%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX163^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:25 AM UTC 2026
% Result : Theorem 1.58s 0.51s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX163^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.15 % Computer : n026.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Sep 29 16:11:57 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.23 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=300 /export/starexec/sandbox/tmp/tmp.PxFhX1VfEH/E---3.1_793636.p
% 1.58/0.51 % Version: 3.5.1-ho
% 1.58/0.51 % partial match(1): HSLMSMSSSSMNHSA
% 1.58/0.51 % Preprocessing class: HSLMSLSSSSMNHSA.
% 1.58/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.58/0.51 % Starting new_ho_10 with 1500s (5) cores
% 1.58/0.51 % Starting sh5l with 300s (1) cores
% 1.58/0.51 % Starting new_bool_1 with 300s (1) cores
% 1.58/0.51 % Starting new_bool_2 with 300s (1) cores
% 1.58/0.51 % new_ho_10 with pid 793649 completed with status 0
% 1.58/0.51 % Result found by new_ho_10
% 1.58/0.51 % partial match(1): HSLMSMSSSSMNHSA
% 1.58/0.51 % Preprocessing class: HSLMSLSSSSMNHSA.
% 1.58/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.58/0.51 % Starting new_ho_10 with 1500s (5) cores
% 1.58/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.58/0.51 % No SInE strategy applied
% 1.58/0.51 % Search class: HGHSM-SMLM31-MHSFFMBN
% 1.58/0.51 % partial match(1): HGHSM-SMLM31-MHSFFSBN
% 1.58/0.51 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.58/0.51 % Starting SubtermCWHack with 151s (1) cores
% 1.58/0.51 % Starting new_ho_10 with 901s (1) cores
% 1.58/0.51 % Starting new_bool_1 with 151s (1) cores
% 1.58/0.51 % Starting new_bool_2 with 151s (1) cores
% 1.58/0.51 % Starting new_bool_9 with 146s (1) cores
% 1.58/0.51 % new_ho_10 with pid 793659 completed with status 0
% 1.58/0.51 % Result found by new_ho_10
% 1.58/0.51 % partial match(1): HSLMSMSSSSMNHSA
% 1.58/0.51 % Preprocessing class: HSLMSLSSSSMNHSA.
% 1.58/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.58/0.51 % Starting new_ho_10 with 1500s (5) cores
% 1.58/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.58/0.51 % No SInE strategy applied
% 1.58/0.51 % Search class: HGHSM-SMLM31-MHSFFMBN
% 1.58/0.51 % partial match(1): HGHSM-SMLM31-MHSFFSBN
% 1.58/0.51 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.58/0.51 % Starting SubtermCWHack with 151s (1) cores
% 1.58/0.51 % Starting new_ho_10 with 901s (1) cores
% 1.58/0.51 % Preprocessing time : 0.032 s
% 1.58/0.51 % Presaturation interreduction done
% 1.58/0.51
% 1.58/0.51 % Proof found!
% 1.58/0.51 % SZS status Theorem
% 1.58/0.51 % SZS output start CNFRefutation
% 1.58/0.51 thf(decl_sort1, type, term: $tType).
% 1.58/0.51 thf(decl_sort2, type, subst: $tType).
% 1.58/0.51 thf(decl_sort3, type, d_term: $tType).
% 1.58/0.51 thf(decl_sort4, type, d_subst: $tType).
% 1.58/0.51 thf(decl_23, type, one: term).
% 1.58/0.51 thf(decl_24, type, ap: term > term > term).
% 1.58/0.51 thf(decl_25, type, lam: term > term).
% 1.58/0.51 thf(decl_26, type, sub: term > subst > term).
% 1.58/0.51 thf(decl_27, type, id: subst).
% 1.58/0.51 thf(decl_28, type, sh: subst).
% 1.58/0.51 thf(decl_29, type, push: term > subst > subst).
% 1.58/0.51 thf(decl_30, type, comp: subst > subst > subst).
% 1.58/0.51 thf(decl_31, type, var: term > $o).
% 1.58/0.51 thf(decl_32, type, pushprop_lem1v2: $o).
