > subst > term > term).
% 0.45/0.38 thf(decl_194, type, esk34_0: term).
% 0.45/0.38 thf(decl_195, type, esk35_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_196, type, esk36_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_197, type, epred13_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_198, type, esk37_1: (term > $o) > term).
% 0.45/0.38 thf(decl_199, type, epred14_0: term > $o).
% 0.45/0.38 thf(decl_200, type, esk38_0: term).
% 0.45/0.38 thf(decl_201, type, esk39_1: term > term).
% 0.45/0.38 thf(decl_202, type, esk40_0: term).
% 0.45/0.38 thf(decl_203, type, epred15_1: (subst > term > subst > $o) > term > $o).
% 0.45/0.38 thf(decl_204, type, esk41_1: (term > $o) > term).
% 0.45/0.38 thf(decl_205, type, esk42_1: (term > $o) > term).
% 0.45/0.38 thf(decl_206, type, esk43_1: (term > $o) > term).
% 0.45/0.38 thf(decl_207, type, esk44_1: (term > $o) > term).
% 0.45/0.38 thf(decl_208, type, esk45_2: (subst > term > term) > (subst > term > term) > subst).
% 0.45/0.38 thf(decl_209, type, esk46_2: (subst > term > term) > (subst > term > term) > term).
% 0.45/0.38 thf(decl_210, type, esk47_2: (subst > term > term) > (subst > term > term) > subst).
% 0.45/0.38 thf(decl_211, type, esk48_2: (subst > term > term) > (subst > term > term) > subst).
% 0.45/0.38 thf(decl_212, type, esk49_2: (subst > term > term) > (subst > term > term) > term).
% 0.45/0.38 thf(decl_213, type, esk50_2: (subst > term > term) > (subst > term > term) > subst).
% 0.45/0.38 thf(decl_214, type, esk51_0: subst > term > term).
% 0.45/0.38 thf(decl_215, type, esk52_0: subst > term > term).
% 0.45/0.38 thf(decl_216, type, esk53_0: subst).
% 0.45/0.38 thf(decl_217, type, esk54_0: term).
% 0.45/0.38 thf(decl_218, type, esk55_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.45/0.38 thf(decl_219, type, esk56_2: (subst > term > subst > $o) > term > term).
% 0.45/0.38 thf(decl_220, type, esk57_2: (subst > term > subst > $o) > term > term).
% 0.45/0.38 thf(decl_221, type, epred16_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_222, type, esk58_0: term).
% 0.45/0.38 thf(decl_223, type, esk59_2: (subst > term > term) > term > term).
% 0.45/0.38 thf(decl_224, type, esk60_2: (subst > term > term) > term > subst).
% 0.45/0.38 thf(decl_225, type, esk61_2: (subst > term > term) > term > term).
% 0.45/0.38 thf(decl_226, type, esk62_2: (subst > term > term) > term > subst).
% 0.45/0.38 thf(decl_227, type, esk63_2: (subst > term > term) > term > subst).
% 0.45/0.38 thf(decl_228, type, esk64_2: (subst > term > term) > term > term).
% 0.45/0.38 thf(decl_229, type, esk65_2: (subst > term > term) > term > subst).
% 0.45/0.38 thf(decl_230, type, esk66_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.45/0.38 thf(decl_231, type, esk67_2: (subst > term > subst > $o) > term > term).
% 0.45/0.38 thf(decl_232, type, epred17_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_233, type, esk68_0: term).
% 0.45/0.38 thf(decl_234, type, esk69_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_235, type, esk70_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_236, type, esk71_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_237, type, esk72_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_238, type, esk73_2: (subst > term > subst > $o) > term > subst).
% 0.45/0.38 thf(decl_239, type, esk74_2: (subst > term > subst > $o) > term > term).
% 0.45/0.38 thf(decl_240, type, esk75_2: (subst > term > subst > $o) > term > subst).
% 0.45/0.38 thf(decl_241, type, esk76_2: (subst > term > subst > $o) > term > subst).
% 0.45/0.38 thf(decl_242, type, esk77_2: (subst > term > subst > $o) > term > subst).
% 0.45/0.38 thf(decl_243, type, esk78_2: (subst > term > subst > $o) > term > term).
% 0.45/0.38 thf(decl_244, type, esk79_2: (subst > term > subst > $o) > term > subst).
% 0.45/0.38 thf(decl_245, type, esk80_2: (subst > term > subst > $o) > term > subst).
% 0.45/0.38 thf(decl_246, type, esk81_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.45/0.38 thf(decl_247, type, esk82_2: (subst > term > subst > $o) > term > term).
% 0.45/0.38 thf(decl_248, type, epred18_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_249, type, esk83_0: term).
% 0.45/0.38 thf(decl_250, type, esk84_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_251, type, esk85_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_252, type, esk86_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_253, type, esk87_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_254, type, esk88_3: (subst > term > subst > $o) > term > term > subst).
% 0.45/0.38 thf(decl_255, type, esk89_3: (subst > term > subst > $o) > term > term > term).
% 0.45/0.38 thf(decl_256, type, esk90_3: (subst > term > subst > $o) > term > term > subst).
% 0.45/0.38 thf(decl_257, type, esk91_3: (subst > term > subst > $o) > term > term > subst).
% 0.45/0.38 thf(decl_258, type, esk92_3: (subst > term > subst > $o) > term > term > subst).
% 0.45/0.38 thf(decl_259, type, esk93_3: (subst > term > subst > $o) > term > term > term).
% 0.45/0.38 thf(decl_260, type, esk94_3: (subst > term > subst > $o) > term > term > subst).
% 0.45/0.38 thf(decl_261, type, esk95_3: (subst > term > subst > $o) > term > term > subst).
% 0.45/0.38 thf(decl_262, type, esk96_3: (subst > term > subst > $o) > term > term > term).
% 0.45/0.38 thf(decl_263, type, esk97_3: (subst > term > subst > $o) > term > term > term).
% 0.45/0.38 thf(decl_264, type, epred19_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_265, type, esk98_0: term).
% 0.45/0.38 thf(decl_266, type, esk99_0: term).
% 0.45/0.38 thf(decl_267, type, esk100_0: term).
% 0.45/0.38 thf(decl_268, type, esk101_0: subst).
% 0.45/0.38 thf(decl_269, type, esk102_4: (term > $o) > (term > $o) > term > subst > term).
% 0.45/0.38 thf(decl_270, type, epred20_0: term > $o).
% 0.45/0.38 thf(decl_271, type, epred21_0: term > $o).
% 0.45/0.38 thf(decl_272, type, esk103_0: term).
% 0.45/0.38 thf(decl_273, type, esk104_0: subst).
% 0.45/0.38 thf(decl_274, type, epred22_1: (subst > term > subst > $o) > term > $o).
% 0.45/0.38 thf(decl_275, type, epred23_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_276, type, esk105_1: (term > $o) > term).
% 0.45/0.38 thf(decl_277, type, epred24_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_278, type, esk106_0: term).
% 0.45/0.38 thf(decl_279, type, esk107_1: term > subst > term > term).
% 0.45/0.38 thf(decl_280, type, esk108_0: term).
% 0.45/0.38 thf(decl_281, type, esk109_1: (term > $o) > term).
% 0.45/0.38 thf(decl_282, type, esk110_1: (term > $o) > term).
% 0.45/0.38 thf(decl_283, type, esk111_1: (term > $o) > term).
% 0.45/0.38 thf(decl_284, type, esk112_1: (term > $o) > term).
% 0.45/0.38 thf(decl_285, type, epred25_0: term > $o).
% 0.45/0.38 thf(decl_286, type, esk113_0: term).
% 0.45/0.38 thf(decl_287, type, esk114_0: term).
% 0.45/0.38 thf(decl_288, type, epred26_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_289, type, esk115_0: term).
% 0.45/0.38 thf(decl_290, type, esk116_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_291, type, esk117_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_292, type, esk118_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_293, type, esk119_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_294, type, esk120_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.45/0.38 thf(decl_295, type, esk121_2: (subst > term > subst > $o) > term > term).
% 0.45/0.38 thf(decl_296, type, esk122_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.45/0.38 thf(decl_297, type, esk123_2: (subst > term > subst > $o) > term > term).
% 0.45/0.38 thf(decl_298, type, epred27_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_299, type, esk124_0: term).
% 0.45/0.38 thf(decl_300, type, esk125_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_301, type, esk126_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_302, type, esk127_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_303, type, esk128_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_304, type, esk129_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.45/0.38 thf(decl_305, type, esk130_2: (subst > term > subst > $o) > term > term).
% 0.45/0.38 thf(decl_306, type, epred28_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_307, type, esk131_0: term).
% 0.45/0.38 thf(decl_308, type, esk132_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_309, type, esk133_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_310, type, esk134_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_311, type, esk135_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_312, type, esk136_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.45/0.38 thf(decl_313, type, esk137_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.45/0.38 thf(decl_314, type, esk138_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.45/0.38 thf(decl_315, type, esk139_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.45/0.38 thf(decl_316, type, esk140_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.45/0.38 thf(decl_317, type, esk141_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.45/0.38 thf(decl_318, type, esk142_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.45/0.38 thf(decl_319, type, esk143_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.45/0.38 thf(decl_320, type, esk144_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.45/0.38 thf(decl_321, type, esk145_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.45/0.38 thf(decl_322, type, esk146_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.45/0.38 thf(decl_323, type, epred29_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_324, type, epred30_0: term > $o).
% 0.45/0.38 thf(decl_325, type, esk147_0: term).
% 0.45/0.38 thf(decl_326, type, esk148_0: term).
% 0.45/0.38 thf(decl_327, type, esk149_0: term).
% 0.45/0.38 thf(decl_328, type, esk150_0: term).
% 0.45/0.38 thf(decl_329, type, esk151_0: term).
% 0.45/0.38 thf(decl_330, type, esk152_0: term).
% 0.45/0.38 thf(decl_331, type, esk153_0: term).
% 0.45/0.38 thf(decl_332, type, esk154_0: term).
% 0.45/0.38 thf(decl_333, type, esk155_0: term).
% 0.45/0.38 thf(decl_334, type, esk156_0: term).
