0.00/0.04	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.07	% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.17/0.42	% Computer : n026.cluster.edu
0.17/0.42	% Model    : x86_64 x86_64
0.17/0.42	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.17/0.42	% Memory   : 8046.5625MB
0.17/0.42	% OS       : Linux 6.8.0-71-generic
0.17/0.42	% CPULimit : 1440
0.17/0.42	% WCLimit  : 180
0.17/0.42	% DateTime : Mon Jul 27 13:51:34 UTC 2026
0.17/0.43	% CPUTime  : 
0.17/0.43	Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.17/0.50	Running higher-order theorem proving
0.27/0.56	Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.yrpyPezLI8/E---3.1_2727653.p
0.33/0.94	% Version: 3.5.1-ho
0.33/0.94	% partial match(1): HSLMSMSSSSMNHSA
0.33/0.94	% Preprocessing class: HSLMSLSSSSMNHSA.
0.33/0.94	% Scheduled 4 strats onto 8 cores with 180 seconds (1440 total)
0.33/0.94	% Starting new_ho_10 with 900s (5) cores
0.33/0.94	% Starting sh5l with 180s (1) cores
0.33/0.94	% Starting new_bool_1 with 180s (1) cores
0.33/0.94	% Starting new_bool_2 with 180s (1) cores
0.33/0.94	% new_ho_10 with pid 2727666 completed with status 0
0.33/0.94	% Result found by new_ho_10
0.33/0.94	% partial match(1): HSLMSMSSSSMNHSA
0.33/0.94	% Preprocessing class: HSLMSLSSSSMNHSA.
0.33/0.94	% Scheduled 4 strats onto 8 cores with 180 seconds (1440 total)
0.33/0.94	% Starting new_ho_10 with 900s (5) cores
0.33/0.94	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
0.33/0.94	% No SInE strategy applied
0.33/0.94	% Search class: HGHSM-SMLM31-MHSFFMBN
0.33/0.94	% partial match(1): HGHSM-SMLM31-MHSFFSBN
0.33/0.94	% Scheduled 5 strats onto 5 cores with 900 seconds (900 total)
0.33/0.94	% Starting SubtermCWHack with 91s (1) cores
0.33/0.94	% Starting new_ho_10 with 541s (1) cores
0.33/0.94	% Starting new_bool_1 with 91s (1) cores
0.33/0.94	% Starting new_bool_2 with 91s (1) cores
0.33/0.94	% Starting new_bool_9 with 86s (1) cores
0.33/0.94	% new_ho_10 with pid 2727676 completed with status 0
0.33/0.94	% Result found by new_ho_10
0.33/0.94	% partial match(1): HSLMSMSSSSMNHSA
0.33/0.94	% Preprocessing class: HSLMSLSSSSMNHSA.
0.33/0.94	% Scheduled 4 strats onto 8 cores with 180 seconds (1440 total)
0.33/0.94	% Starting new_ho_10 with 900s (5) cores
0.33/0.94	% (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
0.33/0.94	% No SInE strategy applied
0.33/0.94	% Search class: HGHSM-SMLM31-MHSFFMBN
0.33/0.94	% partial match(1): HGHSM-SMLM31-MHSFFSBN
0.33/0.94	% Scheduled 5 strats onto 5 cores with 900 seconds (900 total)
0.33/0.94	% Starting SubtermCWHack with 91s (1) cores
0.33/0.94	% Starting new_ho_10 with 541s (1) cores
0.33/0.94	% Preprocessing time       : 0.056 s
0.33/0.94	% Presaturation interreduction done
0.33/0.94	
0.33/0.94	% Proof found!
0.33/0.94	% SZS status Theorem
0.33/0.94	% SZS output start CNFRefutation
0.33/0.94	thf(decl_sort1, type, term: $tType).
0.33/0.94	thf(decl_sort2, type, subst: $tType).
0.33/0.94	thf(decl_sort3, type, d_term: $tType).
0.33/0.94	thf(decl_sort4, type, d_subst: $tType).
0.33/0.94	thf(decl_23, type, one: term).
0.33/0.94	thf(decl_24, type, ap: term > term > term).
0.33/0.94	thf(decl_25, type, lam: term > term).
0.33/0.94	thf(decl_26, type, sub: term > subst > term).
0.33/0.94	thf(decl_27, type, id: subst).
0.33/0.94	thf(decl_28, type, sh: subst).
0.33/0.94	thf(decl_29, type, push: term > subst > subst).
0.33/0.94	thf(decl_30, type, comp: subst > subst > subst).
0.33/0.94	thf(decl_31, type, var: term > $o).
0.33/0.94	thf(decl_32, type, pushprop_lem1v2: $o).
0.33/0.94	thf(decl_33, type, pushprop_lem1_gthm: $o).
0.33/0.94	thf(decl_34, type, axmap: $o).
0.33/0.94	thf(decl_35, type, pushprop_lem0_gthm: $o).
0.33/0.94	thf(decl_36, type, shinj: $o).
0.33/0.94	thf(decl_37, type, hoasinduction_lem1v2: $o).
0.33/0.94	thf(decl_38, type, hoasinduction_lem1v2_gthm: $o).
0.33/0.94	thf(decl_39, type, hoasap: subst > term > subst > term > term).
0.33/0.94	thf(decl_40, type, induction2lem: $o).
0.33/0.94	thf(decl_41, type, hoasinduction_lem3v2_f: $o).
0.33/0.94	thf(decl_42, type, axvarshift: $o).
0.33/0.94	thf(decl_43, type, hoasapinj2: $o).
0.33/0.94	thf(decl_44, type, hoasapnotvar_gthm: $o).
0.33/0.94	thf(decl_45, type, hoasapinj1: $o).
0.33/0.94	thf(decl_46, type, ulamvar1: $o).
0.33/0.94	thf(decl_47, type, induction2lem_lthm: $o).
0.33/0.94	thf(decl_48, type, hoasinduction_lem3v2_gthm: $o).
0.33/0.94	thf(decl_49, type, apnotvar: $o).
0.33/0.94	thf(decl_50, type, pushprop_lthm_orig: $o).
0.33/0.94	thf(decl_51, type, hoasinduction_lem3v2_f_lthm: $o).
0.33/0.94	thf(decl_52, type, hoasinduction_lthm: $o).
0.33/0.94	thf(decl_53, type, hoasinduction_no_psi_cond_lthm: $o).
0.33/0.94	thf(decl_54, type, hoaslaminj: $o).
0.33/0.94	thf(decl_55, type, hoasinduction_lem3aaa: $o).
0.33/0.94	thf(decl_56, type, induction2lem_gthm: $o).
0.33/0.94	thf(decl_57, type, hoasinduction_lem3aa_lthm: $o).
0.33/0.94	thf(decl_58, type, hoasinduction_lem3: $o).
0.33/0.94	thf(decl_59, type, hoasinduction_lem2: $o).
0.33/0.94	thf(decl_60, type, termmset_lthm: $o).
0.33/0.94	thf(decl_61, type, hoasinduction_lem1: $o).
0.33/0.94	thf(decl_62, type, hoaslamnotap_lthm: $o).
0.33/0.94	thf(decl_63, type, pushprop_lem1v2_lthm: $o).
0.33/0.94	thf(decl_64, type, hoasapnotvar: $o).
0.33/0.94	thf(decl_65, type, hoasinduction_lem0: $o).
0.33/0.94	thf(decl_66, type, hoasinduction: $o).
0.33/0.94	thf(decl_67, type, hoasinduction_gthm: $o).
0.33/0.94	thf(decl_68, type, axapp: $o).
0.33/0.94	thf(decl_69, type, hoaslamnotvar_lthm: $o).
0.33/0.94	thf(decl_70, type, pushprop_lem3v2_lthm: $o).
0.33/0.94	thf(decl_71, type, hoasinduction_lem3b_lthm: $o).
0.33/0.94	thf(decl_72, type, ulamvarind: $o).
0.33/0.94	thf(decl_73, type, induction: $o).
0.33/0.94	thf(decl_74, type, hoasinduction_lem3a_lthm: $o).
0.33/0.94	thf(decl_75, type, termmset_gthm: $o).
0.33/0.94	thf(decl_76, type, hoasinduction_lem3aa: $o).
0.33/0.94	thf(decl_77, type, pushprop_lem1v2_gthm: $o).
0.33/0.94	thf(decl_78, type, hoaslamnotap_gthm: $o).
0.33/0.94	thf(decl_79, type, hoaslamnotvar_gthm: $o).
0.33/0.94	thf(decl_80, type, hoasinduction_lem3b_gthm: $o).
0.33/0.94	thf(decl_81, type, pushprop_lem2v2: $o).
0.33/0.94	thf(decl_82, type, hoasinduction_lem3a_gthm: $o).
0.33/0.94	thf(decl_83, type, axclos: $o).
0.33/0.94	thf(decl_84, type, axassoc: $o).
0.33/0.94	thf(decl_85, type, hoasinduction_lem2v2: $o).
0.33/0.94	thf(decl_86, type, pushprop_lthm: $o).
0.33/0.94	thf(decl_87, type, apinj2: $o).
0.33/0.94	thf(decl_88, type, apinj1: $o).
0.33/0.94	thf(decl_89, type, hoasapinj2_lthm: $o).
0.33/0.94	thf(decl_90, type, hoasinduction_lem3v2a: $o).
0.33/0.94	thf(decl_91, type, hoasapinj1_lthm: $o).
0.33/0.94	thf(decl_92, type, hoaslaminj_lthm: $o).
0.33/0.94	thf(decl_93, type, axvarcons: $o).
0.33/0.94	thf(decl_94, type, hoaslam: subst > (subst > term > term) > term).
0.33/0.94	thf(decl_95, type, axscons: $o).
0.33/0.94	thf(decl_96, type, hoasinduction_lem2v2_gthm: $o).
0.33/0.94	thf(decl_97, type, axidr: $o).
0.33/0.94	thf(decl_98, type, pushprop_lem1: $o).
0.33/0.94	thf(decl_99, type, laminj: $o).
0.33/0.94	thf(decl_100, type, hoasinduction_lem3_lthm: $o).
0.33/0.94	thf(decl_101, type, pushprop_lem0: $o).
0.33/0.94	thf(decl_102, type, pushprop_gthm: $o).
0.33/0.94	thf(decl_103, type, axabs: $o).
0.33/0.94	thf(decl_104, type, hoasinduction_lem3v2a_lthm: $o).
0.33/0.94	thf(decl_105, type, hoasinduction_lem2_lthm: $o).
0.33/0.94	thf(decl_106, type, hoasapinj2_gthm: $o).
0.33/0.94	thf(decl_107, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
0.33/0.94	thf(decl_108, type, hoasinduction_lem1_lthm: $o).
0.33/0.94	thf(decl_109, type, lamnotap: $o).
0.33/0.94	thf(decl_110, type, hoasapinj1_gthm: $o).
0.33/0.94	thf(decl_111, type, hoaslamnotvar: $o).
0.33/0.94	thf(decl_112, type, axidl: $o).
0.33/0.94	thf(decl_113, type, hoaslaminj_gthm: $o).
0.33/0.94	thf(decl_114, type, induction2_lthm: $o).
0.33/0.94	thf(decl_115, type, hoasinduction_lem0_lthm: $o).
0.33/0.94	thf(decl_116, type, substmonoid_lthm: $o).
0.33/0.94	thf(decl_117, type, pushprop: $o).
0.33/0.94	thf(decl_118, type, hoasinduction_lem3_gthm: $o).
0.33/0.94	thf(decl_119, type, hoasinduction_lem2_gthm: $o).
0.33/0.94	thf(decl_120, type, hoasinduction_lem3b: $o).
0.33/0.94	thf(decl_121, type, substmonoid: $o).
0.33/0.94	thf(decl_122, type, lamnotvar: $o).
0.33/0.94	thf(decl_123, type, hoasinduction_lem3a: $o).
0.33/0.94	thf(decl_124, type, hoasinduction_lem1_gthm: $o).
0.33/0.94	thf(decl_125, type, hoasinduction_no_psi_cond: $o).
0.33/0.94	thf(decl_126, type, induction2_gthm: $o).
0.33/0.94	thf(decl_127, type, pushprop_lem2v2_lthm: $o).
0.33/0.94	thf(decl_128, type, hoasvar: subst > term > subst > $o).
0.33/0.94	thf(decl_129, type, hoaslamnotap: $o).
0.33/0.94	thf(decl_130, type, substmonoid_gthm: $o).
0.33/0.94	thf(decl_131, type, ulamvarsh: $o).
0.33/0.94	thf(decl_132, type, induction2: $o).
0.33/0.94	thf(decl_133, type, pushprop_lem3v2: $o).
0.33/0.94	thf(decl_134, type, pushprop_lem2v2_gthm: $o).
0.33/0.94	thf(decl_135, type, pushprop_lem1_lthm: $o).
0.33/0.94	thf(decl_136, type, hoasinduction_lem3v2: $o).
0.33/0.94	thf(decl_137, type, axshiftcons: $o).
0.33/0.94	thf(decl_138, type, termmset: $o).
0.33/0.94	thf(decl_139, type, pushprop_lem0_lthm: $o).
0.33/0.94	thf(decl_140, type, hoasapnotvar_lthm: $o).
0.33/0.94	thf(decl_141, type, hoasinduction_lem3v2_lthm: $o).
0.33/0.94	thf(decl_142, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
0.33/0.94	thf(decl_143, type, axvarid: $o).
0.33/0.94	thf(decl_144, type, hoasinduction_lthm_3: $o).
0.33/0.94	thf(decl_145, type, d2term: d_term > term).
0.33/0.94	thf(decl_146, type, d2subst: d_subst > subst).
0.33/0.94	thf(decl_147, type, d_one: d_term).
0.33/0.94	thf(decl_148, type, d_id: d_subst).
0.33/0.94	thf(decl_149, type, epred1_0: $o).
0.33/0.94	thf(decl_150, type, epred2_0: $o).
0.33/0.94	thf(decl_151, type, epred3_0: $o).
0.33/0.94	thf(decl_153, type, epred5_0: $o).
0.33/0.94	thf(decl_154, type, epred6_0: $o).
0.33/0.94	thf(decl_155, type, epred7_0: $o).
0.33/0.94	thf(decl_156, type, epred8_2: (subst > term > subst > $o) > term > $o).
0.33/0.94	thf(decl_157, type, epred9_0: $o).
0.33/0.94	thf(decl_160, type, epred12_0: $o).
0.33/0.94	thf(decl_161, type, esk1_1: term > d_term).
0.33/0.94	thf(decl_162, type, esk2_4: term > subst > (term > $o) > (term > $o) > term).
0.33/0.94	thf(decl_163, type, esk3_4: (term > $o) > (term > $o) > term > subst > term).
0.33/0.94	thf(decl_164, type, epred13_0: term > $o).
0.33/0.94	thf(decl_165, type, epred14_0: term > $o).
0.33/0.94	thf(decl_166, type, esk4_0: term).
0.33/0.94	thf(decl_167, type, esk5_0: subst).
0.33/0.94	thf(decl_168, type, esk6_0: term).
0.33/0.94	thf(decl_169, type, esk7_0: term).
0.33/0.94	thf(decl_170, type, esk8_0: term).
0.33/0.94	thf(decl_171, type, esk9_1: (subst > term > term) > term).
0.33/0.94	thf(decl_172, type, esk10_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_173, type, esk11_1: term > subst > term > term).
0.33/0.94	thf(decl_174, type, esk12_0: term).
0.33/0.94	thf(decl_175, type, esk13_0: term).
0.33/0.94	thf(decl_176, type, esk14_0: term).
0.33/0.94	thf(decl_177, type, esk15_0: term).
0.33/0.94	thf(decl_178, type, esk16_0: term).
0.33/0.94	thf(decl_179, type, esk17_0: subst).
0.33/0.94	thf(decl_180, type, esk18_0: term).
0.33/0.94	thf(decl_181, type, esk19_0: subst).
0.33/0.94	thf(decl_182, type, esk20_0: subst).
0.33/0.94	thf(decl_183, type, esk21_0: subst > term > term).
0.33/0.94	thf(decl_184, type, esk22_0: subst > term > term).
0.33/0.94	thf(decl_185, type, esk23_0: subst).
0.33/0.94	thf(decl_186, type, esk24_0: term).
0.33/0.94	thf(decl_187, type, esk25_2: (subst > term > term) > (subst > term > term) > subst).
0.33/0.94	thf(decl_188, type, esk26_2: (subst > term > term) > (subst > term > term) > term).
0.33/0.94	thf(decl_189, type, esk27_2: (subst > term > term) > (subst > term > term) > subst).
0.33/0.94	thf(decl_190, type, esk28_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_191, type, esk29_1: (subst > term > term) > term).
0.33/0.94	thf(decl_192, type, esk30_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_193, type, esk31_2: (subst > term > subst > $o) > term > subst > term > term).
0.33/0.94	thf(decl_194, type, esk32_2: (subst > term > subst > $o) > term > term).
0.33/0.94	thf(decl_195, type, esk33_2: (subst > term > subst > $o) > term > term).
0.33/0.94	thf(decl_196, type, epred15_0: subst > term > subst > $o).
0.33/0.94	thf(decl_197, type, esk34_0: term).
0.33/0.94	thf(decl_198, type, esk35_2: (subst > term > term) > term > subst).
0.33/0.94	thf(decl_199, type, esk36_2: (subst > term > term) > term > term).
0.33/0.94	thf(decl_200, type, esk37_2: (subst > term > term) > term > subst).
0.33/0.94	thf(decl_201, type, esk38_2: (subst > term > term) > term > subst).
0.33/0.94	thf(decl_202, type, esk39_2: (subst > term > term) > term > term).
0.33/0.94	thf(decl_203, type, esk40_2: (subst > term > term) > term > subst).
0.33/0.94	thf(decl_204, type, esk41_2: (subst > term > term) > term > term).
0.33/0.94	thf(decl_205, type, epred16_0: subst > term > subst > $o).
0.33/0.94	thf(decl_206, type, esk42_0: term).
0.33/0.94	thf(decl_207, type, esk43_0: term).
0.33/0.94	thf(decl_208, type, esk44_3: (subst > term > subst > $o) > term > term > subst).
0.33/0.94	thf(decl_209, type, esk45_3: (subst > term > subst > $o) > term > term > term).
0.33/0.94	thf(decl_210, type, esk46_3: (subst > term > subst > $o) > term > term > subst).
0.33/0.94	thf(decl_211, type, esk47_3: (subst > term > subst > $o) > term > term > subst).
0.33/0.94	thf(decl_212, type, esk48_3: (subst > term > subst > $o) > term > term > subst).
0.33/0.94	thf(decl_213, type, esk49_3: (subst > term > subst > $o) > term > term > term).
0.33/0.94	thf(decl_214, type, esk50_3: (subst > term > subst > $o) > term > term > subst).
0.33/0.94	thf(decl_215, type, esk51_3: (subst > term > subst > $o) > term > term > subst).
0.33/0.94	thf(decl_216, type, esk52_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_217, type, esk53_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_218, type, epred17_0: subst > term > subst > $o).
0.33/0.94	thf(decl_219, type, esk54_1: (term > $o) > term).
0.33/0.94	thf(decl_220, type, epred18_1: (subst > term > subst > $o) > term > $o).
0.33/0.94	thf(decl_221, type, esk55_0: term).
0.33/0.94	thf(decl_222, type, epred19_0: subst > term > subst > $o).
0.33/0.94	thf(decl_223, type, esk56_0: term).
0.33/0.94	thf(decl_224, type, esk57_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_225, type, esk58_1: (subst > term > term) > term).
0.33/0.94	thf(decl_226, type, esk59_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_227, type, esk60_1: (subst > term > term) > term).
0.33/0.94	thf(decl_228, type, esk61_2: (subst > term > subst > $o) > term > term).
0.33/0.94	thf(decl_229, type, esk62_1: (subst > term > subst > $o) > subst > term > term).
0.33/0.94	thf(decl_230, type, esk63_2: (subst > term > subst > $o) > term > term).
0.33/0.94	thf(decl_231, type, esk64_1: (subst > term > subst > $o) > subst > term > term).
0.33/0.94	thf(decl_232, type, epred20_0: subst > term > subst > $o).
0.33/0.94	thf(decl_233, type, esk65_0: term).
0.33/0.94	thf(decl_234, type, esk66_1: (subst > term > term) > term).
0.33/0.94	thf(decl_235, type, esk67_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_236, type, esk68_1: (subst > term > term) > term).