% 1.58/0.51 thf(decl_33, type, pushprop_lem1_gthm: $o).
% 1.58/0.51 thf(decl_34, type, axmap: $o).
% 1.58/0.51 thf(decl_35, type, pushprop_lem0_gthm: $o).
% 1.58/0.51 thf(decl_36, type, shinj: $o).
% 1.58/0.51 thf(decl_37, type, hoasinduction_lem1v2: $o).
% 1.58/0.51 thf(decl_38, type, hoasinduction_lem1v2_gthm: $o).
% 1.58/0.51 thf(decl_39, type, hoasap: subst > term > subst > term > term).
% 1.58/0.51 thf(decl_40, type, induction2lem: $o).
% 1.58/0.51 thf(decl_41, type, hoasinduction_lem3v2_f: $o).
% 1.58/0.51 thf(decl_42, type, axvarshift: $o).
% 1.58/0.51 thf(decl_43, type, hoasapinj2: $o).
% 1.58/0.51 thf(decl_44, type, hoasapnotvar_gthm: $o).
% 1.58/0.51 thf(decl_45, type, hoasapinj1: $o).
% 1.58/0.51 thf(decl_46, type, ulamvar1: $o).
% 1.58/0.51 thf(decl_47, type, induction2lem_lthm: $o).
% 1.58/0.51 thf(decl_48, type, hoasinduction_lem3v2_gthm: $o).
% 1.58/0.51 thf(decl_49, type, apnotvar: $o).
% 1.58/0.51 thf(decl_50, type, pushprop_lthm_orig: $o).
% 1.58/0.51 thf(decl_51, type, hoasinduction_lem3v2_f_lthm: $o).
% 1.58/0.51 thf(decl_52, type, hoasinduction_lthm: $o).
% 1.58/0.51 thf(decl_53, type, hoasinduction_no_psi_cond_lthm: $o).
% 1.58/0.51 thf(decl_54, type, hoaslaminj: $o).
% 1.58/0.51 thf(decl_55, type, hoasinduction_lem3aaa: $o).
% 1.58/0.51 thf(decl_56, type, induction2lem_gthm: $o).
% 1.58/0.51 thf(decl_57, type, hoasinduction_lem3aa_lthm: $o).
% 1.58/0.51 thf(decl_58, type, hoasinduction_lem3: $o).
% 1.58/0.51 thf(decl_59, type, hoasinduction_lem2: $o).
% 1.58/0.51 thf(decl_60, type, termmset_lthm: $o).
% 1.58/0.51 thf(decl_61, type, hoasinduction_lem1: $o).
% 1.58/0.51 thf(decl_62, type, hoaslamnotap_lthm: $o).
% 1.58/0.51 thf(decl_63, type, pushprop_lem1v2_lthm: $o).
% 1.58/0.51 thf(decl_64, type, hoasapnotvar: $o).
% 1.58/0.51 thf(decl_65, type, hoasinduction_lem0: $o).
% 1.58/0.51 thf(decl_66, type, hoasinduction: $o).
% 1.58/0.51 thf(decl_67, type, hoasinduction_gthm: $o).
% 1.58/0.51 thf(decl_68, type, axapp: $o).
% 1.58/0.51 thf(decl_69, type, hoaslamnotvar_lthm: $o).
% 1.58/0.51 thf(decl_70, type, pushprop_lem3v2_lthm: $o).
% 1.58/0.51 thf(decl_71, type, hoasinduction_lem3b_lthm: $o).
% 1.58/0.51 thf(decl_72, type, ulamvarind: $o).
% 1.58/0.51 thf(decl_73, type, induction: $o).
% 1.58/0.51 thf(decl_74, type, hoasinduction_lem3a_lthm: $o).
% 1.58/0.51 thf(decl_75, type, termmset_gthm: $o).
% 1.58/0.51 thf(decl_76, type, hoasinduction_lem3aa: $o).
% 1.58/0.51 thf(decl_77, type, pushprop_lem1v2_gthm: $o).
% 1.58/0.51 thf(decl_78, type, hoaslamnotap_gthm: $o).
