E---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SWX162^1 : 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 : n009.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 08:40:25 AM UTC 2026

% Result   : Theorem 0.22s 0.38s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWX162^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18  % Computer : n009.cluster.edu
% 0.07/0.18  % Model    : x86_64 x86_64
% 0.07/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18  % Memory   : 8046.5625MB
% 0.07/0.18  % OS       : Linux 6.8.0-71-generic
% 0.07/0.18  % CPULimit : 300
% 0.07/0.18  % WCLimit  : 300
% 0.07/0.18  % DateTime : Tue Sep 29 16:09:15 UTC 2026
% 0.07/0.19  % CPUTime  : 
% 0.07/0.19  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23  Running higher-order theorem proving
% 0.07/0.25  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.Y1wHunPQUw/E---3.1_4190355.p
% 0.22/0.38  % Version: 3.5.1-ho
% 0.22/0.38  % partial match(1): HSLMSLSMSSSNHSA
% 0.22/0.38  % Preprocessing class: HSLMSLSSSSSNHSA.
% 0.22/0.38  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.38  % Starting new_ho_10 with 600s (2) cores
% 0.22/0.38  % Starting sh3 with 600s (2) cores
% 0.22/0.38  % Starting ho_unfolding_3 with 600s (2) cores
% 0.22/0.38  % Starting new_ho_10_cnf2 with 600s (2) cores
% 0.22/0.38  % sh3 with pid 4190374 completed with status 0
% 0.22/0.38  % Result found by sh3
% 0.22/0.38  % partial match(1): HSLMSLSMSSSNHSA
% 0.22/0.38  % Preprocessing class: HSLMSLSSSSSNHSA.
% 0.22/0.38  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.38  % Starting new_ho_10 with 600s (2) cores
% 0.22/0.38  % Starting sh3 with 600s (2) cores
% 0.22/0.38  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.38  % No SInE strategy applied
% 0.22/0.38  % Search class: HGHSM-SMLM31-MHSFFMBN
% 0.22/0.38  % partial match(1): HGHSM-SMLM31-MHSFFSBN
% 0.22/0.38  % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.22/0.38  % Starting SubtermCWHack with 55s (1) cores
% 0.22/0.38  % Starting sh3 with 61s (1) cores
% 0.22/0.38  % sh3 with pid 4190382 completed with status 0
% 0.22/0.38  % Result found by sh3
% 0.22/0.38  % partial match(1): HSLMSLSMSSSNHSA
% 0.22/0.38  % Preprocessing class: HSLMSLSSSSSNHSA.
% 0.22/0.38  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.38  % Starting new_ho_10 with 600s (2) cores
% 0.22/0.38  % Starting sh3 with 600s (2) cores
% 0.22/0.38  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.38  % No SInE strategy applied
% 0.22/0.38  % Search class: HGHSM-SMLM31-MHSFFMBN
% 0.22/0.38  % partial match(1): HGHSM-SMLM31-MHSFFSBN
% 0.22/0.38  % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.22/0.38  % Starting SubtermCWHack with 55s (1) cores
% 0.22/0.38  % Starting sh3 with 61s (1) cores
% 0.22/0.38  % Preprocessing time       : 0.028 s
% 0.22/0.38  % Presaturation interreduction done
% 0.22/0.38  
% 0.22/0.38  % Proof found!
% 0.22/0.38  % SZS status Theorem
% 0.22/0.38  % SZS output start CNFRefutation
% 0.22/0.38  thf(decl_sort1, type, term: $tType).
% 0.22/0.38  thf(decl_sort2, type, subst: $tType).
% 0.22/0.38  thf(decl_sort3, type, d_term: $tType).
% 0.22/0.38  thf(decl_sort4, type, d_subst: $tType).
% 0.22/0.38  thf(decl_23, type, one: term).
% 0.22/0.38  thf(decl_24, type, ap: term > term > term).
% 0.22/0.38  thf(decl_25, type, lam: term > term).
% 0.22/0.38  thf(decl_26, type, sub: term > subst > term).
% 0.22/0.38  thf(decl_27, type, id: subst).
% 0.22/0.38  thf(decl_28, type, sh: subst).
% 0.22/0.38  thf(decl_29, type, push: term > subst > subst).
% 0.22/0.38  thf(decl_30, type, comp: subst > subst > subst).
% 0.22/0.38  thf(decl_31, type, var: term > $o).
% 0.22/0.38  thf(decl_32, type, pushprop_lem1v2: $o).
% 0.22/0.38  thf(decl_33, type, pushprop_lem1_gthm: $o).
% 0.22/0.38  thf(decl_34, type, axmap: $o).
% 0.22/0.38  thf(decl_35, type, pushprop_lem0_gthm: $o).
% 0.22/0.38  thf(decl_36, type, shinj: $o).
% 0.22/0.38  thf(decl_37, type, hoasinduction_lem1v2: $o).
% 0.22/0.38  thf(decl_38, type, hoasinduction_lem1v2_gthm: $o).
% 0.22/0.38  thf(decl_39, type, hoasap: subst > term > subst > term > term).
% 0.22/0.38  thf(decl_40, type, induction2lem: $o).
% 0.22/0.38  thf(decl_41, type, hoasinduction_lem3v2_f: $o).
% 0.22/0.38  thf(decl_42, type, axvarshift: $o).
% 0.22/0.38  thf(decl_43, type, hoasapinj2: $o).
% 0.22/0.38  thf(decl_44, type, hoasapnotvar_gthm: $o).
% 0.22/0.38  thf(decl_45, type, hoasapinj1: $o).
% 0.22/0.38  thf(decl_46, type, ulamvar1: $o).
% 0.22/0.38  thf(decl_47, type, induction2lem_lthm: $o).
% 0.22/0.38  thf(decl_48, type, hoasinduction_lem3v2_gthm: $o).
% 0.22/0.38  thf(decl_49, type, apnotvar: $o).
% 0.22/0.38  thf(decl_50, type, pushprop_lthm_orig: $o).
% 0.22/0.38  thf(decl_51, type, hoasinduction_lem3v2_f_lthm: $o).
% 0.22/0.38  thf(decl_52, type, hoasinduction_lthm: $o).
% 0.22/0.38  thf(decl_53, type, hoasinduction_no_psi_cond_lthm: $o).
% 0.22/0.38  thf(decl_54, type, hoaslaminj: $o).
% 0.22/0.38  thf(decl_55, type, hoasinduction_lem3aaa: $o).
% 0.22/0.38  thf(decl_56, type, induction2lem_gthm: $o).
% 0.22/0.38  thf(decl_57, type, hoasinduction_lem3aa_lthm: $o).
% 0.22/0.38  thf(decl_58, type, hoasinduction_lem3: $o).
% 0.22/0.38  thf(decl_59, type, hoasinduction_lem2: $o).
% 0.22/0.38  thf(decl_60, type, termmset_lthm: $o).
% 0.22/0.38  thf(decl_61, type, hoasinduction_lem1: $o).
% 0.22/0.38  thf(decl_62, type, hoaslamnotap_lthm: $o).
% 0.22/0.38  thf(decl_63, type, pushprop_lem1v2_lthm: $o).
% 0.22/0.38  thf(decl_64, type, hoasapnotvar: $o).
% 0.22/0.38  thf(decl_65, type, hoasinduction_lem0: $o).
% 0.22/0.38  thf(decl_66, type, hoasinduction: $o).
% 0.22/0.38  thf(decl_67, type, hoasinduction_gthm: $o).
% 0.22/0.38  thf(decl_68, type, axapp: $o).
% 0.22/0.38  thf(decl_69, type, hoaslamnotvar_lthm: $o).
% 0.22/0.38  thf(decl_70, type, pushprop_lem3v2_lthm: $o).
% 0.22/0.38  thf(decl_71, type, hoasinduction_lem3b_lthm: $o).
% 0.22/0.38  thf(decl_72, type, ulamvarind: $o).
% 0.22/0.38  thf(decl_73, type, induction: $o).
% 0.22/0.38  thf(decl_74, type, hoasinduction_lem3a_lthm: $o).
% 0.22/0.38  thf(decl_75, type, termmset_gthm: $o).
% 0.22/0.38  thf(decl_76, type, hoasinduction_lem3aa: $o).
% 0.22/0.38  thf(decl_77, type, pushprop_lem1v2_gthm: $o).
% 0.22/0.38  thf(decl_78, type, hoaslamnotap_gthm: $o).
% 0.22/0.38  thf(decl_79, type, hoaslamnotvar_gthm: $o).
% 0.22/0.38  thf(decl_80, type, hoasinduction_lem3b_gthm: $o).
% 0.22/0.38  thf(decl_81, type, pushprop_lem2v2: $o).
% 0.22/0.38  thf(decl_82, type, hoasinduction_lem3a_gthm: $o).
% 0.22/0.38  thf(decl_83, type, axclos: $o).
% 0.22/0.38  thf(decl_84, type, axassoc: $o).
% 0.22/0.38  thf(decl_85, type, hoasinduction_lem2v2: $o).
% 0.22/0.38  thf(decl_86, type, pushprop_lthm: $o).
% 0.22/0.38  thf(decl_87, type, apinj2: $o).
% 0.22/0.38  thf(decl_88, type, apinj1: $o).
% 0.22/0.38  thf(decl_89, type, hoasapinj2_lthm: $o).
% 0.22/0.38  thf(decl_90, type, hoasinduction_lem3v2a: $o).
% 0.22/0.38  thf(decl_91, type, hoasapinj1_lthm: $o).
% 0.22/0.38  thf(decl_92, type, hoaslaminj_lthm: $o).
% 0.22/0.38  thf(decl_93, type, axvarcons: $o).
% 0.22/0.38  thf(decl_94, type, hoaslam: subst > (subst > term > term) > term).
% 0.22/0.38  thf(decl_95, type, axscons: $o).
% 0.22/0.38  thf(decl_96, type, hoasinduction_lem2v2_gthm: $o).
% 0.22/0.38  thf(decl_97, type, axidr: $o).
% 0.22/0.38  thf(decl_98, type, pushprop_lem1: $o).
% 0.22/0.38  thf(decl_99, type, laminj: $o).
% 0.22/0.38  thf(decl_100, type, hoasinduction_lem3_lthm: $o).
% 0.22/0.38  thf(decl_101, type, pushprop_lem0: $o).
% 0.22/0.38  thf(decl_102, type, pushprop_gthm: $o).
% 0.22/0.38  thf(decl_103, type, axabs: $o).
% 0.22/0.38  thf(decl_104, type, hoasinduction_lem3v2a_lthm: $o).
% 0.22/0.38  thf(decl_105, type, hoasinduction_lem2_lthm: $o).
% 0.22/0.38  thf(decl_106, type, hoasapinj2_gthm: $o).
% 0.22/0.38  thf(decl_107, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 0.22/0.38  thf(decl_108, type, hoasinduction_lem1_lthm: $o).
% 0.22/0.38  thf(decl_109, type, lamnotap: $o).
% 0.22/0.38  thf(decl_110, type, hoasapinj1_gthm: $o).
% 0.22/0.38  thf(decl_111, type, hoaslamnotvar: $o).
% 0.22/0.38  thf(decl_112, type, axidl: $o).
% 0.22/0.38  thf(decl_113, type, hoaslaminj_gthm: $o).
% 0.22/0.38  thf(decl_114, type, induction2_lthm: $o).
% 0.22/0.38  thf(decl_115, type, hoasinduction_lem0_lthm: $o).
% 0.22/0.38  thf(decl_116, type, substmonoid_lthm: $o).
% 0.22/0.38  thf(decl_117, type, pushprop: $o).
% 0.22/0.38  thf(decl_118, type, hoasinduction_lem3_gthm: $o).
% 0.22/0.38  thf(decl_119, type, hoasinduction_lem2_gthm: $o).
% 0.22/0.38  thf(decl_120, type, hoasinduction_lem3b: $o).
% 0.22/0.38  thf(decl_121, type, substmonoid: $o).