0.33/0.94	thf(decl_237, type, esk69_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_238, type, esk70_2: (subst > term > subst > $o) > term > subst > term > term).
0.33/0.94	thf(decl_239, type, esk71_2: (subst > term > subst > $o) > term > term).
0.33/0.94	thf(decl_240, type, epred21_0: subst > term > subst > $o).
0.33/0.94	thf(decl_241, type, esk72_0: term).
0.33/0.94	thf(decl_242, type, esk73_1: (subst > term > term) > term).
0.33/0.94	thf(decl_243, type, esk74_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_244, type, esk75_1: (subst > term > term) > term).
0.33/0.94	thf(decl_245, type, esk76_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_246, type, esk77_0: term).
0.33/0.94	thf(decl_247, type, esk78_0: term).
0.33/0.94	thf(decl_248, type, esk79_0: term).
0.33/0.94	thf(decl_249, type, esk80_0: term).
0.33/0.94	thf(decl_250, type, esk81_0: term).
0.33/0.94	thf(decl_251, type, esk82_0: term).
0.33/0.94	thf(decl_252, type, esk83_0: term).
0.33/0.94	thf(decl_253, type, esk84_0: term).
0.33/0.94	thf(decl_254, type, esk85_0: term).
0.33/0.94	thf(decl_255, type, esk86_0: term).
0.33/0.94	thf(decl_256, type, esk87_0: term).
0.33/0.94	thf(decl_257, type, esk88_0: term).
0.33/0.94	thf(decl_258, type, esk89_0: subst).
0.33/0.94	thf(decl_259, type, esk90_0: subst).
0.33/0.94	thf(decl_260, type, esk91_0: term).
0.33/0.94	thf(decl_261, type, epred22_3: (term > $o) > term > subst > term > $o).
0.33/0.94	thf(decl_262, type, epred23_0: term > $o).
0.33/0.94	thf(decl_263, type, esk92_0: term).
0.33/0.94	thf(decl_264, type, esk93_0: subst).
0.33/0.94	thf(decl_265, type, esk94_1: (term > $o) > term).
0.33/0.94	thf(decl_266, type, esk95_0: term).
0.33/0.94	thf(decl_267, type, esk96_1: (subst > term > term) > term).
0.33/0.94	thf(decl_268, type, esk97_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_269, type, esk98_0: term).
0.33/0.94	thf(decl_270, type, esk99_3: (subst > term > subst > $o) > (term > $o) > term > term).
0.33/0.94	thf(decl_271, type, esk100_3: (subst > term > subst > $o) > (term > $o) > term > term).
0.33/0.94	thf(decl_272, type, esk101_1: (subst > term > subst > $o) > subst > term > term).
0.33/0.94	thf(decl_273, type, esk102_1: term > subst > term > term).
0.33/0.94	thf(decl_274, type, epred24_0: subst > term > subst > $o).
0.33/0.94	thf(decl_275, type, epred25_0: term > $o).
0.33/0.94	thf(decl_276, type, esk103_0: term).
0.33/0.94	thf(decl_277, type, esk104_1: (subst > term > term) > term).
0.33/0.94	thf(decl_278, type, esk105_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_279, type, esk106_1: (subst > term > term) > term).
0.33/0.94	thf(decl_280, type, esk107_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_281, type, esk108_0: term).
0.33/0.94	thf(decl_282, type, esk109_0: term).
0.33/0.94	thf(decl_283, type, esk110_1: term > subst > term > term).
0.33/0.94	thf(decl_284, type, esk111_0: subst > term > term).
0.33/0.94	thf(decl_285, type, esk112_0: term).
0.33/0.94	thf(decl_286, type, esk113_0: term).
0.33/0.94	thf(decl_287, type, esk114_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_288, type, esk115_1: (subst > term > term) > term).
0.33/0.94	thf(decl_289, type, esk116_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_290, type, esk117_0: term).
0.33/0.94	thf(decl_291, type, esk118_0: subst).
0.33/0.94	thf(decl_292, type, epred26_0: term > $o).
0.33/0.94	thf(decl_293, type, esk119_0: term).
0.33/0.94	thf(decl_294, type, esk120_0: subst).
0.33/0.94	thf(decl_295, type, esk121_1: (term > $o) > term).
0.33/0.94	thf(decl_296, type, epred27_3: (term > $o) > term > subst > term > $o).
0.33/0.94	thf(decl_297, type, esk122_0: term).
0.33/0.94	thf(decl_298, type, epred28_0: subst > term > subst > $o).
0.33/0.94	thf(decl_299, type, esk123_1: (term > $o) > term).
0.33/0.94	thf(decl_300, type, epred29_1: (subst > term > subst > $o) > term > $o).
0.33/0.94	thf(decl_301, type, esk124_0: term).
0.33/0.94	thf(decl_302, type, esk125_0: term).
0.33/0.94	thf(decl_303, type, esk126_0: term).
0.33/0.94	thf(decl_304, type, esk127_0: subst).
0.33/0.94	thf(decl_305, type, esk128_0: term).
0.33/0.94	thf(decl_306, type, esk129_0: subst).
0.33/0.94	thf(decl_307, type, epred30_0: term > $o).
0.33/0.94	thf(decl_308, type, epred31_0: term > $o).
0.33/0.94	thf(decl_309, type, esk130_0: term).
0.33/0.94	thf(decl_310, type, esk131_0: subst).
0.33/0.94	thf(decl_311, type, esk132_0: term).
0.33/0.94	thf(decl_312, type, epred32_0: term > $o).
0.33/0.94	thf(decl_313, type, esk133_0: term).
0.33/0.94	thf(decl_314, type, esk134_1: term > term).
0.33/0.94	thf(decl_315, type, esk135_1: (term > $o) > term).
0.33/0.94	thf(decl_316, type, esk136_1: (term > $o) > term).
0.33/0.94	thf(decl_317, type, esk137_1: (term > $o) > term).
0.33/0.94	thf(decl_318, type, esk138_1: (term > $o) > term).
0.33/0.94	thf(decl_319, type, esk139_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_320, type, esk140_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_321, type, esk141_1: (subst > term > subst > $o) > subst > term > term).
0.33/0.94	thf(decl_322, type, epred33_0: subst > term > subst > $o).
0.33/0.94	thf(decl_323, type, esk142_0: term).
0.33/0.94	thf(decl_324, type, esk143_1: (subst > term > term) > term).
0.33/0.94	thf(decl_325, type, esk144_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_326, type, esk145_1: (subst > term > term) > term).
0.33/0.94	thf(decl_327, type, esk146_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_328, type, esk147_2: (subst > term > subst > $o) > term > subst > term > term).
0.33/0.94	thf(decl_329, type, esk148_2: (subst > term > subst > $o) > term > term).
0.33/0.94	thf(decl_330, type, epred34_0: subst > term > subst > $o).
0.33/0.94	thf(decl_331, type, esk149_0: term).
0.33/0.94	thf(decl_332, type, esk150_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_333, type, esk151_1: (subst > term > term) > term).
0.33/0.94	thf(decl_334, type, esk152_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_335, type, esk153_1: (subst > term > term) > term).
0.33/0.94	thf(decl_336, type, esk154_0: subst).
0.33/0.94	thf(decl_337, type, esk155_0: subst).
0.33/0.94	thf(decl_338, type, esk156_0: subst).
0.33/0.94	thf(decl_339, type, esk157_0: subst).
0.33/0.94	thf(decl_340, type, esk158_0: subst).
0.33/0.94	thf(decl_341, type, esk159_0: subst).
0.33/0.94	thf(decl_342, type, epred35_0: subst > term > subst > $o).
0.33/0.94	thf(decl_343, type, esk160_1: (term > $o) > term).
0.33/0.94	thf(decl_344, type, epred36_1: (subst > term > subst > $o) > term > $o).
0.33/0.94	thf(decl_345, type, esk161_0: subst).
0.33/0.94	thf(decl_346, type, esk162_0: term).
0.33/0.94	thf(decl_347, type, esk163_0: term).
0.33/0.94	thf(decl_348, type, epred37_0: term > $o).
0.33/0.94	thf(decl_349, type, epred38_0: term > $o).
0.33/0.94	thf(decl_350, type, esk164_0: term).
0.33/0.94	thf(decl_351, type, esk165_0: subst).
0.33/0.94	thf(decl_352, type, esk166_0: term).
0.33/0.94	thf(decl_353, type, esk167_0: term).
0.33/0.94	thf(decl_354, type, esk168_0: subst).
0.33/0.94	thf(decl_355, type, esk169_0: term).
0.33/0.94	thf(decl_356, type, esk170_0: subst).
0.33/0.94	thf(decl_357, type, esk171_0: term).
0.33/0.94	thf(decl_358, type, esk172_0: subst).
0.33/0.94	thf(decl_359, type, esk173_0: term).
0.33/0.94	thf(decl_360, type, esk174_0: term).
0.33/0.94	thf(decl_361, type, esk175_2: (subst > term > term) > (subst > term > term) > subst).
0.33/0.94	thf(decl_362, type, esk176_2: (subst > term > term) > (subst > term > term) > term).
0.33/0.94	thf(decl_363, type, esk177_2: (subst > term > term) > (subst > term > term) > subst).
0.33/0.94	thf(decl_364, type, esk178_2: (subst > term > term) > (subst > term > term) > subst).
0.33/0.94	thf(decl_365, type, esk179_2: (subst > term > term) > (subst > term > term) > term).
0.33/0.94	thf(decl_366, type, esk180_2: (subst > term > term) > (subst > term > term) > subst).
0.33/0.94	thf(decl_367, type, esk181_0: subst > term > term).
0.33/0.94	thf(decl_368, type, esk182_0: subst > term > term).
0.33/0.94	thf(decl_369, type, esk183_0: subst).
0.33/0.94	thf(decl_370, type, esk184_0: term).
0.33/0.94	thf(decl_371, type, esk185_0: term).
0.33/0.94	thf(decl_372, type, esk186_0: term).
0.33/0.94	thf(decl_373, type, esk187_0: term).
0.33/0.94	thf(decl_374, type, esk188_0: term).
0.33/0.94	thf(decl_375, type, esk189_0: term).
0.33/0.94	thf(decl_376, type, esk190_0: term).
0.33/0.94	thf(decl_377, type, esk191_0: term).
0.33/0.94	thf(decl_378, type, esk192_0: term).
0.33/0.94	thf(decl_379, type, esk193_0: term).
0.33/0.94	thf(decl_380, type, esk194_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
0.33/0.94	thf(decl_381, type, esk195_3: (subst > term > subst > $o) > (term > $o) > term > term).
0.33/0.94	thf(decl_382, type, esk196_3: (subst > term > subst > $o) > (term > $o) > term > term).
0.33/0.94	thf(decl_383, type, epred39_0: subst > term > subst > $o).
0.33/0.94	thf(decl_384, type, epred40_0: term > $o).
0.33/0.94	thf(decl_385, type, esk197_0: term).
0.33/0.94	thf(decl_386, type, esk198_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_387, type, esk199_1: (subst > term > term) > term).
0.33/0.94	thf(decl_388, type, esk200_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_389, type, esk201_1: (subst > term > term) > term).
0.33/0.94	thf(decl_390, type, esk202_0: term).
0.33/0.94	thf(decl_391, type, esk203_0: term).
0.33/0.94	thf(decl_392, type, esk204_0: term).
0.33/0.94	thf(decl_393, type, esk205_0: term).
0.33/0.94	thf(decl_394, type, esk206_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
0.33/0.94	thf(decl_395, type, esk207_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
0.33/0.94	thf(decl_396, type, esk208_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
0.33/0.94	thf(decl_397, type, esk209_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
0.33/0.94	thf(decl_398, type, esk210_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
0.33/0.94	thf(decl_399, type, esk211_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
0.33/0.94	thf(decl_400, type, esk212_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
0.33/0.94	thf(decl_401, type, esk213_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
0.33/0.94	thf(decl_402, type, esk214_2: (subst > term > subst > $o) > (term > $o) > term).
0.33/0.94	thf(decl_403, type, esk215_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_404, type, esk216_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_405, type, epred41_0: subst > term > subst > $o).
0.33/0.94	thf(decl_406, type, epred42_0: term > $o).
0.33/0.94	thf(decl_407, type, esk217_0: term).
0.33/0.94	thf(decl_408, type, esk218_0: term).
0.33/0.94	thf(decl_409, type, epred43_0: term > $o).
0.33/0.94	thf(decl_410, type, esk219_0: term).
0.33/0.94	thf(decl_411, type, esk220_1: (term > $o) > term).
0.33/0.94	thf(decl_412, type, esk221_1: (term > $o) > term).
0.33/0.94	thf(decl_413, type, esk222_1: (term > $o) > term).
0.33/0.94	thf(decl_414, type, esk223_1: (term > $o) > term).
0.33/0.94	thf(decl_415, type, esk224_0: term).
0.33/0.94	thf(decl_416, type, esk225_1: term > subst > term > term).
0.33/0.94	thf(decl_417, type, esk226_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_418, type, esk227_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_419, type, esk228_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_420, type, esk229_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_421, type, epred44_0: subst > term > subst > $o).
0.33/0.94	thf(decl_422, type, esk230_0: term).
0.33/0.94	thf(decl_423, type, epred45_0: term > $o).
0.33/0.94	thf(decl_424, type, epred46_0: term > $o).
0.33/0.94	thf(decl_425, type, esk231_0: term).
0.33/0.94	thf(decl_426, type, esk232_0: subst).
0.33/0.94	thf(decl_427, type, esk233_0: term).
0.33/0.94	thf(decl_428, type, esk234_0: subst).
0.33/0.94	thf(decl_429, type, esk235_4: (term > $o) > (term > $o) > term > subst > term).
0.33/0.94	thf(decl_430, type, epred47_0: subst > term > subst > $o).
0.33/0.94	thf(decl_431, type, esk236_0: term).
0.33/0.94	thf(decl_432, type, esk237_1: (subst > term > term) > term).
0.33/0.94	thf(decl_433, type, esk238_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_434, type, esk239_1: (subst > term > term) > term).
0.33/0.94	thf(decl_435, type, esk240_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_436, type, esk241_2: (subst > term > subst > $o) > term > subst).
0.33/0.94	thf(decl_437, type, esk242_2: (subst > term > subst > $o) > term > term).
0.33/0.94	thf(decl_438, type, esk243_2: (subst > term > subst > $o) > term > subst).
0.33/0.94	thf(decl_439, type, esk244_2: (subst > term > subst > $o) > term > subst).
0.33/0.94	thf(decl_440, type, esk245_2: (subst > term > subst > $o) > term > term).
0.33/0.94	thf(decl_441, type, esk246_1: (subst > term > subst > $o) > subst > term > term).
0.33/0.94	thf(decl_442, type, esk247_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_443, type, esk248_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_444, type, esk249_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_445, type, esk250_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_446, type, esk251_2: (subst > term > subst > $o) > term > subst > term > term).
0.33/0.94	thf(decl_447, type, esk252_2: (subst > term > subst > $o) > term > term).
0.33/0.94	thf(decl_448, type, epred48_0: subst > term > subst > $o).
0.33/0.94	thf(decl_449, type, esk253_0: term).
0.33/0.94	thf(decl_450, type, esk254_1: (subst > term > term) > term).
0.33/0.94	thf(decl_451, type, esk255_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_452, type, esk256_1: (subst > term > term) > term).
0.33/0.94	thf(decl_453, type, esk257_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_454, type, epred49_0: subst > term > subst > $o).
0.33/0.94	thf(decl_455, type, esk258_1: (term > $o) > term).
0.33/0.94	thf(decl_456, type, epred50_0: term > $o).
0.33/0.94	thf(decl_457, type, esk259_0: term).
0.33/0.94	thf(decl_458, type, esk260_1: term > term).
0.33/0.94	thf(decl_459, type, esk261_0: term).
0.33/0.94	thf(decl_460, type, epred51_1: (subst > term > subst > $o) > term > $o).
0.33/0.94	thf(decl_461, type, esk262_1: (term > $o) > term).
0.33/0.94	thf(decl_462, type, esk263_1: (term > $o) > term).
0.33/0.94	thf(decl_463, type, esk264_1: (term > $o) > term).
0.33/0.94	thf(decl_464, type, esk265_1: (term > $o) > term).
0.33/0.94	thf(decl_465, type, esk266_1: term > subst > term > term).
0.33/0.94	thf(decl_466, type, esk267_0: term).
0.33/0.94	thf(decl_467, type, esk268_1: (subst > term > term) > term).
0.33/0.94	thf(decl_468, type, esk269_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_469, type, esk270_0: term).
0.33/0.94	thf(decl_470, type, esk271_0: term).
0.33/0.94	thf(decl_471, type, esk272_0: term).
0.33/0.94	thf(decl_472, type, esk273_0: term).
0.33/0.94	thf(decl_473, type, esk274_3: (term > $o) > term > subst > term).
0.33/0.94	thf(decl_474, type, esk275_3: (term > $o) > term > subst > term).
0.33/0.94	thf(decl_475, type, esk276_3: (term > $o) > term > subst > term).
0.33/0.94	thf(decl_476, type, esk277_3: (term > $o) > term > subst > term).
0.33/0.94	thf(decl_477, type, epred52_0: term > $o).
0.33/0.94	thf(decl_478, type, esk278_0: term).
0.33/0.94	thf(decl_479, type, esk279_0: subst).
0.33/0.94	thf(decl_480, type, esk280_1: term > term).
0.33/0.94	thf(decl_481, type, esk281_2: (subst > term > subst > $o) > (term > $o) > term).
0.33/0.94	thf(decl_482, type, esk282_1: subst > d_subst).
0.33/0.94	thf(decl_483, type, epred53_0: subst > term > subst > $o).
0.33/0.94	thf(decl_484, type, epred54_0: term > $o).
0.33/0.94	thf(decl_485, type, esk283_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_486, type, esk284_1: (subst > term > term) > term).
0.33/0.94	thf(decl_487, type, esk285_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_488, type, esk286_1: (subst > term > term) > term).
0.33/0.94	thf(decl_489, type, esk287_0: term).
0.33/0.94	thf(decl_490, type, esk288_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_491, type, esk289_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_492, type, esk290_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_493, type, esk291_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_494, type, esk292_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_495, type, esk293_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_496, type, esk294_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_497, type, esk295_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_498, type, esk296_1: (subst > term > subst > $o) > subst > term > term).
0.33/0.94	thf(decl_499, type, esk297_3: (subst > term > subst > $o) > (term > $o) > term > term).
0.33/0.94	thf(decl_607, type, esk393_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
0.33/0.94	thf(decl_608, type, esk394_3: (subst > term > subst > $o) > (term > $o) > term > term).
0.33/0.94	thf(decl_609, type, esk395_3: (subst > term > subst > $o) > (term > $o) > term > term).
0.33/0.94	thf(decl_610, type, esk396_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_611, type, esk397_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_612, type, esk398_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_613, type, esk399_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_614, type, esk400_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_615, type, esk401_1: (subst > term > subst > $o) > term).
0.33/0.94	thf(decl_616, type, esk402_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_617, type, esk403_1: (subst > term > subst > $o) > subst).
0.33/0.94	thf(decl_618, type, epred67_0: subst > term > subst > $o).
0.33/0.94	thf(decl_619, type, epred68_0: term > $o).
0.33/0.94	thf(decl_620, type, esk404_0: term).
0.33/0.94	thf(decl_621, type, esk405_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_622, type, esk406_1: (subst > term > term) > term).
0.33/0.94	thf(decl_623, type, esk407_1: (subst > term > term) > subst).
0.33/0.94	thf(decl_624, type, esk408_1: (subst > term > term) > term).