% 1.58/0.51 thf(decl_79, type, hoaslamnotvar_gthm: $o).
% 1.58/0.51 thf(decl_80, type, hoasinduction_lem3b_gthm: $o).
% 1.58/0.51 thf(decl_81, type, pushprop_lem2v2: $o).
% 1.58/0.51 thf(decl_82, type, hoasinduction_lem3a_gthm: $o).
% 1.58/0.51 thf(decl_83, type, axclos: $o).
% 1.58/0.51 thf(decl_84, type, axassoc: $o).
% 1.58/0.51 thf(decl_85, type, hoasinduction_lem2v2: $o).
% 1.58/0.51 thf(decl_86, type, pushprop_lthm: $o).
% 1.58/0.51 thf(decl_87, type, apinj2: $o).
% 1.58/0.51 thf(decl_88, type, apinj1: $o).
% 1.58/0.51 thf(decl_89, type, hoasapinj2_lthm: $o).
% 1.58/0.51 thf(decl_90, type, hoasinduction_lem3v2a: $o).
% 1.58/0.51 thf(decl_91, type, hoasapinj1_lthm: $o).
% 1.58/0.51 thf(decl_92, type, hoaslaminj_lthm: $o).
% 1.58/0.51 thf(decl_93, type, axvarcons: $o).
% 1.58/0.51 thf(decl_94, type, hoaslam: subst > (subst > term > term) > term).
% 1.58/0.51 thf(decl_95, type, axscons: $o).
% 1.58/0.51 thf(decl_96, type, hoasinduction_lem2v2_gthm: $o).
% 1.58/0.51 thf(decl_97, type, axidr: $o).
% 1.58/0.51 thf(decl_98, type, pushprop_lem1: $o).
% 1.58/0.51 thf(decl_99, type, laminj: $o).
% 1.58/0.51 thf(decl_100, type, hoasinduction_lem3_lthm: $o).
% 1.58/0.51 thf(decl_101, type, pushprop_lem0: $o).
% 1.58/0.51 thf(decl_102, type, pushprop_gthm: $o).
% 1.58/0.51 thf(decl_103, type, axabs: $o).
% 1.58/0.51 thf(decl_104, type, hoasinduction_lem3v2a_lthm: $o).
% 1.58/0.51 thf(decl_105, type, hoasinduction_lem2_lthm: $o).
% 1.58/0.51 thf(decl_106, type, hoasapinj2_gthm: $o).
% 1.58/0.51 thf(decl_107, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 1.58/0.51 thf(decl_108, type, hoasinduction_lem1_lthm: $o).
% 1.58/0.51 thf(decl_109, type, lamnotap: $o).
% 1.58/0.51 thf(decl_110, type, hoasapinj1_gthm: $o).
% 1.58/0.51 thf(decl_111, type, hoaslamnotvar: $o).
% 1.58/0.51 thf(decl_112, type, axidl: $o).
% 1.58/0.51 thf(decl_113, type, hoaslaminj_gthm: $o).
% 1.58/0.51 thf(decl_114, type, induction2_lthm: $o).
% 1.58/0.51 thf(decl_115, type, hoasinduction_lem0_lthm: $o).
% 1.58/0.51 thf(decl_116, type, substmonoid_lthm: $o).
% 1.58/0.51 thf(decl_117, type, pushprop: $o).
% 1.58/0.51 thf(decl_118, type, hoasinduction_lem3_gthm: $o).
% 1.58/0.51 thf(decl_119, type, hoasinduction_lem2_gthm: $o).
% 1.58/0.51 thf(decl_120, type, hoasinduction_lem3b: $o).
% 1.58/0.51 thf(decl_121, type, substmonoid: $o).
% 1.58/0.51 thf(decl_122, type, lamnotvar: $o).
% 1.58/0.51 thf(decl_123, type, hoasinduction_lem3a: $o).
% 1.58/0.51 thf(decl_124, type, hoasinduction_lem1_gthm: $o).
% 1.58/0.51 thf(decl_125, type, hoasinduction_no_psi_cond: $o).
% 1.58/0.51 thf(decl_126, type, induction2_gthm: $o).