% 0.22/0.38  thf(decl_122, type, lamnotvar: $o).
% 0.22/0.38  thf(decl_123, type, hoasinduction_lem3a: $o).
% 0.22/0.38  thf(decl_124, type, hoasinduction_lem1_gthm: $o).
% 0.22/0.38  thf(decl_125, type, hoasinduction_no_psi_cond: $o).
% 0.22/0.38  thf(decl_126, type, induction2_gthm: $o).
% 0.22/0.38  thf(decl_127, type, pushprop_lem2v2_lthm: $o).
% 0.22/0.38  thf(decl_128, type, hoasvar: subst > term > subst > $o).
% 0.22/0.38  thf(decl_129, type, hoaslamnotap: $o).
% 0.22/0.38  thf(decl_130, type, substmonoid_gthm: $o).
% 0.22/0.38  thf(decl_131, type, ulamvarsh: $o).
% 0.22/0.38  thf(decl_132, type, induction2: $o).
% 0.22/0.38  thf(decl_133, type, pushprop_lem3v2: $o).
% 0.22/0.38  thf(decl_134, type, pushprop_lem2v2_gthm: $o).
% 0.22/0.38  thf(decl_135, type, pushprop_lem1_lthm: $o).
% 0.22/0.38  thf(decl_136, type, hoasinduction_lem3v2: $o).
% 0.22/0.38  thf(decl_137, type, axshiftcons: $o).
% 0.22/0.38  thf(decl_138, type, termmset: $o).
% 0.22/0.38  thf(decl_139, type, pushprop_lem0_lthm: $o).
% 0.22/0.38  thf(decl_140, type, hoasapnotvar_lthm: $o).
% 0.22/0.38  thf(decl_141, type, hoasinduction_lem3v2_lthm: $o).
% 0.22/0.38  thf(decl_142, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 0.22/0.38  thf(decl_143, type, axvarid: $o).
% 0.22/0.38  thf(decl_144, type, hoasinduction_lthm_3: $o).
% 0.22/0.38  thf(decl_145, type, d2term: d_term > term).
% 0.22/0.38  thf(decl_146, type, d2subst: d_subst > subst).
% 0.22/0.38  thf(decl_147, type, d_one: d_term).
% 0.22/0.38  thf(decl_148, type, d_id: d_subst).
% 0.22/0.38  thf(decl_149, type, epred1_0: $o).
% 0.22/0.38  thf(decl_150, type, epred2_1: (subst > term > subst > $o) > $o).
% 0.22/0.38  thf(decl_152, type, epred4_0: $o).
% 0.22/0.38  thf(decl_153, type, epred5_0: $o).
% 0.22/0.38  thf(decl_154, type, epred6_0: $o).
% 0.22/0.38  thf(decl_155, type, epred7_0: $o).
% 0.22/0.38  thf(decl_156, type, epred8_3: term > (term > $o) > (subst > term > subst > $o) > $o).
% 0.22/0.38  thf(decl_157, type, epred9_0: $o).
% 0.22/0.38  thf(decl_158, type, esk1_1: term > d_term).
% 0.22/0.38  thf(decl_159, type, esk2_1: subst > d_subst).
% 0.22/0.38  thf(decl_160, type, esk3_2: (subst > term > subst > $o) > (term > $o) > term).
% 0.22/0.38  thf(decl_161, type, esk4_4: term > subst > (term > $o) > (term > $o) > term).
% 0.22/0.38  thf(decl_162, type, esk5_4: (term > $o) > (term > $o) > term > subst > term).
% 0.22/0.38  thf(decl_163, type, epred10_0: term > $o).
% 0.22/0.38  thf(decl_164, type, epred11_0: term > $o).
% 0.22/0.38  thf(decl_165, type, esk6_0: term).
% 0.22/0.38  thf(decl_166, type, esk7_0: subst).
% 0.22/0.38  thf(decl_167, type, esk8_0: term).
% 0.22/0.38  thf(decl_168, type, esk9_0: term).
% 0.22/0.38  thf(decl_169, type, esk10_3: (term > $o) > term > subst > term).
% 0.22/0.38  thf(decl_170, type, esk11_3: (term > $o) > term > subst > term).
% 0.22/0.38  thf(decl_171, type, esk12_3: (term > $o) > term > subst > term).
% 0.22/0.38  thf(decl_172, type, esk13_3: (term > $o) > term > subst > term).
% 0.22/0.38  thf(decl_173, type, epred12_0: term > $o).
% 0.22/0.38  thf(decl_174, type, esk14_0: term).
% 0.22/0.38  thf(decl_175, type, esk15_0: subst).
% 0.22/0.38  thf(decl_176, type, esk16_1: term > term).
% 0.22/0.38  thf(decl_177, type, esk17_1: term > subst > term > term).
% 0.22/0.38  thf(decl_178, type, esk18_0: term).
% 0.22/0.38  thf(decl_179, type, esk19_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_180, type, esk20_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_181, type, esk21_0: term).
% 0.22/0.38  thf(decl_182, type, esk22_0: term).
% 0.22/0.38  thf(decl_183, type, esk23_0: term).
% 0.22/0.38  thf(decl_184, type, esk24_0: term).
% 0.22/0.38  thf(decl_185, type, esk25_0: term).
% 0.22/0.38  thf(decl_186, type, esk26_0: term).
% 0.22/0.38  thf(decl_187, type, esk27_0: term).
% 0.22/0.38  thf(decl_188, type, esk28_0: term).
% 0.22/0.38  thf(decl_189, type, esk29_0: term).
% 0.22/0.38  thf(decl_190, type, esk30_0: subst).
% 0.22/0.38  thf(decl_191, type, esk31_0: term).
% 0.22/0.38  thf(decl_192, type, esk32_0: subst).
% 0.22/0.38  thf(decl_193, type, esk33_0: subst).
% 0.22/0.38  thf(decl_194, type, esk34_1: term > subst > term > term).
% 0.22/0.38  thf(decl_195, type, esk35_0: term).
% 0.22/0.38  thf(decl_196, type, esk36_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_197, type, esk37_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_198, type, epred13_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_199, type, esk38_1: (term > $o) > term).
% 0.22/0.38  thf(decl_200, type, epred14_0: term > $o).
% 0.22/0.38  thf(decl_201, type, esk39_0: term).
% 0.22/0.38  thf(decl_202, type, esk40_1: term > term).
% 0.22/0.38  thf(decl_203, type, esk41_0: term).
% 0.22/0.38  thf(decl_204, type, epred15_1: (subst > term > subst > $o) > term > $o).
% 0.22/0.38  thf(decl_205, type, esk42_1: (term > $o) > term).
% 0.22/0.38  thf(decl_206, type, esk43_1: (term > $o) > term).
% 0.22/0.38  thf(decl_207, type, esk44_1: (term > $o) > term).
% 0.22/0.38  thf(decl_208, type, esk45_1: (term > $o) > term).
% 0.22/0.38  thf(decl_209, type, esk46_2: (subst > term > term) > (subst > term > term) > subst).
% 0.22/0.38  thf(decl_210, type, esk47_2: (subst > term > term) > (subst > term > term) > term).
% 0.22/0.38  thf(decl_211, type, esk48_2: (subst > term > term) > (subst > term > term) > subst).
% 0.22/0.38  thf(decl_212, type, esk49_2: (subst > term > term) > (subst > term > term) > subst).
% 0.22/0.38  thf(decl_213, type, esk50_2: (subst > term > term) > (subst > term > term) > term).
% 0.22/0.38  thf(decl_214, type, esk51_2: (subst > term > term) > (subst > term > term) > subst).
% 0.22/0.38  thf(decl_215, type, esk52_0: subst > term > term).
% 0.22/0.38  thf(decl_216, type, esk53_0: subst > term > term).
% 0.22/0.38  thf(decl_217, type, esk54_0: subst).
% 0.22/0.38  thf(decl_218, type, esk55_0: term).
% 0.22/0.38  thf(decl_219, type, esk56_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.22/0.38  thf(decl_220, type, esk57_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_221, type, esk58_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_222, type, epred16_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_223, type, esk59_0: term).
% 0.22/0.38  thf(decl_224, type, esk60_2: (subst > term > term) > term > term).
% 0.22/0.38  thf(decl_225, type, esk61_2: (subst > term > term) > term > subst).
% 0.22/0.38  thf(decl_226, type, esk62_2: (subst > term > term) > term > term).
% 0.22/0.38  thf(decl_227, type, esk63_2: (subst > term > term) > term > subst).
% 0.22/0.38  thf(decl_228, type, esk64_2: (subst > term > term) > term > subst).
% 0.22/0.38  thf(decl_229, type, esk65_2: (subst > term > term) > term > term).
% 0.22/0.38  thf(decl_230, type, esk66_2: (subst > term > term) > term > subst).
% 0.22/0.38  thf(decl_231, type, esk67_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.22/0.38  thf(decl_232, type, esk68_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_233, type, epred17_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_234, type, esk69_0: term).
% 0.22/0.38  thf(decl_235, type, esk70_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_236, type, esk71_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_237, type, esk72_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_238, type, esk73_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_239, type, esk74_2: (subst > term > subst > $o) > term > subst).
% 0.22/0.38  thf(decl_240, type, esk75_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_241, type, esk76_2: (subst > term > subst > $o) > term > subst).
% 0.22/0.38  thf(decl_242, type, esk77_2: (subst > term > subst > $o) > term > subst).
% 0.22/0.38  thf(decl_243, type, esk78_2: (subst > term > subst > $o) > term > subst).
% 0.22/0.38  thf(decl_244, type, esk79_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_245, type, esk80_2: (subst > term > subst > $o) > term > subst).
% 0.22/0.38  thf(decl_246, type, esk81_2: (subst > term > subst > $o) > term > subst).
% 0.22/0.38  thf(decl_247, type, esk82_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.22/0.38  thf(decl_248, type, esk83_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_249, type, epred18_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_250, type, esk84_0: term).
% 0.22/0.38  thf(decl_251, type, esk85_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_252, type, esk86_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_253, type, esk87_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_254, type, esk88_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_255, type, esk89_3: (subst > term > subst > $o) > term > term > subst).
% 0.22/0.38  thf(decl_256, type, esk90_3: (subst > term > subst > $o) > term > term > term).
% 0.22/0.38  thf(decl_257, type, esk91_3: (subst > term > subst > $o) > term > term > subst).
% 0.22/0.38  thf(decl_258, type, esk92_3: (subst > term > subst > $o) > term > term > subst).
% 0.22/0.38  thf(decl_259, type, esk93_3: (subst > term > subst > $o) > term > term > subst).
% 0.22/0.38  thf(decl_260, type, esk94_3: (subst > term > subst > $o) > term > term > term).
% 0.22/0.38  thf(decl_261, type, esk95_3: (subst > term > subst > $o) > term > term > subst).
% 0.22/0.38  thf(decl_262, type, esk96_3: (subst > term > subst > $o) > term > term > subst).
% 0.22/0.38  thf(decl_263, type, esk97_3: (subst > term > subst > $o) > term > term > term).
% 0.22/0.38  thf(decl_264, type, esk98_3: (subst > term > subst > $o) > term > term > term).
% 0.22/0.38  thf(decl_265, type, epred19_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_266, type, esk99_0: term).
% 0.22/0.38  thf(decl_267, type, esk100_0: term).
% 0.22/0.38  thf(decl_268, type, esk101_0: term).
% 0.22/0.38  thf(decl_269, type, esk102_0: subst).
% 0.22/0.38  thf(decl_270, type, esk103_4: (term > $o) > (term > $o) > term > subst > term).
% 0.22/0.38  thf(decl_271, type, epred20_0: term > $o).
% 0.22/0.38  thf(decl_272, type, epred21_0: term > $o).
% 0.22/0.38  thf(decl_273, type, esk104_0: term).
% 0.22/0.38  thf(decl_274, type, esk105_0: subst).