0.33/0.94	thf(alg444_1, axiom, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X1:term]:(?[X2:d_term]:(((X1)=(d2term @ X2))))&![X2:d_term]:(((X2)=(d_one))))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(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)=(^[X3:subst, X4:subst > term > term]:(d2term @ d_one))))&((pushprop_p_and_p_prime)=(^[X5:term, X6:subst, X7:term > $o, X8:term > $o]:(![X9:term]:((((X8 @ X9))<=>((X7 @ (sub @ X9 @ (push @ X5 @ X6))))))))))&~((var @ (d2term @ d_one))))&((pushprop_lem1v2)<=>![X7:term > $o, X8:term > $o, X5:term, X6:subst]:((~((X7 @ X5))|~(![X9:term]:(((X8 @ X9)<=>(X7 @ (sub @ X9 @ (push @ X5 @ X6))))))|(X8 @ one)))))&(pushprop_lem1_gthm))&((shinj)<=>![X5:term, X10:term]:((((sub @ X5 @ sh)!=(sub @ X10 @ sh))|((X5)=(X10))))))&(hoasinduction_lem1v2))&(![X10:term]:(~(![X11:subst > term > term]:(~(![X5:term, X6:subst]:(((sub @ X10 @ (push @ X5 @ X6))=(X11 @ X6 @ X5)))))))<=>(hoasinduction_lem3v2_f)))&(hoasapnotvar_gthm))&(![X5:term, X10:term, X12:term, X13:term]:((((ap @ (sub @ X5 @ id) @ X12)!=(ap @ (sub @ X10 @ id) @ X13))|((X5)=(X10))))<=>(hoasapinj1)))&((induction2lem_lthm)<=>(![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6))))=>(![X5:term, X6:subst]:(((X6)=(comp @ sh @ (push @ X5 @ X6))))=>((![X7:term > $o, X14:term, X15:subst]:((~(![X5:term, X10:term]:(((X7 @ (ap @ X5 @ X10))|~((X7 @ X10))|~((X7 @ X5)))))|~(![X5:term]:((~(![X10:term]:(((X7 @ (sub @ X5 @ (push @ X10 @ id)))|~((X7 @ X10)))))|(X7 @ (lam @ X5)))))|(X7 @ (sub @ X14 @ X15))|~(![X10:term]:(((X7 @ (sub @ X10 @ X15))|~((var @ X10)))))))<=![X7:term > $o, X16:term]:((~(![X5:term]:(((X7 @ X5)|~((var @ X5)))))|~(![X5:term, X10:term]:(((X7 @ (ap @ X5 @ X10))|~((X7 @ X10))|~((X7 @ X5)))))|~(![X5:term]:(((X7 @ (lam @ X5))|~((X7 @ X5)))))|(X7 @ X16))))<=![X6:subst]:(((X6)=(comp @ X6 @ id))))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&(![X11:subst > term > term, X17:subst > term > term, X18:subst, X19:term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X17 @ X6 @ X5) @ X20)=(X17 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|((X11 @ X18 @ X19)=(X17 @ X18 @ X19))|((lam @ (X11 @ sh @ one))!=(lam @ (X17 @ sh @ one)))|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))))<=>(hoaslaminj)))&((hoasinduction_lem3aaa)<=>![X21:subst > term > subst > $o, X22:term]:((~(![X11:subst > term > term, X23:term]:(((X21 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X24:subst, X25:term, X26:subst]:(((X11 @ (comp @ X24 @ X26) @ (sub @ X25 @ X26))=(sub @ X23 @ (push @ (sub @ X25 @ X26) @ (comp @ X24 @ X26))))))|~(![X27:subst, X28:term, X29:subst]:(((sub @ (X11 @ X27 @ X28) @ X29)=(sub @ (sub @ X23 @ (push @ X28 @ X27)) @ X29))))|~(![X5:term]:((~((X21 @ id @ X5 @ id))|(X21 @ id @ (X11 @ id @ X5) @ id)))))))|(X21 @ id @ (lam @ (sub @ X22 @ (push @ one @ sh))) @ id)|~(![X10:term]:((~((X21 @ id @ X10 @ id))|(X21 @ id @ (sub @ X22 @ (push @ X10 @ id)) @ id))))))))&(![X30:subst > term > subst > $o, X31:term, X32:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X30 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X30 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X30 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X30 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))|~((X30 @ id @ X32 @ id))|(X30 @ id @ (ap @ X31 @ X32) @ id)|~((X30 @ id @ X31 @ id))|~(![X5:term, X10:term]:((~((X30 @ id @ X5 @ id))|(X30 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X30 @ id @ X10 @ id)))))))<=>(hoasinduction_lem2)))&((![X5:term]:(((X5)=(sub @ X5 @ id)))=>![X5:term]:(((X5)=(sub @ X5 @ id))))<=>(termmset_lthm)))&(hoasinduction_lem1))&(![X34:subst > term > subst > $o]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X34 @ id @ X9 @ id)))))))<=>(hoasinduction_lem0)))&(hoaslamnotvar_lthm))&(pushprop_lem3v2_lthm))&(ulamvarind))&((hoasinduction_lem3a_lthm)<=>((![X35:subst > term > subst > $o, X36:term]:((~(![X10:term]:(((X35 @ id @ (sub @ X36 @ (push @ X10 @ id)) @ id)|~((X35 @ id @ X10 @ id)))))|(X35 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X35 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X35 @ id @ (X11 @ id @ X5) @ id)|~((X35 @ id @ X5 @ id))))))))))=>![X37:subst > term > subst > $o, X38:term]:((~(![X10:term]:(((X37 @ id @ (sub @ X38 @ (push @ X10 @ id)) @ id)|~((X37 @ id @ X10 @ id)))))|(X37 @ id @ (lam @ X38) @ id)|~(![X11:subst > term > term]:((~(![X5:term]:((~((X37 @ id @ X5 @ id))|(X37 @ id @ (X11 @ id @ X5) @ id))))|(X37 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))))))))<=![X5:term]:(((X5)=(sub @ X5 @ id))))))&(termmset_gthm))&((hoasinduction_lem3aa)<=>![X39:subst > term > subst > $o, X36:term]:((~(![X11:subst > term > term]:((~(![X5:term]:((~((X39 @ id @ X5 @ id))|(X39 @ id @ (X11 @ id @ X5) @ id))))|(X39 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|~(![X10:term]:(((X39 @ id @ (sub @ X36 @ (push @ X10 @ id)) @ id)|~((X39 @ id @ X10 @ id)))))|(X39 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)))))&(hoasinduction_lem3a_gthm))&(axclos))&((apinj1)<=>![X5:term, X10:term, X12:term, X13:term]:((((X5)=(X10))|((ap @ X5 @ X12)!=(ap @ X10 @ X13))))))&((hoasapinj2_lthm)<=>(![X5:term, X10:term, X12:term, X13:term]:((((X12)=(X13))|((ap @ (sub @ X5 @ id) @ X12)!=(ap @ (sub @ X10 @ id) @ X13))))<=![X5:term, X10:term, X12:term, X13:term]:((((X12)=(X13))|((ap @ X5 @ X12)!=(ap @ X10 @ X13)))))))&(![X6:subst]:(((X6)=(push @ (sub @ one @ X6) @ (comp @ sh @ X6))))<=>(axscons)))&(hoasinduction_lem2v2_gthm))&((axidr)<=>![X6:subst]:(((X6)=(comp @ X6 @ id)))))&(((![X40:subst > term > subst > $o, X36:term]:((~(![X10:term]:((~((X40 @ id @ X10 @ id))|(X40 @ id @ (sub @ X36 @ (push @ X10 @ id)) @ id))))|(X40 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:(((X40 @ id @ (X11 @ id @ X5) @ id)|~((X40 @ id @ X5 @ id)))))|(X40 @ id @ (lam @ (X11 @ sh @ one)) @ id))))))=>![X41:subst > term > subst > $o, X42:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X41 @ X6 @ X5 @ (comp @ X33 @ X20)))|(X41 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))))|~(![X10:term]:(((X41 @ id @ (sub @ X42 @ (push @ X10 @ id)) @ id)|~((X41 @ id @ X10 @ id)))))|(X41 @ id @ (lam @ X42) @ id)|~(![X11:subst > term > term]:((~(![X5:term]:(((X41 @ id @ (X11 @ id @ X5) @ id)|~((X41 @ id @ X5 @ id)))))|(X41 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X41 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X41 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))))))))<=![X5:term]:(((X5)=(sub @ X5 @ id))))<=>(hoasinduction_lem3_lthm)))&((pushprop_lem0)<=>![X7:term > $o, X5:term, X6:subst]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X7 @ (sub @ X9 @ (push @ X5 @ X6)))))))))))&((hoasinduction_lem3v2a_lthm)<=>((![X5:term]:(((X5)=(sub @ X5 @ id)))=>![X43:subst > term > subst > $o, X8:term > $o, X44:term]:((~(![X9:term]:(((X8 @ X9)<=>(X43 @ id @ X9 @ id))))|(X8 @ (lam @ X44))|~(![X10:term]:(((X8 @ (sub @ X44 @ (push @ X10 @ id)))|~((X8 @ X10)))))|~(![X11:subst > term > term]:(((X43 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X43 @ id @ (X11 @ id @ X5) @ id)|~((X43 @ id @ X5 @ id)))))|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))))))))<=![X10:term]:(~(![X11:subst > term > term]:(~(![X5:term, X6:subst]:(((sub @ X10 @ (push @ X5 @ X6))=(X11 @ X6 @ X5))))))))))&(hoasinduction_lem1_lthm))&~((lamnotap)))&(hoasapinj1_gthm))&(hoaslamnotvar))&(hoaslaminj_gthm))&(((![X7:term > $o, X45:term]:((~(![X5:term]:(((X7 @ X5)|~((var @ X5)))))|~(![X5:term, X10:term]:((~((X7 @ X10))|(X7 @ (ap @ X5 @ X10))|~((X7 @ X5)))))|(X7 @ X45)|~(![X5:term]:((~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id))))))|(X7 @ (lam @ X5)))))))<=![X7:term > $o, X14:term, X15:subst]:((~(![X5:term, X10:term]:((~((X7 @ X5))|~((X7 @ X10))|(X7 @ (ap @ X5 @ X10)))))|(X7 @ (sub @ X14 @ X15))|~(![X10:term]:((~((var @ X10))|(X7 @ (sub @ X10 @ X15)))))|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id))))))))))))<=![X5:term]:(((X5)=(sub @ X5 @ id))))<=>(induction2_lthm)))&(pushprop))&(![X10:term]:(~(![X11:subst > term > term]:(((X11 @ sh @ one)!=(sub @ X10 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b)))&~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))&(![X11:subst > term > term, X46:term, X47:term]:((((lam @ (X11 @ sh @ one))!=(ap @ (sub @ X46 @ id) @ X47))|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))))<=>(hoaslamnotap)))&(ulamvarsh))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((axshiftcons)<=>![X5:term, X6:subst]:(((X6)=(comp @ sh @ (push @ X5 @ X6))))))&(![X7:term > $o, X5:term, X6:subst]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X7 @ (sub @ X9 @ (push @ X5 @ X6)))))))))<=>(pushprop_lem0_lthm)))&(![X5:term]:(((X5)=(sub @ X5 @ id)))<=>(axvarid)))&((hoasinduction_lthm_3)<=>(((![X5:term]:(((X5)=(sub @ X5 @ id)))=>(![X48:subst > term > subst > $o, X8:term > $o, X44:term]:((~(![X9:term]:(((X8 @ X9)<=>(X48 @ id @ X9 @ id))))|(X8 @ (lam @ X44))|~(![X10:term]:((~((X8 @ X10))|(X8 @ (sub @ X44 @ (push @ X10 @ id))))))|~(![X11:subst > term > term]:((~(![X5:term]:(((X48 @ id @ (X11 @ id @ X5) @ id)|~((X48 @ id @ X5 @ id)))))|(X48 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))))=>![X49:subst > term > subst > $o, X50:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X49 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X49 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X49 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))|(X49 @ X6 @ X5 @ (comp @ X33 @ X20)))))|~(![X5:term, X10:term]:((~((X49 @ id @ X5 @ id))|~((X49 @ id @ X10 @ id))|(X49 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id))))|(X49 @ id @ X50 @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:((~((X49 @ id @ X5 @ id))|(X49 @ id @ (X11 @ id @ X5) @ id))))|(X49 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X5:term]:((~((var @ (sub @ X5 @ id)))|(X49 @ id @ X5 @ id))))))))<=![X7:term > $o, X45:term]:((~(![X5:term, X10:term]:((~((X7 @ X5))|~((X7 @ X10))|(X7 @ (ap @ X5 @ X10)))))|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id)))))))))|(X7 @ X45)|~(![X5:term]:(((X7 @ X5)|~((var @ X5))))))))<=![X51:subst > term > subst > $o]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X51 @ id @ X9 @ id))))))))))&((hoasinduction_lem3v2_lthm)<=>(![X5:term]:(((X5)=(sub @ X5 @ id)))=>![X52:subst > term > subst > $o, X8:term > $o, X53:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X52 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X52 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X52 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X52 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))|~(![X9:term]:(((X8 @ X9)<=>(X52 @ id @ X9 @ id))))|(X8 @ (lam @ X53))|~(![X10:term]:((~((X8 @ X10))|(X8 @ (sub @ X53 @ (push @ X10 @ id))))))|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:((~((X52 @ id @ X5 @ id))|(X52 @ id @ (X11 @ id @ X5) @ id))))|(X52 @ id @ (lam @ (X11 @ sh @ one)) @ id)))))))))&(hoasapnotvar_lthm))&((termmset)<=>![X5:term]:(((X5)=(sub @ X5 @ id)))))&(![X54:subst > term > subst > $o, X8:term > $o, X53:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:(((X54 @ id @ (X11 @ id @ X5) @ id)|~((X54 @ id @ X5 @ id)))))|(X54 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X9:term]:(((X8 @ X9)<=>(X54 @ id @ X9 @ id))))|~(![X10:term]:(((X8 @ (sub @ X53 @ (push @ X10 @ id)))|~((X8 @ X10)))))|(X8 @ (lam @ X53))|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X54 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))|(X54 @ X6 @ X5 @ (comp @ X33 @ X20)))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X54 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X54 @ X6 @ X5 @ (comp @ X33 @ X20))))))))<=>(hoasinduction_lem3v2)))&((pushprop_lem1_lthm)<=>((![X7:term > $o, X55:term > $o, X5:term, X6:subst, X10:term]:(((X55 @ (sub @ X5 @ (push @ X10 @ X6)))|~((X7 @ X5))))<=![X5:term, X6:subst]:(((X6)=(comp @ sh @ (push @ X5 @ X6)))))<=![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6)))))))&(![X7:term > $o, X45:term]:((~(![X5:term]:(((X7 @ X5)|~((var @ X5)))))|(X7 @ X45)|~(![X5:term]:((~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id))))))|(X7 @ (lam @ X5)))))|~(![X5:term, X10:term]:(((X7 @ (ap @ X5 @ X10))|~((X7 @ X10))|~((X7 @ X5)))))))<=>(induction2)))&(substmonoid_gthm))&(pushprop_lem2v2_lthm))&(induction2_gthm))&((hoasinduction_no_psi_cond)<=>![X56:subst > term > subst > $o, X57:term]:((~(![X5:term, X10:term]:(((X56 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X56 @ id @ X10 @ id))|~((X56 @ id @ X5 @ id)))))|~(![X11:subst > term > term]:((~(![X5:term]:(((X56 @ id @ (X11 @ id @ X5) @ id)|~((X56 @ id @ X5 @ id)))))|(X56 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|(X56 @ id @ X57 @ id)))))&(hoasinduction_lem1_gthm))&((hoasinduction_lem3a)<=>![X58:subst > term > subst > $o, X38:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X58 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X58 @ id @ (X11 @ id @ X5) @ id)|~((X58 @ id @ X5 @ id))))))))|~(![X10:term]:(((X58 @ id @ (sub @ X38 @ (push @ X10 @ id)) @ id)|~((X58 @ id @ X10 @ id)))))|(X58 @ id @ (lam @ X38) @ id)))))&(lamnotvar))&((substmonoid)<=>(![X6:subst]:(((X6)=(comp @ id @ X6)))&![X6:subst]:(((X6)=(comp @ X6 @ id))))))&(hoasinduction_lem2_gthm))&(hoasinduction_lem3_gthm))&((![X6:subst]:(((X6)=(comp @ id @ X6)))=>(![X6:subst]:(((X6)=(comp @ X6 @ id)))=>(![X6:subst]:(((X6)=(comp @ id @ X6)))&![X6:subst]:(((X6)=(comp @ X6 @ id))))))<=>(substmonoid_lthm)))&(![X59:subst > term > subst > $o]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X59 @ id @ X9 @ id)))))))<=>(hoasinduction_lem0_lthm)))&((axidl)<=>![X6:subst]:(((X6)=(comp @ id @ X6)))))&(hoasapinj2_gthm))&(hoasinduction_lem2_lthm))&(axabs))&(pushprop_gthm))&((laminj)<=>![X5:term, X10:term]:((((lam @ X5)!=(lam @ X10))|((X5)=(X10))))))&((pushprop_lem1)<=>![X7:term > $o, X60:term > $o, X5:term, X6:subst, X10:term]:(((X60 @ (sub @ X5 @ (push @ X10 @ X6)))|~((X7 @ X5))))))&((axvarcons)<=>![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6))))))&((hoaslaminj_lthm)<=>((![X5:term, X6:subst]:(((X6)=(comp @ sh @ (push @ X5 @ X6))))=>(![X5:term, X10:term]:((((lam @ X5)!=(lam @ X10))|((X5)=(X10))))=>![X11:subst > term > term, X17:subst > term > term, X18:subst, X19:term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|((X11 @ X18 @ X19)=(X17 @ X18 @ X19))|((lam @ (X11 @ sh @ one))!=(lam @ (X17 @ sh @ one)))|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X17 @ X6 @ X5) @ X20)=(X17 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))))))<=![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6)))))))&((![X5:term]:(((X5)=(sub @ X5 @ id)))=>(![X5:term, X10:term, X12:term, X13:term]:((((ap @ X5 @ X12)!=(ap @ X10 @ X13))|((X5)=(X10))))=>![X5:term, X10:term, X12:term, X13:term]:((((ap @ (sub @ X5 @ id) @ X12)!=(ap @ (sub @ X10 @ id) @ X13))|((X5)=(X10))))))<=>(hoasapinj1_lthm)))&((hoasinduction_lem3v2a)<=>![X61:subst > term > subst > $o, X8:term > $o, X44:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:(((X61 @ id @ (X11 @ id @ X5) @ id)|~((X61 @ id @ X5 @ id)))))|(X61 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X9:term]:(((X8 @ X9)<=>(X61 @ id @ X9 @ id))))|(X8 @ (lam @ X44))|~(![X10:term]:((~((X8 @ X10))|(X8 @ (sub @ X44 @ (push @ X10 @ id))))))))))&(![X5:term, X10:term, X12:term, X13:term]:((((ap @ X5 @ X12)!=(ap @ X10 @ X13))|((X12)=(X13))))<=>(apinj2)))&(pushprop_lthm))&((hoasinduction_lem2v2)<=>![X62:subst > term > subst > $o, X8:term > $o, X63:term, X64:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X62 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X62 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X62 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))|(X62 @ X6 @ X5 @ (comp @ X33 @ X20)))))|~((X8 @ X63))|(X8 @ (ap @ X63 @ X64))|~((X8 @ X64))|~(![X9:term]:(((X8 @ X9)<=>(X62 @ id @ X9 @ id))))|~(![X5:term, X10:term]:(((X62 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X62 @ id @ X10 @ id))|~((X62 @ id @ X5 @ id)))))))))&(axassoc))&(pushprop_lem2v2))&(hoasinduction_lem3b_gthm))&(hoaslamnotvar_gthm))&(hoaslamnotap_gthm))&(pushprop_lem1v2_gthm))&(![X7:term > $o, X16:term]:(((X7 @ X16)|~(![X5:term]:(((X7 @ (lam @ X5))|~((X7 @ X5)))))|~(![X5:term, X10:term]:((~((X7 @ X5))|(X7 @ (ap @ X5 @ X10))|~((X7 @ X10)))))|~(![X5:term]:((~((var @ X5))|(X7 @ X5))))))<=>(induction)))&(![X10:term]:(~(![X11:subst > term > term]:(((X11 @ sh @ one)!