% 0.45/0.38 thf(decl_335, type, esk157_0: term).
% 0.45/0.38 thf(decl_336, type, esk158_0: term).
% 0.45/0.38 thf(decl_337, type, esk159_0: term).
% 0.45/0.38 thf(decl_338, type, esk160_0: term).
% 0.45/0.38 thf(decl_339, type, esk161_0: term).
% 0.45/0.38 thf(decl_340, type, esk162_0: term).
% 0.45/0.38 thf(decl_341, type, esk163_0: term).
% 0.45/0.38 thf(decl_342, type, esk164_0: term).
% 0.45/0.38 thf(decl_343, type, esk165_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
% 0.45/0.38 thf(decl_344, type, esk166_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.45/0.38 thf(decl_345, type, esk167_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.45/0.38 thf(decl_346, type, epred31_0: subst > term > subst > $o).
% 0.45/0.38 thf(decl_347, type, epred32_0: term > $o).
% 0.45/0.38 thf(decl_348, type, esk168_0: term).
% 0.45/0.38 thf(decl_349, type, esk169_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_350, type, esk170_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_351, type, esk171_1: (subst > term > term) > subst).
% 0.45/0.38 thf(decl_352, type, esk172_1: (subst > term > term) > term).
% 0.45/0.38 thf(decl_353, type, esk173_0: term).
% 0.45/0.38 thf(decl_354, type, esk174_0: term).
% 0.45/0.38 thf(decl_355, type, esk175_0: term).
% 0.45/0.38 thf(decl_356, type, esk176_0: term).
% 0.45/0.38 thf(decl_357, type, esk177_0: term).
% 0.45/0.38 thf(decl_358, type, esk178_0: term).
% 0.45/0.38 thf(decl_359, type, esk179_0: term).
% 0.45/0.38 thf(decl_360, type, esk180_0: term).
% 0.45/0.38 thf(decl_361, type, esk181_0: term).
% 0.45/0.38 thf(decl_362, type, esk182_0: term).
% 0.45/0.39 thf(decl_363, type, esk183_0: subst).
% 0.45/0.39 thf(decl_364, type, esk184_0: term).
% 0.45/0.39 thf(decl_365, type, esk185_0: subst).
% 0.45/0.39 thf(decl_366, type, esk186_0: term).
% 0.45/0.39 thf(decl_367, type, esk187_0: term).
% 0.45/0.39 thf(decl_368, type, esk188_2: (subst > term > term) > (subst > term > term) > subst).
% 0.45/0.39 thf(decl_369, type, esk189_2: (subst > term > term) > (subst > term > term) > term).
% 0.45/0.39 thf(decl_370, type, esk190_2: (subst > term > term) > (subst > term > term) > subst).
% 0.45/0.39 thf(decl_371, type, esk191_2: (subst > term > term) > (subst > term > term) > subst).
% 0.45/0.39 thf(decl_372, type, esk192_2: (subst > term > term) > (subst > term > term) > term).
% 0.45/0.39 thf(decl_373, type, esk193_2: (subst > term > term) > (subst > term > term) > subst).
% 0.45/0.39 thf(decl_374, type, esk194_0: subst > term > term).
% 0.45/0.39 thf(decl_375, type, esk195_0: subst > term > term).
% 0.45/0.39 thf(decl_376, type, esk196_0: subst).
% 0.45/0.39 thf(decl_377, type, esk197_0: term).
% 0.45/0.39 thf(decl_378, type, esk198_0: term).
% 0.45/0.39 thf(decl_379, type, esk199_0: subst).
% 0.45/0.39 thf(decl_380, type, esk200_0: subst).
% 0.45/0.39 thf(decl_381, type, esk201_0: subst).
% 0.45/0.39 thf(decl_382, type, epred33_0: term > $o).
% 0.45/0.39 thf(decl_383, type, epred34_0: term > $o).
% 0.45/0.39 thf(decl_384, type, esk202_0: term).
% 0.45/0.39 thf(decl_385, type, esk203_0: subst).
% 0.45/0.39 thf(decl_386, type, esk204_0: term).
% 0.45/0.39 thf(decl_387, type, esk205_0: term).
% 0.45/0.39 thf(decl_388, type, esk206_0: term).
% 0.45/0.39 thf(decl_389, type, esk207_0: term).
% 0.45/0.39 thf(decl_390, type, epred35_3: (term > $o) > term > subst > term > $o).
% 0.45/0.39 thf(decl_391, type, epred36_0: term > $o).
% 0.45/0.39 thf(decl_392, type, esk208_0: term).
% 0.45/0.39 thf(decl_393, type, esk209_0: subst).
% 0.45/0.39 thf(decl_394, type, esk210_1: (term > $o) > term).
% 0.45/0.39 thf(decl_395, type, esk211_0: term).
% 0.45/0.39 thf(decl_396, type, esk212_1: (subst > term > term) > term).
% 0.45/0.39 thf(decl_397, type, esk213_1: (subst > term > term) > subst).
% 0.45/0.39 thf(decl_398, type, esk214_0: term).
% 0.45/0.39 thf(decl_399, type, esk215_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
% 0.45/0.39 thf(decl_400, type, esk216_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.45/0.39 thf(decl_401, type, esk217_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.45/0.39 thf(decl_402, type, esk218_1: term > subst > term > term).
% 0.45/0.39 thf(decl_403, type, epred37_0: subst > term > subst > $o).
% 0.45/0.39 thf(decl_404, type, epred38_0: term > $o).
% 0.45/0.39 thf(decl_405, type, esk219_0: term).
% 0.45/0.39 thf(decl_406, type, esk220_1: (subst > term > term) > subst).
% 0.45/0.39 thf(decl_407, type, esk221_1: (subst > term > term) > term).
% 0.45/0.39 thf(decl_408, type, esk222_1: (subst > term > term) > subst).
% 0.45/0.39 thf(decl_409, type, esk223_1: (subst > term > term) > term).
% 0.45/0.39 thf(decl_410, type, esk224_0: subst).
% 0.45/0.39 thf(decl_411, type, esk225_0: term).
% 0.45/0.39 thf(decl_412, type, epred39_1: (subst > term > subst > $o) > term > $o).
% 0.45/0.39 thf(decl_413, type, epred40_0: subst > term > subst > $o).
% 0.45/0.39 thf(decl_414, type, esk226_1: (term > $o) > term).
% 0.45/0.39 thf(decl_415, type, esk227_0: subst).
% 0.45/0.39 thf(decl_416, type, esk228_0: subst).
% 0.45/0.39 thf(decl_417, type, esk229_0: subst).
% 0.45/0.39 thf(decl_418, type, esk230_0: subst).
% 0.45/0.39 thf(decl_419, type, esk231_1: term > subst > term > term).
% 0.45/0.39 thf(decl_420, type, esk232_0: term).
% 0.45/0.39 thf(decl_421, type, esk233_0: subst).
% 0.45/0.39 thf(decl_422, type, esk234_0: subst).
% 0.45/0.39 thf(decl_423, type, esk235_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.45/0.39 thf(decl_424, type, esk236_2: (subst > term > subst > $o) > term > term).
% 0.45/0.39 thf(decl_425, type, epred41_0: subst > term > subst > $o).
% 0.45/0.39 thf(decl_426, type, esk237_0: term).
% 0.45/0.39 thf(decl_427, type, esk238_1: (subst > term > term) > subst).
% 0.45/0.39 thf(decl_428, type, esk239_1: (subst > term > term) > term).
% 0.45/0.39 thf(decl_429, type, esk240_1: (subst > term > term) > subst).
% 0.45/0.39 thf(decl_430, type, esk241_1: (subst > term > term) > term).
% 0.45/0.39 thf(decl_431, type, esk242_1: (subst > term > subst > $o) > term).
% 0.45/0.39 thf(decl_432, type, esk243_1: (subst > term > subst > $o) > term).
% 0.45/0.39 thf(decl_433, type, esk244_1: (subst > term > subst > $o) > subst > term > term).
% 0.45/0.39 thf(decl_434, type, epred42_0: subst > term > subst > $o).
% 0.45/0.39 thf(decl_435, type, esk245_0: term).
% 0.45/0.39 thf(decl_436, type, esk246_1: (subst > term > term) > subst).
% 0.45/0.39 thf(decl_437, type, esk247_1: (subst > term > term) > term).
% 0.45/0.39 thf(decl_438, type, esk248_1: (subst > term > term) > subst).
% 0.45/0.39 thf(decl_439, type, esk249_1: (subst > term > term) > term).
% 0.45/0.39 thf(decl_440, type, esk250_1: (subst > term > term) > subst).
% 0.45/0.39 thf(decl_441, type, esk251_1: (subst > term > term) > term).
% 0.45/0.39 thf(decl_442, type, esk252_1: (subst > term > term) > subst).
% 0.45/0.39 thf(decl_443, type, esk253_0: subst > term > term).
% 0.45/0.39 thf(decl_444, type, esk254_0: term).
% 0.45/0.39 thf(decl_445, type, esk255_0: term).
% 0.45/0.39 thf(decl_446, type, esk256_1: (term > $o) > term).
% 0.45/0.39 thf(decl_447, type, esk257_1: (term > $o) > term).
% 0.45/0.39 thf(decl_448, type, esk258_1: (term > $o) > term).
% 0.45/0.39 thf(decl_449, type, esk259_1: (term > $o) > term).
% 0.45/0.39 thf(decl_450, type, epred43_0: term > $o).
% 0.45/0.39 thf(decl_451, type, esk260_0: term).
% 0.45/0.39 thf(decl_452, type, esk261_1: term > term).
% 0.45/0.39 thf(decl_453, type, esk262_0: term).
% 0.45/0.39 thf(decl_454, type, esk263_0: subst).
% 0.45/0.39 thf(decl_455, type, esk264_0: term).
% 0.45/0.39 thf(decl_456, type, esk265_0: subst).
% 0.45/0.39 thf(decl_457, type, epred44_0: term > $o).
% 0.45/0.39 thf(decl_458, type, epred45_0: term > $o).
% 0.45/0.39 thf(decl_459, type, esk266_0: term).
% 0.45/0.39 thf(decl_460, type, esk267_0: subst).