% 0.22/0.38  thf(decl_275, type, epred22_1: (subst > term > subst > $o) > term > $o).
% 0.22/0.38  thf(decl_276, type, epred23_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_277, type, esk106_1: (term > $o) > term).
% 0.22/0.38  thf(decl_278, type, epred24_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_279, type, esk107_0: term).
% 0.22/0.38  thf(decl_280, type, esk108_1: term > subst > term > term).
% 0.22/0.38  thf(decl_281, type, esk109_0: term).
% 0.22/0.38  thf(decl_282, type, esk110_1: (term > $o) > term).
% 0.22/0.38  thf(decl_283, type, esk111_1: (term > $o) > term).
% 0.22/0.38  thf(decl_284, type, esk112_1: (term > $o) > term).
% 0.22/0.38  thf(decl_285, type, esk113_1: (term > $o) > term).
% 0.22/0.38  thf(decl_286, type, epred25_0: term > $o).
% 0.22/0.38  thf(decl_287, type, esk114_0: term).
% 0.22/0.38  thf(decl_288, type, esk115_0: term).
% 0.22/0.38  thf(decl_289, type, epred26_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_290, type, esk116_0: term).
% 0.22/0.38  thf(decl_291, type, esk117_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_292, type, esk118_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_293, type, esk119_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_294, type, esk120_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_295, type, esk121_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.22/0.38  thf(decl_296, type, esk122_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_297, type, esk123_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.22/0.38  thf(decl_298, type, esk124_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_299, type, epred27_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_300, type, esk125_0: term).
% 0.22/0.38  thf(decl_301, type, esk126_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_302, type, esk127_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_303, type, esk128_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_304, type, esk129_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_305, type, esk130_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.22/0.38  thf(decl_306, type, esk131_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_307, type, epred28_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_308, type, esk132_0: term).
% 0.22/0.38  thf(decl_309, type, esk133_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_310, type, esk134_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_311, type, esk135_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_312, type, esk136_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_313, type, esk137_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.22/0.38  thf(decl_314, type, esk138_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.22/0.38  thf(decl_315, type, esk139_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.22/0.38  thf(decl_316, type, esk140_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.22/0.38  thf(decl_317, type, esk141_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.22/0.38  thf(decl_318, type, esk142_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.22/0.38  thf(decl_319, type, esk143_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.22/0.38  thf(decl_320, type, esk144_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.22/0.38  thf(decl_321, type, esk145_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.22/0.38  thf(decl_322, type, esk146_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.22/0.38  thf(decl_323, type, esk147_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.22/0.38  thf(decl_324, type, epred29_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_325, type, epred30_0: term > $o).
% 0.22/0.38  thf(decl_326, type, esk148_0: term).
% 0.22/0.38  thf(decl_327, type, esk149_0: term).
% 0.22/0.38  thf(decl_328, type, esk150_0: term).
% 0.22/0.38  thf(decl_329, type, esk151_0: term).
% 0.22/0.38  thf(decl_330, type, esk152_0: term).
% 0.22/0.38  thf(decl_331, type, esk153_0: term).
% 0.22/0.38  thf(decl_332, type, esk154_0: term).
% 0.22/0.38  thf(decl_333, type, esk155_0: term).
% 0.22/0.38  thf(decl_334, type, esk156_0: term).
% 0.22/0.38  thf(decl_335, type, esk157_0: term).
% 0.22/0.38  thf(decl_336, type, esk158_0: term).
% 0.22/0.38  thf(decl_337, type, esk159_0: term).
% 0.22/0.38  thf(decl_338, type, esk160_0: term).
% 0.22/0.38  thf(decl_339, type, esk161_0: term).
% 0.22/0.38  thf(decl_340, type, esk162_0: term).
% 0.22/0.38  thf(decl_341, type, esk163_0: term).
% 0.22/0.38  thf(decl_342, type, esk164_0: term).
% 0.22/0.38  thf(decl_343, type, esk165_0: term).
% 0.22/0.38  thf(decl_344, type, esk166_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
% 0.22/0.38  thf(decl_345, type, esk167_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.22/0.38  thf(decl_346, type, esk168_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.22/0.38  thf(decl_347, type, epred31_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_348, type, epred32_0: term > $o).
% 0.22/0.38  thf(decl_349, type, esk169_0: term).
% 0.22/0.38  thf(decl_350, type, esk170_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_351, type, esk171_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_352, type, esk172_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_353, type, esk173_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_354, type, esk174_0: term).
% 0.22/0.38  thf(decl_355, type, esk175_0: term).
% 0.22/0.38  thf(decl_356, type, esk176_0: term).
% 0.22/0.38  thf(decl_357, type, esk177_0: term).
% 0.22/0.38  thf(decl_358, type, esk178_0: term).
% 0.22/0.38  thf(decl_359, type, esk179_0: term).
% 0.22/0.38  thf(decl_360, type, esk180_0: term).
% 0.22/0.38  thf(decl_361, type, esk181_0: term).
% 0.22/0.38  thf(decl_362, type, esk182_0: term).
% 0.22/0.38  thf(decl_363, type, esk183_0: term).
% 0.22/0.38  thf(decl_364, type, esk184_0: subst).
% 0.22/0.38  thf(decl_365, type, esk185_0: term).
% 0.22/0.38  thf(decl_366, type, esk186_0: subst).
% 0.22/0.38  thf(decl_367, type, esk187_0: term).
% 0.22/0.38  thf(decl_368, type, esk188_0: term).
% 0.22/0.38  thf(decl_369, type, esk189_2: (subst > term > term) > (subst > term > term) > subst).
% 0.22/0.38  thf(decl_370, type, esk190_2: (subst > term > term) > (subst > term > term) > term).
% 0.22/0.38  thf(decl_371, type, esk191_2: (subst > term > term) > (subst > term > term) > subst).
% 0.22/0.38  thf(decl_372, type, esk192_2: (subst > term > term) > (subst > term > term) > subst).
% 0.22/0.38  thf(decl_373, type, esk193_2: (subst > term > term) > (subst > term > term) > term).
% 0.22/0.38  thf(decl_374, type, esk194_2: (subst > term > term) > (subst > term > term) > subst).
% 0.22/0.38  thf(decl_375, type, esk195_0: subst > term > term).
% 0.22/0.38  thf(decl_376, type, esk196_0: subst > term > term).
% 0.22/0.38  thf(decl_377, type, esk197_0: subst).
% 0.22/0.38  thf(decl_378, type, esk198_0: term).
% 0.22/0.38  thf(decl_379, type, esk199_0: term).
% 0.22/0.38  thf(decl_380, type, esk200_0: subst).
% 0.22/0.38  thf(decl_381, type, esk201_0: subst).
% 0.22/0.38  thf(decl_382, type, esk202_0: subst).
% 0.22/0.38  thf(decl_383, type, epred33_0: term > $o).
% 0.22/0.38  thf(decl_384, type, epred34_0: term > $o).
% 0.22/0.38  thf(decl_385, type, esk203_0: term).
% 0.22/0.38  thf(decl_386, type, esk204_0: subst).
% 0.22/0.38  thf(decl_387, type, esk205_0: term).
% 0.22/0.38  thf(decl_388, type, esk206_0: term).
% 0.22/0.38  thf(decl_389, type, esk207_0: term).
% 0.22/0.38  thf(decl_390, type, esk208_0: term).
% 0.22/0.38  thf(decl_391, type, epred35_3: (term > $o) > term > subst > term > $o).
% 0.22/0.38  thf(decl_392, type, epred36_0: term > $o).
% 0.22/0.38  thf(decl_393, type, esk209_0: term).
% 0.22/0.38  thf(decl_394, type, esk210_0: subst).
% 0.22/0.38  thf(decl_395, type, esk211_1: (term > $o) > term).
% 0.22/0.38  thf(decl_396, type, esk212_0: term).
% 0.22/0.38  thf(decl_397, type, esk213_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_398, type, esk214_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_399, type, esk215_0: term).
% 0.22/0.38  thf(decl_400, type, esk216_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
% 0.22/0.38  thf(decl_401, type, esk217_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.22/0.38  thf(decl_402, type, esk218_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.22/0.38  thf(decl_403, type, esk219_1: term > subst > term > term).
% 0.22/0.38  thf(decl_404, type, epred37_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_405, type, epred38_0: term > $o).
% 0.22/0.38  thf(decl_406, type, esk220_0: term).
% 0.22/0.38  thf(decl_407, type, esk221_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_408, type, esk222_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_409, type, esk223_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_410, type, esk224_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_411, type, esk225_0: subst).
% 0.22/0.38  thf(decl_412, type, esk226_0: term).
% 0.22/0.38  thf(decl_413, type, epred39_1: (subst > term > subst > $o) > term > $o).
% 0.22/0.38  thf(decl_414, type, epred40_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_415, type, esk227_1: (term > $o) > term).
% 0.22/0.38  thf(decl_416, type, esk228_0: subst).
% 0.22/0.38  thf(decl_417, type, esk229_0: subst).
% 0.22/0.38  thf(decl_418, type, esk230_0: subst).
% 0.22/0.38  thf(decl_419, type, esk231_0: subst).
% 0.22/0.38  thf(decl_420, type, esk232_1: term > subst > term > term).
% 0.22/0.38  thf(decl_421, type, esk233_0: term).
% 0.22/0.38  thf(decl_422, type, esk234_0: subst).
% 0.22/0.38  thf(decl_423, type, esk235_0: subst).
% 0.22/0.38  thf(decl_424, type, esk236_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.22/0.38  thf(decl_425, type, esk237_2: (subst > term > subst > $o) > term > term).
% 0.22/0.38  thf(decl_426, type, epred41_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_427, type, esk238_0: term).
% 0.22/0.38  thf(decl_428, type, esk239_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_429, type, esk240_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_430, type, esk241_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_431, type, esk242_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_432, type, esk243_1: (subst > term > subst > $o) > term).
% 0.22/0.38  thf(decl_433, type, esk244_1: (subst > term > subst > $o) > term).
% 0.22/0.38  thf(decl_434, type, esk245_1: (subst > term > subst > $o) > subst > term > term).
% 0.22/0.38  thf(decl_435, type, epred42_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_436, type, esk246_0: term).
% 0.22/0.38  thf(decl_437, type, esk247_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_438, type, esk248_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_439, type, esk249_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_440, type, esk250_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_441, type, esk251_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_442, type, esk252_1: (subst > term > term) > term).
% 0.22/0.38  thf(decl_443, type, esk253_1: (subst > term > term) > subst).
% 0.22/0.38  thf(decl_444, type, esk254_0: subst > term > term).
% 0.22/0.38  thf(decl_445, type, esk255_0: term).
% 0.22/0.38  thf(decl_446, type, esk256_0: term).
% 0.22/0.38  thf(decl_447, type, esk257_1: (term > $o) > term).
% 0.22/0.38  thf(decl_448, type, esk258_1: (term > $o) > term).
% 0.22/0.38  thf(decl_449, type, esk259_1: (term > $o) > term).
% 0.22/0.38  thf(decl_450, type, esk260_1: (term > $o) > term).
% 0.22/0.38  thf(decl_451, type, epred43_0: term > $o).
% 0.22/0.38  thf(decl_452, type, esk261_0: term).
% 0.22/0.38  thf(decl_453, type, esk262_1: term > term).
% 0.22/0.38  thf(decl_454, type, esk263_0: term).
% 0.22/0.38  thf(decl_455, type, esk264_0: subst).
% 0.22/0.38  thf(decl_456, type, esk265_0: term).
% 0.22/0.38  thf(decl_457, type, esk266_0: subst).
% 0.22/0.38  thf(decl_458, type, epred44_0: term > $o).
% 0.22/0.38  thf(decl_459, type, epred45_0: term > $o).
% 0.22/0.38  thf(decl_460, type, esk267_0: term).
% 0.22/0.38  thf(decl_461, type, esk268_0: subst).
% 0.22/0.38  thf(decl_462, type, esk269_0: term).