=(sub @ X10 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b_lthm)))&(axapp))&(hoasinduction_gthm))&((hoasinduction)<=>![X65:subst > term > subst > $o, X50:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X65 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X65 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))|~(![X5:term, X10:term]:((~((X65 @ id @ X5 @ id))|(X65 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X65 @ id @ X10 @ id)))))|(X65 @ id @ X50 @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X65 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X65 @ id @ (X11 @ id @ X5) @ id)|~((X65 @ id @ X5 @ id))))))))|~(![X5:term]:((~((var @ (sub @ X5 @ id)))|(X65 @ id @ X5 @ id))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X65 @ X6 @ X5 @ (comp @ X33 @ X20)))|(X65 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))))))))&(hoasapnotvar))&((![X7:term > $o, X8:term > $o, X5:term, X6:subst]:((~(![X9:term]:(((X8 @ X9)<=>(X7 @ (sub @ X9 @ (push @ X5 @ X6))))))|(X8 @ one)|~((X7 @ X5))))<=![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6)))))<=>(pushprop_lem1v2_lthm)))&(hoaslamnotap_lthm))&(![X66:subst > term > subst > $o, X42:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X66 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X66 @ X6 @ X5 @ (comp @ X33 @ X20))))))|(X66 @ id @ (lam @ X42) @ id)|~(![X10:term]:((~((X66 @ id @ X10 @ id))|(X66 @ id @ (sub @ X42 @ (push @ X10 @ id)) @ id))))|~(![X11:subst > term > term]:((~(![X5:term]:(((X66 @ id @ (X11 @ id @ X5) @ id)|~((X66 @ id @ X5 @ id)))))|(X66 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X66 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X66 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))))<=>(hoasinduction_lem3)))&((hoasinduction_lem3aa_lthm)<=>![X67:subst > term > subst > $o, X36:term]:((~(![X11:subst > term > term]:((~(![X5:term]:(((X67 @ id @ (X11 @ id @ X5) @ id)|~((X67 @ id @ X5 @ id)))))|(X67 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|(X67 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X10:term]:((~((X67 @ id @ X10 @ id))|(X67 @ id @ (sub @ X36 @ (push @ X10 @ id)) @ id))))))))&(induction2lem_gthm))&((hoasinduction_no_psi_cond_lthm)<=>((((![X68:subst > term > subst > $o, X8:term > $o, X44:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X68 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X68 @ id @ (X11 @ id @ X5) @ id)|~((X68 @ id @ X5 @ id))))))))|(X8 @ (lam @ X44))|~(![X10:term]:(((X8 @ (sub @ X44 @ (push @ X10 @ id)))|~((X8 @ X10)))))|~(![X9:term]:(((X8 @ X9)<=>(X68 @ id @ X9 @ id))))))=>![X69:subst > term > subst > $o, X57:term]:(((X69 @ id @ X57 @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:((~((X69 @ id @ X5 @ id))|(X69 @ id @ (X11 @ id @ X5) @ id))))|(X69 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X5:term, X10:term]:((~((X69 @ id @ X5 @ id))|~((X69 @ id @ X10 @ id))|(X69 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)))))))<=![X5:term]:(((X5)=(sub @ X5 @ id))))<=![X7:term > $o, X45:term]:((~(![X5:term]:((~((var @ X5))|(X7 @ X5))))|(X7 @ X45)|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id)))))))))|~(![X5:term, X10:term]:((~((X7 @ X10))|(X7 @ (ap @ X5 @ X10))|~((X7 @ X5))))))))<=![X70:subst > term > subst > $o]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X70 @ id @ X9 @ id))))))))))&((hoasinduction_lthm)<=>(![X7:term > $o, X45:term]:((~(![X5:term]:((~((var @ X5))|(X7 @ X5))))|~(![X5:term, X10:term]:((~((X7 @ X5))|(X7 @ (ap @ X5 @ X10))|~((X7 @ X10)))))|(X7 @ X45)|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id)))))))))))=>(![X71:subst > term > subst > $o, X31:term, X32:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X71 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X71 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~((X71 @ id @ X31 @ id))|~((X71 @ id @ X32 @ id))|(X71 @ id @ (ap @ X31 @ X32) @ id)|~(![X5:term, X10:term]:(((X71 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X71 @ id @ X10 @ id))|~((X71 @ id @ X5 @ id)))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X71 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X71 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))))=>(![X72:subst > term > subst > $o, X50:term]:((~(![X5:term]:(((X72 @ id @ X5 @ id)|~((var @ (sub @ X5 @ id))))))|~(![X5:term, X10:term]:((~((X72 @ id @ X5 @ id))|~((X72 @ id @ X10 @ id))|(X72 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id))))|(X72 @ id @ X50 @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:((~((X72 @ id @ X5 @ id))|(X72 @ id @ (X11 @ id @ X5) @ id))))|(X72 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X72 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X72 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X72 @ X6 @ X5 @ (comp @ X33 @ X20)))|(X72 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))))))<=![X73:subst > term > subst > $o, X42:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X73 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X73 @ id @ (X11 @ id @ X5) @ id)|~((X73 @ id @ X5 @ id))))))))|~(![X10:term]:((~((X73 @ id @ X10 @ id))|(X73 @ id @ (sub @ X42 @ (push @ X10 @ id)) @ id))))|(X73 @ id @ (lam @ X42) @ id)|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X73 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))|(X73 @ X6 @ X5 @ (comp @ X33 @ X20)))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X73 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X73 @ X6 @ X5 @ (comp @ X33 @ X20)))))))))))))&((hoasinduction_lem3v2_f_lthm)<=>![X10:term]:(~(![X11:subst > term > term]:(~(![X5:term, X6:subst]:(((sub @ X10 @ (push @ X5 @ X6))=(X11 @ X6 @ X5)))))))))&~((ulamvar1)))&((hoasapinj2)<=>![X5:term, X10:term, X12:term, X13:term]:((((X12)=(X13))|((ap @ (sub @ X5 @ id) @ X12)!=(ap @ (sub @ X10 @ id) @ X13))))))&(axvarshift))&((induction2lem)<=>![X7:term > $o, X14:term, X15:subst]:((~(![X5:term, X10:term]:((~((X7 @ X5))|~((X7 @ X10))|(X7 @ (ap @ X5 @ X10)))))|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:(((X7 @ (sub @ X5 @ (push @ X10 @ id)))|~((X7 @ X10))))))))|(X7 @ (sub @ X14 @ X15))|~(![X10:term]:((~((var @ X10))|(X7 @ (sub @ X10 @ X15)))))))))&(hoasinduction_lem1v2_gthm))&(pushprop_lem0_gthm))&(axmap))&((hoasinduction_p_and_p_prime)=(^[X74:subst > term > subst > $o, X8:term > $o]:(![X9:term]:((((X8 @ X9))<=>((X74 @ id @ X9 @ id))))))))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((one)=(d2term @ d_one)))&![X75:d_subst, X76:d_subst]:((((d2subst @ X75)=(d2subst @ X76))=>((X75)=(X76)))))&![X77:d_subst]:(((X77)=(d_id))))&![X78:subst]:(?[X77:d_subst]:(((X78)=(d2subst @ X77)))))&![X79:d_term, X80:d_term]:((((X79)=(X80))<=((d2term @ X79)=(d2term @ X80))))), file('/export/starexec/sandbox/tmp/tmp.yrpyPezLI8/E---3.1_2727653.p', alg444_1)).
0.33/0.94	thf(hoasinduction_lem3v2, conjecture, ((hoasinduction_lem3v2)<=>![X81:subst > term > subst > $o, X8:term > $o]:((![X6:subst, X5:term, X20:subst, X33:subst]:(((X81 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)<=(X81 @ X6 @ X5 @ (comp @ X33 @ X20))))=>(![X6:subst, X5:term, X20:subst, X33:subst]:(((X81 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)=>(X81 @ X6 @ X5 @ (comp @ X33 @ X20))))=>(![X11:subst > term > term]:((((X81 @ id @ (hoaslam @ id @ (^[X6:subst, X5:term]:(X11 @ X6 @ X5))) @ id)<=![X5:term]:(((X81 @ id @ (X11 @ id @ X5) @ id)<=(X81 @ id @ X5 @ id))))<=![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))=>(![X5:term]:(((X8 @ (lam @ X5))<=![X10:term]:(((X8 @ (sub @ X5 @ (push @ X10 @ id)))<=(X8 @ X10)))))<=(hoasinduction_p_and_p_prime @ X81 @ X8))))))), file('/export/starexec/sandbox/tmp/tmp.yrpyPezLI8/E---3.1_2727653.p', hoasinduction_lem3v2)).
0.33/0.94	thf(c_0_2, plain, ((epred1_0)<=>(![X7:term > $o, X16:term]:((~(![X5:term]:(((X7 @ X5)|~(var @ X5))))|~(![X5:term, X10:term]:(((X7 @ (ap @ X5 @ X10))|~((X7 @ X10))|~((X7 @ X5)))))|~(![X5:term]:(((X7 @ (lam @ X5))|~((X7 @ X5)))))|(X7 @ X16)))=>![X7:term > $o, X14:term, X15:subst]:((~(![X5:term, X10:term]:(((X7 @ (ap @ X5 @ X10))|~((X7 @ X10))|~((X7 @ X5)))))|~(![X5:term]:((~(![X10:term]:(((X7 @ (sub @ X5 @ (push @ X10 @ id)))|~((X7 @ X10)))))|(X7 @ (lam @ X5)))))|(X7 @ (sub @ X14 @ X15))|~(![X10:term]:(((X7 @ (sub @ X10 @ X15))|~(var @ X10)))))))), introduced(definition)).
0.33/0.94	thf(c_0_3, plain, ((epred2_0)<=>(![X40:subst > term > subst > $o, X36:term]:((~(![X10:term]:((~((X40 @ id @ X10 @ id))|(X40 @ id @ (sub @ X36 @ (push @ X10 @ id)) @ id))))|(X40 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:(((X40 @ id @ (X11 @ id @ X5) @ id)|~((X40 @ id @ X5 @ id)))))|(X40 @ id @ (lam @ (X11 @ sh @ one)) @ id))))))=>![X41:subst > term > subst > $o, X42:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X41 @ X6 @ X5 @ (comp @ X33 @ X20)))|(X41 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))))|~(![X10:term]:(((X41 @ id @ (sub @ X42 @ (push @ X10 @ id)) @ id)|~((X41 @ id @ X10 @ id)))))|(X41 @ id @ (lam @ X42) @ id)|~(![X11:subst > term > term]:((~(![X5:term]:(((X41 @ id @ (X11 @ id @ X5) @ id)|~((X41 @ id @ X5 @ id)))))|(X41 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X41 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X41 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))))))))), introduced(definition)).
0.33/0.94	thf(c_0_4, plain, ((epred3_0)<=>(![X7:term > $o, X14:term, X15:subst]:((~(![X5:term, X10:term]:((~((X7 @ X5))|~((X7 @ X10))|(X7 @ (ap @ X5 @ X10)))))|(X7 @ (sub @ X14 @ X15))|~(![X10:term]:((~(var @ X10)|(X7 @ (sub @ X10 @ X15)))))|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id)))))))))))=>![X7:term > $o, X45:term]:((~(![X5:term]:(((X7 @ X5)|~(var @ X5))))|~(![X5:term, X10:term]:((~((X7 @ X10))|(X7 @ (ap @ X5 @ X10))|~((X7 @ X5)))))|(X7 @ X45)|~(![X5:term]:((~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id))))))|(X7 @ (lam @ X5))))))))), introduced(definition)).
0.33/0.94	thf(c_0_5, plain, ((epred5_0)<=>(![X7:term > $o, X45:term]:((~(![X5:term, X10:term]:((~((X7 @ X5))|~((X7 @ X10))|(X7 @ (ap @ X5 @ X10)))))|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id)))))))))|(X7 @ X45)|~(![X5:term]:(((X7 @ X5)|~(var @ X5))))))=>(![X5:term]:(((X5)=(sub @ X5 @ id)))=>(![X48:subst > term > subst > $o, X8:term > $o, X44:term]:((~(![X9:term]:(((X8 @ X9)<=>(X48 @ id @ X9 @ id))))|(X8 @ (lam @ X44))|~(![X10:term]:((~((X8 @ X10))|(X8 @ (sub @ X44 @ (push @ X10 @ id))))))|~(![X11:subst > term > term]:((~(![X5:term]:(((X48 @ id @ (X11 @ id @ X5) @ id)|~((X48 @ id @ X5 @ id)))))|(X48 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))))=>![X49:subst > term > subst > $o, X50:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X49 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X49 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X49 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))|(X49 @ X6 @ X5 @ (comp @ X33 @ X20)))))|~(![X5:term, X10:term]:((~((X49 @ id @ X5 @ id))|~((X49 @ id @ X10 @ id))|(X49 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id))))|(X49 @ id @ X50 @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:((~((X49 @ id @ X5 @ id))|(X49 @ id @ (X11 @ id @ X5) @ id))))|(X49 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X5:term]:((~(var @ (sub @ X5 @ id))|(X49 @ id @ X5 @ id)))))))))), introduced(definition)).
0.33/0.94	thf(c_0_6, plain, ((epred6_0)<=>![X52:subst > term > subst > $o, X8:term > $o, X53:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X52 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X52 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X52 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X52 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))|~(![X9:term]:(((X8 @ X9)<=>(X52 @ id @ X9 @ id))))|(X8 @ (lam @ X53))|~(![X10:term]:((~((X8 @ X10))|(X8 @ (sub @ X53 @ (push @ X10 @ id))))))|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:((~((X52 @ id @ X5 @ id))|(X52 @ id @ (X11 @ id @ X5) @ id))))|(X52 @ id @ (lam @ (X11 @ sh @ one)) @ id))))))), introduced(definition)).
0.33/0.94	thf(c_0_7, plain, ((epred7_0)<=>![X54:subst > term > subst > $o, X8:term > $o, X53:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:(((X54 @ id @ (X11 @ id @ X5) @ id)|~((X54 @ id @ X5 @ id)))))|(X54 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X9:term]:(((X8 @ X9)<=>(X54 @ id @ X9 @ id))))|~(![X10:term]:(((X8 @ (sub @ X53 @ (push @ X10 @ id)))|~((X8 @ X10)))))|(X8 @ (lam @ X53))|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X54 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))|(X54 @ X6 @ X5 @ (comp @ X33 @ X20)))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X54 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X54 @ X6 @ X5 @ (comp @ X33 @ X20))))))))), introduced(definition)).
0.33/0.94	thf(c_0_8, plain, ![X50:term, X65:subst > term > subst > $o]:(((epred8_2 @ X65 @ X50)<=>(~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X65 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X65 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))|~(![X5:term, X10:term]:((~((X65 @ id @ X5 @ id))|(X65 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X65 @ id @ X10 @ id)))))|(X65 @ id @ X50 @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X65 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X65 @ id @ (X11 @ id @ X5) @ id)|~((X65 @ id @ X5 @ id))))))))|~(![X5:term]:((~(var @ (sub @ X5 @ id))|(X65 @ id @ X5 @ id))))))), introduced(definition)).
0.33/0.94	thf(c_0_9, plain, ((epred9_0)<=>(![X68:subst > term > subst > $o, X8:term > $o, X44:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X68 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X68 @ id @ (X11 @ id @ X5) @ id)|~((X68 @ id @ X5 @ id))))))))|(X8 @ (lam @ X44))|~(![X10:term]:(((X8 @ (sub @ X44 @ (push @ X10 @ id)))|~((X8 @ X10)))))|~(![X9:term]:(((X8 @ X9)<=>(X68 @ id @ X9 @ id))))))=>![X69:subst > term > subst > $o, X57:term]:(((X69 @ id @ X57 @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:((~((X69 @ id @ X5 @ id))|(X69 @ id @ (X11 @ id @ X5) @ id))))|(X69 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X5:term, X10:term]:((~((X69 @ id @ X5 @ id))|~((X69 @ id @ X10 @ id))|(X69 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)))))))), introduced(definition)).
0.33/0.94	thf(c_0_10, plain, ((epred12_0)<=>(![X7:term > $o, X45:term]:((~(![X5:term]:((~(var @ X5)|(X7 @ X5))))|~(![X5:term, X10:term]:((~((X7 @ X5))|(X7 @ (ap @ X5 @ X10))|~((X7 @ X10)))))|(X7 @ X45)|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id)))))))))))=>(![X71:subst > term > subst > $o, X31:term, X32:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X71 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X71 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~((X71 @ id @ X31 @ id))|~((X71 @ id @ X32 @ id))|(X71 @ id @ (ap @ X31 @ X32) @ id)|~(![X5:term, X10:term]:(((X71 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X71 @ id @ X10 @ id))|~((X71 @ id @ X5 @ id)))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X71 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X71 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))))=>(![X73:subst > term > subst > $o, X42:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X73 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X73 @ id @ (X11 @ id @ X5) @ id)|~((X73 @ id @ X5 @ id))))))))|~(![X10:term]:((~((X73 @ id @ X10 @ id))|(X73 @ id @ (sub @ X42 @ (push @ X10 @ id)) @ id))))|(X73 @ id @ (lam @ X42) @ id)|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X73 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))|(X73 @ X6 @ X5 @ (comp @ X33 @ X20)))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X73 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X73 @ X6 @ X5 @ (comp @ X33 @ X20))))))))=>![X72:subst > term > subst > $o, X50:term]:((~(![X5:term]:(((X72 @ id @ X5 @ id)|~(var @ (sub @ X5 @ id)))))|~(![X5:term, X10:term]:((~((X72 @ id @ X5 @ id))|~((X72 @ id @ X10 @ id))|(X72 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id))))|(X72 @ id @ X50 @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:((~((X72 @ id @ X5 @ id))|(X72 @ id @ (X11 @ id @ X5) @ id))))|(X72 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X72 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X72 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X72 @ X6 @ X5 @ (comp @ X33 @ X20)))|(X72 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))))))), introduced(definition)).