% 0.45/0.39 thf(decl_461, type, esk268_0: term).
% 0.45/0.39 thf(decl_462, type, epred46_0: subst > term > subst > $o).
% 0.45/0.39 thf(decl_463, type, epred47_0: term > $o).
% 0.45/0.39 thf(decl_464, type, esk269_0: term).
% 0.45/0.39 thf(decl_465, type, esk270_0: term).
% 0.45/0.39 thf(decl_466, type, esk271_0: subst).
% 0.45/0.39 thf(decl_467, type, esk272_0: term).
% 0.45/0.39 thf(decl_468, type, epred48_3: (term > $o) > term > subst > term > $o).
% 0.45/0.39 thf(decl_469, type, epred49_0: term > $o).
% 0.45/0.39 thf(decl_470, type, esk273_0: term).
% 0.45/0.39 thf(decl_471, type, esk274_0: subst).
% 0.45/0.39 thf(decl_472, type, esk275_1: (term > $o) > term).
% 0.45/0.39 thf(decl_473, type, esk276_0: term).
% 0.45/0.39 thf(decl_474, type, epred50_0: subst > term > subst > $o).
% 0.45/0.39 thf(decl_475, type, epred51_0: term > $o).
% 0.45/0.39 thf(decl_476, type, esk277_0: term).
% 0.45/0.39 thf(decl_477, type, esk278_0: term).
% 0.45/0.39 thf(decl_478, type, epred52_0: subst > term > subst > $o).
% 0.45/0.39 thf(decl_479, type, esk279_1: (term > $o) > term).
% 0.45/0.39 thf(decl_480, type, epred53_1: (subst > term > subst > $o) > term > $o).
% 0.45/0.39 thf(alg444_1, axiom, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X1:term]:(?[X2:d_term]:(((X1)=(d2term @ X2))))&![X2:d_term]:(((X2)=(d_one))))&![X3:d_term, X4:d_term]:((((d2term @ X3)=(d2term @ X4))=>((X3)=(X4)))))&![X5:subst]:(?[X6:d_subst]:(((X5)=(d2subst @ X6)))))&![X6:d_subst]:(((X6)=(d_id))))&![X7:d_subst, X8:d_subst]:((((d2subst @ X7)=(d2subst @ X8))=>((X7)=(X8)))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((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)=(^[X9:subst, X10:subst > term > term]:(d2term @ d_one))))&((hoasinduction_p_and_p_prime)=(^[X11:subst > term > subst > $o, X12:term > $o]:(![X13:term]:((((X12 @ X13))<=>((X11 @ id @ X13 @ id))))))))&((pushprop_p_and_p_prime)=(^[X14:term, X15:subst, X16:term > $o, X12:term > $o]:(![X13:term]:((((X12 @ X13))<=>((X16 @ (sub @ X13 @ (push @ X14 @ X15))))))))))&~((var @ (d2term @ d_one))))&((pushprop_lem1v2)<=>![X17:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X17 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X17 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one)))))&(pushprop_lem1_gthm))&(axmap))&(pushprop_lem0_gthm))&((shinj)<=>![X14:term, X18:term]:((((sub @ X14 @ sh)!=(sub @ X18 @ sh))|((X14)=(X18))))))&(hoasinduction_lem1v2))&(hoasinduction_lem1v2_gthm))&((induction2lem)<=>![X19:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X19 @ X14))|~((X19 @ X18))|(X19 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X19 @ X18))|(X19 @ (sub @ X14 @ (push @ X18 @ id))))))|(X19 @ (lam @ X14)))))|~(![X18:term]:((~((var @ X18))|(X19 @ (sub @ X18 @ X21)))))|(X19 @ (sub @ X20 @ X21))))))&((hoasinduction_lem3v2_f)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&(axvarshift))&((hoasapinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24))))))&(hoasapnotvar_gthm))&((hoasapinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))&~((ulamvar1)))&((induction2lem_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(![X25:term > $o, X26:term]:((~(![X14:term]:((~((var @ X14))|(X25 @ X14))))|~(![X14:term, X18:term]:((~((X25 @ X14))|~((X25 @ X18))|(X25 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X25 @ X14))|(X25 @ (lam @ X14)))))|(X25 @ X26)))=>![X27:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X27 @ X14))|~((X27 @ X18))|(X27 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X27 @ X18))|(X27 @ (sub @ X14 @ (push @ X18 @ id))))))|(X27 @ (lam @ X14)))))|~(![X18:term]:((~((var @ X18))|(X27 @ (sub @ X18 @ X21)))))|(X27 @ (sub @ X20 @ X21))))))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((hoasinduction_lem3v2_f_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&((hoasinduction_lthm)<=>(![X28:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X28 @ X14))))|~(![X14:term, X18:term]:((~((X28 @ X14))|~((X28 @ X18))|(X28 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X28 @ X18))|(X28 @ (sub @ X14 @ (push @ X18 @ id))))))|(X28 @ (lam @ X14)))))|(X28 @ X29)))=>(![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))=>(![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~((var @ (sub @ X14 @ id)))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))))&((hoasinduction_no_psi_cond_lthm)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(![X36:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X36 @ X14))))|~(![X14:term, X18:term]:((~((X36 @ X14))|~((X36 @ X18))|(X36 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X36 @ X18))|(X36 @ (sub @ X14 @ (push @ X18 @ id))))))|(X36 @ (lam @ X14)))))|(X36 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id)))))))))&((hoaslaminj)<=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41))))))&((hoasinduction_lem3aaa)<=>![X11:subst > term > subst > $o, X42:term]:((~(![X22:subst > term > term, X43:term]:((~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id)|~(![X44:subst, X45:term, X46:subst]:(((sub @ (X22 @ X44 @ X45) @ X46)=(sub @ (sub @ X43 @ (push @ X45 @ X44)) @ X46))))|~(![X47:subst, X48:term, X49:subst]:(((X22 @ (comp @ X47 @ X49) @ (sub @ X48 @ X49))=(sub @ X43 @ (push @ (sub @ X48 @ X49) @ (comp @ X47 @ X49)))))))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X42 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)))))&(induction2lem_gthm))&((hoasinduction_lem3aa_lthm)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&((hoasinduction_lem3)<=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))))&((hoasinduction_lem2)<=>![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))))&((termmset_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X14:term]:(((X14)=(sub @ X14 @ id))))))&(hoasinduction_lem1))&(hoaslamnotap_lthm))&((pushprop_lem1v2_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>![X51:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X51 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X51 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one))))))&(hoasapnotvar))&((hoasinduction_lem0)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((hoasinduction)<=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~((var @ (sub @ X14 @ id)))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id)))))&(hoasinduction_gthm))&(axapp))&(hoaslamnotvar_lthm))&(pushprop_lem3v2_lthm))&((hoasinduction_lem3b_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&(ulamvarind))&((induction)<=>![X52:term > $o, X26:term]:((~(![X14:term]:((~((var @ X14))|(X52 @ X14))))|~(![X14:term, X18:term]:((~((X52 @ X14))|~((X52 @ X18))|(X52 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X52 @ X14))|(X52 @ (lam @ X14)))))|(X52 @ X26)))))&((hoasinduction_lem3a_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))))&(termmset_gthm))&((hoasinduction_lem3aa)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&(pushprop_lem1v2_gthm))&(hoaslamnotap_gthm))&(hoaslamnotvar_gthm))&(hoasinduction_lem3b_gthm))&(pushprop_lem2v2))&(hoasinduction_lem3a_gthm))&(axclos))&(axassoc))&((hoasinduction_lem2v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X54:term, X55:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~((X12 @ X54))|~((X12 @ X55))|(X12 @ (ap @ X54 @ X55))))))&(pushprop_lthm))&((apinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))))&((apinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))))&((hoasapinj2_lthm)<=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24)))))))&((hoasinduction_lem3v2a)<=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))&((hoasapinj1_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))))&((hoaslaminj_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41)))))))))&((axvarcons)<=>![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))))&((axscons)<=>![X15:subst]:(((X15)=(push @ (sub @ one @ X15) @ (comp @ sh @ X15))))))&(hoasinduction_lem2v2_gthm))&((axidr)<=>![X15:subst]:(((X15)=(comp @ X15 @ id)))))&((pushprop_lem1)<=>![X56:term > $o, X57:term > $o, X14:term, X15:subst, X18:term]:((~((X56 @ X14))|(X57 @ (sub @ X14 @ (push @ X18 @ X15)))))))&((laminj)<=>![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))))&((hoasinduction_lem3_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))))))&((pushprop_lem0)<=>![X58:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X58 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(pushprop_gthm))&(axabs))&((hoasinduction_lem3v2a_lthm)<=>(![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))))&(hoasinduction_lem2_lthm))&(hoasapinj2_gthm))&(hoasinduction_lem1_lthm))&~((lamnotap)))&(hoasapinj1_gthm))&(hoaslamnotvar))&((axidl)<=>![X15:subst]:(((X15)=(comp @ id @ X15)))))&(hoaslaminj_gthm))&((induction2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X59:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X59 @ X14))|~((X59 @ X18))|(X59 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X59 @ X18))|(X59 @ (sub @ X14 @ (push @ X18 @ id))))))|(X59 @ (lam @ X14)))))|~(![X18:term]:((~((var @ X18))|(X59 @ (sub @ X18 @ X21)))))|(X59 @ (sub @ X20 @ X21))))=>![X60:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X60 @ X14))))|~(![X14:term, X18:term]:((~((X60 @ X14))|~((X60 @ X18))|(X60 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X60 @ X18))|(X60 @ (sub @ X14 @ (push @ X18 @ id))))))|(X60 @ (lam @ X14)))))|(X60 @ X29)))))))&((hoasinduction_lem0_lthm)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((substmonoid_lthm)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))))&(pushprop))&(hoasinduction_lem3_gthm))&(hoasinduction_lem2_gthm))&((hoasinduction_lem3b)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&((substmonoid)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))&(lamnotvar))&((hoasinduction_lem3a)<=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))&(hoasinduction_lem1_gthm))&((hoasinduction_no_psi_cond)<=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id)))))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))&((hoaslamnotap)<=>![X22:subst > term > term, X61:term, X62:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(ap @ (sub @ X61 @ id) @ X62))))))&(substmonoid_gthm))&(ulamvarsh))&((induction2)<=>![X63:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X63 @ X14))))|~(![X14:term, X18:term]:((~((X63 @ X14))|~((X63 @ X18))|(X63 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X63 @ X18))|(X63 @ (sub @ X14 @ (push @ X18 @ id))))))|(X63 @ (lam @ X14)))))|(X63 @ X29)))))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((pushprop_lem1_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>![X64:term > $o, X65:term > $o, X14:term, X15:subst, X18:term]:((~((X64 @ X14))|(X65 @ (sub @ X14 @ (push @ X18 @ X15)))))))))&((hoasinduction_lem3v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X66 @ (push @ X18 @ id))))))|(X12 @ (lam @ X66))))))&((axshiftcons)<=>![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))))&((termmset)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((pushprop_lem0_lthm)<=>![X67:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X67 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(hoasapnotvar_lthm))&((hoasinduction_lem3v2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X66 @ (push @ X18 @ id))))))|(X12 @ (lam @ X66)))))))&((axvarid)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((hoasinduction_lthm_3)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(![X68:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X68 @ X14))))|~(![X14:term, X18:term]:((~((X68 @ X14))|~((X68 @ X18))|(X68 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X68 @ X18))|(X68 @ (sub @ X14 @ (push @ X18 @ id))))))|(X68 @ (lam @ X14)))))|(X68 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~((var @ (sub @ X14 @ id)))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))))), file('/export/starexec/sandbox2/tmp/tmp.Nz5wer6szc/E---3.1_1484892.p', alg444_1)).