% 0.22/0.38  thf(decl_463, type, epred46_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_464, type, epred47_0: term > $o).
% 0.22/0.38  thf(decl_465, type, esk270_0: term).
% 0.22/0.38  thf(decl_466, type, esk271_0: term).
% 0.22/0.38  thf(decl_467, type, esk272_0: subst).
% 0.22/0.38  thf(decl_468, type, esk273_0: term).
% 0.22/0.38  thf(decl_469, type, epred48_3: (term > $o) > term > subst > term > $o).
% 0.22/0.38  thf(decl_470, type, epred49_0: term > $o).
% 0.22/0.38  thf(decl_471, type, esk274_0: term).
% 0.22/0.38  thf(decl_472, type, esk275_0: subst).
% 0.22/0.38  thf(decl_473, type, esk276_1: (term > $o) > term).
% 0.22/0.38  thf(decl_474, type, esk277_0: term).
% 0.22/0.38  thf(decl_475, type, epred50_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_476, type, epred51_0: term > $o).
% 0.22/0.38  thf(decl_477, type, esk278_0: term).
% 0.22/0.38  thf(decl_478, type, esk279_0: term).
% 0.22/0.38  thf(decl_479, type, epred52_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_480, type, esk280_1: (term > $o) > term).
% 0.22/0.38  thf(decl_481, type, epred53_1: (subst > term > subst > $o) > term > $o).
% 0.22/0.38  thf(decl_482, type, epred54_0: subst > term > subst > $o).
% 0.22/0.38  thf(decl_483, type, epred55_0: term > $o).
% 0.22/0.38  thf(decl_484, type, esk281_0: term).
% 0.22/0.38  thf(decl_485, type, esk282_0: term).
% 0.22/0.38  thf(decl_486, type, esk283_1: (subst > term > subst > $o) > subst).
% 0.22/0.38  thf(decl_487, type, esk284_1: (subst > term > subst > $o) > term).
% 0.22/0.38  thf(decl_488, type, esk285_1: (subst > term > subst > $o) > subst).
% 0.22/0.38  thf(decl_489, type, esk286_1: (subst > term > subst > $o) > subst).
% 0.22/0.38  thf(decl_490, type, esk287_1: (subst > term > subst > $o) > subst).
% 0.22/0.38  thf(decl_491, type, esk288_1: (subst > term > subst > $o) > term).
% 0.22/0.38  thf(decl_492, type, esk289_1: (subst > term > subst > $o) > subst).
% 0.22/0.38  thf(decl_493, type, esk290_1: (subst > term > subst > $o) > subst).
% 0.22/0.38  thf(decl_494, type, esk291_1: (subst > term > subst > $o) > term).
% 0.22/0.38  thf(decl_495, type, esk292_1: (subst > term > subst > $o) > term).
% 0.22/0.38  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.Y1wHunPQUw/E---3.1_4190355.p', alg444_1)).
% 0.22/0.38  thf(hoasinduction_lem2v2, conjecture, ((hoasinduction_lem2v2)<=>![X11:subst > term > subst > $o, X12:term > $o]:((![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 @ (hoasap @ id @ X14 @ id @ X18) @ id))))=>((hoasinduction_p_and_p_prime @ X11 @ X12)=>![X14:term, X18:term]:(((X12 @ X14)=>((X12 @ X18)=>(X12 @ (ap @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/tmp/tmp.Y1wHunPQUw/E---3.1_4190355.p', hoasinduction_lem2v2)).
% 0.22/0.38  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)).
% 0.22/0.38  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)).
% 0.22/0.38  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)).
% 0.22/0.38  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)).
% 0.22/0.38  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)).
% 0.22/0.38  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)).
% 0.22/0.38  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)).
% 0.22/0.38  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)).
% 0.22/0.38  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)))&![X623:subst, X624:subst > term > term]:(((hoaslam @ X623 @ X624)=(d2term @ d_one))))&![X625:subst > term > subst > $o, X626:term > $o]:(((hoasinduction_p_and_p_prime @ X625 @ X626)<=>![X13:term]:(((X626 @ X13)<=>(X625 @ id @ X13 @ id))))))&![X627:term, X628:subst, X629:term > $o, X630:term > $o]:(((pushprop_p_and_p_prime @ X627 @ X628 @ X629 @ X630)<=>![X13:term]:(((X630 @ X13)<=>(X629 @ (sub @ X13 @ (push @ X627 @ X628))))))))&~(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)],[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])).
% 0.22/0.38  thf(c_0_11, negated_conjecture, ~(((hoasinduction_lem2v2)<=>![X11:subst > term > subst > $o, X12:term > $o]:((![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 @ (hoasap @ id @ X14 @ id @ X18) @ id))))=>((hoasinduction_p_and_p_prime @ X11 @ X12)=>![X14:term, X18:term]:(((X12 @ X14)=>((X12 @ X18)=>(X12 @ (ap @ X14 @ X18)))))))))))), inference(assume_negation,[status(cth)],[hoasinduction_lem2v2])).
% 0.22/0.38  thf(c_0_12, plain, ![X631:term, X633:d_term, X634:d_term, X635:d_term, X636:subst, X638:d_subst, X639:d_subst, X640:d_subst, X641:subst, X642:subst > term > term, X643:subst > term > subst > $o, X644:term > $o, X645:term, X646:term, X647:subst > term > subst > $o, X648:term > $o, X650:term, X651:subst, X652:term > $o, X653:term > $o, X654:term, X655:term, X656:term, X657:subst, X658:term > $o, X659:term > $o, X661:term > $o, X662:term > $o, X663:term, X664:subst, X670:term, X671:term, X672:term, X675:term > $o, X676:term, X677:subst, X681:term, X686:term, X687:term, X688:term, X690:term, X691:term, X693:term, X694:subst, X696:subst > term > term, X699:term, X700:term, X701:term, X702:term, X707:term, X708:term, X709:term, X710:term, X720:term, X721:subst, X722:term, X723:subst, X724:subst, X725:term, X727:term, X728:subst, X730:subst > term > term, X734:term > $o, X738:term, X739:term, X740:term, X741:term, X744:subst > term > subst > $o, X746:term, X747:term, X748:term > $o, X753:term, X754:term, X755:term, X756:subst > term > term, X757:subst > term > term, X764:subst, X765:term, X770:subst, X771:term, X772:subst, X773:subst, X774:term, X775:subst, X776:subst > term > subst > $o, X777:term, X780:term, X781:subst, X782:term, X783:subst, X784:subst, X785:term, X786:subst, X790:subst > term > term, X791:term, X799:term, X800:subst > term > subst > $o, X801:term, X803:subst, X804:term, X805:subst, X806:term, X810:subst > term > term, X815:term, X816:subst > term > subst > $o, X817:term, X827:subst, X828:term, X829:subst, X830:term, X834:subst, X835:term, X836:subst, X837:subst, X838:subst, X839:term, X840:subst, X841:subst, X842:subst > term > term, X847:term, X848:subst > term > subst > $o, X849:term, X850:term, X864:subst, X865:term, X866:subst, X867:subst, X868:subst, X869:term, X870:subst, X871:subst, X872:term, X873:term, X876:term > $o, X877:term > $o, X878:term, X879:subst, X881:term, X882:subst, X887:term, X888:subst > term > subst > $o, X890:term, X891:term, X893:term > $o, X895:subst > term > subst > $o, X896:term, X899:term, X902:subst > term > term, X903:term > $o, X908:term, X911:term, X912:term, X913:term, X914:term, X918:subst > term > term, X923:term, X924:subst > term > subst > $o, X925:term, X927:subst, X928:term, X929:subst, X930:term, X932:term, X933:subst > term > subst > $o, X934:term, X936:subst, X937:term, X938:subst, X939:term, X943:subst > term > term, X948:term, X949:subst > term > subst > $o, X950:term, X952:subst, X953:term, X954:subst, X955:term, X959:subst > term > term, X964:term, X965:subst > term > subst > $o, X966:term > $o, X967:term, X968:term, X984:subst, X985:term, X986:subst, X987:subst, X988:subst, X989:term, X990:subst, X991:subst, X992:term, X993:term, X994:term, X995:term, X996:term, X997:term, X998:term, X1003:term, X1004:term, X1005:term, X1006:term, X1015:term, X1016:term, X1017:term, X1018:term, X1019:term, X1020:term, X1021:term, X1022:term, X1027:subst > term > subst > $o, X1028:term > $o, X1029:term, X1031:subst, X1032:term, X1033:subst, X1034:term, X1040:subst > term > term, X1045:term, X1046:term, X1052:term, X1053:term, X1054:term, X1055:term, X1056:term, X1057:term, X1058:term, X1059:term, X1060:term, X1071:subst > term > term, X1072:subst > term > term, X1079:subst, X1080:term, X1081:term, X1082:subst, X1083:term, X1084:subst, X1085:term, X1086:term, X1091:subst, X1092:term, X1093:subst, X1094:subst, X1095:term, X1096:subst, X1097:term, X1098:subst, X1101:subst, X1103:subst, X1105:term > $o, X1106:term > $o, X1107:term, X1108:subst, X1109:term, X1115:term, X1116:term, X1120:term, X1121:term > $o, X1122:term, X1123:subst, X1125:term, X1126:term, X1130:term > $o, X1133:subst > term > term, X1137:subst > term > subst > $o, X1138:term > $o, X1139:term, X1141:subst, X1142:term, X1143:subst, X1144:term, X1147:term, X1149:term, X1150:subst, X1151:term, X1155:subst > term > term, X1160:term, X1161:term, X1162:subst, X1165:term, X1166:subst > term > subst > $o, X1168:term, X1169:term, X1171:term > $o, X1175:subst, X1176:subst, X1177:subst, X1178:subst, X1181:term, X1184:subst > term > term, X1185:subst, X1186:subst, X1189:subst > term > subst > $o, X1190:term, X1192:subst, X1193:term, X1194:subst, X1195:term, X1199:subst > term > term, X1204:term, X1205:subst > term > subst > $o, X1209:subst, X1210:term, X1211:subst, X1212:term, X1213:term, X1216:term, X1217:term, X1218:subst > term > term, X1223:subst > term > term, X1227:term, X1228:term, X1232:subst, X1233:term, X1234:subst, X1235:term > $o, X1240:term, X1241:term, X1244:term, X1245:term, X1246:term, X1247:term, X1253:term > $o, X1254:term > $o, X1255:term, X1256:subst, X1257:term, X1258:term, X1259:subst, X1260:term, X1261:subst, X1267:subst > term > subst > $o, X1268:term > $o, X1269:term, X1273:term, X1274:subst, X1277:term, X1279:term > $o, X1280:term, X1281:subst, X1283:term, X1284:term, X1288:term > $o, X1291:subst > term > subst > $o, X1292:term > $o, X1293:term, X1294:term, X1298:term, X1301:term > $o, X1303:subst > term > subst > $o, X1305:term, X1306:term]:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((X631)=(d2term @ (esk1_1 @ X631)))&((X633)=(d_one)))&(((d2term @ X634)!=(d2term @ X635))|((X634)=(X635))))&((X636)=(d2subst @ (esk2_1 @ X636))))&((X638)=(d_id)))&(((d2subst @ X639)!=(d2subst @ X640))|((X639)=(X640))))&((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 @ X641 @ X642)=(d2term @ d_one)))&(((~(X644 @ X645)|(X643 @ id @ X645 @ id)|~(hoasinduction_p_and_p_prime @ X643 @ X644))&(~(X643 @ id @ X646 @ id)|(X644 @ X646)|~(hoasinduction_p_and_p_prime @ X643 @ X644)))&((~(X648 @ (esk3_2 @ X647 @ X648))|~(X647 @ id @ (esk3_2 @ X647 @ X648) @ id)|(hoasinduction_p_and_p_prime @ X647 @ X648))&((X648 @ (esk3_2 @ X647 @ X648))|(X647 @ id @ (esk3_2 @ X647 @ X648) @ id)|(hoasinduction_p_and_p_prime @ X647 @ X648)))))&(((~(X653 @ X654)|(X652 @ (sub @ X654 @ (push @ X650 @ X651)))|~(pushprop_p_and_p_prime @ X650 @ X651 @ X652 @ X653))&(~(X652 @ (sub @ X655 @ (push @ X650 @ X651)))|(X653 @ X655)|~(pushprop_p_and_p_prime @ X650 @ X651 @ X652 @ X653)))&((~(X659 @ (esk4_4 @ X656 @ X657 @ X658 @ X659))|~(X658 @ (sub @ (esk4_4 @ X656 @ X657 @ X658 @ X659) @ (push @ X656 @ X657)))|(pushprop_p_and_p_prime @ X656 @ X657 @ X658 @ X659))&((X659 @ (esk4_4 @ X656 @ X657 @ X658 @ X659))|(X658 @ (sub @ (esk4_4 @ X656 @ X657 @ X658 @ X659) @ (push @ X656 @ X657)))|(pushprop_p_and_p_prime @ X656 @ X657 @ X658 @ X659)))))&~(var @ (d2term @ d_one)))&(((~(X662 @ (esk5_4 @ X661 @ X662 @ X663 @ X664))|~(X661 @ (sub @ (esk5_4 @ X661 @ X662 @ X663 @ X664) @ (push @ X663 @ X664)))|~(X661 @ X663)|(X662 @ one)|~(pushprop_lem1v2))&((X662 @ (esk5_4 @ X661 @ X662 @ X663 @ X664))|(X661 @ (sub @ (esk5_4 @ X661 @ X662 @ X663 @ X664) @ (push @ X663 @ X664)))|~(X661 @ X663)|(X662 @ one)|~(pushprop_lem1v2)))&((((epred10_0 @ esk6_0)|(pushprop_lem1v2))&((~(epred11_0 @ X670)|(epred10_0 @ (sub @ X670 @ (push @ esk6_0 @ esk7_0)))|(pushprop_lem1v2))&(~(epred10_0 @ (sub @ X670 @ (push @ esk6_0 @ esk7_0)))|(epred11_0 @ X670)|(pushprop_lem1v2))))&(~(epred11_0 @ one)|(pushprop_lem1v2)))))&(pushprop_lem1_gthm))&(axmap))&(pushprop_lem0_gthm))&((~(shinj)|(((sub @ X671 @ sh)!=(sub @ X672 @ sh))|((X671)=(X672))))&((((sub @ esk8_0 @ sh)=(sub @ esk9_0 @ sh))|(shinj))&(((esk8_0)!=(esk9_0))|(shinj)))))&(hoasinduction_lem1v2))&(hoasinduction_lem1v2_gthm))&(((((((var @ (esk13_3 @ X675 @ X676 @ X677))|(~(X675 @ X681)|(X675 @ (sub @ (esk12_3 @ X675 @ X676 @ X677) @ (push @ X681 @ id)))|(X675 @ (esk10_3 @ X675 @ X676 @ X677)))|(X675 @ (sub @ X676 @ X677))|~(induction2lem))&(~(X675 @ (sub @ (esk13_3 @ X675 @ X676 @ X677) @ X677))|(~(X675 @ X681)|(X675 @ (sub @ (esk12_3 @ X675 @ X676 @ X677) @ (push @ X681 @ id)))|(X675 @ (esk10_3 @ X675 @ X676 @ X677)))|(X675 @ (sub @ X676 @ X677))|~(induction2lem)))&(((var @ (esk13_3 @ X675 @ X676 @ X677))|(~(X675 @ (lam @ (esk12_3 @ X675 @ X676 @ X677)))|(X675 @ (esk10_3 @ X675 @ X676 @ X677)))|(X675 @ (sub @ X676 @ X677))|~(induction2lem))&(~(X675 @ (sub @ (esk13_3 @ X675 @ X676 @ X677) @ X677))|(~(X675 @ (lam @ (esk12_3 @ X675 @ X676 @ X677)))|(X675 @ (esk10_3 @ X675 @ X676 @ X677)))|(X675 @ (sub @ X676 @ X677))|~(induction2lem))))&((((var @ (esk13_3 @ X675 @ X676 @ X677))|(~(X675 @ X681)|(X675 @ (sub @ (esk12_3 @ X675 @ X676 @ X677) @ (push @ X681 @ id)))|(X675 @ (esk11_3 @ X675 @ X676 @ X677)))|(X675 @ (sub @ X676 @ X677))|~(induction2lem))&(~(X675 @ (sub @ (esk13_3 @ X675 @ X676 @ X677) @ X677))|(~(X675 @ X681)|(X675 @ (sub @ (esk12_3 @ X675 @ X676 @ X677) @ (push @ X681 @ id)))|(X675 @ (esk11_3 @ X675 @ X676 @ X677)))|(X675 @ (sub @ X676 @ X677))|~(induction2lem)))&(((var @ (esk13_3 @ X675 @ X676 @ X677))|(~(X675 @ (lam @ (esk12_3 @ X675 @ X676 @ X677)))|(X675 @ (esk11_3 @ X675 @ X676 @ X677)))|(X675 @ (sub @ X676 @ X677))|~(induction2lem))&(~(X675 @ (sub @ (esk13_3 @ X675 @ X676 @ X677) @ X677))|(~(X675 @ (lam @ (esk12_3 @ X675 @ X676 @ X677)))|(X675 @ (esk11_3 @ X675 @ X676 @ X677)))|(X675 @ (sub @ X676 @ X677))|~(induction2lem)))))&((((var @ (esk13_3 @ X675 @ X676 @ X677))|(~(X675 @ X681)|(X675 @ (sub @ (esk12_3 @ X675 @ X676 @ X677) @ (push @ X681 @ id)))|~(X675 @ (ap @ (esk10_3 @ X675 @ X676 @ X677) @ (esk11_3 @ X675 @ X676 @ X677))))|(X675 @ (sub @ X676 @ X677))|~(induction2lem))&(~(X675 @ (sub @ (esk13_3 @ X675 @ X676 @ X677) @ X677))|(~(X675 @ X681)|(X675 @ (sub @ (esk12_3 @ X675 @ X676 @ X677) @ (push @ X681 @ id)))|~(X675 @ (ap @ (esk10_3 @ X675 @ X676 @ X677) @ (esk11_3 @ X675 @ X676 @ X677))))|(X675 @ (sub @ X676 @ X677))|~(induction2lem)))&(((var @ (esk13_3 @ X675 @ X676 @ X677))|(~(X675 @ (lam @ (esk12_3 @ X675 @ X676 @ X677)))|~(X675 @ (ap @ (esk10_3 @ X675 @ X676 @ X677) @ (esk11_3 @ X675 @ X676 @ X677))))|(X675 @ (sub @ X676 @ X677))|~(induction2lem))&(~(X675 @ (sub @ (esk13_3 @ X675 @ X676 @ X677) @ X677))|(~(X675 @ (lam @ (esk12_3 @ X675 @ X676 @ X677)))|~(X675 @ (ap @ (esk10_3 @ X675 @ X676 @ X677) @ (esk11_3 @ X675 @ X676 @ X677))))|(X675 @ (sub @ X676 @ X677))|~(induction2lem)))))&((((~(epred12_0 @ X686)|~(epred12_0 @ X687)|(epred12_0 @ (ap @ X686 @ X687))|(induction2lem))&(((epred12_0 @ (esk16_1 @ X688))|(epred12_0 @ (lam @ X688))|(induction2lem))&(~(epred12_0 @ (sub @ X688 @ (push @ (esk16_1 @ X688) @ id)))|(epred12_0 @ (lam @ X688))|(induction2lem))))&(~(var @ X690)|(epred12_0 @ (sub @ X690 @ esk15_0))|(induction2lem)))&(~(epred12_0 @ (sub @ esk14_0 @ esk15_0))|(induction2lem)))))&((~(hoasinduction_lem3v2_f)|((sub @ X691 @ (push @ X693 @ X694))=(esk17_1 @ X691 @ X694 @ X693)))&(((sub @ esk18_0 @ (push @ (esk19_1 @ X696) @ (esk20_1 @ X696)))!=(X696 @ (esk20_1 @ X696) @ (esk19_1 @ X696)))|(hoasinduction_lem3v2_f))))&(axvarshift))&((~(hoasapinj2)|(((ap @ (sub @ X699 @ id) @ X701)!=(ap @ (sub @ X700 @ id) @ X702))|((X701)=(X702))))&((((ap @ (sub @ esk21_0 @ id) @ esk23_0)=(ap @ (sub @ esk22_0 @ id) @ esk24_0))|(hoasapinj2))&(((esk23_0)!=(esk24_0))|(hoasapinj2)))))&(hoasapnotvar_gthm))&((~(hoasapinj1)|(((ap @ (sub @ X707 @ id) @ X709)!=(ap @ (sub @ X708 @ id) @ X710))|((X707)=(X708))))&((((ap @ (sub @ esk25_0 @ id) @ esk27_0)=(ap @ (sub @ esk26_0 @ id) @ esk28_0))|(hoasapinj1))&(((esk25_0)!=(esk26_0))|(hoasapinj1)))))&~(ulamvar1))&((~(induction2lem_lthm)|(((esk29_0)!=(sub @ one @ (push @ esk29_0 @ esk30_0)))|(((esk32_0)!