0.33/0.94	thf(c_0_11, plain, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X1:term]:(?[X2:d_term]:(((X1)=(d2term @ X2))))&![X2:d_term]:(((X2)=(d_one))))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(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)))&![X639:subst, X640:subst > term > term]:(((hoaslam @ X639 @ X640)=(d2term @ d_one))))&![X641:term, X642:subst, X643:term > $o, X644:term > $o]:(((pushprop_p_and_p_prime @ X641 @ X642 @ X643 @ X644)<=>![X9:term]:(((X644 @ X9)<=>(X643 @ (sub @ X9 @ (push @ X641 @ X642))))))))&~(var @ (d2term @ d_one)))&((pushprop_lem1v2)<=>![X7:term > $o, X8:term > $o, X5:term, X6:subst]:((~((X7 @ X5))|~(![X9:term]:(((X8 @ X9)<=>(X7 @ (sub @ X9 @ (push @ X5 @ X6))))))|(X8 @ one)))))&(pushprop_lem1_gthm))&((shinj)<=>![X5:term, X10:term]:((((sub @ X5 @ sh)!=(sub @ X10 @ sh))|((X5)=(X10))))))&(hoasinduction_lem1v2))&(![X10:term]:(~(![X11:subst > term > term]:(~(![X5:term, X6:subst]:(((sub @ X10 @ (push @ X5 @ X6))=(X11 @ X6 @ X5)))))))<=>(hoasinduction_lem3v2_f)))&(hoasapnotvar_gthm))&(![X5:term, X10:term, X12:term, X13:term]:((((ap @ (sub @ X5 @ id) @ X12)!=(ap @ (sub @ X10 @ id) @ X13))|((X5)=(X10))))<=>(hoasapinj1)))&((induction2lem_lthm)<=>(![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6))))=>(![X5:term, X6:subst]:(((X6)=(comp @ sh @ (push @ X5 @ X6))))=>(![X6:subst]:(((X6)=(comp @ X6 @ id)))=>(epred1_0))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&(![X11:subst > term > term, X17:subst > term > term, X18:subst, X19:term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X17 @ X6 @ X5) @ X20)=(X17 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|((X11 @ X18 @ X19)=(X17 @ X18 @ X19))|((lam @ (X11 @ sh @ one))!=(lam @ (X17 @ sh @ one)))|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))))<=>(hoaslaminj)))&((hoasinduction_lem3aaa)<=>![X21:subst > term > subst > $o, X22:term]:((~(![X11:subst > term > term, X23:term]:(((X21 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X24:subst, X25:term, X26:subst]:(((X11 @ (comp @ X24 @ X26) @ (sub @ X25 @ X26))=(sub @ X23 @ (push @ (sub @ X25 @ X26) @ (comp @ X24 @ X26))))))|~(![X27:subst, X28:term, X29:subst]:(((sub @ (X11 @ X27 @ X28) @ X29)=(sub @ (sub @ X23 @ (push @ X28 @ X27)) @ X29))))|~(![X5:term]:((~((X21 @ id @ X5 @ id))|(X21 @ id @ (X11 @ id @ X5) @ id)))))))|(X21 @ id @ (lam @ (sub @ X22 @ (push @ one @ sh))) @ id)|~(![X10:term]:((~((X21 @ id @ X10 @ id))|(X21 @ id @ (sub @ X22 @ (push @ X10 @ id)) @ id))))))))&(![X30:subst > term > subst > $o, X31:term, X32:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X30 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X30 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X30 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X30 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))|~((X30 @ id @ X32 @ id))|(X30 @ id @ (ap @ X31 @ X32) @ id)|~((X30 @ id @ X31 @ id))|~(![X5:term, X10:term]:((~((X30 @ id @ X5 @ id))|(X30 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X30 @ id @ X10 @ id)))))))<=>(hoasinduction_lem2)))&(termmset_lthm))&(hoasinduction_lem1))&(![X34:subst > term > subst > $o]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X34 @ id @ X9 @ id)))))))<=>(hoasinduction_lem0)))&(hoaslamnotvar_lthm))&(pushprop_lem3v2_lthm))&(ulamvarind))&((hoasinduction_lem3a_lthm)<=>(![X5:term]:(((X5)=(sub @ X5 @ id)))=>(![X35:subst > term > subst > $o, X36:term]:((~(![X10:term]:(((X35 @ id @ (sub @ X36 @ (push @ X10 @ id)) @ id)|~((X35 @ id @ X10 @ id)))))|(X35 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X35 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X35 @ id @ (X11 @ id @ X5) @ id)|~((X35 @ id @ X5 @ id))))))))))=>![X37:subst > term > subst > $o, X38:term]:((~(![X10:term]:(((X37 @ id @ (sub @ X38 @ (push @ X10 @ id)) @ id)|~((X37 @ id @ X10 @ id)))))|(X37 @ id @ (lam @ X38) @ id)|~(![X11:subst > term > term]:((~(![X5:term]:((~((X37 @ id @ X5 @ id))|(X37 @ id @ (X11 @ id @ X5) @ id))))|(X37 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))))))))&(termmset_gthm))&((hoasinduction_lem3aa)<=>![X39:subst > term > subst > $o, X36:term]:((~(![X11:subst > term > term]:((~(![X5:term]:((~((X39 @ id @ X5 @ id))|(X39 @ id @ (X11 @ id @ X5) @ id))))|(X39 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|~(![X10:term]:(((X39 @ id @ (sub @ X36 @ (push @ X10 @ id)) @ id)|~((X39 @ id @ X10 @ id)))))|(X39 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)))))&(hoasinduction_lem3a_gthm))&(axclos))&((apinj1)<=>![X5:term, X10:term, X12:term, X13:term]:((((X5)=(X10))|((ap @ X5 @ X12)!=(ap @ X10 @ X13))))))&((hoasapinj2_lthm)<=>(![X5:term, X10:term, X12:term, X13:term]:((((X12)=(X13))|((ap @ X5 @ X12)!=(ap @ X10 @ X13))))=>![X5:term, X10:term, X12:term, X13:term]:((((X12)=(X13))|((ap @ (sub @ X5 @ id) @ X12)!=(ap @ (sub @ X10 @ id) @ X13)))))))&(![X6:subst]:(((X6)=(push @ (sub @ one @ X6) @ (comp @ sh @ X6))))<=>(axscons)))&(hoasinduction_lem2v2_gthm))&((axidr)<=>![X6:subst]:(((X6)=(comp @ X6 @ id)))))&((![X5:term]:(((X5)=(sub @ X5 @ id)))=>(epred2_0))<=>(hoasinduction_lem3_lthm)))&((pushprop_lem0)<=>![X7:term > $o, X5:term, X6:subst]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X7 @ (sub @ X9 @ (push @ X5 @ X6)))))))))))&((hoasinduction_lem3v2a_lthm)<=>(![X10:term]:(~(![X11:subst > term > term]:(~(![X5:term, X6:subst]:(((sub @ X10 @ (push @ X5 @ X6))=(X11 @ X6 @ X5)))))))=>(![X5:term]:(((X5)=(sub @ X5 @ id)))=>![X43:subst > term > subst > $o, X8:term > $o, X44:term]:((~(![X9:term]:(((X8 @ X9)<=>(X43 @ id @ X9 @ id))))|(X8 @ (lam @ X44))|~(![X10:term]:(((X8 @ (sub @ X44 @ (push @ X10 @ id)))|~((X8 @ X10)))))|~(![X11:subst > term > term]:(((X43 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X43 @ id @ (X11 @ id @ X5) @ id)|~((X43 @ id @ X5 @ id)))))|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))))))))&(hoasinduction_lem1_lthm))&~(lamnotap))&(hoasapinj1_gthm))&(hoaslamnotvar))&(hoaslaminj_gthm))&((![X5:term]:(((X5)=(sub @ X5 @ id)))=>(epred3_0))<=>(induction2_lthm)))&(pushprop))&(![X10:term]:(~(![X11:subst > term > term]:(((X11 @ sh @ one)!=(sub @ X10 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b)))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&(![X11:subst > term > term, X46:term, X47:term]:((((lam @ (X11 @ sh @ one))!=(ap @ (sub @ X46 @ id) @ X47))|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))))<=>(hoaslamnotap)))&(ulamvarsh))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((axshiftcons)<=>![X5:term, X6:subst]:(((X6)=(comp @ sh @ (push @ X5 @ X6))))))&(![X7:term > $o, X5:term, X6:subst]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X7 @ (sub @ X9 @ (push @ X5 @ X6)))))))))<=>(pushprop_lem0_lthm)))&(![X5:term]:(((X5)=(sub @ X5 @ id)))<=>(axvarid)))&((hoasinduction_lthm_3)<=>(![X51:subst > term > subst > $o]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X51 @ id @ X9 @ id)))))))=>(epred5_0))))&((hoasinduction_lem3v2_lthm)<=>(![X5:term]:(((X5)=(sub @ X5 @ id)))=>(epred6_0))))&(hoasapnotvar_lthm))&((termmset)<=>![X5:term]:(((X5)=(sub @ X5 @ id)))))&((epred7_0)<=>(hoasinduction_lem3v2)))&((pushprop_lem1_lthm)<=>(![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6))))=>(![X5:term, X6:subst]:(((X6)=(comp @ sh @ (push @ X5 @ X6))))=>![X7:term > $o, X55:term > $o, X5:term, X6:subst, X10:term]:(((X55 @ (sub @ X5 @ (push @ X10 @ X6)))|~((X7 @ X5))))))))&(![X7:term > $o, X45:term]:((~(![X5:term]:(((X7 @ X5)|~(var @ X5))))|(X7 @ X45)|~(![X5:term]:((~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id))))))|(X7 @ (lam @ X5)))))|~(![X5:term, X10:term]:(((X7 @ (ap @ X5 @ X10))|~((X7 @ X10))|~((X7 @ X5)))))))<=>(induction2)))&(substmonoid_gthm))&(pushprop_lem2v2_lthm))&(induction2_gthm))&((hoasinduction_no_psi_cond)<=>![X56:subst > term > subst > $o, X57:term]:((~(![X5:term, X10:term]:(((X56 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X56 @ id @ X10 @ id))|~((X56 @ id @ X5 @ id)))))|~(![X11:subst > term > term]:((~(![X5:term]:(((X56 @ id @ (X11 @ id @ X5) @ id)|~((X56 @ id @ X5 @ id)))))|(X56 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|(X56 @ id @ X57 @ id)))))&(hoasinduction_lem1_gthm))&((hoasinduction_lem3a)<=>![X58:subst > term > subst > $o, X38:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|(X58 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X5:term]:(((X58 @ id @ (X11 @ id @ X5) @ id)|~((X58 @ id @ X5 @ id))))))))|~(![X10:term]:(((X58 @ id @ (sub @ X38 @ (push @ X10 @ id)) @ id)|~((X58 @ id @ X10 @ id)))))|(X58 @ id @ (lam @ X38) @ id)))))&(lamnotvar))&((substmonoid)<=>(![X6:subst]:(((X6)=(comp @ id @ X6)))&![X6:subst]:(((X6)=(comp @ X6 @ id))))))&(hoasinduction_lem2_gthm))&(hoasinduction_lem3_gthm))&((![X6:subst]:(((X6)=(comp @ id @ X6)))=>(![X6:subst]:(((X6)=(comp @ X6 @ id)))=>(![X6:subst]:(((X6)=(comp @ id @ X6)))&![X6:subst]:(((X6)=(comp @ X6 @ id))))))<=>(substmonoid_lthm)))&(![X59:subst > term > subst > $o]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X59 @ id @ X9 @ id)))))))<=>(hoasinduction_lem0_lthm)))&((axidl)<=>![X6:subst]:(((X6)=(comp @ id @ X6)))))&(hoasapinj2_gthm))&(hoasinduction_lem2_lthm))&(axabs))&(pushprop_gthm))&((laminj)<=>![X5:term, X10:term]:((((lam @ X5)!=(lam @ X10))|((X5)=(X10))))))&((pushprop_lem1)<=>![X7:term > $o, X60:term > $o, X5:term, X6:subst, X10:term]:(((X60 @ (sub @ X5 @ (push @ X10 @ X6)))|~((X7 @ X5))))))&((axvarcons)<=>![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6))))))&((hoaslaminj_lthm)<=>(![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6))))=>(![X5:term, X6:subst]:(((X6)=(comp @ sh @ (push @ X5 @ X6))))=>(![X5:term, X10:term]:((((lam @ X5)!=(lam @ X10))|((X5)=(X10))))=>![X11:subst > term > term, X17:subst > term > term, X18:subst, X19:term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|((X11 @ X18 @ X19)=(X17 @ X18 @ X19))|((lam @ (X11 @ sh @ one))!=(lam @ (X17 @ sh @ one)))|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X17 @ X6 @ X5) @ X20)=(X17 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))))))&((![X5:term]:(((X5)=(sub @ X5 @ id)))=>(![X5:term, X10:term, X12:term, X13:term]:((((ap @ X5 @ X12)!=(ap @ X10 @ X13))|((X5)=(X10))))=>![X5:term, X10:term, X12:term, X13:term]:((((ap @ (sub @ X5 @ id) @ X12)!=(ap @ (sub @ X10 @ id) @ X13))|((X5)=(X10))))))<=>(hoasapinj1_lthm)))&((hoasinduction_lem3v2a)<=>![X61:subst > term > subst > $o, X8:term > $o, X44:term]:((~(![X11:subst > term > term]:((~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20)))))|~(![X5:term]:(((X61 @ id @ (X11 @ id @ X5) @ id)|~((X61 @ id @ X5 @ id)))))|(X61 @ id @ (lam @ (X11 @ sh @ one)) @ id))))|~(![X9:term]:(((X8 @ X9)<=>(X61 @ id @ X9 @ id))))|(X8 @ (lam @ X44))|~(![X10:term]:((~((X8 @ X10))|(X8 @ (sub @ X44 @ (push @ X10 @ id))))))))))&(![X5:term, X10:term, X12:term, X13:term]:((((ap @ X5 @ X12)!=(ap @ X10 @ X13))|((X12)=(X13))))<=>(apinj2)))&(pushprop_lthm))&((hoasinduction_lem2v2)<=>![X62:subst > term > subst > $o, X8:term > $o, X63:term, X64:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X62 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X62 @ X6 @ X5 @ (comp @ X33 @ X20))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X62 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))|(X62 @ X6 @ X5 @ (comp @ X33 @ X20)))))|~((X8 @ X63))|(X8 @ (ap @ X63 @ X64))|~((X8 @ X64))|~(![X9:term]:(((X8 @ X9)<=>(X62 @ id @ X9 @ id))))|~(![X5:term, X10:term]:(((X62 @ id @ (ap @ (sub @ X5 @ id) @ X10) @ id)|~((X62 @ id @ X10 @ id))|~((X62 @ id @ X5 @ id)))))))))&(axassoc))&(pushprop_lem2v2))&(hoasinduction_lem3b_gthm))&(hoaslamnotvar_gthm))&(hoaslamnotap_gthm))&(pushprop_lem1v2_gthm))&(![X7:term > $o, X16:term]:(((X7 @ X16)|~(![X5:term]:(((X7 @ (lam @ X5))|~((X7 @ X5)))))|~(![X5:term, X10:term]:((~((X7 @ X5))|(X7 @ (ap @ X5 @ X10))|~((X7 @ X10)))))|~(![X5:term]:((~(var @ X5)|(X7 @ X5))))))<=>(induction)))&(![X10:term]:(~(![X11:subst > term > term]:(((X11 @ sh @ one)!=(sub @ X10 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b_lthm)))&(axapp))&(hoasinduction_gthm))&((hoasinduction)<=>![X65:subst > term > subst > $o, X50:term]:(((epred8_2 @ X65 @ X50)|~(![X6:subst, X5:term, X20:subst, X33:subst]:((~((X65 @ X6 @ X5 @ (comp @ X33 @ X20)))|(X65 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20))))))))&(hoasapnotvar))&((![X5:term, X6:subst]:(((X5)=(sub @ one @ (push @ X5 @ X6))))=>![X7:term > $o, X8:term > $o, X5:term, X6:subst]:((~(![X9:term]:(((X8 @ X9)<=>(X7 @ (sub @ X9 @ (push @ X5 @ X6))))))|(X8 @ one)|~((X7 @ X5)))))<=>(pushprop_lem1v2_lthm)))&(hoaslamnotap_lthm))&(![X66:subst > term > subst > $o, X42:term]:((~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X66 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)|~((X66 @ X6 @ X5 @ (comp @ X33 @ X20))))))|(X66 @ id @ (lam @ X42) @ id)|~(![X10:term]:((~((X66 @ id @ X10 @ id))|(X66 @ id @ (sub @ X42 @ (push @ X10 @ id)) @ id))))|~(![X11:subst > term > term]:((~(![X5:term]:(((X66 @ id @ (X11 @ id @ X5) @ id)|~((X66 @ id @ X5 @ id)))))|(X66 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|~(![X6:subst, X5:term, X20:subst, X33:subst]:(((X66 @ X6 @ X5 @ (comp @ X33 @ X20))|~((X66 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))))))<=>(hoasinduction_lem3)))&((hoasinduction_lem3aa_lthm)<=>![X67:subst > term > subst > $o, X36:term]:((~(![X11:subst > term > term]:((~(![X5:term]:(((X67 @ id @ (X11 @ id @ X5) @ id)|~((X67 @ id @ X5 @ id)))))|(X67 @ id @ (lam @ (X11 @ sh @ one)) @ id)|~(![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))))|(X67 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id)|~(![X10:term]:((~((X67 @ id @ X10 @ id))|(X67 @ id @ (sub @ X36 @ (push @ X10 @ id)) @ id))))))))&(induction2lem_gthm))&((hoasinduction_no_psi_cond_lthm)<=>(![X70:subst > term > subst > $o]:(~(![X8:term > $o]:(~(![X9:term]:(((X8 @ X9)<=>(X70 @ id @ X9 @ id)))))))=>(![X7:term > $o, X45:term]:((~(![X5:term]:((~(var @ X5)|(X7 @ X5))))|(X7 @ X45)|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:((~((X7 @ X10))|(X7 @ (sub @ X5 @ (push @ X10 @ id)))))))))|~(![X5:term, X10:term]:((~((X7 @ X10))|(X7 @ (ap @ X5 @ X10))|~((X7 @ X5)))))))=>(![X5:term]:(((X5)=(sub @ X5 @ id)))=>(epred9_0))))))&((hoasinduction_lthm)<=>(epred12_0)))&((hoasinduction_lem3v2_f_lthm)<=>![X10:term]:(~(![X11:subst > term > term]:(~(![X5:term, X6:subst]:(((sub @ X10 @ (push @ X5 @ X6))=(X11 @ X6 @ X5)))))))))&~(ulamvar1))&((hoasapinj2)<=>![X5:term, X10:term, X12:term, X13:term]:((((X12)=(X13))|((ap @ (sub @ X5 @ id) @ X12)!=(ap @ (sub @ X10 @ id) @ X13))))))&(axvarshift))&((induction2lem)<=>![X7:term > $o, X14:term, X15:subst]:((~(![X5:term, X10:term]:((~((X7 @ X5))|~((X7 @ X10))|(X7 @ (ap @ X5 @ X10)))))|~(![X5:term]:(((X7 @ (lam @ X5))|~(![X10:term]:(((X7 @ (sub @ X5 @ (push @ X10 @ id)))|~((X7 @ X10))))))))|(X7 @ (sub @ X14 @ X15))|~(![X10:term]:((~(var @ X10)|(X7 @ (sub @ X10 @ X15)))))))))&(hoasinduction_lem1v2_gthm))&(pushprop_lem0_gthm))&(axmap))&![X645:subst > term > subst > $o, X646:term > $o]:(((hoasinduction_p_and_p_prime @ X645 @ X646)<=>![X9:term]:(((X646 @ X9)<=>(X645 @ id @ X9 @ id))))))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((one)=(d2term @ d_one)))&![X75:d_subst, X76:d_subst]:((((d2subst @ X75)=(d2subst @ X76))=>((X75)=(X76)))))&![X77:d_subst]:(((X77)=(d_id))))&![X78:subst]:(?[X77:d_subst]:(((X78)=(d2subst @ X77)))))&![X79:d_term, X80:d_term]:((((d2term @ X79)=(d2term @ X80))=>((X79)=(X80))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[alg444_1])])]), c_0_2]), c_0_3]), c_0_4]), c_0_5]), c_0_6]), c_0_7]), c_0_8]), c_0_9]), c_0_10])).