% 0.45/0.39 thf(lamnotvar, conjecture, ((lamnotvar)<=>![X14:term]:(~((var @ (lam @ X14))))), file('/export/starexec/sandbox2/tmp/tmp.Nz5wer6szc/E---3.1_1484892.p', lamnotvar)).
% 0.45/0.39 thf(c_0_2, plain, ((epred1_0)<=>(![X25:term > $o, X26:term]:((~(![X14:term]:((~(var @ X14)|(X25 @ X14))))|~(![X14:term, X18:term]:((~((X25 @ X14))|~((X25 @ X18))|(X25 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X25 @ X14))|(X25 @ (lam @ X14)))))|(X25 @ X26)))=>![X27:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X27 @ X14))|~((X27 @ X18))|(X27 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X27 @ X18))|(X27 @ (sub @ X14 @ (push @ X18 @ id))))))|(X27 @ (lam @ X14)))))|~(![X18:term]:((~(var @ X18)|(X27 @ (sub @ X18 @ X21)))))|(X27 @ (sub @ X20 @ X21)))))), introduced(definition)).
% 0.45/0.39 thf(c_0_3, plain, ((epred4_0)<=>(![X28:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X28 @ X14))))|~(![X14:term, X18:term]:((~((X28 @ X14))|~((X28 @ X18))|(X28 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X28 @ X18))|(X28 @ (sub @ X14 @ (push @ X18 @ id))))))|(X28 @ (lam @ X14)))))|(X28 @ X29)))=>(![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))=>(![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~(var @ (sub @ X14 @ id))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))), introduced(definition)).
% 0.45/0.39 thf(c_0_4, plain, ((epred5_0)<=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id))))), introduced(definition)).
% 0.45/0.39 thf(c_0_5, plain, ![X11:subst > term > subst > $o]:(((epred2_1 @ X11)<=>(~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~(var @ (sub @ X14 @ id))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))))), introduced(definition)).
% 0.45/0.39 thf(c_0_6, plain, ((epred6_0)<=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id))))), introduced(definition)).
% 0.45/0.39 thf(c_0_7, plain, ((epred7_0)<=>(![X59:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X59 @ X14))|~((X59 @ X18))|(X59 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X59 @ X18))|(X59 @ (sub @ X14 @ (push @ X18 @ id))))))|(X59 @ (lam @ X14)))))|~(![X18:term]:((~(var @ X18)|(X59 @ (sub @ X18 @ X21)))))|(X59 @ (sub @ X20 @ X21))))=>![X60:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X60 @ X14))))|~(![X14:term, X18:term]:((~((X60 @ X14))|~((X60 @ X18))|(X60 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X60 @ X18))|(X60 @ (sub @ X14 @ (push @ X18 @ id))))))|(X60 @ (lam @ X14)))))|(X60 @ X29))))), introduced(definition)).
% 0.45/0.39 thf(c_0_8, plain, ![X11:subst > term > subst > $o, X12:term > $o, X66:term]:(((epred8_3 @ X66 @ X12 @ X11)<=>(~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X66 @ (push @ X18 @ id))))))))), introduced(definition)).
% 0.45/0.39 thf(c_0_9, plain, ((epred9_0)<=>(![X68:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X68 @ X14))))|~(![X14:term, X18:term]:((~((X68 @ X14))|~((X68 @ X18))|(X68 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X68 @ X18))|(X68 @ (sub @ X14 @ (push @ X18 @ id))))))|(X68 @ (lam @ X14)))))|(X68 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~(var @ (sub @ X14 @ id))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))), introduced(definition)).
% 0.45/0.39 thf(c_0_10, plain, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X1:term]:(?[X2:d_term]:(((X1)=(d2term @ X2))))&![X2:d_term]:(((X2)=(d_one))))&![X3:d_term, X4:d_term]:((((d2term @ X3)=(d2term @ X4))=>((X3)=(X4)))))&![X5:subst]:(?[X6:d_subst]:(((X5)=(d2subst @ X6)))))&![X6:d_subst]:(((X6)=(d_id))))&![X7:d_subst, X8:d_subst]:((((d2subst @ X7)=(d2subst @ X8))=>((X7)=(X8)))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((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)=(^[Z0:subst, Z1:subst > term > term]:(d2term @ d_one))))&((hoasinduction_p_and_p_prime)=(^[Z0:subst > term > subst > $o, Z1:term > $o]:(![X13:term]:(((Z1 @ X13)<=>(Z0 @ id @ X13 @ id)))))))&((pushprop_p_and_p_prime)=(^[Z0:term, Z1:subst, Z2:term > $o, Z3:term > $o]:(![X13:term]:(((Z3 @ X13)<=>(Z2 @ (sub @ X13 @ (push @ Z0 @ Z1)))))))))&~(var @ (d2term @ d_one)))&((pushprop_lem1v2)<=>![X17:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X17 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X17 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one)))))&(pushprop_lem1_gthm))&(axmap))&(pushprop_lem0_gthm))&((shinj)<=>![X14:term, X18:term]:((((sub @ X14 @ sh)!=(sub @ X18 @ sh))|((X14)=(X18))))))&(hoasinduction_lem1v2))&(hoasinduction_lem1v2_gthm))&((induction2lem)<=>![X19:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X19 @ X14))|~((X19 @ X18))|(X19 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X19 @ X18))|(X19 @ (sub @ X14 @ (push @ X18 @ id))))))|(X19 @ (lam @ X14)))))|~(![X18:term]:((~(var @ X18)|(X19 @ (sub @ X18 @ X21)))))|(X19 @ (sub @ X20 @ X21))))))&((hoasinduction_lem3v2_f)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&(axvarshift))&((hoasapinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24))))))&(hoasapnotvar_gthm))&((hoasapinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))&~(ulamvar1))&((induction2lem_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(epred1_0))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((hoasinduction_lem3v2_f_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&((hoasinduction_lthm)<=>(epred4_0)))&((hoasinduction_no_psi_cond_lthm)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(![X36:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X36 @ X14))))|~(![X14:term, X18:term]:((~((X36 @ X14))|~((X36 @ X18))|(X36 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X36 @ X18))|(X36 @ (sub @ X14 @ (push @ X18 @ id))))))|(X36 @ (lam @ X14)))))|(X36 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(epred5_0))))))&((hoaslaminj)<=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41))))))&((hoasinduction_lem3aaa)<=>![X11:subst > term > subst > $o, X42:term]:((~(![X22:subst > term > term, X43:term]:((~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id)|~(![X44:subst, X45:term, X46:subst]:(((sub @ (X22 @ X44 @ X45) @ X46)=(sub @ (sub @ X43 @ (push @ X45 @ X44)) @ X46))))|~(![X47:subst, X48:term, X49:subst]:(((X22 @ (comp @ X47 @ X49) @ (sub @ X48 @ X49))=(sub @ X43 @ (push @ (sub @ X48 @ X49) @ (comp @ X47 @ X49)))))))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X42 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)))))&(induction2lem_gthm))&((hoasinduction_lem3aa_lthm)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&((hoasinduction_lem3)<=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))))&((hoasinduction_lem2)<=>![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))))&(termmset_lthm))&(hoasinduction_lem1))&(hoaslamnotap_lthm))&((pushprop_lem1v2_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>![X51:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X51 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X51 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one))))))&(hoasapnotvar))&((hoasinduction_lem0)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((hoasinduction)<=>![X11:subst > term > subst > $o, X35:term]:(((epred2_1 @ X11)|(X11 @ id @ X35 @ id)))))&(hoasinduction_gthm))&(axapp))&(hoaslamnotvar_lthm))&(pushprop_lem3v2_lthm))&((hoasinduction_lem3b_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&(ulamvarind))&((induction)<=>![X52:term > $o, X26:term]:((~(![X14:term]:((~(var @ X14)|(X52 @ X14))))|~(![X14:term, X18:term]:((~((X52 @ X14))|~((X52 @ X18))|(X52 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X52 @ X14))|(X52 @ (lam @ X14)))))|(X52 @ X26)))))&((hoasinduction_lem3a_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))))&(termmset_gthm))&((hoasinduction_lem3aa)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&(pushprop_lem1v2_gthm))&(hoaslamnotap_gthm))&(hoaslamnotvar_gthm))&(hoasinduction_lem3b_gthm))&(pushprop_lem2v2))&(hoasinduction_lem3a_gthm))&(axclos))&(axassoc))&((hoasinduction_lem2v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X54:term, X55:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~((X12 @ X54))|~((X12 @ X55))|(X12 @ (ap @ X54 @ X55))))))&(pushprop_lthm))&((apinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))))&((apinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))))&((hoasapinj2_lthm)<=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24)))))))&((hoasinduction_lem3v2a)<=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))&((hoasapinj1_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))))&((hoaslaminj_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41)))))))))&((axvarcons)<=>![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))))&((axscons)<=>![X15:subst]:(((X15)=(push @ (sub @ one @ X15) @ (comp @ sh @ X15))))))&(hoasinduction_lem2v2_gthm))&((axidr)<=>![X15:subst]:(((X15)=(comp @ X15 @ id)))))&((pushprop_lem1)<=>![X56:term > $o, X57:term > $o, X14:term, X15:subst, X18:term]:((~((X56 @ X14))|(X57 @ (sub @ X14 @ (push @ X18 @ X15)))))))&((laminj)<=>![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))))&((hoasinduction_lem3_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(epred6_0))))&((pushprop_lem0)<=>![X58:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X58 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(pushprop_gthm))&(axabs))&((hoasinduction_lem3v2a_lthm)<=>(![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))))&(hoasinduction_lem2_lthm))&(hoasapinj2_gthm))&(hoasinduction_lem1_lthm))&~(lamnotap))&(hoasapinj1_gthm))&(hoaslamnotvar))&((axidl)<=>![X15:subst]:(((X15)=(comp @ id @ X15)))))&(hoaslaminj_gthm))&((induction2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(epred7_0))))&((hoasinduction_lem0_lthm)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((substmonoid_lthm)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))))&(pushprop))&(hoasinduction_lem3_gthm))&(hoasinduction_lem2_gthm))&((hoasinduction_lem3b)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&((substmonoid)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))&(lamnotvar))&((hoasinduction_lem3a)<=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))&(hoasinduction_lem1_gthm))&((hoasinduction_no_psi_cond)<=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id)))))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&((hoaslamnotap)<=>![X22:subst > term > term, X61:term, X62:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(ap @ (sub @ X61 @ id) @ X62))))))&(substmonoid_gthm))&(ulamvarsh))&((induction2)<=>![X63:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X63 @ X14))))|~(![X14:term, X18:term]:((~((X63 @ X14))|~((X63 @ X18))|(X63 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X63 @ X18))|(X63 @ (sub @ X14 @ (push @ X18 @ id))))))|(X63 @ (lam @ X14)))))|(X63 @ X29)))))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((pushprop_lem1_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>![X64:term > $o, X65:term > $o, X14:term, X15:subst, X18:term]:((~((X64 @ X14))|(X65 @ (sub @ X14 @ (push @ X18 @ X15)))))))))&((hoasinduction_lem3v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:(((epred8_3 @ X66 @ X12 @ X11)|(X12 @ (lam @ X66))))))&((axshiftcons)<=>![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))))&((termmset)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((pushprop_lem0_lthm)<=>![X67:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X67 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(hoasapnotvar_lthm))&((hoasinduction_lem3v2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:(((epred8_3 @ X66 @ X12 @ X11)|(X12 @ (lam @ X66)))))))&((axvarid)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((hoasinduction_lthm_3)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(epred9_0)))), 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)],[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_8]), c_0_9])).
% 0.45/0.39 thf(c_0_11, negated_conjecture, ~(((lamnotvar)<=>![X14:term]:(~((var @ (lam @ X14)))))), inference(assume_negation,[status(cth)],[lamnotvar])).
% 0.45/0.39 thf(c_0_12, plain, ![X612:term, X614:d_term, X615:d_term, X616:d_term, X617:subst, X619:d_subst, X620:d_subst, X621:d_subst, X622:term > $o, X623:term > $o, X624:term, X625:subst, X631:term, X632:term, X633:term, X636:term > $o, X637:term, X638:subst, X642:term, X647:term, X648:term, X649:term, X651:term, X652:term, X654:term, X655:subst, X657:subst > term > term, X660:term, X661:term, X662:term, X663:term, X668:term, X669:term, X670:term, X671:term, X681:term, X682:subst, X683:term, X684:subst, X685:subst, X686:term, X688:term, X689:subst, X691:subst > term > term, X695:term > $o, X699:term, X700:term, X701:term, X702:term, X705:subst > term > subst > $o, X707:term, X708:term, X709:term > $o, X714:term, X715:term, X716:term, X717:subst > term > term, X718:subst > term > term, X725:subst, X726:term, X731:subst, X732:term, X733:subst, X734:subst, X735:term, X736:subst, X737:subst > term > subst > $o, X738:term, X741:term, X742:subst, X743:term, X744:subst, X745:subst, X746:term, X747:subst, X751:subst > term > term, X752:term, X760:term, X761:subst > term > subst > $o, X762:term, X764:subst, X765:term, X766:subst, X767:term, X771:subst > term > term, X776:term, X777:subst > term > subst > $o, X778:term, X788:subst, X789:term, X790:subst, X791:term, X795:subst, X796:term, X797:subst, X798:subst, X799:subst, X800:term, X801:subst, X802:subst, X803:subst > term > term, X808:term, X809:subst > term > subst > $o, X810:term, X811:term, X825:subst, X826:term, X827:subst, X828:subst, X829:subst, X830:term, X831:subst, X832:subst, X833:term, X834:term, X837:term > $o, X838:term > $o, X839:term, X840:subst, X842:term, X843:subst, X848:term, X849:subst > term > subst > $o, X851:term, X852:term, X854:term > $o, X856:subst > term > subst > $o, X857:term, X860:term, X863:subst > term > term, X864:term > $o, X869:term, X872:term, X873:term, X874:term, X875:term, X879:subst > term > term, X884:term, X885:subst > term > subst > $o, X886:term, X888:subst, X889:term, X890:subst, X891:term, X893:term, X894:subst > term > subst > $o, X895:term, X897:subst, X898:term, X899:subst, X900:term, X904:subst > term > term, X909:term, X910:subst > term > subst > $o, X911:term, X913:subst, X914:term, X915:subst, X916:term, X920:subst > term > term, X925:term, X926:subst > term > subst > $o, X927:term > $o, X928:term, X929:term, X945:subst, X946:term, X947:subst, X948:subst, X949:subst, X950:term, X951:subst, X952:subst, X953:term, X954:term, X955:term, X956:term, X957:term, X958:term, X959:term, X964:term, X965:term, X966:term, X967:term, X976:term, X977:term, X978:term, X979:term, X980:term, X981:term, X982:term, X983:term, X988:subst > term > subst > $o, X989:term > $o, X990:term, X992:subst, X993:term, X994:subst, X995:term, X1001:subst > term > term, X1006:term, X1007:term, X1013:term, X1014:term, X1015:term, X1016:term, X1017:term, X1018:term, X1019:term, X1020:term, X1021:term, X1032:subst > term > term, X1033:subst > term > term, X1040:subst, X1041:term, X1042:term, X1043:subst, X1044:term, X1045:subst, X1046:term, X1047:term, X1052:subst, X1053:term, X1054:subst, X1055:subst, X1056:term, X1057:subst, X1058:term, X1059:subst, X1062:subst, X1064:subst, X1066:term > $o, X1067:term > $o, X1068:term, X1069:subst, X1070:term, X1076:term, X1077:term, X1081:term, X1082:term > $o, X1083:term, X1084:subst, X1086:term, X1087:term, X1091:term > $o, X1094:subst > term > term, X1098:subst > term > subst > $o, X1099:term > $o, X1100:term, X1102:subst, X1103:term, X1104:subst, X1105:term, X1108:term, X1110:term, X1111:subst, X1112:term, X1116:subst > term > term, X1121:term, X1122:term, X1123:subst, X1126:term, X1127:subst > term > subst > $o, X1129:term, X1130:term, X1132:term > $o, X1136:subst, X1137:subst, X1138:subst, X1139:subst, X1142:term, X1145:subst > term > term, X1146:subst, X1147:subst, X1150:subst > term > subst > $o, X1151:term, X1153:subst, X1154:term, X1155:subst, X1156:term, X1160:subst > term > term, X1165:term, X1166:subst > term > subst > $o, X1170:subst, X1171:term, X1172:subst, X1173:term, X1174:term, X1177:term, X1178:term, X1179:subst > term > term, X1184:subst > term > term, X1188:term, X1189:term, X1193:subst, X1194:term, X1195:subst, X1196:term > $o, X1201:term, X1202:term, X1205:term, X1206:term, X1207:term, X1208:term, X1214:term > $o, X1215:term > $o, X1216:term, X1217:subst, X1218:term, X1219:term, X1220:subst, X1221:term, X1222:subst, X1228:subst > term > subst > $o, X1229:term > $o, X1230:term, X1234:term, X1235:subst, X1238:term, X1240:term > $o, X1241:term, X1242:subst, X1244:term, X1245:term, X1249:term > $o, X1252:subst > term > subst > $o, X1253:term > $o, X1254:term, X1255:term, X1259:term, X1262:term > $o, X1264:subst > term > subst > $o, X1266:term, X1267:term]:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((X612)=(d2term @ (esk2_1 @ X612)))&((X614)=(d_one)))&(((d2term @ X615)!=(d2term @ X616))|((X615)=(X616))))&((X617)=(d2subst @ (esk3_1 @ X617))))&((X619)=(d_id)))&(((d2subst @ X620)!=(d2subst @ X621))|((X620)=(X621))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((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)=(^[Z0:subst, Z1:subst > term > term]:(d2term @ d_one))))&((hoasinduction_p_and_p_prime)=(^[Z0:subst > term > subst > $o, Z1:term > $o]:(![X13:term]:(((Z1 @ X13)<=>(Z0 @ id @ X13 @ id)))))))&((pushprop_p_and_p_prime)=(^[Z0:term, Z1:subst, Z2:term > $o, Z3:term > $o]:(![X13:term]:(((Z3 @ X13)<=>(Z2 @ (sub @ X13 @ (push @ Z0 @ Z1)))))))))&~(var @ (d2term @ d_one)))&(((~(X623 @ (esk4_4 @ X622 @ X623 @ X624 @ X625))|~(X622 @ (sub @ (esk4_4 @ X622 @ X623 @ X624 @ X625) @ (push @ X624 @ X625)))|~(X622 @ X624)|(X623 @ one)|~(pushprop_lem1v2))&((X623 @ (esk4_4 @ X622 @ X623 @ X624 @ X625))|(X622 @ (sub @ (esk4_4 @ X622 @ X623 @ X624 @ X625) @ (push @ X624 @ X625)))|~(X622 @ X624)|(X623 @ one)|~(pushprop_lem1v2)))&((((epred10_0 @ esk5_0)|(pushprop_lem1v2))&((~(epred11_0 @ X631)|(epred10_0 @ (sub @ X631 @ (push @ esk5_0 @ esk6_0)))|(pushprop_lem1v2))&(~(epred10_0 @ (sub @ X631 @ (push @ esk5_0 @ esk6_0)))|(epred11_0 @ X631)|(pushprop_lem1v2))))&(~(epred11_0 @ one)|(pushprop_lem1v2)))))&(pushprop_lem1_gthm))&(axmap))&(pushprop_lem0_gthm))&((~(shinj)|(((sub @ X632 @ sh)!=(sub @ X633 @ sh))|((X632)=(X633))))&((((sub @ esk7_0 @ sh)=(sub @ esk8_0 @ sh))|(shinj))&(((esk7_0)!=(esk8_0))|(shinj)))))&(hoasinduction_lem1v2))&(hoasinduction_lem1v2_gthm))&(((((((var @ (esk12_3 @ X636 @ X637 @ X638))|(~(X636 @ X642)|(X636 @ (sub @ (esk11_3 @ X636 @ X637 @ X638) @ (push @ X642 @ id)))|(X636 @ (esk9_3 @ X636 @ X637 @ X638)))|(X636 @ (sub @ X637 @ X638))|~(induction2lem))&(~(X636 @ (sub @ (esk12_3 @ X636 @ X637 @ X638) @ X638))|(~(X636 @ X642)|(X636 @ (sub @ (esk11_3 @ X636 @ X637 @ X638) @ (push @ X642 @ id)))|(X636 @ (esk9_3 @ X636 @ X637 @ X638)))|(X636 @ (sub @ X637 @ X638))|~(induction2lem)))&(((var @ (esk12_3 @ X636 @ X637 @ X638))|(~(X636 @ (lam @ (esk11_3 @ X636 @ X637 @ X638)))|(X636 @ (esk9_3 @ X636 @ X637 @ X638)))|(X636 @ (sub @ X637 @ X638))|~(induction2lem))&(~(X636 @ (sub @ (esk12_3 @ X636 @ X637 @ X638) @ X638))|(~(X636 @ (lam @ (esk11_3 @ X636 @ X637 @ X638)))|(X636 @ (esk9_3 @ X636 @ X637 @ X638)))|(X636 @ (sub @ X637 @ X638))|~(induction2lem))))&((((var @ (esk12_3 @ X636 @ X637 @ X638))|(~(X636 @ X642)|(X636 @ (sub @ (esk11_3 @ X636 @ X637 @ X638) @ (push @ X642 @ id)))|(X636 @ (esk10_3 @ X636 @ X637 @ X638)))|(X636 @ (sub @ X637 @ X638))|~(induction2lem))&(~(X636 @ (sub @ (esk12_3 @ X636 @ X637 @ X638) @ X638))|(~(X636 @ X642)|(X636 @ (sub @ (esk11_3 @ X636 @ X637 @ X638) @ (push @ X642 @ id)))|(X636 @ (esk10_3 @ X636 @ X637 @ X638)))|(X636 @ (sub @ X637 @ X638))|~(induction2lem)))&(((var @ (esk12_3 @ X636 @ X637 @ X638))|(~(X636 @ (lam @ (esk11_3 @ X636 @ X637 @ X638)))|(X636 @ (esk10_3 @ X636 @ X637 @ X638)))|(X636 @ (sub @ X637 @ X638))|~(induction2lem))&(~(X636 @ (sub @ (esk12_3 @ X636 @ X637 @ X638) @ X638))|(~(X636 @ (lam @ (esk11_3 @ X636 @ X637 @ X638)))|(X636 @ (esk10_3 @ X636 @ X637 @ X638)))|(X636 @ (sub @ X637 @ X638))|~(induction2lem)))))&((((var @ (esk12_3 @ X636 @ X637 @ X638))|(~(X636 @ X642)|(X636 @ (sub @ (esk11_3 @ X636 @ X637 @ X638) @ (push @ X642 @ id)))|~(X636 @ (ap @ (esk9_3 @ X636 @ X637 @ X638) @ (esk10_3 @ X636 @ X637 @ X638))))|(X636 @ (sub @ X637 @ X638))|~(induction2lem))&(~(X636 @ (sub @ (esk12_3 @ X636 @ X637 @ X638) @ X638))|(~(X636 @ X642)|(X636 @ (sub @ (esk11_3 @ X636 @ X637 @ X638) @ (push @ X642 @ id)))|~(X636 @ (ap @ (esk9_3 @ X636 @ X637 @ X638) @ (esk10_3 @ X636 @ X637 @ X638))))|(X636 @ (sub @ X637 @ X638))|~(induction2lem)))&(((var @ (esk12_3 @ X636 @ X637 @ X638))|(~(X636 @ (lam @ (esk11_3 @ X636 @ X637 @ X638)))|~(X636 @ (ap @ (esk9_3 @ X636 @ X637 @ X638) @ (esk10_3 @ X636 @ X637 @ X638))))|(X636 @ (sub @ X637 @ X638))|~(induction2lem))&(~(X636 @ (sub @ (esk12_3 @ X636 @ X637 @ X638) @ X638))|(~(X636 @ (lam @ (esk11_3 @ X636 @ X637 @ X638)))|~(X636 @ (ap @ (esk9_3 @ X636 @ X637 @ X638) @ (esk10_3 @ X636 @ X637 @ X638))))|(X636 @ (sub @ X637 @ X638))|~(induction2lem)))))&((((~(epred12_0 @ X647)|~(epred12_0 @ X648)|(epred12_0 @ (ap @ X647 @ X648))|(induction2lem))&(((epred12_0 @ (esk15_1 @ X649))|(epred12_0 @ (lam @ X649))|(induction2lem))&(~(epred12_0 @ (sub @ X649 @ (push @ (esk15_1 @ X649) @ id)))|(epred12_0 @ (lam @ X649))|(induction2lem))))&(~(var @ X651)|(epred12_0 @ (sub @ X651 @ esk14_0))|(induction2lem)))&(~(epred12_0 @ (sub @ esk13_0 @ esk14_0))|(induction2lem)))))&((~(hoasinduction_lem3v2_f)|((sub @ X652 @ (push @ X654 @ X655))=(esk16_1 @ X652 @ X655 @ X654)))&(((sub @ esk17_0 @ (push @ (esk18_1 @ X657) @ (esk19_1 @ X657)))!=(X657 @ (esk19_1 @ X657) @ (esk18_1 @ X657)))|(hoasinduction_lem3v2_f))))&(axvarshift))&((~(hoasapinj2)|(((ap @ (sub @ X660 @ id) @ X662)!=(ap @ (sub @ X661 @ id) @ X663))|((X662)=(X663))))&((((ap @ (sub @ esk20_0 @ id) @ esk22_0)=(ap @ (sub @ esk21_0 @ id) @ esk23_0))|(hoasapinj2))&(((esk22_0)!=(esk23_0))|(hoasapinj2)))))&(hoasapnotvar_gthm))&((~(hoasapinj1)|(((ap @ (sub @ X668 @ id) @ X670)!=(ap @ (sub @ X669 @ id) @ X671))|((X668)=(X669))))&((((ap @ (sub @ esk24_0 @ id) @ esk26_0)=(ap @ (sub @ esk25_0 @ id) @ esk27_0))|(hoasapinj1))&(((esk24_0)!=(esk25_0))|(hoasapinj1)))))&~(ulamvar1))&((~(induction2lem_lthm)|(((esk28_0)!=(sub @ one @ (push @ esk28_0 @ esk29_0)))|(((esk31_0)!=(comp @ sh @ (push @ esk30_0 @ esk31_0)))|(((esk32_0)!=(comp @ esk32_0 @ id))|(epred1_0)))))&((((X681)=(sub @ one @ (push @ X681 @ X682)))|(induction2lem_lthm))&((((X684)=(comp @ sh @ (push @ X683 @ X684)))|(induction2lem_lthm))&((((X685)=(comp @ X685 @ id))|(induction2lem_lthm))&(~(epred1_0)|(induction2lem_lthm)))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((~(hoasinduction_lem3v2_f_lthm)|((sub @ X686 @ (push @ X688 @ X689))=(esk33_1 @ X686 @ X689 @ X688)))&(((sub @ esk34_0 @ (push @ (esk35_1 @ X691) @ (esk36_1 @ X691)))!