=(comp @ sh @ (push @ esk31_0 @ esk32_0)))|(((esk33_0)!=(comp @ esk33_0 @ id))|(epred1_0)))))&((((X720)=(sub @ one @ (push @ X720 @ X721)))|(induction2lem_lthm))&((((X723)=(comp @ sh @ (push @ X722 @ X723)))|(induction2lem_lthm))&((((X724)=(comp @ X724 @ id))|(induction2lem_lthm))&(~(epred1_0)|(induction2lem_lthm)))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((~(hoasinduction_lem3v2_f_lthm)|((sub @ X725 @ (push @ X727 @ X728))=(esk34_1 @ X725 @ X728 @ X727)))&(((sub @ esk35_0 @ (push @ (esk36_1 @ X730) @ (esk37_1 @ X730)))!=(X730 @ (esk37_1 @ X730) @ (esk36_1 @ X730)))|(hoasinduction_lem3v2_f_lthm))))&((~(hoasinduction_lthm)|(epred4_0))&(~(epred4_0)|(hoasinduction_lthm))))&((((((~(var @ X738)|(epred14_0 @ X738)|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X734 @ (esk38_1 @ X734))|~(epred13_0 @ id @ (esk38_1 @ X734) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ X739)|~(epred14_0 @ X740)|(epred14_0 @ (ap @ X739 @ X740))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X734 @ (esk38_1 @ X734))|~(epred13_0 @ id @ (esk38_1 @ X734) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred14_0 @ (esk40_1 @ X741))|(epred14_0 @ (lam @ X741))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X734 @ (esk38_1 @ X734))|~(epred13_0 @ id @ (esk38_1 @ X734) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ (sub @ X741 @ (push @ (esk40_1 @ X741) @ id)))|(epred14_0 @ (lam @ X741))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X734 @ (esk38_1 @ X734))|~(epred13_0 @ id @ (esk38_1 @ X734) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred14_0 @ esk39_0)|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X734 @ (esk38_1 @ X734))|~(epred13_0 @ id @ (esk38_1 @ X734) @ id))|~(hoasinduction_no_psi_cond_lthm)))&((((~(var @ X738)|(epred14_0 @ X738)|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|((X734 @ (esk38_1 @ X734))|(epred13_0 @ id @ (esk38_1 @ X734) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ X739)|~(epred14_0 @ X740)|(epred14_0 @ (ap @ X739 @ X740))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|((X734 @ (esk38_1 @ X734))|(epred13_0 @ id @ (esk38_1 @ X734) @ 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(esk218_3 @ X1137 @ X1138 @ X1139) @ id)))|((X1138 @ (esk217_3 @ X1137 @ X1138 @ X1139))|(X1137 @ id @ (esk217_3 @ X1137 @ X1138 @ X1139) @ id)|~(X1137 @ id @ (lam @ (esk216_3 @ X1137 @ X1138 @ X1139 @ sh @ one)) @ id))|(X1138 @ (lam @ X1139))|((esk215_0)!=(sub @ esk215_0 @ id))|((sub @ esk212_0 @ (push @ (esk213_1 @ X1133) @ (esk214_1 @ X1133)))!=(X1133 @ (esk214_1 @ X1133) @ (esk213_1 @ X1133)))|~(hoasinduction_lem3v2a_lthm)))))&((((sub @ X1147 @ (push @ X1149 @ X1150))=(esk219_1 @ X1147 @ X1150 @ X1149))|(hoasinduction_lem3v2a_lthm))&((((X1151)=(sub @ X1151 @ id))|(hoasinduction_lem3v2a_lthm))&((((((epred37_0 @ id @ (esk224_1 @ X1155) @ id)|((sub @ (X1155 @ (esk221_1 @ X1155) @ (esk222_1 @ X1155)) @ (esk223_1 @ X1155))!=(X1155 @ (comp @ (esk221_1 @ X1155) @ (esk223_1 @ X1155)) @ (sub @ (esk222_1 @ X1155) @ (esk223_1 @ X1155))))|(epred37_0 @ id @ (lam @ (X1155 @ sh @ one)) @ id)|(hoasinduction_lem3v2a_lthm))&(~(epred37_0 @ id @ (X1155 @ id @ (esk224_1 @ X1155)) @ id)|((sub @ (X1155 @ (esk221_1 @ X1155) @ (esk222_1 @ X1155)) @ (esk223_1 @ X1155))!=(X1155 @ (comp @ (esk221_1 @ X1155) @ (esk223_1 @ X1155)) @ (sub @ (esk222_1 @ X1155) @ (esk223_1 @ X1155))))|(epred37_0 @ id @ (lam @ (X1155 @ sh @ one)) @ id)|(hoasinduction_lem3v2a_lthm)))&((~(epred38_0 @ X1160)|(epred37_0 @ id @ X1160 @ id)|(hoasinduction_lem3v2a_lthm))&(~(epred37_0 @ id @ X1160 @ id)|(epred38_0 @ X1160)|(hoasinduction_lem3v2a_lthm))))&(~(epred38_0 @ X1161)|(epred38_0 @ (sub @ esk220_0 @ (push @ X1161 @ id)))|(hoasinduction_lem3v2a_lthm)))&(~(epred38_0 @ (lam @ esk220_0))|(hoasinduction_lem3v2a_lthm)))))))&(hoasinduction_lem2_lthm))&(hoasapinj2_gthm))&(hoasinduction_lem1_lthm))&~(lamnotap))&(hoasapinj1_gthm))&(hoaslamnotvar))&((~(axidl)|((X1162)=(comp @ id @ X1162)))&(((esk225_0)!=(comp @ id @ esk225_0))|(axidl))))&(hoaslaminj_gthm))&((~(induction2_lthm)|(((esk226_0)!=(sub @ esk226_0 @ id))|(epred7_0)))&((((X1165)=(sub @ X1165 @ id))|(induction2_lthm))&(~(epred7_0)|(induction2_lthm)))))&(((~(epred39_1 @ X1166 @ X1168)|(X1166 @ id @ X1168 @ id)|~(hoasinduction_lem0_lthm))&(~(X1166 @ id @ X1169 @ id)|(epred39_1 @ X1166 @ X1169)|~(hoasinduction_lem0_lthm)))&((~(X1171 @ (esk227_1 @ X1171))|~(epred40_0 @ id @ (esk227_1 @ X1171) @ id)|(hoasinduction_lem0_lthm))&((X1171 @ (esk227_1 @ X1171))|(epred40_0 @ id @ (esk227_1 @ X1171) @ id)|(hoasinduction_lem0_lthm)))))&(((((X1175)=(comp @ id @ X1175))|((esk229_0)!=(comp @ esk229_0 @ id))|((esk228_0)!=(comp @ id @ esk228_0))|~(substmonoid_lthm))&(((X1176)=(comp @ X1176 @ id))|((esk229_0)!=(comp @ esk229_0 @ id))|((esk228_0)!=(comp @ id @ esk228_0))|~(substmonoid_lthm)))&((((X1177)=(comp @ id @ X1177))|(substmonoid_lthm))&((((X1178)=(comp @ X1178 @ id))|(substmonoid_lthm))&(((esk230_0)!=(comp @ id @ esk230_0))|((esk231_0)!=(comp @ esk231_0 @ id))|(substmonoid_lthm))))))&(pushprop))&(hoasinduction_lem3_gthm))&(hoasinduction_lem2_gthm))&((~(hoasinduction_lem3b)|((esk232_1 @ X1181 @ sh @ one)=(sub @ X1181 @ (push @ one @ sh))))&(((X1184 @ sh @ one)!=(sub @ esk233_0 @ (push @ one @ sh)))|(hoasinduction_lem3b))))&(((((X1185)=(comp @ id @ X1185))|~(substmonoid))&(((X1186)=(comp @ X1186 @ id))|~(substmonoid)))&(((esk234_0)!=(comp @ id @ esk234_0))|((esk235_0)!=(comp @ esk235_0 @ id))|(substmonoid))))&(lamnotvar))&((((((X1189 @ id @ (esk237_2 @ X1189 @ X1190) @ id)|((sub @ (esk236_2 @ X1189 @ X1190 @ X1192 @ X1193) @ X1194)=(esk236_2 @ X1189 @ X1190 @ (comp @ X1192 @ X1194) @ (sub @ X1193 @ X1194)))|(X1189 @ id @ (lam @ X1190) @ id)|~(hoasinduction_lem3a))&(~(X1189 @ id @ (sub @ X1190 @ (push @ (esk237_2 @ X1189 @ X1190) @ id)) @ id)|((sub @ (esk236_2 @ X1189 @ X1190 @ X1192 @ X1193) @ X1194)=(esk236_2 @ X1189 @ X1190 @ (comp @ X1192 @ X1194) @ (sub @ X1193 @ X1194)))|(X1189 @ id @ (lam @ X1190) @ id)|~(hoasinduction_lem3a)))&(((X1189 @ id @ (esk237_2 @ X1189 @ X1190) @ id)|(~(X1189 @ id @ X1195 @ id)|(X1189 @ id @ (esk236_2 @ X1189 @ X1190 @ id @ X1195) @ id))|(X1189 @ id @ (lam @ X1190) @ id)|~(hoasinduction_lem3a))&(~(X1189 @ id @ (sub @ X1190 @ (push @ (esk237_2 @ X1189 @ X1190) @ id)) @ id)|(~(X1189 @ id @ X1195 @ id)|(X1189 @ id @ (esk236_2 @ X1189 @ X1190 @ id @ X1195) @ id))|(X1189 @ id @ (lam @ X1190) @ id)|~(hoasinduction_lem3a))))&(((X1189 @ id @ (esk237_2 @ X1189 @ X1190) @ id)|~(X1189 @ id @ (lam @ (esk236_2 @ X1189 @ X1190 @ sh @ one)) @ id)|(X1189 @ id @ (lam @ X1190) @ id)|~(hoasinduction_lem3a))&(~(X1189 @ id @ (sub @ X1190 @ (push @ (esk237_2 @ X1189 @ X1190) @ id)) @ id)|~(X1189 @ id @ (lam @ (esk236_2 @ X1189 @ X1190 @ sh @ one)) @ id)|(X1189 @ id @ (lam @ X1190) @ id)|~(hoasinduction_lem3a))))&(((((epred41_0 @ id @ (esk242_1 @ X1199) @ id)|((sub @ (X1199 @ (esk239_1 @ X1199) @ (esk240_1 @ X1199)) @ (esk241_1 @ X1199))!=(X1199 @ (comp @ (esk239_1 @ X1199) @ (esk241_1 @ X1199)) @ (sub @ (esk240_1 @ X1199) @ (esk241_1 @ X1199))))|(epred41_0 @ id @ (lam @ (X1199 @ sh @ one)) @ id)|(hoasinduction_lem3a))&(~(epred41_0 @ id @ (X1199 @ id @ (esk242_1 @ X1199)) @ id)|((sub @ (X1199 @ (esk239_1 @ X1199) @ (esk240_1 @ X1199)) @ (esk241_1 @ X1199))!