0.33/0.94	thf(c_0_12, plain, ![X647:term, X649:d_term, X650:subst, X651:subst > term > term, X652:term, X653:subst, X654:term > $o, X655:term > $o, X656:term, X657:term, X658:term, X659:subst, X660:term > $o, X661:term > $o, X663:term > $o, X664:term > $o, X665:term, X666:subst, X672:term, X673:term, X674:term, X678:subst > term > term, X681:term, X683:term, X684:subst, X689:term, X690:term, X691:term, X692:term, X698:term, X699:subst, X700:term, X701:subst, X702:subst, X707:subst, X708:term, X709:subst, X710:subst, X711:term, X712:subst, X713:subst > term > term, X714:subst > term > term, X718:subst, X719:term, X723:subst > term > subst > $o, X724:term, X727:subst, X728:term, X729:subst, X730:subst, X731:term, X732:subst, X733:term, X737:subst > term > term, X738:term, X746:term, X750:subst, X751:term, X752:subst, X753:subst, X754:subst, X755:term, X756:subst, X757:subst, X758:term, X759:term, X760:subst > term > subst > $o, X761:term, X762:term, X774:term > $o, X776:subst > term > subst > $o, X778:term, X779:term, X783:term, X784:subst > term > term, X789:subst > term > subst > $o, X790:term, X793:term, X794:subst, X795:term, X796:subst, X797:term, X798:subst > term > subst > $o, X799:term, X802:subst, X803:term, X804:subst, X805:term, X808:term, X809:subst > term > term, X814:subst > term > subst > $o, X815:term, X817:term, X818:subst, X819:term, X820:subst, X824:subst > term > term, X829:term, X830:term, X831:term, X832:term, X833:term, X842:term, X843:term, X844:term, X845:term, X846:term, X847:term, X848:term, X849:term, X855:subst, X856:subst, X858:term, X860:term > $o, X861:term, X862:subst, X864:term, X865:term, X869:term > $o, X872:subst > term > term, X876:subst > term > subst > $o, X877:term > $o, X878:term, X882:term, X883:subst, X884:term, X885:subst, X886:term, X888:term, X889:subst, X890:term, X894:term, X895:term, X896:subst > term > term, X901:term, X904:subst > term > term, X905:term, X910:subst, X911:term, X912:subst, X913:subst > term > term, X914:term, X915:term, X919:term, X920:subst, X926:term > $o, X928:term > $o, X929:term, X930:subst, X932:term, X933:term, X935:term, X937:term > $o, X939:subst > term > subst > $o, X941:term, X942:term, X944:term, X945:term, X951:term > $o, X952:term > $o, X953:term, X954:subst, X955:term, X956:term, X957:subst, X958:term, X959:subst, X967:term, X968:term, X970:term, X971:term, X972:term > $o, X974:term, X976:term, X979:subst > term > subst > $o, X983:term, X984:subst, X985:term, X986:subst, X987:term, X990:term, X991:term, X992:subst > term > term, X997:subst > term > subst > $o, X998:term, X1000:subst, X1001:term, X1002:subst, X1003:term, X1007:subst > term > term, X1012:term, X1013:subst, X1014:subst, X1017:subst, X1018:subst, X1023:subst, X1024:subst, X1026:term > $o, X1028:subst > term > subst > $o, X1030:term, X1031:term, X1032:subst, X1034:term, X1035:term, X1038:term > $o, X1039:term > $o, X1040:term, X1041:subst, X1042:term, X1048:term, X1049:subst, X1058:subst > term > term, X1059:subst > term > term, X1063:subst, X1064:term, X1068:term, X1069:subst, X1070:term, X1071:subst, X1072:term, X1073:term, X1078:subst, X1079:term, X1080:subst, X1081:subst, X1082:term, X1083:subst, X1084:term, X1085:term, X1086:term, X1087:term, X1088:term, X1098:term, X1099:term, X1100:term, X1101:term, X1102:subst > term > subst > $o, X1103:term > $o, X1104:term, X1106:subst, X1107:term, X1108:subst, X1109:term, X1115:subst > term > term, X1120:term, X1121:term, X1126:term, X1127:term, X1128:term, X1129:term, X1130:subst > term > subst > $o, X1131:term > $o, X1132:term, X1133:term, X1149:subst, X1150:term, X1151:subst, X1152:subst, X1153:subst, X1154:term, X1155:subst, X1156:subst, X1157:term, X1158:term, X1159:term, X1162:term, X1163:term, X1164:term, X1165:term, X1166:term > $o, X1167:term, X1173:subst > term > term, X1174:term, X1176:subst > term > subst > $o, X1177:term, X1184:subst, X1185:term, X1186:subst, X1187:subst, X1188:term, X1189:subst, X1194:term, X1197:term > $o, X1198:term > $o, X1199:term, X1200:subst, X1204:subst, X1205:term, X1206:subst, X1207:subst, X1208:term, X1209:subst > term > term, X1214:subst, X1215:term, X1216:subst, X1217:subst, X1218:subst > term > subst > $o, X1219:term, X1226:term, X1227:subst, X1228:term, X1229:subst, X1234:subst > term > subst > $o, X1235:term, X1237:term, X1238:subst, X1239:term, X1240:subst, X1244:subst > term > term, X1249:term, X1251:term > $o, X1255:term, X1256:term, X1258:term, X1259:term, X1261:subst > term > subst > $o, X1263:term, X1264:term, X1265:term > $o, X1267:term, X1269:term, X1272:term, X1273:term, X1275:term, X1276:subst, X1278:subst > term > term, X1281:term, X1282:term, X1283:term, X1284:term, X1289:term > $o, X1290:term, X1291:subst, X1295:term, X1300:term, X1301:term, X1302:term, X1304:term, X1305:subst > term > subst > $o, X1306:term > $o, X1307:term, X1308:term, X1309:subst > term > subst > $o, X1310:term > $o, X1312:d_subst, X1313:d_subst, X1314:d_subst, X1315:subst, X1317:d_term, X1318:d_term]:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((X647)=(d2term @ (esk1_1 @ X647)))&((X649)=(d_one)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(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 @ X650 @ X651)=(d2term @ d_one)))&(((~(X655 @ X656)|(X654 @ (sub @ X656 @ (push @ X652 @ X653)))|~(pushprop_p_and_p_prime @ X652 @ X653 @ X654 @ X655))&(~(X654 @ (sub @ X657 @ (push @ X652 @ X653)))|(X655 @ X657)|~(pushprop_p_and_p_prime @ X652 @ X653 @ X654 @ X655)))&((~(X661 @ (esk2_4 @ X658 @ X659 @ X660 @ X661))|~(X660 @ (sub @ (esk2_4 @ X658 @ X659 @ X660 @ X661) @ (push @ X658 @ X659)))|(pushprop_p_and_p_prime @ X658 @ X659 @ X660 @ X661))&((X661 @ (esk2_4 @ X658 @ X659 @ X660 @ X661))|(X660 @ (sub @ (esk2_4 @ X658 @ X659 @ X660 @ X661) @ (push @ X658 @ X659)))|(pushprop_p_and_p_prime @ X658 @ X659 @ X660 @ X661)))))&~(var @ (d2term @ d_one)))&(((~(X664 @ (esk3_4 @ X663 @ X664 @ X665 @ X666))|~(X663 @ (sub @ (esk3_4 @ X663 @ X664 @ X665 @ X666) @ (push @ X665 @ X666)))|~(X663 @ X665)|(X664 @ one)|~(pushprop_lem1v2))&((X664 @ (esk3_4 @ X663 @ X664 @ X665 @ X666))|(X663 @ (sub @ (esk3_4 @ X663 @ X664 @ X665 @ X666) @ (push @ X665 @ X666)))|~(X663 @ X665)|(X664 @ one)|~(pushprop_lem1v2)))&((((epred13_0 @ esk4_0)|(pushprop_lem1v2))&((~(epred14_0 @ X672)|(epred13_0 @ (sub @ X672 @ (push @ esk4_0 @ esk5_0)))|(pushprop_lem1v2))&(~(epred13_0 @ (sub @ X672 @ (push @ esk4_0 @ esk5_0)))|(epred14_0 @ X672)|(pushprop_lem1v2))))&(~(epred14_0 @ one)|(pushprop_lem1v2)))))&(pushprop_lem1_gthm))&((~(shinj)|(((sub @ X673 @ sh)!=(sub @ X674 @ sh))|((X673)=(X674))))&((((sub @ esk6_0 @ sh)=(sub @ esk7_0 @ sh))|(shinj))&(((esk6_0)!=(esk7_0))|(shinj)))))&(hoasinduction_lem1v2))&((((sub @ esk8_0 @ (push @ (esk9_1 @ X678) @ (esk10_1 @ X678)))!=(X678 @ (esk10_1 @ X678) @ (esk9_1 @ X678)))|(hoasinduction_lem3v2_f))&(~(hoasinduction_lem3v2_f)|((sub @ X681 @ (push @ X683 @ X684))=(esk11_1 @ X681 @ X684 @ X683)))))&(hoasapnotvar_gthm))&(((((ap @ (sub @ esk12_0 @ id) @ esk14_0)=(ap @ (sub @ esk13_0 @ id) @ esk15_0))|(hoasapinj1))&(((esk12_0)!=(esk13_0))|(hoasapinj1)))&(~(hoasapinj1)|(((ap @ (sub @ X689 @ id) @ X691)!=(ap @ (sub @ X690 @ id) @ X692))|((X689)=(X690))))))&((~(induction2lem_lthm)|(((esk16_0)!=(sub @ one @ (push @ esk16_0 @ esk17_0)))|(((esk19_0)!=(comp @ sh @ (push @ esk18_0 @ esk19_0)))|(((esk20_0)!=(comp @ esk20_0 @ id))|(epred1_0)))))&((((X698)=(sub @ one @ (push @ X698 @ X699)))|(induction2lem_lthm))&((((X701)=(comp @ sh @ (push @ X700 @ X701)))|(induction2lem_lthm))&((((X702)=(comp @ X702 @ id))|(induction2lem_lthm))&(~(epred1_0)|(induction2lem_lthm)))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&(((((((sub @ (esk22_0 @ X707 @ X708) @ X709)=(esk22_0 @ (comp @ X707 @ X709) @ (sub @ X708 @ X709)))|(hoaslaminj))&(((esk21_0 @ esk23_0 @ esk24_0)!=(esk22_0 @ esk23_0 @ esk24_0))|(hoaslaminj)))&(((lam @ (esk21_0 @ sh @ one))=(lam @ (esk22_0 @ sh @ one)))|(hoaslaminj)))&(((sub @ (esk21_0 @ X710 @ X711) @ X712)=(esk21_0 @ (comp @ X710 @ X712) @ (sub @ X711 @ X712)))|(hoaslaminj)))&(~(hoaslaminj)|(((sub @ (X714 @ (esk25_2 @ X713 @ X714) @ (esk26_2 @ X713 @ X714)) @ (esk27_2 @ X713 @ X714))!=(X714 @ (comp @ (esk25_2 @ X713 @ X714) @ (esk27_2 @ X713 @ X714)) @ (sub @ (esk26_2 @ X713 @ X714) @ (esk27_2 @ X713 @ X714))))|((X713 @ X718 @ X719)=(X714 @ X718 @ X719))|((lam @ (X713 @ sh @ one))!=(lam @ (X714 @ sh @ one)))|((sub @ (X713 @ (esk28_1 @ X713) @ (esk29_1 @ X713)) @ (esk30_1 @ X713))!=(X713 @ (comp @ (esk28_1 @ X713) @ (esk30_1 @ X713)) @ (sub @ (esk29_1 @ X713) @ (esk30_1 @ X713))))))))&(((((((X723 @ id @ (esk33_2 @ X723 @ X724) @ id)|(~(X723 @ id @ (lam @ (esk31_2 @ X723 @ X724 @ sh @ one)) @ id)|(X723 @ id @ (lam @ (sub @ X724 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&(~(X723 @ id @ (sub @ X724 @ (push @ (esk33_2 @ X723 @ X724) @ id)) @ id)|(~(X723 @ id @ (lam @ (esk31_2 @ X723 @ X724 @ sh @ one)) @ id)|(X723 @ id @ (lam @ (sub @ X724 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&(((X723 @ id @ (esk33_2 @ X723 @ X724) @ id)|(((esk31_2 @ X723 @ X724 @ (comp @ X727 @ X729) @ (sub @ X728 @ X729))=(sub @ (esk32_2 @ X723 @ X724) @ (push @ (sub @ X728 @ X729) @ (comp @ X727 @ X729))))|(X723 @ id @ (lam @ (sub @ X724 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&(~(X723 @ id @ (sub @ X724 @ (push @ (esk33_2 @ X723 @ X724) @ id)) @ id)|(((esk31_2 @ X723 @ X724 @ (comp @ X727 @ X729) @ (sub @ X728 @ X729))=(sub @ (esk32_2 @ X723 @ X724) @ (push @ (sub @ X728 @ X729) @ (comp @ X727 @ X729))))|(X723 @ id @ (lam @ (sub @ X724 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))))&(((X723 @ id @ (esk33_2 @ X723 @ X724) @ id)|(((sub @ (esk31_2 @ X723 @ X724 @ X730 @ X731) @ X732)=(sub @ (sub @ (esk32_2 @ X723 @ X724) @ (push @ X731 @ X730)) @ X732))|(X723 @ id @ (lam @ (sub @ X724 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&(~(X723 @ id @ (sub @ X724 @ (push @ (esk33_2 @ X723 @ X724) @ id)) @ id)|(((sub @ (esk31_2 @ X723 @ X724 @ X730 @ X731) @ X732)=(sub @ (sub @ (esk32_2 @ X723 @ X724) @ (push @ X731 @ X730)) @ X732))|(X723 @ id @ (lam @ (sub @ X724 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))))&(((X723 @ id @ (esk33_2 @ X723 @ X724) @ id)|(~(X723 @ id @ X733 @ id)|(X723 @ id @ (esk31_2 @ X723 @ X724 @ id @ X733) @ id)|(X723 @ id @ (lam @ (sub @ X724 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&(~(X723 @ id @ (sub @ X724 @ (push @ (esk33_2 @ X723 @ X724) @ id)) @ id)|(~(X723 @ id @ X733 @ id)|(X723 @ id @ (esk31_2 @ X723 @ X724 @ id @ X733) @ id)|(X723 @ id @ (lam @ (sub @ X724 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))))&(((((epred15_0 @ id @ (esk41_2 @ X737 @ X738) @ id)|((epred15_0 @ id @ (lam @ (X737 @ sh @ one)) @ id)|((X737 @ (comp @ (esk35_2 @ X737 @ X738) @ (esk37_2 @ X737 @ X738)) @ (sub @ (esk36_2 @ X737 @ X738) @ (esk37_2 @ X737 @ X738)))!=(sub @ X738 @ (push @ (sub @ (esk36_2 @ X737 @ X738) @ (esk37_2 @ X737 @ X738)) @ (comp @ (esk35_2 @ X737 @ X738) @ (esk37_2 @ X737 @ X738)))))|((sub @ (X737 @ (esk38_2 @ X737 @ X738) @ (esk39_2 @ X737 @ X738)) @ (esk40_2 @ X737 @ X738))!=(sub @ (sub @ X738 @ (push @ (esk39_2 @ X737 @ X738) @ (esk38_2 @ X737 @ X738))) @ (esk40_2 @ X737 @ X738))))|(hoasinduction_lem3aaa))&(~(epred15_0 @ id @ (X737 @ id @ (esk41_2 @ X737 @ X738)) @ id)|((epred15_0 @ id @ (lam @ (X737 @ sh @ one)) @ id)|((X737 @ (comp @ (esk35_2 @ X737 @ X738) @ (esk37_2 @ X737 @ X738)) @ (sub @ (esk36_2 @ X737 @ X738) @ (esk37_2 @ X737 @ X738)))!=(sub @ X738 @ (push @ (sub @ (esk36_2 @ X737 @ X738) @ (esk37_2 @ X737 @ X738)) @ (comp @ (esk35_2 @ X737 @ X738) @ (esk37_2 @ X737 @ X738)))))|((sub @ (X737 @ (esk38_2 @ X737 @ X738) @ (esk39_2 @ X737 @ X738)) @ (esk40_2 @ X737 @ X738))!=(sub @ (sub @ X738 @ (push @ (esk39_2 @ X737 @ X738) @ (esk38_2 @ X737 @ X738))) @ (esk40_2 @ X737 @ X738))))|(hoasinduction_lem3aaa)))&(~(epred15_0 @ id @ (lam @ (sub @ esk34_0 @ (push @ one @ sh))) @ id)|(hoasinduction_lem3aaa)))&(~(epred15_0 @ id @ X746 @ id)|(epred15_0 @ id @ (sub @ esk34_0 @ (push @ X746 @ id)) @ id)|(hoasinduction_lem3aaa)))))&((((((((epred16_0 @ (comp @ X750 @ X753) @ (sub @ X751 @ X753) @ X752)|~(epred16_0 @ X750 @ X751 @ (comp @ X753 @ X752))|(hoasinduction_lem2))&((epred16_0 @ X754 @ X755 @ (comp @ X757 @ X756))|~(epred16_0 @ (comp @ X754 @ X757) @ (sub @ X755 @ X757) @ X756)|(hoasinduction_lem2)))&((epred16_0 @ id @ esk43_0 @ id)|(hoasinduction_lem2)))&(~(epred16_0 @ id @ (ap @ esk42_0 @ esk43_0) @ id)|(hoasinduction_lem2)))&((epred16_0 @ id @ esk42_0 @ id)|(hoasinduction_lem2)))&(~(epred16_0 @ id @ X758 @ id)|(epred16_0 @ id @ (ap @ (sub @ X758 @ id) @ X759) @ id)|~(epred16_0 @ id @ X759 @ id)|(hoasinduction_lem2)))&((((((X760 @ id @ (esk52_1 @ X760) @ id)|(~(X760 @ (esk48_3 @ X760 @ X761 @ X762) @ (esk49_3 @ X760 @ X761 @ X762) @ (comp @ (esk51_3 @ X760 @ X761 @ X762) @ (esk50_3 @ X760 @ X761 @ X762)))|~(X760 @ (comp @ (esk44_3 @ X760 @ X761 @ X762) @ (esk47_3 @ X760 @ X761 @ X762)) @ (sub @ (esk45_3 @ X760 @ X761 @ X762) @ (esk47_3 @ X760 @ X761 @ X762)) @ (esk46_3 @ X760 @ X761 @ X762))|~(X760 @ id @ X762 @ id)|(X760 @ id @ (ap @ X761 @ X762) @ id)|~(X760 @ id @ X761 @ id))|~(hoasinduction_lem2))&(~(X760 @ id @ (ap @ (sub @ (esk52_1 @ X760) @ id) @ (esk53_1 @ X760)) @ id)|(~(X760 @ (esk48_3 @ X760 @ X761 @ X762) @ (esk49_3 @ X760 @ X761 @ X762) @ (comp @ (esk51_3 @ X760 @ X761 @ X762) @ (esk50_3 @ X760 @ X761 @ X762)))|~(X760 @ (comp @ (esk44_3 @ X760 @ X761 @ X762) @ (esk47_3 @ X760 @ X761 @ X762)) @ (sub @ (esk45_3 @ X760 @ X761 @ X762) @ (esk47_3 @ X760 @ X761 @ X762)) @ (esk46_3 @ X760 @ X761 @ X762))|~(X760 @ id @ X762 @ id)|(X760 @ id @ (ap @ X761 @ X762) @ id)|~(X760 @ id @ X761 @ id))|~(hoasinduction_lem2)))&((X760 @ id @ (esk53_1 @ X760) @ id)|(~(X760 @ (esk48_3 @ X760 @ X761 @ X762) @ (esk49_3 @ X760 @ X761 @ X762) @ (comp @ (esk51_3 @ X760 @ X761 @ X762) @ (esk50_3 @ X760 @ X761 @ X762)))|~(X760 @ (comp @ (esk44_3 @ X760 @ X761 @ X762) @ (esk47_3 @ X760 @ X761 @ X762)) @ (sub @ (esk45_3 @ X760 @ X761 @ X762) @ (esk47_3 @ X760 @ X761 @ X762)) @ (esk46_3 @ X760 @ X761 @ X762))|~(X760 @ id @ X762 @ id)|(X760 @ id @ (ap @ X761 @ X762) @ id)|~(X760 @ id @ X761 @ id))|~(hoasinduction_lem2)))&((((X760 @ id @ (esk52_1 @ X760) @ id)|((X760 @ (comp @ (esk48_3 @ X760 @ X761 @ X762) @ (esk51_3 @ X760 @ X761 @ X762)) @ (sub @ (esk49_3 @ X760 @ X761 @ X762) @ (esk51_3 @ X760 @ X761 @ X762)) @ (esk50_3 @ X760 @ X761 @ X762))|~(X760 @ (comp @ (esk44_3 @ X760 @ X761 @ X762) @ (esk47_3 @ X760 @ X761 @ X762)) @ (sub @ (esk45_3 @ X760 @ X761 @ X762) @ (esk47_3 @ X760 @ X761 @ X762)) @ (esk46_3 @ X760 @ X761 @ X762))|~(X760 @ id @ X762 @ id)|(X760 @ id @ (ap @ X761 @ X762) @ id)|~(X760 @ id @ X761 @ id))|~(hoasinduction_lem2))&(~(X760 @ id 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id)|(hoasinduction_lem3aa_lthm)))))&(induction2lem_gthm))&((((((~(var @ X1255)|(epred50_0 @ X1255)|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|(~(X1251 @ (esk258_1 @ X1251))|~(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred50_0 @ esk259_0)|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|(~(X1251 @ (esk258_1 @ X1251))|~(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred50_0 @ (esk260_1 @ X1256))|(epred50_0 @ (lam @ X1256))|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|(~(X1251 @ (esk258_1 @ X1251))|~(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred50_0 @ (sub @ X1256 @ (push @ (esk260_1 @ X1256) @ id)))|(epred50_0 @ (lam @ X1256))|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|(~(X1251 @ (esk258_1 @ X1251))|~(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred50_0 @ X1259)|(epred50_0 @ (ap @ X1258 @ X1259))|~(epred50_0 @ X1258)|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|(~(X1251 @ (esk258_1 @ X1251))|~(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm)))&((((~(var @ X1255)|(epred50_0 @ X1255)|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|((X1251 @ (esk258_1 @ X1251))|(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred50_0 @ esk259_0)|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|((X1251 @ (esk258_1 @ X1251))|(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred50_0 @ (esk260_1 @ X1256))|(epred50_0 @ (lam @ X1256))|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|((X1251 @ (esk258_1 @ X1251))|(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred50_0 @ (sub @ X1256 @ (push @ (esk260_1 @ X1256) @ id)))|(epred50_0 @ (lam @ X1256))|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|((X1251 @ (esk258_1 @ X1251))|(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred50_0 @ X1259)|(epred50_0 @ (ap @ X1258 @ X1259))|~(epred50_0 @ X1258)|(((esk261_0)!