% 1.58/0.51 thf(decl_127, type, pushprop_lem2v2_lthm: $o).
% 1.58/0.51 thf(decl_128, type, hoasvar: subst > term > subst > $o).
% 1.58/0.51 thf(decl_129, type, hoaslamnotap: $o).
% 1.58/0.51 thf(decl_130, type, substmonoid_gthm: $o).
% 1.58/0.51 thf(decl_131, type, ulamvarsh: $o).
% 1.58/0.51 thf(decl_132, type, induction2: $o).
% 1.58/0.51 thf(decl_133, type, pushprop_lem3v2: $o).
% 1.58/0.51 thf(decl_134, type, pushprop_lem2v2_gthm: $o).
% 1.58/0.51 thf(decl_135, type, pushprop_lem1_lthm: $o).
% 1.58/0.51 thf(decl_136, type, hoasinduction_lem3v2: $o).
% 1.58/0.51 thf(decl_137, type, axshiftcons: $o).
% 1.58/0.51 thf(decl_138, type, termmset: $o).
% 1.58/0.51 thf(decl_139, type, pushprop_lem0_lthm: $o).
% 1.58/0.51 thf(decl_140, type, hoasapnotvar_lthm: $o).
% 1.58/0.51 thf(decl_141, type, hoasinduction_lem3v2_lthm: $o).
% 1.58/0.51 thf(decl_142, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 1.58/0.51 thf(decl_143, type, axvarid: $o).
% 1.58/0.51 thf(decl_144, type, hoasinduction_lthm_3: $o).
% 1.58/0.51 thf(decl_145, type, d2term: d_term > term).
% 1.58/0.51 thf(decl_146, type, d2subst: d_subst > subst).
% 1.58/0.51 thf(decl_147, type, d_one: d_term).
% 1.58/0.51 thf(decl_148, type, d_id: d_subst).
% 1.58/0.51 thf(decl_149, type, epred1_0: $o).
% 1.58/0.51 thf(decl_150, type, epred2_1: (subst > term > subst > $o) > $o).
% 1.58/0.51 thf(decl_152, type, epred4_0: $o).
% 1.58/0.51 thf(decl_153, type, epred5_0: $o).
% 1.58/0.51 thf(decl_154, type, epred6_0: $o).
% 1.58/0.51 thf(decl_155, type, epred7_0: $o).
% 1.58/0.51 thf(decl_156, type, epred8_3: term > (term > $o) > (subst > term > subst > $o) > $o).
% 1.58/0.51 thf(decl_157, type, epred9_0: $o).
% 1.58/0.51 thf(decl_158, type, esk1_1: term > d_term).
% 1.58/0.51 thf(decl_159, type, esk2_1: subst > d_subst).
% 1.58/0.51 thf(decl_160, type, esk3_2: (subst > term > subst > $o) > (term > $o) > term).
% 1.58/0.51 thf(decl_161, type, esk4_4: term > subst > (term > $o) > (term > $o) > term).
% 1.58/0.51 thf(decl_162, type, esk5_4: (term > $o) > (term > $o) > term > subst > term).
% 1.58/0.51 thf(decl_163, type, epred10_0: term > $o).
% 1.58/0.51 thf(decl_164, type, epred11_0: term > $o).
% 1.58/0.51 thf(decl_165, type, esk6_0: term).
% 1.58/0.51 thf(decl_166, type, esk7_0: subst).
% 1.58/0.51 thf(decl_167, type, esk8_0: term).
% 1.58/0.51 thf(decl_168, type, esk9_0: term).
% 1.58/0.51 thf(decl_169, type, esk10_3: (term > $o) > term > subst > term).
% 1.58/0.51 thf(decl_170, type, esk11_3: (term > $o) > term > subst > term).
% 1.58/0.51 thf(decl_171, type, esk12_3: (term > $o) > term > subst > term).
% 1.58/0.51 thf(decl_172, type, esk13_3: (term > $o) > term > subst > term).
% 1.58/0.51 thf(decl_173, type, epred12_0: term > $o).