=(X1199 @ (comp @ (esk239_1 @ X1199) @ (esk241_1 @ X1199)) @ (sub @ (esk240_1 @ X1199) @ (esk241_1 @ X1199))))|(epred41_0 @ id @ (lam @ (X1199 @ sh @ one)) @ id)|(hoasinduction_lem3a)))&(~(epred41_0 @ id @ X1204 @ id)|(epred41_0 @ id @ (sub @ esk238_0 @ (push @ X1204 @ id)) @ id)|(hoasinduction_lem3a)))&(~(epred41_0 @ id @ (lam @ esk238_0) @ id)|(hoasinduction_lem3a)))))&(hoasinduction_lem1_gthm))&((((((((sub @ (esk245_1 @ X1205 @ X1209 @ X1210) @ X1211)=(esk245_1 @ X1205 @ (comp @ X1209 @ X1211) @ (sub @ X1210 @ X1211)))|(X1205 @ id @ (esk243_1 @ X1205) @ id)|(X1205 @ id @ X1213 @ id)|~(hoasinduction_no_psi_cond))&(~(X1205 @ id @ X1212 @ id)|(X1205 @ id @ (esk245_1 @ X1205 @ id @ X1212) @ id)|(X1205 @ id @ (esk243_1 @ X1205) @ id)|(X1205 @ id @ X1213 @ id)|~(hoasinduction_no_psi_cond)))&(~(X1205 @ id @ (lam @ (esk245_1 @ X1205 @ sh @ one)) @ id)|(X1205 @ id @ (esk243_1 @ X1205) @ id)|(X1205 @ id @ X1213 @ id)|~(hoasinduction_no_psi_cond)))&(((((sub @ (esk245_1 @ X1205 @ X1209 @ X1210) @ X1211)=(esk245_1 @ X1205 @ (comp @ X1209 @ X1211) @ (sub @ X1210 @ X1211)))|(X1205 @ id @ (esk244_1 @ X1205) @ id)|(X1205 @ id @ X1213 @ id)|~(hoasinduction_no_psi_cond))&(~(X1205 @ id @ X1212 @ id)|(X1205 @ id @ (esk245_1 @ X1205 @ id @ X1212) @ id)|(X1205 @ id @ (esk244_1 @ X1205) @ id)|(X1205 @ id @ X1213 @ id)|~(hoasinduction_no_psi_cond)))&(~(X1205 @ id @ (lam @ (esk245_1 @ X1205 @ sh @ one)) @ id)|(X1205 @ id @ (esk244_1 @ X1205) @ id)|(X1205 @ id @ X1213 @ id)|~(hoasinduction_no_psi_cond))))&(((((sub @ (esk245_1 @ X1205 @ X1209 @ X1210) @ X1211)=(esk245_1 @ X1205 @ (comp @ X1209 @ X1211) @ (sub @ X1210 @ X1211)))|~(X1205 @ id @ (ap @ (sub @ (esk243_1 @ X1205) @ id) @ (esk244_1 @ X1205)) @ id)|(X1205 @ id @ X1213 @ id)|~(hoasinduction_no_psi_cond))&(~(X1205 @ id @ X1212 @ id)|(X1205 @ id @ (esk245_1 @ X1205 @ id @ X1212) @ id)|~(X1205 @ id @ (ap @ (sub @ (esk243_1 @ X1205) @ id) @ (esk244_1 @ X1205)) @ id)|(X1205 @ id @ X1213 @ id)|~(hoasinduction_no_psi_cond)))&(~(X1205 @ id @ (lam @ (esk245_1 @ X1205 @ sh @ one)) @ id)|~(X1205 @ id @ (ap @ (sub @ (esk243_1 @ X1205) @ id) @ (esk244_1 @ X1205)) @ id)|(X1205 @ id @ X1213 @ id)|~(hoasinduction_no_psi_cond))))&(((~(epred42_0 @ id @ X1216 @ id)|~(epred42_0 @ id @ X1217 @ id)|(epred42_0 @ id @ (ap @ (sub @ X1216 @ id) @ X1217) @ id)|(hoasinduction_no_psi_cond))&(((epred42_0 @ id @ (esk250_1 @ X1218) @ id)|((sub @ (X1218 @ (esk247_1 @ X1218) @ (esk248_1 @ X1218)) @ (esk249_1 @ X1218))!=(X1218 @ (comp @ (esk247_1 @ X1218) @ (esk249_1 @ X1218)) @ (sub @ (esk248_1 @ X1218) @ (esk249_1 @ X1218))))|(epred42_0 @ id @ (lam @ (X1218 @ sh @ one)) @ id)|(hoasinduction_no_psi_cond))&(~(epred42_0 @ id @ (X1218 @ id @ (esk250_1 @ X1218)) @ id)|((sub @ (X1218 @ (esk247_1 @ X1218) @ (esk248_1 @ X1218)) @ (esk249_1 @ X1218))!=(X1218 @ (comp @ (esk247_1 @ X1218) @ (esk249_1 @ X1218)) @ (sub @ (esk248_1 @ X1218) @ (esk249_1 @ X1218))))|(epred42_0 @ id @ (lam @ (X1218 @ sh @ one)) @ id)|(hoasinduction_no_psi_cond))))&(~(epred42_0 @ id @ esk246_0 @ id)|(hoasinduction_no_psi_cond)))))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&((~(hoaslamnotap)|(((sub @ (X1223 @ (esk251_1 @ X1223) @ (esk252_1 @ X1223)) @ (esk253_1 @ X1223))!=(X1223 @ (comp @ (esk251_1 @ X1223) @ (esk253_1 @ X1223)) @ (sub @ (esk252_1 @ X1223) @ (esk253_1 @ X1223))))|((lam @ (X1223 @ sh @ one))!=(ap @ (sub @ X1227 @ id) @ X1228))))&((((sub @ (esk254_0 @ X1232 @ X1233) @ X1234)=(esk254_0 @ (comp @ X1232 @ X1234) @ (sub @ X1233 @ X1234)))|(hoaslamnotap))&(((lam @ (esk254_0 @ sh @ one))=(ap @ (sub @ esk255_0 @ id) @ esk256_0))|(hoaslamnotap)))))&(substmonoid_gthm))&(ulamvarsh))&((((((~(X1235 @ X1240)|(X1235 @ (sub @ (esk260_1 @ X1235) @ (push @ X1240 @ id)))|((X1235 @ (esk258_1 @ X1235))|(var @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2))&(~(X1235 @ (lam @ (esk260_1 @ X1235)))|((X1235 @ (esk258_1 @ X1235))|(var @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2)))&((~(X1235 @ X1240)|(X1235 @ (sub @ (esk260_1 @ X1235) @ (push @ X1240 @ id)))|((X1235 @ (esk259_1 @ X1235))|(var @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2))&(~(X1235 @ (lam @ (esk260_1 @ X1235)))|((X1235 @ (esk259_1 @ X1235))|(var @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2))))&((~(X1235 @ X1240)|(X1235 @ (sub @ (esk260_1 @ X1235) @ (push @ X1240 @ id)))|(~(X1235 @ (ap @ (esk258_1 @ X1235) @ (esk259_1 @ X1235)))|(var @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2))&(~(X1235 @ (lam @ (esk260_1 @ X1235)))|(~(X1235 @ (ap @ (esk258_1 @ X1235) @ (esk259_1 @ X1235)))|(var @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2))))&((((~(X1235 @ X1240)|(X1235 @ (sub @ (esk260_1 @ X1235) @ (push @ X1240 @ id)))|((X1235 @ (esk258_1 @ X1235))|~(X1235 @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2))&(~(X1235 @ (lam @ (esk260_1 @ X1235)))|((X1235 @ (esk258_1 @ X1235))|~(X1235 @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2)))&((~(X1235 @ X1240)|(X1235 @ (sub @ (esk260_1 @ X1235) @ (push @ X1240 @ id)))|((X1235 @ (esk259_1 @ X1235))|~(X1235 @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2))&(~(X1235 @ (lam @ (esk260_1 @ X1235)))|((X1235 @ (esk259_1 @ X1235))|~(X1235 @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2))))&((~(X1235 @ X1240)|(X1235 @ (sub @ (esk260_1 @ X1235) @ (push @ X1240 @ id)))|(~(X1235 @ (ap @ (esk258_1 @ X1235) @ (esk259_1 @ X1235)))|~(X1235 @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2))&(~(X1235 @ (lam @ (esk260_1 @ X1235)))|(~(X1235 @ (ap @ (esk258_1 @ X1235) @ (esk259_1 @ X1235)))|~(X1235 @ (esk257_1 @ X1235)))|(X1235 @ X1241)|~(induction2)))))&((((~(var @ X1244)|(epred43_0 @ X1244)|(induction2))&(~(epred43_0 @ X1245)|~(epred43_0 @ X1246)|(epred43_0 @ (ap @ X1245 @ X1246))|(induction2)))&(((epred43_0 @ (esk262_1 @ X1247))|(epred43_0 @ (lam @ X1247))|(induction2))&(~(epred43_0 @ (sub @ X1247 @ (push @ (esk262_1 @ X1247) @ id)))|(epred43_0 @ (lam @ X1247))|(induction2))))&(~(epred43_0 @ esk261_0)|(induction2)))))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((~(pushprop_lem1_lthm)|(((esk263_0)!=(sub @ one @ (push @ esk263_0 @ esk264_0)))|(((esk266_0)!=(comp @ sh @ (push @ esk265_0 @ esk266_0)))|(~(X1253 @ X1255)|(X1254 @ (sub @ X1255 @ (push @ X1257 @ X1256)))))))&((((X1258)=(sub @ one @ (push @ X1258 @ X1259)))|(pushprop_lem1_lthm))&((((X1261)=(comp @ sh @ (push @ X1260 @ X1261)))|(pushprop_lem1_lthm))&(((epred44_0 @ esk267_0)|(pushprop_lem1_lthm))&(~(epred45_0 @ (sub @ esk267_0 @ (push @ esk269_0 @ esk268_0)))|(pushprop_lem1_lthm)))))))&((~(hoasinduction_lem3v2)|((epred8_3 @ X1269 @ X1268 @ X1267)|(X1268 @ (lam @ X1269))))&((~(epred8_3 @ esk270_0 @ epred47_0 @ epred46_0)|(hoasinduction_lem3v2))&(~(epred47_0 @ (lam @ esk270_0))|(hoasinduction_lem3v2)))))&((~(axshiftcons)|((X1274)=(comp @ sh @ (push @ X1273 @ X1274))))&(((esk272_0)!=(comp @ sh @ (push @ esk271_0 @ esk272_0)))|(axshiftcons))))&((~(termmset)|((X1277)=(sub @ X1277 @ id)))&(((esk273_0)!=(sub @ esk273_0 @ id))|(termmset))))&(((~(epred48_3 @ X1279 @ X1280 @ X1281 @ X1283)|(X1279 @ (sub @ X1283 @ (push @ X1280 @ X1281)))|~(pushprop_lem0_lthm))&(~(X1279 @ (sub @ X1284 @ (push @ X1280 @ X1281)))|(epred48_3 @ X1279 @ X1280 @ X1281 @ X1284)|~(pushprop_lem0_lthm)))&((~(X1288 @ (esk276_1 @ X1288))|~(epred49_0 @ (sub @ (esk276_1 @ X1288) @ (push @ esk274_0 @ esk275_0)))|(pushprop_lem0_lthm))&((X1288 @ (esk276_1 @ X1288))|(epred49_0 @ (sub @ (esk276_1 @ X1288) @ (push @ esk274_0 @ esk275_0)))|(pushprop_lem0_lthm)))))&(hoasapnotvar_lthm))&((~(hoasinduction_lem3v2_lthm)|(((esk277_0)!=(sub @ esk277_0 @ id))|((epred8_3 @ X1293 @ X1292 @ X1291)|(X1292 @ (lam @ X1293)))))&((((X1294)=(sub @ X1294 @ id))|(hoasinduction_lem3v2_lthm))&((~(epred8_3 @ esk278_0 @ epred51_0 @ epred50_0)|(hoasinduction_lem3v2_lthm))&(~(epred51_0 @ (lam @ esk278_0))|(hoasinduction_lem3v2_lthm))))))&((~(axvarid)|((X1298)=(sub @ X1298 @ id)))&(((esk279_0)!=(sub @ esk279_0 @ id))|(axvarid))))&(((~(X1301 @ (esk280_1 @ X1301))|~(epred52_0 @ id @ (esk280_1 @ X1301) @ id)|(epred9_0)|~(hoasinduction_lthm_3))&((X1301 @ (esk280_1 @ X1301))|(epred52_0 @ id @ (esk280_1 @ X1301) @ id)|(epred9_0)|~(hoasinduction_lthm_3)))&(((~(epred53_1 @ X1303 @ X1305)|(X1303 @ id @ X1305 @ id)|(hoasinduction_lthm_3))&(~(X1303 @ id @ X1306 @ id)|(epred53_1 @ X1303 @ X1306)|(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])])])])])])])).