=(X691 @ (esk36_1 @ X691) @ (esk35_1 @ X691)))|(hoasinduction_lem3v2_f_lthm))))&((~(hoasinduction_lthm)|(epred4_0))&(~(epred4_0)|(hoasinduction_lthm))))&((((((~(var @ X699)|(epred14_0 @ X699)|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|(~(X695 @ (esk37_1 @ X695))|~(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ X700)|~(epred14_0 @ X701)|(epred14_0 @ (ap @ X700 @ X701))|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|(~(X695 @ (esk37_1 @ X695))|~(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred14_0 @ (esk39_1 @ X702))|(epred14_0 @ (lam @ X702))|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|(~(X695 @ (esk37_1 @ X695))|~(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ (sub @ X702 @ (push @ (esk39_1 @ X702) @ id)))|(epred14_0 @ (lam @ X702))|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|(~(X695 @ (esk37_1 @ X695))|~(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred14_0 @ esk38_0)|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|(~(X695 @ (esk37_1 @ X695))|~(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm)))&((((~(var @ X699)|(epred14_0 @ X699)|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|((X695 @ (esk37_1 @ X695))|(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ X700)|~(epred14_0 @ X701)|(epred14_0 @ (ap @ X700 @ X701))|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|((X695 @ (esk37_1 @ X695))|(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred14_0 @ (esk39_1 @ X702))|(epred14_0 @ (lam @ X702))|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|((X695 @ (esk37_1 @ X695))|(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ (sub @ X702 @ (push @ (esk39_1 @ X702) @ id)))|(epred14_0 @ (lam @ X702))|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|((X695 @ (esk37_1 @ X695))|(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred14_0 @ esk38_0)|(((esk40_0)!=(sub @ esk40_0 @ id))|(epred5_0))|((X695 @ (esk37_1 @ X695))|(epred13_0 @ id @ (esk37_1 @ X695) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(((~(epred15_1 @ X705 @ X707)|(X705 @ id @ X707 @ id)|(hoasinduction_no_psi_cond_lthm))&(~(X705 @ id @ X708 @ id)|(epred15_1 @ X705 @ X708)|(hoasinduction_no_psi_cond_lthm)))&((((((~(X709 @ X714)|(X709 @ (sub @ (esk44_1 @ X709) @ (push @ X714 @ id)))|((X709 @ (esk42_1 @ X709))|(var @ (esk41_1 @ X709)))|(X709 @ X715)|(hoasinduction_no_psi_cond_lthm))&(~(X709 @ (lam @ (esk44_1 @ X709)))|((X709 @ (esk42_1 @ X709))|(var @ (esk41_1 @ X709)))|(X709 @ X715)|(hoasinduction_no_psi_cond_lthm)))&((~(X709 @ X714)|(X709 @ (sub @ (esk44_1 @ X709) @ (push @ X714 @ id)))|((X709 @ (esk43_1 @ X709))|(var @ (esk41_1 @ X709)))|(X709 @ X715)|(hoasinduction_no_psi_cond_lthm))&(~(X709 @ (lam @ (esk44_1 @ X709)))|((X709 @ (esk43_1 @ X709))|(var @ (esk41_1 @ X709)))|(X709 @ X715)|(hoasinduction_no_psi_cond_lthm))))&((~(X709 @ X714)|(X709 @ (sub @ (esk44_1 @ X709) @ (push @ X714 @ id)))|(~(X709 @ (ap @ (esk42_1 @ X709) @ (esk43_1 @ X709)))|(var @ (esk41_1 @ X709)))|(X709 @ X715)|(hoasinduction_no_psi_cond_lthm))&(~(X709 @ (lam @ (esk44_1 @ X709)))|(~(X709 @ (ap @ (esk42_1 @ X709) @ (esk43_1 @ X709)))|(var @ (esk41_1 @ X709)))|(X709 @ X715)|(hoasinduction_no_psi_cond_lthm))))&((((~(X709 @ X714)|(X709 @ (sub @ (esk44_1 @ X709) @ (push @ X714 @ id)))|((X709 @ (esk42_1 @ X709))|~(X709 @ (esk41_1 @ X709)))|(X709 @ 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id)|~(hoasinduction_no_psi_cond))&(~(X1166 @ id @ X1173 @ id)|(X1166 @ id @ (esk244_1 @ X1166 @ id @ X1173) @ id)|(X1166 @ id @ (esk243_1 @ X1166) @ id)|(X1166 @ id @ X1174 @ id)|~(hoasinduction_no_psi_cond)))&(~(X1166 @ id @ (lam @ (esk244_1 @ X1166 @ sh @ one)) @ id)|(X1166 @ id @ (esk243_1 @ X1166) @ id)|(X1166 @ id @ X1174 @ id)|~(hoasinduction_no_psi_cond))))&(((((sub @ (esk244_1 @ X1166 @ X1170 @ X1171) @ X1172)=(esk244_1 @ X1166 @ (comp @ X1170 @ X1172) @ (sub @ X1171 @ X1172)))|~(X1166 @ id @ (ap @ (sub @ (esk242_1 @ X1166) @ id) @ (esk243_1 @ X1166)) @ id)|(X1166 @ id @ X1174 @ id)|~(hoasinduction_no_psi_cond))&(~(X1166 @ id @ X1173 @ id)|(X1166 @ id @ (esk244_1 @ X1166 @ id @ X1173) @ id)|~(X1166 @ id @ (ap @ (sub @ (esk242_1 @ X1166) @ id) @ (esk243_1 @ X1166)) @ id)|(X1166 @ id @ X1174 @ id)|~(hoasinduction_no_psi_cond)))&(~(X1166 @ id @ (lam @ (esk244_1 @ X1166 @ sh @ one)) @ id)|~(X1166 @ id @ (ap @ (sub @ (esk242_1 @ X1166) @ id) @ (esk243_1 @ X1166)) @ id)|(X1166 @ id @ X1174 @ id)|~(hoasinduction_no_psi_cond))))&(((~(epred42_0 @ id @ X1177 @ id)|~(epred42_0 @ id @ X1178 @ id)|(epred42_0 @ id @ (ap @ (sub @ X1177 @ id) @ X1178) @ id)|(hoasinduction_no_psi_cond))&(((epred42_0 @ id @ (esk249_1 @ X1179) @ id)|((sub @ (X1179 @ (esk246_1 @ X1179) @ (esk247_1 @ X1179)) @ (esk248_1 @ X1179))!=(X1179 @ (comp @ (esk246_1 @ X1179) @ (esk248_1 @ X1179)) @ (sub @ (esk247_1 @ X1179) @ (esk248_1 @ X1179))))|(epred42_0 @ id @ (lam @ (X1179 @ sh @ one)) @ id)|(hoasinduction_no_psi_cond))&(~(epred42_0 @ id @ (X1179 @ id @ (esk249_1 @ X1179)) @ id)|((sub @ (X1179 @ (esk246_1 @ X1179) @ (esk247_1 @ X1179)) @ (esk248_1 @ X1179))!=(X1179 @ (comp @ (esk246_1 @ X1179) @ (esk248_1 @ X1179)) @ (sub @ (esk247_1 @ X1179) @ (esk248_1 @ X1179))))|(epred42_0 @ id @ (lam @ (X1179 @ sh @ one)) @ id)|(hoasinduction_no_psi_cond))))&(~(epred42_0 @ id @ esk245_0 @ id)|(hoasinduction_no_psi_cond)))))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&((~(hoaslamnotap)|(((sub @ (X1184 @ (esk250_1 @ X1184) @ (esk251_1 @ X1184)) @ (esk252_1 @ X1184))!=(X1184 @ (comp @ (esk250_1 @ X1184) @ (esk252_1 @ X1184)) @ (sub @ (esk251_1 @ X1184) @ (esk252_1 @ X1184))))|((lam @ (X1184 @ sh @ one))!=(ap @ (sub @ X1188 @ id) @ X1189))))&((((sub @ (esk253_0 @ X1193 @ X1194) @ X1195)=(esk253_0 @ (comp @ X1193 @ X1195) @ (sub @ X1194 @ X1195)))|(hoaslamnotap))&(((lam @ (esk253_0 @ sh @ one))=(ap @ (sub @ esk254_0 @ id) @ esk255_0))|(hoaslamnotap)))))&(substmonoid_gthm))&(ulamvarsh))&((((((~(X1196 @ X1201)|(X1196 @ (sub @ (esk259_1 @ X1196) @ (push @ X1201 @ id)))|((X1196 @ (esk257_1 @ X1196))|(var @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2))&(~(X1196 @ (lam @ (esk259_1 @ X1196)))|((X1196 @ (esk257_1 @ X1196))|(var @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2)))&((~(X1196 @ X1201)|(X1196 @ (sub @ (esk259_1 @ X1196) @ (push @ X1201 @ id)))|((X1196 @ (esk258_1 @ X1196))|(var @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2))&(~(X1196 @ (lam @ (esk259_1 @ X1196)))|((X1196 @ (esk258_1 @ X1196))|(var @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2))))&((~(X1196 @ X1201)|(X1196 @ (sub @ (esk259_1 @ X1196) @ (push @ X1201 @ id)))|(~(X1196 @ (ap @ (esk257_1 @ X1196) @ (esk258_1 @ X1196)))|(var @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2))&(~(X1196 @ (lam @ (esk259_1 @ X1196)))|(~(X1196 @ (ap @ (esk257_1 @ X1196) @ (esk258_1 @ X1196)))|(var @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2))))&((((~(X1196 @ X1201)|(X1196 @ (sub @ (esk259_1 @ X1196) @ (push @ X1201 @ id)))|((X1196 @ (esk257_1 @ X1196))|~(X1196 @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2))&(~(X1196 @ (lam @ (esk259_1 @ X1196)))|((X1196 @ (esk257_1 @ X1196))|~(X1196 @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2)))&((~(X1196 @ X1201)|(X1196 @ (sub @ (esk259_1 @ X1196) @ (push @ X1201 @ id)))|((X1196 @ (esk258_1 @ X1196))|~(X1196 @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2))&(~(X1196 @ (lam @ (esk259_1 @ X1196)))|((X1196 @ (esk258_1 @ X1196))|~(X1196 @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2))))&((~(X1196 @ X1201)|(X1196 @ (sub @ (esk259_1 @ X1196) @ (push @ X1201 @ id)))|(~(X1196 @ (ap @ (esk257_1 @ X1196) @ (esk258_1 @ X1196)))|~(X1196 @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2))&(~(X1196 @ (lam @ (esk259_1 @ X1196)))|(~(X1196 @ (ap @ (esk257_1 @ X1196) @ (esk258_1 @ X1196)))|~(X1196 @ (esk256_1 @ X1196)))|(X1196 @ X1202)|~(induction2)))))&((((~(var @ X1205)|(epred43_0 @ X1205)|(induction2))&(~(epred43_0 @ X1206)|~(epred43_0 @ X1207)|(epred43_0 @ (ap @ X1206 @ X1207))|(induction2)))&(((epred43_0 @ (esk261_1 @ X1208))|(epred43_0 @ (lam @ X1208))|(induction2))&(~(epred43_0 @ (sub @ X1208 @ (push @ (esk261_1 @ X1208) @ id)))|(epred43_0 @ (lam @ X1208))|(induction2))))&(~(epred43_0 @ esk260_0)|(induction2)))))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((~(pushprop_lem1_lthm)|(((esk262_0)!