=(sub @ esk261_0 @ id))|(epred9_0))|((X1251 @ (esk258_1 @ X1251))|(epred49_0 @ id @ (esk258_1 @ X1251) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(((~(epred51_1 @ X1261 @ X1263)|(X1261 @ id @ X1263 @ id)|(hoasinduction_no_psi_cond_lthm))&(~(X1261 @ id @ X1264 @ id)|(epred51_1 @ X1261 @ X1264)|(hoasinduction_no_psi_cond_lthm)))&(((((((X1265 @ (esk265_1 @ X1265))|(~(X1265 @ (lam @ (esk263_1 @ X1265)))|((var @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm))&(~(X1265 @ (ap @ (esk264_1 @ X1265) @ (esk265_1 @ X1265)))|(~(X1265 @ (lam @ (esk263_1 @ X1265)))|((var @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm)))&((X1265 @ (esk264_1 @ X1265))|(~(X1265 @ (lam @ (esk263_1 @ X1265)))|((var @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm)))&((((X1265 @ (esk265_1 @ X1265))|(~(X1265 @ X1269)|(X1265 @ (sub @ (esk263_1 @ X1265) @ (push @ X1269 @ id)))|((var @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm))&(~(X1265 @ (ap @ (esk264_1 @ X1265) @ (esk265_1 @ X1265)))|(~(X1265 @ X1269)|(X1265 @ (sub @ (esk263_1 @ X1265) @ (push @ X1269 @ id)))|((var @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm)))&((X1265 @ (esk264_1 @ X1265))|(~(X1265 @ X1269)|(X1265 @ (sub @ (esk263_1 @ X1265) @ (push @ X1269 @ id)))|((var @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm))))&(((((X1265 @ (esk265_1 @ X1265))|(~(X1265 @ (lam @ (esk263_1 @ X1265)))|(~(X1265 @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm))&(~(X1265 @ (ap @ (esk264_1 @ X1265) @ (esk265_1 @ X1265)))|(~(X1265 @ (lam @ (esk263_1 @ X1265)))|(~(X1265 @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm)))&((X1265 @ (esk264_1 @ X1265))|(~(X1265 @ (lam @ (esk263_1 @ X1265)))|(~(X1265 @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm)))&((((X1265 @ (esk265_1 @ X1265))|(~(X1265 @ X1269)|(X1265 @ (sub @ (esk263_1 @ X1265) @ (push @ X1269 @ id)))|(~(X1265 @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm))&(~(X1265 @ (ap @ (esk264_1 @ X1265) @ (esk265_1 @ X1265)))|(~(X1265 @ X1269)|(X1265 @ (sub @ (esk263_1 @ X1265) @ (push @ X1269 @ id)))|(~(X1265 @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm)))&((X1265 @ (esk264_1 @ X1265))|(~(X1265 @ X1269)|(X1265 @ (sub @ (esk263_1 @ X1265) @ (push @ X1269 @ id)))|(~(X1265 @ (esk262_1 @ X1265))|(X1265 @ X1267)))|(hoasinduction_no_psi_cond_lthm)))))&((((X1272)=(sub @ X1272 @ id))|(hoasinduction_no_psi_cond_lthm))&(~(epred9_0)|(hoasinduction_no_psi_cond_lthm)))))))&((~(hoasinduction_lthm)|(epred12_0))&(~(epred12_0)|(hoasinduction_lthm))))&((~(hoasinduction_lem3v2_f_lthm)|((sub @ X1273 @ (push @ X1275 @ X1276))=(esk266_1 @ X1273 @ X1276 @ X1275)))&(((sub @ esk267_0 @ (push @ (esk268_1 @ X1278) @ (esk269_1 @ X1278)))!=(X1278 @ (esk269_1 @ X1278) @ (esk268_1 @ X1278)))|(hoasinduction_lem3v2_f_lthm))))&~(ulamvar1))&((~(hoasapinj2)|(((X1283)=(X1284))|((ap @ (sub @ X1281 @ id) @ X1283)!=(ap @ (sub @ X1282 @ id) @ X1284))))&((((esk272_0)!=(esk273_0))|(hoasapinj2))&(((ap @ (sub @ esk270_0 @ id) @ esk272_0)=(ap @ (sub @ esk271_0 @ id) @ esk273_0))|(hoasapinj2)))))&(axvarshift))&(((((((var @ (esk277_3 @ X1289 @ X1290 @ X1291))|(~(X1289 @ (lam @ (esk276_3 @ X1289 @ X1290 @ X1291)))|(X1289 @ (esk274_3 @ X1289 @ X1290 @ X1291))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem))&(~(X1289 @ (sub @ (esk277_3 @ X1289 @ X1290 @ X1291) @ X1291))|(~(X1289 @ (lam @ (esk276_3 @ X1289 @ X1290 @ X1291)))|(X1289 @ (esk274_3 @ X1289 @ X1290 @ X1291))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem)))&(((var @ (esk277_3 @ X1289 @ X1290 @ X1291))|((X1289 @ (sub @ (esk276_3 @ X1289 @ X1290 @ X1291) @ (push @ X1295 @ id)))|~(X1289 @ X1295)|(X1289 @ (esk274_3 @ X1289 @ X1290 @ X1291))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem))&(~(X1289 @ (sub @ (esk277_3 @ X1289 @ X1290 @ X1291) @ X1291))|((X1289 @ (sub @ (esk276_3 @ X1289 @ X1290 @ X1291) @ (push @ X1295 @ id)))|~(X1289 @ X1295)|(X1289 @ (esk274_3 @ X1289 @ X1290 @ X1291))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem))))&((((var @ (esk277_3 @ X1289 @ X1290 @ X1291))|(~(X1289 @ (lam @ (esk276_3 @ X1289 @ X1290 @ X1291)))|(X1289 @ (esk275_3 @ X1289 @ X1290 @ X1291))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem))&(~(X1289 @ (sub @ (esk277_3 @ X1289 @ X1290 @ X1291) @ X1291))|(~(X1289 @ (lam @ (esk276_3 @ X1289 @ X1290 @ X1291)))|(X1289 @ (esk275_3 @ X1289 @ X1290 @ X1291))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem)))&(((var @ (esk277_3 @ X1289 @ X1290 @ X1291))|((X1289 @ (sub @ (esk276_3 @ X1289 @ X1290 @ X1291) @ (push @ X1295 @ id)))|~(X1289 @ X1295)|(X1289 @ (esk275_3 @ X1289 @ X1290 @ X1291))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem))&(~(X1289 @ (sub @ (esk277_3 @ X1289 @ X1290 @ X1291) @ X1291))|((X1289 @ (sub @ (esk276_3 @ X1289 @ X1290 @ X1291) @ (push @ X1295 @ id)))|~(X1289 @ X1295)|(X1289 @ (esk275_3 @ X1289 @ X1290 @ X1291))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem)))))&((((var @ (esk277_3 @ X1289 @ X1290 @ X1291))|(~(X1289 @ (lam @ (esk276_3 @ X1289 @ X1290 @ X1291)))|~(X1289 @ (ap @ (esk274_3 @ X1289 @ X1290 @ X1291) @ (esk275_3 @ X1289 @ X1290 @ X1291)))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem))&(~(X1289 @ (sub @ (esk277_3 @ X1289 @ X1290 @ X1291) @ X1291))|(~(X1289 @ (lam @ (esk276_3 @ X1289 @ X1290 @ X1291)))|~(X1289 @ (ap @ (esk274_3 @ X1289 @ X1290 @ X1291) @ (esk275_3 @ X1289 @ X1290 @ X1291)))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem)))&(((var @ (esk277_3 @ X1289 @ X1290 @ X1291))|((X1289 @ (sub @ (esk276_3 @ X1289 @ X1290 @ X1291) @ (push @ X1295 @ id)))|~(X1289 @ X1295)|~(X1289 @ (ap @ (esk274_3 @ X1289 @ X1290 @ X1291) @ (esk275_3 @ X1289 @ X1290 @ X1291)))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem))&(~(X1289 @ (sub @ (esk277_3 @ X1289 @ X1290 @ X1291) @ X1291))|((X1289 @ (sub @ (esk276_3 @ X1289 @ X1290 @ X1291) @ (push @ X1295 @ id)))|~(X1289 @ X1295)|~(X1289 @ (ap @ (esk274_3 @ X1289 @ X1290 @ X1291) @ (esk275_3 @ X1289 @ X1290 @ X1291)))|(X1289 @ (sub @ X1290 @ X1291)))|~(induction2lem)))))&((((~(epred52_0 @ X1300)|~(epred52_0 @ X1301)|(epred52_0 @ (ap @ X1300 @ X1301))|(induction2lem))&((~(epred52_0 @ (sub @ X1302 @ (push @ (esk280_1 @ X1302) @ id)))|(epred52_0 @ (lam @ X1302))|(induction2lem))&((epred52_0 @ (esk280_1 @ X1302))|(epred52_0 @ (lam @ X1302))|(induction2lem))))&(~(epred52_0 @ (sub @ esk278_0 @ esk279_0))|(induction2lem)))&(~(var @ X1304)|(epred52_0 @ (sub @ X1304 @ esk279_0))|(induction2lem)))))&(hoasinduction_lem1v2_gthm))&(pushprop_lem0_gthm))&(axmap))&(((~(X1306 @ X1307)|(X1305 @ id @ X1307 @ id)|~(hoasinduction_p_and_p_prime @ X1305 @ X1306))&(~(X1305 @ id @ X1308 @ id)|(X1306 @ X1308)|~(hoasinduction_p_and_p_prime @ X1305 @ X1306)))&((~(X1310 @ (esk281_2 @ X1309 @ X1310))|~(X1309 @ id @ (esk281_2 @ X1309 @ X1310) @ id)|(hoasinduction_p_and_p_prime @ X1309 @ X1310))&((X1310 @ (esk281_2 @ X1309 @ X1310))|(X1309 @ id @ (esk281_2 @ X1309 @ X1310) @ id)|(hoasinduction_p_and_p_prime @ X1309 @ X1310)))))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((one)=(d2term @ d_one)))&(((d2subst @ X1312)!=(d2subst @ X1313))|((X1312)=(X1313))))&((X1314)=(d_id)))&((X1315)=(d2subst @ (esk282_1 @ X1315))))&(((d2term @ X1317)!=(d2term @ X1318))|((X1317)=(X1318))))), 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])])])])])])])).
0.33/0.94	thf(c_0_13, plain, ![X1:term]:(((X1)=(d2term @ (esk1_1 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_14, plain, ![X2:d_term]:(((X2)=(d_one))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_15, plain, ((one)=(d2term @ d_one)), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_16, plain, ((laminj)|((esk162_0)!=(esk163_0))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_17, plain, ![X1:term]:(((one)=(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_14]), c_0_15])).
0.33/0.94	thf(c_0_18, plain, ![X1571:subst > term > subst > $o, X1572:term > $o, X1573:term, X1575:subst, X1576:term, X1577:subst, X1578:term, X1592:subst > term > term, X1597:term, X1598:term, X1599:subst, X1600:term, X1601:subst, X1602:subst, X1603:subst, X1604:term, X1605:subst, X1606:subst]:(((((((((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((sub @ (esk393_3 @ X1571 @ X1572 @ X1573 @ X1575 @ X1576) @ X1577)=(esk393_3 @ X1571 @ X1572 @ X1573 @ (comp @ X1575 @ X1577) @ (sub @ X1576 @ X1577))))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((sub @ (esk393_3 @ X1571 @ X1572 @ X1573 @ X1575 @ X1576) @ X1577)=(esk393_3 @ X1571 @ X1572 @ X1573 @ (comp @ X1575 @ X1577) @ (sub @ X1576 @ X1577))))|(X1572 @ (lam @ X1573))))|~(epred7_0)))&((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((sub @ (esk393_3 @ X1571 @ X1572 @ X1573 @ X1575 @ X1576) @ X1577)=(esk393_3 @ X1571 @ X1572 @ X1573 @ (comp @ X1575 @ X1577) @ (sub @ X1576 @ X1577))))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((sub @ (esk393_3 @ X1571 @ X1572 @ X1573 @ X1575 @ X1576) @ X1577)=(esk393_3 @ X1571 @ X1572 @ X1573 @ (comp @ X1575 @ X1577) @ (sub @ X1576 @ X1577))))|(X1572 @ (lam @ X1573))))|~(epred7_0))))&(((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((sub @ (esk393_3 @ X1571 @ X1572 @ X1573 @ X1575 @ X1576) @ X1577)=(esk393_3 @ X1571 @ X1572 @ X1573 @ (comp @ X1575 @ X1577) @ (sub @ X1576 @ X1577))))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((sub @ (esk393_3 @ X1571 @ X1572 @ X1573 @ X1575 @ X1576) @ X1577)=(esk393_3 @ X1571 @ X1572 @ X1573 @ (comp @ X1575 @ X1577) @ (sub @ X1576 @ X1577))))|(X1572 @ (lam @ X1573))))|~(epred7_0)))&((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((sub @ (esk393_3 @ X1571 @ X1572 @ X1573 @ X1575 @ X1576) @ X1577)=(esk393_3 @ X1571 @ X1572 @ X1573 @ (comp @ X1575 @ X1577) @ (sub @ X1576 @ X1577))))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((sub @ (esk393_3 @ X1571 @ X1572 @ X1573 @ X1575 @ X1576) @ X1577)=(esk393_3 @ X1571 @ X1572 @ X1573 @ (comp @ X1575 @ X1577) @ (sub @ 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(esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((X1571 @ id @ (esk393_3 @ X1571 @ X1572 @ X1573 @ id @ X1578) @ id)|~(X1571 @ id @ X1578 @ id)))|(X1572 @ (lam @ X1573))))|~(epred7_0)))&((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((X1571 @ id @ (esk393_3 @ X1571 @ X1572 @ X1573 @ id @ X1578) @ id)|~(X1571 @ id @ X1578 @ id)))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|((X1571 @ id @ (esk393_3 @ X1571 @ X1572 @ X1573 @ id @ X1578) @ id)|~(X1571 @ id @ X1578 @ id)))|(X1572 @ (lam @ X1573))))|~(epred7_0)))))))&(((((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0)))&((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))))&(((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0)))&((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|(~(X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|~(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0)))))&((((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0)))&((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|(~(X1572 @ (sub @ X1573 @ (push @ (esk395_3 @ X1571 @ X1572 @ X1573) @ id)))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))))&(((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|((X1571 @ (comp @ (esk396_1 @ X1571) @ (esk399_1 @ X1571)) @ (sub @ (esk397_1 @ X1571) @ (esk399_1 @ X1571)) @ (esk398_1 @ X1571))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0)))&((~(X1571 @ (comp @ (esk400_1 @ X1571) @ (esk403_1 @ X1571)) @ (sub @ (esk401_1 @ X1571) @ (esk403_1 @ X1571)) @ (esk402_1 @ X1571))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0))&((X1571 @ (esk400_1 @ X1571) @ (esk401_1 @ X1571) @ (comp @ (esk403_1 @ X1571) @ (esk402_1 @ X1571)))|(~(X1571 @ (esk396_1 @ X1571) @ (esk397_1 @ X1571) @ (comp @ (esk399_1 @ X1571) @ (esk398_1 @ X1571)))|((X1572 @ (esk395_3 @ X1571 @ X1572 @ X1573))|((X1572 @ (esk394_3 @ X1571 @ X1572 @ X1573))|(X1571 @ id @ (esk394_3 @ X1571 @ X1572 @ X1573) @ id)|~(X1571 @ id @ (lam @ (esk393_3 @ X1571 @ X1572 @ X1573 @ sh @ one)) @ id))|(X1572 @ (lam @ X1573))))|~(epred7_0)))))))&(((((((~(epred67_0 @ id @ (X1592 @ id @ (esk408_1 @ X1592)) @ id)|((sub @ (X1592 @ (esk405_1 @ X1592) @ (esk406_1 @ X1592)) @ (esk407_1 @ X1592))!=(X1592 @ (comp @ (esk405_1 @ X1592) @ (esk407_1 @ X1592)) @ (sub @ (esk406_1 @ X1592) @ (esk407_1 @ X1592))))|(epred67_0 @ id @ (lam @ (X1592 @ sh @ one)) @ id)|(epred7_0))&((epred67_0 @ id @ (esk408_1 @ X1592) @ id)|((sub @ (X1592 @ (esk405_1 @ X1592) @ (esk406_1 @ X1592)) @ (esk407_1 @ X1592))!=(X1592 @ (comp @ (esk405_1 @ X1592) @ (esk407_1 @ X1592)) @ (sub @ (esk406_1 @ X1592) @ (esk407_1 @ X1592))))|(epred67_0 @ id @ (lam @ (X1592 @ sh @ one)) @ id)|(epred7_0)))&((~(epred68_0 @ X1597)|(epred67_0 @ id @ X1597 @ id)|(epred7_0))&(~(epred67_0 @ id @ X1597 @ id)|(epred68_0 @ X1597)|(epred7_0))))&((epred68_0 @ (sub @ esk404_0 @ (push @ X1598 @ id)))|~(epred68_0 @ X1598)|(epred7_0)))&(~(epred68_0 @ (lam @ esk404_0))|(epred7_0)))&(~(epred67_0 @ (comp @ X1599 @ X1602) @ (sub @ X1600 @ X1602) @ X1601)|(epred67_0 @ X1599 @ X1600 @ (comp @ X1602 @ X1601))|(epred7_0)))&((epred67_0 @ (comp @ X1603 @ X1606) @ (sub @ X1604 @ X1606) @ X1605)|~(epred67_0 @ X1603 @ X1604 @ (comp @ X1606 @ X1605))|(epred7_0))))), 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_7])])])])])])])).
0.33/0.94	thf(c_0_19, plain, ![X1:term, X5:term]:((((X1)=(X5))|~((laminj))|((lam @ X1)!=(lam @ X5)))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_20, plain, (laminj), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17]), c_0_17])])).
0.33/0.94	thf(c_0_21, plain, ![X3:subst]:(((X3)=(d2subst @ (esk282_1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_22, plain, ![X75:d_subst]:(((X75)=(d_id))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_23, plain, ((id)=(d2subst @ d_id)), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_24, plain, ((epred7_0)|~((epred68_0 @ (lam @ esk404_0)))), inference(split_conjunct,[status(thm)],[c_0_18])).
0.33/0.94	thf(c_0_25, negated_conjecture, ~(((hoasinduction_lem3v2)<=>![X81:subst > term > subst > $o, X8:term > $o]:((![X6:subst, X5:term, X20:subst, X33:subst]:(((X81 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)<=(X81 @ X6 @ X5 @ (comp @ X33 @ X20))))=>(![X6:subst, X5:term, X20:subst, X33:subst]:(((X81 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)=>(X81 @ X6 @ X5 @ (comp @ X33 @ X20))))=>(![X11:subst > term > term]:((((X81 @ id @ (hoaslam @ id @ (^[X6:subst, X5:term]:(X11 @ X6 @ X5))) @ id)<=![X5:term]:(((X81 @ id @ (X11 @ id @ X5) @ id)<=(X81 @ id @ X5 @ id))))<=![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))))=>(![X5:term]:(((X8 @ (lam @ X5))<=![X10:term]:(((X8 @ (sub @ X5 @ (push @ X10 @ id)))<=(X8 @ X10)))))<=(hoasinduction_p_and_p_prime @ X81 @ X8)))))))), inference(assume_negation,[status(cth)],[hoasinduction_lem3v2])).
0.33/0.94	thf(c_0_26, plain, ![X1:term]:(((epred68_0 @ (sub @ esk404_0 @ (push @ X1 @ id)))|(epred7_0)|~((epred68_0 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_18])).
0.33/0.94	thf(c_0_27, plain, ![X1:term, X5:term]:(((X1)=(X5))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_17]), c_0_17]), c_0_20])])).
0.33/0.94	thf(c_0_28, plain, ![X3:subst]:(((id)=(X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_22]), c_0_23])).
0.33/0.94	thf(c_0_29, plain, ((epred7_0)|~((epred68_0 @ one))), inference(rw,[status(thm)],[c_0_24, c_0_17])).
0.33/0.94	thf(c_0_30, plain, ((hoasinduction_no_psi_cond)|~((epred33_0 @ id @ esk142_0 @ id))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_31, negated_conjecture, ~(((hoasinduction_lem3v2)<=>![X81:subst > term > subst > $o, X8:term > $o]:((![X6:subst, X5:term, X20:subst, X33:subst]:(((X81 @ X6 @ X5 @ (comp @ X33 @ X20))=>(X81 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)))=>(![X6:subst, X5:term, X20:subst, X33:subst]:(((X81 @ (comp @ X6 @ X33) @ (sub @ X5 @ X33) @ X20)=>(X81 @ X6 @ X5 @ (comp @ X33 @ X20))))=>(![X11:subst > term > term]:((![X6:subst, X5:term, X20:subst]:(((sub @ (X11 @ X6 @ X5) @ X20)=(X11 @ (comp @ X6 @ X20) @ (sub @ X5 @ X20))))=>(![X5:term]:(((X81 @ id @ X5 @ id)=>(X81 @ id @ (X11 @ id @ X5) @ id)))=>(X81 @ id @ (hoaslam @ id @ (^[Z0:subst, Z1:term]:(X11 @ Z0 @ Z1))) @ id))))=>((hoasinduction_p_and_p_prime @ X81 @ X8)=>![X5:term]:((![X10:term]:(((X8 @ X10)=>(X8 @ (sub @ X5 @ (push @ X10 @ id)))))=>(X8 @ (lam @ X5))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_25])])).