% 0.22/0.38  thf(c_0_13, negated_conjecture, ![X1309:subst, X1310:term, X1311:subst, X1312:subst, X1313:subst, X1314:term, X1315:subst, X1316:subst, X1317:term, X1318:term, X1321:subst > term > subst > $o, X1332:term > $o, X1333:term, X1334:term]:((((~(epred54_0 @ X1309 @ X1310 @ (comp @ X1312 @ X1311))|(epred54_0 @ (comp @ X1309 @ X1312) @ (sub @ X1310 @ X1312) @ X1311)|~(hoasinduction_lem2v2))&((~(epred54_0 @ (comp @ X1313 @ X1316) @ (sub @ X1314 @ X1316) @ X1315)|(epred54_0 @ X1313 @ X1314 @ (comp @ X1316 @ X1315))|~(hoasinduction_lem2v2))&((~(epred54_0 @ id @ X1317 @ id)|(~(epred54_0 @ id @ X1318 @ id)|(epred54_0 @ id @ (hoasap @ id @ X1317 @ id @ X1318) @ id))|~(hoasinduction_lem2v2))&(((hoasinduction_p_and_p_prime @ epred54_0 @ epred55_0)|~(hoasinduction_lem2v2))&(((epred55_0 @ esk281_0)|~(hoasinduction_lem2v2))&(((epred55_0 @ esk282_0)|~(hoasinduction_lem2v2))&(~(epred55_0 @ (ap @ esk281_0 @ esk282_0))|~(hoasinduction_lem2v2))))))))&(((((X1321 @ id @ (esk291_1 @ X1321) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|(X1321 @ (comp @ (esk287_1 @ X1321) @ (esk290_1 @ X1321)) @ (sub @ (esk288_1 @ X1321) @ (esk290_1 @ X1321)) @ (esk289_1 @ X1321))|(X1321 @ (esk283_1 @ X1321) @ (esk284_1 @ X1321) @ (comp @ (esk286_1 @ X1321) @ (esk285_1 @ X1321)))|(hoasinduction_lem2v2))&(((X1321 @ id @ (esk292_1 @ X1321) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|(X1321 @ (comp @ (esk287_1 @ X1321) @ (esk290_1 @ X1321)) @ (sub @ (esk288_1 @ X1321) @ (esk290_1 @ X1321)) @ (esk289_1 @ X1321))|(X1321 @ (esk283_1 @ X1321) @ (esk284_1 @ X1321) @ (comp @ (esk286_1 @ X1321) @ (esk285_1 @ X1321)))|(hoasinduction_lem2v2))&(~(X1321 @ id @ (hoasap @ id @ (esk291_1 @ X1321) @ id @ (esk292_1 @ X1321)) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|(X1321 @ (comp @ (esk287_1 @ X1321) @ (esk290_1 @ X1321)) @ (sub @ (esk288_1 @ X1321) @ (esk290_1 @ X1321)) @ (esk289_1 @ X1321))|(X1321 @ (esk283_1 @ X1321) @ (esk284_1 @ X1321) @ (comp @ (esk286_1 @ X1321) @ (esk285_1 @ X1321)))|(hoasinduction_lem2v2))))&(((X1321 @ id @ (esk291_1 @ X1321) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|~(X1321 @ (esk287_1 @ X1321) @ (esk288_1 @ X1321) @ (comp @ (esk290_1 @ X1321) @ (esk289_1 @ X1321)))|(X1321 @ (esk283_1 @ X1321) @ (esk284_1 @ X1321) @ (comp @ (esk286_1 @ X1321) @ (esk285_1 @ X1321)))|(hoasinduction_lem2v2))&(((X1321 @ id @ (esk292_1 @ X1321) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|~(X1321 @ (esk287_1 @ X1321) @ (esk288_1 @ X1321) @ (comp @ (esk290_1 @ X1321) @ (esk289_1 @ X1321)))|(X1321 @ (esk283_1 @ X1321) @ (esk284_1 @ X1321) @ (comp @ (esk286_1 @ X1321) @ (esk285_1 @ X1321)))|(hoasinduction_lem2v2))&(~(X1321 @ id @ (hoasap @ id @ (esk291_1 @ X1321) @ id @ (esk292_1 @ X1321)) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|~(X1321 @ (esk287_1 @ X1321) @ (esk288_1 @ X1321) @ (comp @ (esk290_1 @ X1321) @ (esk289_1 @ X1321)))|(X1321 @ (esk283_1 @ X1321) @ (esk284_1 @ X1321) @ (comp @ (esk286_1 @ X1321) @ (esk285_1 @ X1321)))|(hoasinduction_lem2v2)))))&((((X1321 @ id @ (esk291_1 @ X1321) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|(X1321 @ (comp @ (esk287_1 @ X1321) @ (esk290_1 @ X1321)) @ (sub @ (esk288_1 @ X1321) @ (esk290_1 @ X1321)) @ (esk289_1 @ X1321))|~(X1321 @ (comp @ (esk283_1 @ X1321) @ (esk286_1 @ X1321)) @ (sub @ (esk284_1 @ X1321) @ (esk286_1 @ X1321)) @ (esk285_1 @ X1321))|(hoasinduction_lem2v2))&(((X1321 @ id @ (esk292_1 @ X1321) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|(X1321 @ (comp @ (esk287_1 @ X1321) @ (esk290_1 @ X1321)) @ (sub @ (esk288_1 @ X1321) @ (esk290_1 @ X1321)) @ (esk289_1 @ X1321))|~(X1321 @ (comp @ (esk283_1 @ X1321) @ (esk286_1 @ X1321)) @ (sub @ (esk284_1 @ X1321) @ (esk286_1 @ X1321)) @ (esk285_1 @ X1321))|(hoasinduction_lem2v2))&(~(X1321 @ id @ (hoasap @ id @ (esk291_1 @ X1321) @ id @ (esk292_1 @ X1321)) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|(X1321 @ (comp @ (esk287_1 @ X1321) @ (esk290_1 @ X1321)) @ (sub @ (esk288_1 @ X1321) @ (esk290_1 @ X1321)) @ (esk289_1 @ X1321))|~(X1321 @ (comp @ (esk283_1 @ X1321) @ (esk286_1 @ X1321)) @ (sub @ (esk284_1 @ X1321) @ (esk286_1 @ X1321)) @ (esk285_1 @ X1321))|(hoasinduction_lem2v2))))&(((X1321 @ id @ (esk291_1 @ X1321) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|~(X1321 @ (esk287_1 @ X1321) @ (esk288_1 @ X1321) @ (comp @ (esk290_1 @ X1321) @ (esk289_1 @ X1321)))|~(X1321 @ (comp @ (esk283_1 @ X1321) @ (esk286_1 @ X1321)) @ (sub @ (esk284_1 @ X1321) @ (esk286_1 @ X1321)) @ (esk285_1 @ X1321))|(hoasinduction_lem2v2))&(((X1321 @ id @ (esk292_1 @ X1321) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|~(X1321 @ (esk287_1 @ X1321) @ (esk288_1 @ X1321) @ (comp @ (esk290_1 @ X1321) @ (esk289_1 @ X1321)))|~(X1321 @ (comp @ (esk283_1 @ X1321) @ (esk286_1 @ X1321)) @ (sub @ (esk284_1 @ X1321) @ (esk286_1 @ X1321)) @ (esk285_1 @ X1321))|(hoasinduction_lem2v2))&(~(X1321 @ id @ (hoasap @ id @ (esk291_1 @ X1321) @ id @ (esk292_1 @ X1321)) @ id)|(~(hoasinduction_p_and_p_prime @ X1321 @ X1332)|(~(X1332 @ X1333)|(~(X1332 @ X1334)|(X1332 @ (ap @ X1333 @ X1334)))))|~(X1321 @ (esk287_1 @ X1321) @ (esk288_1 @ X1321) @ (comp @ (esk290_1 @ X1321) @ (esk289_1 @ X1321)))|~(X1321 @ (comp @ (esk283_1 @ X1321) @ (esk286_1 @ X1321)) @ (sub @ (esk284_1 @ X1321) @ (esk286_1 @ X1321)) @ (esk285_1 @ X1321))|(hoasinduction_lem2v2)))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])])])).
% 0.22/0.38  thf(c_0_14, plain, ![X1:term]:(((X1)=(d2term @ (esk1_1 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.22/0.38  thf(c_0_15, plain, ![X2:d_term]:(((X2)=(d_one))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.22/0.38  thf(c_0_16, plain, ((one)=(d2term @ d_one)), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.22/0.38  thf(c_0_17, negated_conjecture, (~((epred55_0 @ (ap @ esk281_0 @ esk282_0)))|~((hoasinduction_lem2v2))), inference(split_conjunct,[status(thm)],[c_0_13])).
% 0.22/0.38  thf(c_0_18, plain, ![X1:term]:(((one)=(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15]), c_0_16])).
% 0.22/0.38  thf(c_0_19, negated_conjecture, ((epred55_0 @ esk281_0)|~((hoasinduction_lem2v2))), inference(split_conjunct,[status(thm)],[c_0_13])).
% 0.22/0.38  thf(c_0_20, negated_conjecture, (~((epred55_0 @ one))|~((hoasinduction_lem2v2))), inference(rw,[status(thm)],[c_0_17, c_0_18])).
% 0.22/0.38  thf(c_0_21, plain, ((hoasinduction_lem2v2)|~((epred30_0 @ (ap @ esk148_0 @ esk149_0)))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.22/0.38  thf(c_0_22, plain, ((epred30_0 @ esk148_0)|(hoasinduction_lem2v2)), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.22/0.38  thf(c_0_23, negated_conjecture, ~((hoasinduction_lem2v2)), inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_18]), c_0_20])).
% 0.22/0.38  thf(c_0_24, plain, ((hoasinduction_lem2v2)|~((epred30_0 @ one))), inference(rw,[status(thm)],[c_0_21, c_0_18])).
% 0.22/0.38  thf(c_0_25, plain, (epred30_0 @ one), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_18]), c_0_23])).
% 0.22/0.38  thf(c_0_26, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])]), c_0_23]), ['proof']).
% 0.22/0.38  % SZS output end CNFRefutation
% 0.22/0.38  % Parsed axioms                        : 132
% 0.22/0.38  % Removed by relevancy pruning/SinE    : 0
% 0.22/0.38  % Initial clauses                      : 1250
% 0.22/0.38  % Removed in clause preprocessing      : 130
% 0.22/0.38  % Initial clauses in saturation        : 1120
% 0.22/0.38  % Processed clauses                    : 150
% 0.22/0.38  % ...of these trivial                  : 1
% 0.22/0.38  % ...subsumed                          : 1
% 0.22/0.38  % ...remaining for further processing  : 148
% 0.22/0.38  % Other redundant clauses eliminated   : 0
% 0.22/0.38  % Clauses deleted for lack of memory   : 0
% 0.22/0.38  % Backward-subsumed                    : 4
% 0.22/0.38  % Backward-rewritten                   : 36
% 0.22/0.38  % Generated clauses                    : 0
% 0.22/0.38  % ...of the previous two non-redundant : 32
% 0.22/0.38  % ...aggressively subsumed             : 0
% 0.22/0.38  % Contextual simplify-reflections      : 1
% 0.22/0.38  % Paramodulations                      : 0
% 0.22/0.38  % Factorizations                       : 0
% 0.22/0.38  % NegExts                              : 0
% 0.22/0.38  % Equation resolutions                 : 0
% 0.22/0.38  % Disequality decompositions           : 0
% 0.22/0.38  % Total rewrite steps                  : 86
% 0.22/0.38  % ...of those cached                   : 10
% 0.22/0.38  % Propositional unsat checks           : 0
% 0.22/0.38  %    Propositional check models        : 0
% 0.22/0.38  %    Propositional check unsatisfiable : 0
% 0.22/0.38  %    Propositional clauses             : 0
% 0.22/0.38  %    Propositional clauses after purity: 0
% 0.22/0.38  %    Propositional unsat core size     : 0
% 0.22/0.38  %    Propositional preprocessing time  : 0.000
% 0.22/0.38  %    Propositional encoding time       : 0.000
% 0.22/0.38  %    Propositional solver time         : 0.000
% 0.22/0.38  %    Success case prop preproc time    : 0.000
% 0.22/0.38  %    Success case prop encoding time   : 0.000
% 0.22/0.38  %    Success case prop solver time     : 0.000
% 0.22/0.38  % Current number of processed clauses  : 108
% 0.22/0.38  %    Positive orientable unit clauses  : 66
% 0.22/0.38  %    Positive unorientable unit clauses: 4
% 0.22/0.38  %    Negative unit clauses             : 4
% 0.22/0.38  %    Non-unit-clauses                  : 34
% 0.22/0.38  % Current number of unprocessed clauses: 1002
% 0.22/0.38  % ...number of literals in the above   : 5986
% 0.22/0.38  % Current number of archived formulas  : 0
% 0.22/0.38  % Current number of archived clauses   : 40
% 0.22/0.38  % Clause-clause subsumption calls (NU) : 799
% 0.22/0.38  % Rec. Clause-clause subsumption calls : 707
% 0.22/0.38  % Non-unit clause-clause subsumptions  : 1
% 0.22/0.38  % Unit Clause-clause subsumption calls : 772
% 0.22/0.38  % Rewrite failures with RHS unbound    : 16
% 0.22/0.38  % BW rewrite match attempts            : 907
% 0.22/0.38  % BW rewrite match successes           : 56
% 0.22/0.38  % Condensation attempts                : 0
% 0.22/0.38  % Condensation successes               : 0
% 0.22/0.38  % Termbank termtop insertions          : 111603
% 0.22/0.38  % Search garbage collected termcells   : 22884
% 0.22/0.38  
% 0.22/0.38  % -------------------------------------------------
% 0.22/0.38  % User time                : 0.081 s
% 0.22/0.38  % System time              : 0.017 s
% 0.22/0.38  % Total time               : 0.098 s
% 0.22/0.38  % Maximum resident set size: 8004 pages
% 0.22/0.38  
% 0.22/0.38  % -------------------------------------------------
% 0.22/0.38  % User time                : 0.125 s
% 0.22/0.38  % System time              : 0.030 s
% 0.22/0.38  % Total time               : 0.155 s
% 0.22/0.38  % Maximum resident set size: 5376 pages
% 0.22/0.38  % E exiting
%------------------------------------------------------------------------------