=(sub @ one @ (push @ esk262_0 @ esk263_0)))|(((esk265_0)!=(comp @ sh @ (push @ esk264_0 @ esk265_0)))|(~(X1214 @ X1216)|(X1215 @ (sub @ X1216 @ (push @ X1218 @ X1217)))))))&((((X1219)=(sub @ one @ (push @ X1219 @ X1220)))|(pushprop_lem1_lthm))&((((X1222)=(comp @ sh @ (push @ X1221 @ X1222)))|(pushprop_lem1_lthm))&(((epred44_0 @ esk266_0)|(pushprop_lem1_lthm))&(~(epred45_0 @ (sub @ esk266_0 @ (push @ esk268_0 @ esk267_0)))|(pushprop_lem1_lthm)))))))&((~(hoasinduction_lem3v2)|((epred8_3 @ X1230 @ X1229 @ X1228)|(X1229 @ (lam @ X1230))))&((~(epred8_3 @ esk269_0 @ epred47_0 @ epred46_0)|(hoasinduction_lem3v2))&(~(epred47_0 @ (lam @ esk269_0))|(hoasinduction_lem3v2)))))&((~(axshiftcons)|((X1235)=(comp @ sh @ (push @ X1234 @ X1235))))&(((esk271_0)!=(comp @ sh @ (push @ esk270_0 @ esk271_0)))|(axshiftcons))))&((~(termmset)|((X1238)=(sub @ X1238 @ id)))&(((esk272_0)!=(sub @ esk272_0 @ id))|(termmset))))&(((~(epred48_3 @ X1240 @ X1241 @ X1242 @ X1244)|(X1240 @ (sub @ X1244 @ (push @ X1241 @ X1242)))|~(pushprop_lem0_lthm))&(~(X1240 @ (sub @ X1245 @ (push @ X1241 @ X1242)))|(epred48_3 @ X1240 @ X1241 @ X1242 @ X1245)|~(pushprop_lem0_lthm)))&((~(X1249 @ (esk275_1 @ X1249))|~(epred49_0 @ (sub @ (esk275_1 @ X1249) @ (push @ esk273_0 @ esk274_0)))|(pushprop_lem0_lthm))&((X1249 @ (esk275_1 @ X1249))|(epred49_0 @ (sub @ (esk275_1 @ X1249) @ (push @ esk273_0 @ esk274_0)))|(pushprop_lem0_lthm)))))&(hoasapnotvar_lthm))&((~(hoasinduction_lem3v2_lthm)|(((esk276_0)!=(sub @ esk276_0 @ id))|((epred8_3 @ X1254 @ X1253 @ X1252)|(X1253 @ (lam @ X1254)))))&((((X1255)=(sub @ X1255 @ id))|(hoasinduction_lem3v2_lthm))&((~(epred8_3 @ esk277_0 @ epred51_0 @ epred50_0)|(hoasinduction_lem3v2_lthm))&(~(epred51_0 @ (lam @ esk277_0))|(hoasinduction_lem3v2_lthm))))))&((~(axvarid)|((X1259)=(sub @ X1259 @ id)))&(((esk278_0)!=(sub @ esk278_0 @ id))|(axvarid))))&(((~(X1262 @ (esk279_1 @ X1262))|~(epred52_0 @ id @ (esk279_1 @ X1262) @ id)|(epred9_0)|~(hoasinduction_lthm_3))&((X1262 @ (esk279_1 @ X1262))|(epred52_0 @ id @ (esk279_1 @ X1262) @ id)|(epred9_0)|~(hoasinduction_lthm_3)))&(((~(epred53_1 @ X1264 @ X1266)|(X1264 @ id @ X1266 @ id)|(hoasinduction_lthm_3))&(~(X1264 @ id @ X1267 @ id)|(epred53_1 @ X1264 @ X1267)|(hoasinduction_lthm_3)))&(~(epred9_0)|(hoasinduction_lthm_3)))))), 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_10])])])])])])])).
% 0.45/0.39 thf(c_0_13, negated_conjecture, ~(((lamnotvar)<=>![X14:term]:(~(var @ (lam @ X14))))), inference(fof_simplification,[status(thm)],[c_0_11])).
% 0.45/0.39 thf(c_0_14, plain, ![X2:d_term]:(((X2)=(d_one))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.45/0.39 thf(c_0_15, negated_conjecture, ![X611:term]:(((~(lamnotvar)|(var @ (lam @ esk1_0)))&((lamnotvar)|~(var @ (lam @ X611))))), 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_13])])])])])).
% 0.45/0.39 thf(c_0_16, plain, ((one)=(d2term @ d_one)), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.45/0.39 thf(c_0_17, plain, ![X2:d_term, X3:d_term]:(((X2)=(X3))), inference(spm,[status(thm)],[c_0_14, c_0_14])).
% 0.45/0.39 thf(c_0_18, plain, ~((var @ (d2term @ d_one))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.45/0.39 thf(c_0_19, negated_conjecture, ((var @ (lam @ esk1_0))|~((lamnotvar))), inference(split_conjunct,[status(thm)],[c_0_15])).
% 0.45/0.39 thf(c_0_20, plain, (lamnotvar), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.45/0.39 thf(c_0_21, plain, ![X1:term]:(((X1)=(d2term @ (esk2_1 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.45/0.39 thf(c_0_22, plain, ![X2:d_term]:(((d2term @ X2)=(one))), inference(spm,[status(thm)],[c_0_16, c_0_17])).
% 0.45/0.39 thf(c_0_23, plain, ![X2:d_term]:(~((var @ (d2term @ X2)))), inference(spm,[status(thm)],[c_0_18, c_0_17])).
% 0.45/0.39 thf(c_0_24, negated_conjecture, (var @ (lam @ esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 0.45/0.39 thf(c_0_25, plain, ![X1:term]:(((X1)=(one))), inference(rw,[status(thm)],[c_0_21, c_0_22])).
% 0.45/0.39 thf(c_0_26, plain, ~((var @ one)), inference(spm,[status(thm)],[c_0_23, c_0_16])).
% 0.45/0.39 thf(c_0_27, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25]), c_0_26]), ['proof']).
% 0.45/0.39 % SZS output end CNFRefutation
% 0.45/0.39 % Parsed axioms : 132
% 0.45/0.39 % Removed by relevancy pruning/SinE : 130
% 0.45/0.39 % Initial clauses : 1097
% 0.45/0.39 % Removed in clause preprocessing : 0
% 0.45/0.39 % Initial clauses in saturation : 1097
% 0.45/0.39 % Processed clauses : 105
% 0.45/0.39 % ...of these trivial : 1
% 0.45/0.39 % ...subsumed : 1
% 0.45/0.39 % ...remaining for further processing : 103
% 0.45/0.39 % Other redundant clauses eliminated : 0
% 0.45/0.39 % Clauses deleted for lack of memory : 0
% 0.45/0.39 % Backward-subsumed : 3
% 0.45/0.39 % Backward-rewritten : 27
% 0.45/0.39 % Generated clauses : 24
% 0.45/0.39 % ...of the previous two non-redundant : 16
% 0.45/0.39 % ...aggressively subsumed : 0
% 0.45/0.39 % Contextual simplify-reflections : 0
% 0.45/0.39 % Paramodulations : 22
% 0.45/0.39 % Factorizations : 0
% 0.45/0.39 % NegExts : 0
% 0.45/0.39 % Equation resolutions : 0
% 0.45/0.39 % Disequality decompositions : 0
% 0.45/0.39 % Total rewrite steps : 9
% 0.45/0.39 % ...of those cached : 0
% 0.45/0.39 % Propositional unsat checks : 0
% 0.45/0.39 % Propositional check models : 0
% 0.45/0.39 % Propositional check unsatisfiable : 0
% 0.45/0.39 % Propositional clauses : 0
% 0.45/0.39 % Propositional clauses after purity: 0
% 0.45/0.39 % Propositional unsat core size : 0
% 0.45/0.39 % Propositional preprocessing time : 0.000
% 0.45/0.39 % Propositional encoding time : 0.000
% 0.45/0.39 % Propositional solver time : 0.000
% 0.45/0.39 % Success case prop preproc time : 0.000
% 0.45/0.39 % Success case prop encoding time : 0.000
% 0.45/0.39 % Success case prop solver time : 0.000
% 0.45/0.39 % Current number of processed clauses : 73
% 0.45/0.39 % Positive orientable unit clauses : 54
% 0.45/0.39 % Positive unorientable unit clauses: 3
% 0.45/0.39 % Negative unit clauses : 3
% 0.45/0.39 % Non-unit-clauses : 13
% 0.45/0.39 % Current number of unprocessed clauses: 1001
% 0.45/0.39 % ...number of literals in the above : 5901
% 0.45/0.39 % Current number of archived formulas : 0
% 0.45/0.39 % Current number of archived clauses : 30
% 0.45/0.39 % Clause-clause subsumption calls (NU) : 245
% 0.45/0.39 % Rec. Clause-clause subsumption calls : 218
% 0.45/0.39 % Non-unit clause-clause subsumptions : 0
% 0.45/0.39 % Unit Clause-clause subsumption calls : 346
% 0.45/0.39 % Rewrite failures with RHS unbound : 21
% 0.45/0.39 % BW rewrite match attempts : 723
% 0.45/0.39 % BW rewrite match successes : 42
% 0.45/0.39 % Condensation attempts : 0
% 0.45/0.39 % Condensation successes : 0
% 0.45/0.39 % Termbank termtop insertions : 107128
% 0.45/0.39 % Search garbage collected termcells : 21964
% 0.45/0.39
% 0.45/0.39 % -------------------------------------------------
% 0.45/0.39 % User time : 0.098 s
% 0.45/0.39 % System time : 0.013 s
% 0.45/0.39 % Total time : 0.111 s
% 0.45/0.39 % Maximum resident set size: 8256 pages
% 0.45/0.39
% 0.45/0.39 % -------------------------------------------------
% 0.45/0.39 % User time : 0.163 s
% 0.45/0.39 % System time : 0.062 s
% 0.45/0.39 % Total time : 0.224 s
% 0.45/0.39 % Maximum resident set size: 5376 pages
% 0.45/0.39 % E exiting
%------------------------------------------------------------------------------