0.33/0.94	thf(c_0_32, plain, ![X1:term]:(((epred68_0 @ X1)|(epred7_0)|~((epred67_0 @ id @ X1 @ id)))), inference(split_conjunct,[status(thm)],[c_0_18])).
0.33/0.94	thf(c_0_33, plain, ![X1:term]:(((epred7_0)|~((epred68_0 @ X1)))), inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27]), c_0_28]), c_0_17]), c_0_29])).
0.33/0.94	thf(c_0_34, plain, ![X4:subst > term > term]:(((epred67_0 @ id @ (esk408_1 @ X4) @ id)|(epred67_0 @ id @ (lam @ (X4 @ sh @ one)) @ id)|(epred7_0)|((sub @ (X4 @ (esk405_1 @ X4) @ (esk406_1 @ X4)) @ (esk407_1 @ X4))!=(X4 @ (comp @ (esk405_1 @ X4) @ (esk407_1 @ X4)) @ (sub @ (esk406_1 @ X4) @ (esk407_1 @ X4)))))), inference(split_conjunct,[status(thm)],[c_0_18])).
0.33/0.94	thf(c_0_35, plain, ![X1:term, X21:subst > term > subst > $o]:(((X21 @ id @ X1 @ id)|~((X21 @ id @ (lam @ (esk141_1 @ X21 @ sh @ one)) @ id))|~((X21 @ id @ (ap @ (sub @ (esk139_1 @ X21) @ id) @ (esk140_1 @ X21)) @ id))|~((hoasinduction_no_psi_cond)))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_36, plain, ![X5:term, X1:term]:(((epred33_0 @ id @ (ap @ (sub @ X1 @ id) @ X5) @ id)|(hoasinduction_no_psi_cond)|~((epred33_0 @ id @ X5 @ id))|~((epred33_0 @ id @ X1 @ id)))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_37, plain, ((hoasinduction_no_psi_cond)|~((epred33_0 @ id @ one @ id))), inference(rw,[status(thm)],[c_0_30, c_0_17])).
0.33/0.94	thf(c_0_38, negated_conjecture, ![X1321:subst, X1322:term, X1323:subst, X1324:subst, X1325:subst, X1326:term, X1327:subst, X1328:subst, X1329:subst > term > term, X1335:term, X1336:subst > term > subst > $o, X1346:subst, X1347:term, X1348:subst, X1349:term, X1350:term > $o, X1351:term]:((((~(epred53_0 @ X1321 @ X1322 @ (comp @ X1324 @ X1323))|(epred53_0 @ (comp @ X1321 @ X1324) @ (sub @ X1322 @ X1324) @ X1323)|~(hoasinduction_lem3v2))&((~(epred53_0 @ (comp @ X1325 @ X1328) @ (sub @ X1326 @ X1328) @ X1327)|(epred53_0 @ X1325 @ X1326 @ (comp @ X1328 @ X1327))|~(hoasinduction_lem3v2))&((((epred53_0 @ id @ (esk286_1 @ X1329) @ id)|(epred53_0 @ id @ (hoaslam @ id @ X1329) @ id)|((sub @ (X1329 @ (esk283_1 @ X1329) @ (esk284_1 @ X1329)) @ (esk285_1 @ X1329))!=(X1329 @ (comp @ (esk283_1 @ X1329) @ (esk285_1 @ X1329)) @ (sub @ (esk284_1 @ X1329) @ (esk285_1 @ X1329))))|~(hoasinduction_lem3v2))&(~(epred53_0 @ id @ (X1329 @ id @ (esk286_1 @ X1329)) @ id)|(epred53_0 @ id @ (hoaslam @ id @ X1329) @ id)|((sub @ (X1329 @ (esk283_1 @ X1329) @ (esk284_1 @ X1329)) @ (esk285_1 @ X1329))!=(X1329 @ (comp @ (esk283_1 @ X1329) @ (esk285_1 @ X1329)) @ (sub @ (esk284_1 @ X1329) @ (esk285_1 @ X1329))))|~(hoasinduction_lem3v2)))&(((hoasinduction_p_and_p_prime @ epred53_0 @ epred54_0)|~(hoasinduction_lem3v2))&((~(epred54_0 @ X1335)|(epred54_0 @ (sub @ esk287_0 @ (push @ X1335 @ id)))|~(hoasinduction_lem3v2))&(~(epred54_0 @ (lam @ esk287_0))|~(hoasinduction_lem3v2)))))))&((((((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|((sub @ (esk296_1 @ X1336 @ X1346 @ X1347) @ X1348)=(esk296_1 @ X1336 @ (comp @ X1346 @ X1348) @ (sub @ X1347 @ X1348)))|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|((sub @ (esk296_1 @ X1336 @ X1346 @ X1347) @ X1348)=(esk296_1 @ X1336 @ (comp @ X1346 @ X1348) @ (sub @ X1347 @ X1348)))|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2)))&((((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|(~(X1336 @ id @ X1349 @ id)|(X1336 @ id @ (esk296_1 @ X1336 @ id @ X1349) @ id))|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|(~(X1336 @ id @ X1349 @ id)|(X1336 @ id @ (esk296_1 @ X1336 @ id @ X1349) @ id))|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2)))&(((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|~(X1336 @ id @ (hoaslam @ id @ (esk296_1 @ X1336)) @ id)|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|~(X1336 @ id @ (hoaslam @ id @ (esk296_1 @ X1336)) @ id)|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2)))))&((((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|((sub @ (esk296_1 @ X1336 @ X1346 @ X1347) @ X1348)=(esk296_1 @ X1336 @ (comp @ X1346 @ X1348) @ (sub @ X1347 @ X1348)))|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|((sub @ (esk296_1 @ X1336 @ X1346 @ X1347) @ X1348)=(esk296_1 @ X1336 @ (comp @ X1346 @ X1348) @ (sub @ X1347 @ X1348)))|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2)))&((((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|(~(X1336 @ id @ X1349 @ id)|(X1336 @ id @ (esk296_1 @ X1336 @ id @ X1349) @ id))|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|(~(X1336 @ id @ X1349 @ id)|(X1336 @ id @ (esk296_1 @ X1336 @ id @ X1349) @ id))|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2)))&(((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|~(X1336 @ id @ (hoaslam @ id @ (esk296_1 @ X1336)) @ id)|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|~(X1336 @ id @ (hoaslam @ id @ (esk296_1 @ X1336)) @ id)|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|(X1336 @ (esk288_1 @ X1336) @ (esk289_1 @ X1336) @ (comp @ (esk291_1 @ X1336) @ (esk290_1 @ X1336)))|(hoasinduction_lem3v2))))))&(((((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|((sub @ (esk296_1 @ X1336 @ X1346 @ X1347) @ X1348)=(esk296_1 @ X1336 @ (comp @ X1346 @ X1348) @ (sub @ X1347 @ X1348)))|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|((sub @ (esk296_1 @ X1336 @ X1346 @ X1347) @ X1348)=(esk296_1 @ X1336 @ (comp @ X1346 @ X1348) @ (sub @ X1347 @ X1348)))|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2)))&((((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|(~(X1336 @ id @ X1349 @ id)|(X1336 @ id @ (esk296_1 @ X1336 @ id @ X1349) @ id))|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|(~(X1336 @ id @ X1349 @ id)|(X1336 @ id @ (esk296_1 @ X1336 @ id @ X1349) @ id))|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2)))&(((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|~(X1336 @ id @ (hoaslam @ id @ (esk296_1 @ X1336)) @ id)|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|~(X1336 @ id @ (hoaslam @ id @ (esk296_1 @ X1336)) @ id)|(X1336 @ (comp @ (esk292_1 @ X1336) @ (esk295_1 @ X1336)) @ (sub @ (esk293_1 @ X1336) @ (esk295_1 @ X1336)) @ (esk294_1 @ X1336))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2)))))&((((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|((sub @ (esk296_1 @ X1336 @ X1346 @ X1347) @ X1348)=(esk296_1 @ X1336 @ (comp @ X1346 @ X1348) @ (sub @ X1347 @ X1348)))|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|((sub @ (esk296_1 @ X1336 @ X1346 @ X1347) @ X1348)=(esk296_1 @ X1336 @ (comp @ X1346 @ X1348) @ (sub @ X1347 @ X1348)))|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2)))&((((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|(~(X1336 @ id @ X1349 @ id)|(X1336 @ id @ (esk296_1 @ X1336 @ id @ X1349) @ id))|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|(~(X1336 @ id @ X1349 @ id)|(X1336 @ id @ (esk296_1 @ X1336 @ id @ X1349) @ id))|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2)))&(((X1350 @ (esk297_3 @ X1336 @ X1350 @ X1351))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|~(X1336 @ id @ (hoaslam @ id @ (esk296_1 @ X1336)) @ id)|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2))&(~(X1350 @ (sub @ X1351 @ (push @ (esk297_3 @ X1336 @ X1350 @ X1351) @ id)))|(X1350 @ (lam @ X1351))|~(hoasinduction_p_and_p_prime @ X1336 @ X1350)|~(X1336 @ id @ (hoaslam @ id @ (esk296_1 @ X1336)) @ id)|~(X1336 @ (esk292_1 @ X1336) @ (esk293_1 @ X1336) @ (comp @ (esk295_1 @ X1336) @ (esk294_1 @ X1336)))|~(X1336 @ (comp @ (esk288_1 @ X1336) @ (esk291_1 @ X1336)) @ (sub @ (esk289_1 @ X1336) @ (esk291_1 @ X1336)) @ (esk290_1 @ X1336))|(hoasinduction_lem3v2))))))))), 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_31])])])])])])])).
0.33/0.94	thf(c_0_39, plain, ![X1:term]:(((epred7_0)|~((epred67_0 @ id @ X1 @ id)))), inference(csr,[status(thm)],[c_0_32, c_0_33])).
0.33/0.94	thf(c_0_40, plain, ((epred67_0 @ id @ one @ id)|(epred7_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_27]), c_0_17]), c_0_28]), c_0_28]), c_0_28]), c_0_27]), c_0_28]), c_0_17]), c_0_27]), c_0_28]), c_0_27]), c_0_27]), c_0_28]), c_0_17])])).
0.33/0.94	thf(c_0_41, plain, ![X21:subst > term > subst > $o, X5:term, X1:term]:(((X21 @ id @ (esk141_1 @ X21 @ id @ X1) @ id)|(X21 @ id @ (esk139_1 @ X21) @ id)|(X21 @ id @ X5 @ id)|~((X21 @ id @ X1 @ id))|~((hoasinduction_no_psi_cond)))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_42, plain, ![X1:term, X21:subst > term > subst > $o]:(((X21 @ id @ X1 @ id)|~((X21 @ id @ one @ id))|~((hoasinduction_no_psi_cond)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_28]), c_0_27]), c_0_17]), c_0_27]), c_0_17]), c_0_27]), c_0_17])])).
0.33/0.94	thf(c_0_43, plain, ![X4:subst > term > term]:(((epred33_0 @ id @ (esk143_1 @ X4) @ id)|(epred33_0 @ id @ (lam @ (X4 @ sh @ one)) @ id)|(hoasinduction_no_psi_cond)|((sub @ (X4 @ (esk144_1 @ X4) @ (esk145_1 @ X4)) @ (esk146_1 @ X4))!=(X4 @ (comp @ (esk144_1 @ X4) @ (esk146_1 @ X4)) @ (sub @ (esk145_1 @ X4) @ (esk146_1 @ X4)))))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_44, plain, ![X1:term]:(((hoasinduction_no_psi_cond)|~((epred33_0 @ id @ X1 @ id)))), inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_17])]), c_0_37])).
0.33/0.94	thf(c_0_45, negated_conjecture, ![X4:subst > term > term]:(((epred53_0 @ id @ (esk286_1 @ X4) @ id)|(epred53_0 @ id @ (hoaslam @ id @ X4) @ id)|((sub @ (X4 @ (esk283_1 @ X4) @ (esk284_1 @ X4)) @ (esk285_1 @ X4))!=(X4 @ (comp @ (esk283_1 @ X4) @ (esk285_1 @ X4)) @ (sub @ (esk284_1 @ X4) @ (esk285_1 @ X4))))|~((hoasinduction_lem3v2)))), inference(split_conjunct,[status(thm)],[c_0_38])).
0.33/0.94	thf(c_0_46, plain, ((hoasinduction_lem3v2)|~((epred7_0))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_47, plain, (epred7_0), inference(spm,[status(thm)],[c_0_39, c_0_40])).
0.33/0.94	thf(c_0_48, negated_conjecture, (~((epred54_0 @ (lam @ esk287_0)))|~((hoasinduction_lem3v2))), inference(split_conjunct,[status(thm)],[c_0_38])).
0.33/0.94	thf(c_0_49, plain, ![X1:term, X21:subst > term > subst > $o, X5:term]:(((X21 @ id @ X1 @ id)|~((X21 @ id @ X5 @ id))|~((hoasinduction_no_psi_cond)))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_27]), c_0_27])]), c_0_42])).
0.33/0.94	thf(c_0_50, plain, (hoasinduction_no_psi_cond), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_27]), c_0_17]), c_0_28]), c_0_28]), c_0_28]), c_0_27]), c_0_28]), c_0_17]), c_0_27]), c_0_28]), c_0_27]), c_0_27]), c_0_28]), c_0_17])]), c_0_44])).
0.33/0.94	thf(c_0_51, negated_conjecture, ((epred53_0 @ id @ one @ id)|~((hoasinduction_lem3v2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_27]), c_0_27]), c_0_28]), c_0_28]), c_0_28]), c_0_27]), c_0_28]), c_0_17]), c_0_27]), c_0_28]), c_0_27]), c_0_27]), c_0_28]), c_0_17])])).
0.33/0.94	thf(c_0_52, plain, (hoasinduction_lem3v2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46, c_0_47])])).
0.33/0.94	thf(c_0_53, negated_conjecture, ![X1:term]:(((epred54_0 @ (sub @ esk287_0 @ (push @ X1 @ id)))|~((epred54_0 @ X1))|~((hoasinduction_lem3v2)))), inference(split_conjunct,[status(thm)],[c_0_38])).
0.33/0.94	thf(c_0_54, negated_conjecture, (~((epred54_0 @ one))|~((hoasinduction_lem3v2))), inference(rw,[status(thm)],[c_0_48, c_0_17])).
0.33/0.94	thf(c_0_55, negated_conjecture, ((hoasinduction_p_and_p_prime @ epred53_0 @ epred54_0)|~((hoasinduction_lem3v2))), inference(split_conjunct,[status(thm)],[c_0_38])).
0.33/0.94	thf(c_0_56, plain, ![X1:term, X21:subst > term > subst > $o, X5:term]:(((X21 @ id @ X1 @ id)|~((X21 @ id @ X5 @ id)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50])])).
0.33/0.94	thf(c_0_57, negated_conjecture, (epred53_0 @ id @ one @ id), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])).
0.33/0.94	thf(c_0_58, negated_conjecture, ![X1:term]:((~((epred54_0 @ X1))|~((hoasinduction_lem3v2)))), inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_17]), c_0_54])).
0.33/0.94	thf(c_0_59, plain, ![X1:term, X21:subst > term > subst > $o, X7:term > $o]:(((X7 @ X1)|~((X21 @ id @ X1 @ id))|~((hoasinduction_p_and_p_prime @ X21 @ X7)))), inference(split_conjunct,[status(thm)],[c_0_12])).
0.33/0.94	thf(c_0_60, negated_conjecture, (hoasinduction_p_and_p_prime @ epred53_0 @ epred54_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55, c_0_52])])).
0.33/0.94	thf(c_0_61, negated_conjecture, ![X1:term]:((epred53_0 @ id @ X1 @ id)), inference(spm,[status(thm)],[c_0_56, c_0_57])).
0.33/0.94	thf(c_0_62, negated_conjecture, ![X1:term]:(~((epred54_0 @ X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58, c_0_52])])).
0.33/0.94	thf(c_0_63, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60]), c_0_61])]), c_0_62]), ['proof']).
0.33/0.94	% SZS output end CNFRefutation
0.33/0.94	% Parsed axioms                        : 132
0.33/0.94	% Removed by relevancy pruning/SinE    : 0
0.33/0.94	% Initial clauses                      : 1402
0.33/0.94	% Removed in clause preprocessing      : 130
0.33/0.94	% Initial clauses in saturation        : 1272
0.33/0.94	% Processed clauses                    : 1530
0.33/0.94	% ...of these trivial                  : 803
0.33/0.94	% ...subsumed                          : 171
0.33/0.94	% ...remaining for further processing  : 556
0.33/0.94	% Other redundant clauses eliminated   : 0
0.33/0.94	% Clauses deleted for lack of memory   : 0
0.33/0.94	% Backward-subsumed                    : 82
0.33/0.94	% Backward-rewritten                   : 120
0.33/0.94	% Generated clauses                    : 244
0.33/0.94	% ...of the previous two non-redundant : 287
0.33/0.94	% ...aggressively subsumed             : 0
0.33/0.94	% Contextual simplify-reflections      : 66
0.33/0.94	% Paramodulations                      : 243
0.33/0.94	% Factorizations                       : 0
0.33/0.94	% NegExts                              : 0
0.33/0.94	% Equation resolutions                 : 0
0.33/0.94	% Disequality decompositions           : 0
0.33/0.94	% Total rewrite steps                  : 14243
0.33/0.94	% ...of those cached                   : 13537
0.33/0.94	% Propositional unsat checks           : 0
0.33/0.94	%    Propositional check models        : 0
0.33/0.94	%    Propositional check unsatisfiable : 0
0.33/0.94	%    Propositional clauses             : 0
0.33/0.94	%    Propositional clauses after purity: 0
0.33/0.94	%    Propositional unsat core size     : 0
0.33/0.94	%    Propositional preprocessing time  : 0.000
0.33/0.94	%    Propositional encoding time       : 0.000
0.33/0.94	%    Propositional solver time         : 0.000
0.33/0.94	%    Success case prop preproc time    : 0.000
0.33/0.94	%    Success case prop encoding time   : 0.000
0.33/0.94	%    Success case prop solver time     : 0.000
0.33/0.94	% Current number of processed clauses  : 156
0.33/0.94	%    Positive orientable unit clauses  : 108
0.33/0.94	%    Positive unorientable unit clauses: 4
0.33/0.94	%    Negative unit clauses             : 9
0.33/0.94	%    Non-unit-clauses                  : 35
0.33/0.94	% Current number of unprocessed clauses: 193
0.33/0.94	% ...number of literals in the above   : 455
0.33/0.94	% Current number of archived formulas  : 0
0.33/0.94	% Current number of archived clauses   : 400
0.33/0.94	% Clause-clause subsumption calls (NU) : 19742
0.33/0.94	% Rec. Clause-clause subsumption calls : 10476
0.33/0.94	% Non-unit clause-clause subsumptions  : 402
0.33/0.94	% Unit Clause-clause subsumption calls : 3267
0.33/0.94	% Rewrite failures with RHS unbound    : 0
0.33/0.94	% BW rewrite match attempts            : 2483
0.33/0.94	% BW rewrite match successes           : 109
0.33/0.94	% Condensation attempts                : 1533
0.33/0.94	% Condensation successes               : 129
0.33/0.94	% Termbank termtop insertions          : 151821
0.33/0.94	% Search garbage collected termcells   : 25461
0.33/0.94	
0.33/0.94	% -------------------------------------------------
0.33/0.94	% User time                : 0.312 s
0.33/0.94	% System time              : 0.024 s
0.33/0.94	% Total time               : 0.336 s
0.33/0.94	% Maximum resident set size: 8344 pages
0.33/0.94	
0.33/0.94	% -------------------------------------------------
0.33/0.94	% User time                : 0.987 s
0.33/0.94	% System time              : 0.080 s
0.33/0.94	% Total time               : 1.067 s
0.33/0.94	% Maximum resident set size: 5376 pages
0.33/0.94	% E exiting
0.33/0.95	EOF