% 1.58/0.51 thf(decl_174, type, esk14_0: term).
% 1.58/0.51 thf(decl_175, type, esk15_0: subst).
% 1.58/0.51 thf(decl_176, type, esk16_1: term > term).
% 1.58/0.51 thf(decl_177, type, esk17_1: term > subst > term > term).
% 1.58/0.51 thf(decl_178, type, esk18_0: term).
% 1.58/0.51 thf(decl_179, type, esk19_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_180, type, esk20_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_181, type, esk21_0: term).
% 1.58/0.51 thf(decl_182, type, esk22_0: term).
% 1.58/0.51 thf(decl_183, type, esk23_0: term).
% 1.58/0.51 thf(decl_184, type, esk24_0: term).
% 1.58/0.51 thf(decl_185, type, esk25_0: term).
% 1.58/0.51 thf(decl_186, type, esk26_0: term).
% 1.58/0.51 thf(decl_187, type, esk27_0: term).
% 1.58/0.51 thf(decl_188, type, esk28_0: term).
% 1.58/0.51 thf(decl_189, type, esk29_0: term).
% 1.58/0.51 thf(decl_190, type, esk30_0: subst).
% 1.58/0.51 thf(decl_191, type, esk31_0: term).
% 1.58/0.51 thf(decl_192, type, esk32_0: subst).
% 1.58/0.51 thf(decl_193, type, esk33_0: subst).
% 1.58/0.51 thf(decl_194, type, esk34_1: term > subst > term > term).
% 1.58/0.51 thf(decl_195, type, esk35_0: term).
% 1.58/0.51 thf(decl_196, type, esk36_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_197, type, esk37_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_198, type, epred13_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_199, type, esk38_1: (term > $o) > term).
% 1.58/0.51 thf(decl_200, type, epred14_0: term > $o).
% 1.58/0.51 thf(decl_201, type, esk39_0: term).
% 1.58/0.51 thf(decl_202, type, esk40_1: term > term).
% 1.58/0.51 thf(decl_203, type, esk41_0: term).
% 1.58/0.51 thf(decl_204, type, epred15_1: (subst > term > subst > $o) > term > $o).
% 1.58/0.51 thf(decl_205, type, esk42_1: (term > $o) > term).
% 1.58/0.51 thf(decl_206, type, esk43_1: (term > $o) > term).
% 1.58/0.51 thf(decl_207, type, esk44_1: (term > $o) > term).
% 1.58/0.51 thf(decl_208, type, esk45_1: (term > $o) > term).
% 1.58/0.51 thf(decl_209, type, esk46_2: (subst > term > term) > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_210, type, esk47_2: (subst > term > term) > (subst > term > term) > term).
% 1.58/0.51 thf(decl_211, type, esk48_2: (subst > term > term) > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_212, type, esk49_2: (subst > term > term) > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_213, type, esk50_2: (subst > term > term) > (subst > term > term) > term).
% 1.58/0.51 thf(decl_214, type, esk51_2: (subst > term > term) > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_215, type, esk52_0: subst > term > term).
% 1.58/0.51 thf(decl_216, type, esk53_0: subst > term > term).
% 1.58/0.51 thf(decl_217, type, esk54_0: subst).
% 1.58/0.51 thf(decl_218, type, esk55_0: term).
% 1.58/0.51 thf(decl_219, type, esk56_2: (subst > term > subst > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_220, type, esk57_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_221, type, esk58_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_222, type, epred16_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_223, type, esk59_0: term).
% 1.58/0.51 thf(decl_224, type, esk60_2: (subst > term > term) > term > term).
% 1.58/0.51 thf(decl_225, type, esk61_2: (subst > term > term) > term > subst).
% 1.58/0.51 thf(decl_226, type, esk62_2: (subst > term > term) > term > term).
% 1.58/0.51 thf(decl_227, type, esk63_2: (subst > term > term) > term > subst).
% 1.58/0.51 thf(decl_228, type, esk64_2: (subst > term > term) > term > subst).
% 1.58/0.51 thf(decl_229, type, esk65_2: (subst > term > term) > term > term).
% 1.58/0.51 thf(decl_230, type, esk66_2: (subst > term > term) > term > subst).
% 1.58/0.51 thf(decl_231, type, esk67_2: (subst > term > subst > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_232, type, esk68_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_233, type, epred17_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_234, type, esk69_0: term).
% 1.58/0.51 thf(decl_235, type, esk70_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_236, type, esk71_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_237, type, esk72_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_238, type, esk73_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_239, type, esk74_2: (subst > term > subst > $o) > term > subst).
% 1.58/0.51 thf(decl_240, type, esk75_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_241, type, esk76_2: (subst > term > subst > $o) > term > subst).
% 1.58/0.51 thf(decl_242, type, esk77_2: (subst > term > subst > $o) > term > subst).
% 1.58/0.51 thf(decl_243, type, esk78_2: (subst > term > subst > $o) > term > subst).
% 1.58/0.51 thf(decl_244, type, esk79_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_245, type, esk80_2: (subst > term > subst > $o) > term > subst).
% 1.58/0.51 thf(decl_246, type, esk81_2: (subst > term > subst > $o) > term > subst).
% 1.58/0.51 thf(decl_247, type, esk82_2: (subst > term > subst > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_248, type, esk83_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_249, type, epred18_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_250, type, esk84_0: term).
% 1.58/0.51 thf(decl_251, type, esk85_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_252, type, esk86_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_253, type, esk87_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_254, type, esk88_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_255, type, esk89_3: (subst > term > subst > $o) > term > term > subst).
% 1.58/0.51 thf(decl_256, type, esk90_3: (subst > term > subst > $o) > term > term > term).
% 1.58/0.51 thf(decl_257, type, esk91_3: (subst > term > subst > $o) > term > term > subst).
% 1.58/0.51 thf(decl_258, type, esk92_3: (subst > term > subst > $o) > term > term > subst).
% 1.58/0.51 thf(decl_259, type, esk93_3: (subst > term > subst > $o) > term > term > subst).
% 1.58/0.51 thf(decl_260, type, esk94_3: (subst > term > subst > $o) > term > term > term).
% 1.58/0.51 thf(decl_261, type, esk95_3: (subst > term > subst > $o) > term > term > subst).
% 1.58/0.51 thf(decl_262, type, esk96_3: (subst > term > subst > $o) > term > term > subst).
% 1.58/0.51 thf(decl_263, type, esk97_3: (subst > term > subst > $o) > term > term > term).
% 1.58/0.51 thf(decl_264, type, esk98_3: (subst > term > subst > $o) > term > term > term).
% 1.58/0.51 thf(decl_265, type, epred19_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_266, type, esk99_0: term).
% 1.58/0.51 thf(decl_267, type, esk100_0: term).
% 1.58/0.51 thf(decl_268, type, esk101_0: term).
% 1.58/0.51 thf(decl_269, type, esk102_0: subst).
% 1.58/0.51 thf(decl_270, type, esk103_4: (term > $o) > (term > $o) > term > subst > term).
% 1.58/0.51 thf(decl_271, type, epred20_0: term > $o).
% 1.58/0.51 thf(decl_272, type, epred21_0: term > $o).
% 1.58/0.51 thf(decl_273, type, esk104_0: term).
% 1.58/0.51 thf(decl_274, type, esk105_0: subst).
% 1.58/0.51 thf(decl_275, type, epred22_1: (subst > term > subst > $o) > term > $o).
% 1.58/0.51 thf(decl_276, type, epred23_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_277, type, esk106_1: (term > $o) > term).
% 1.58/0.51 thf(decl_278, type, epred24_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_279, type, esk107_0: term).
% 1.58/0.51 thf(decl_280, type, esk108_1: term > subst > term > term).
% 1.58/0.51 thf(decl_281, type, esk109_0: term).
% 1.58/0.51 thf(decl_282, type, esk110_1: (term > $o) > term).
% 1.58/0.51 thf(decl_283, type, esk111_1: (term > $o) > term).
% 1.58/0.51 thf(decl_284, type, esk112_1: (term > $o) > term).
% 1.58/0.51 thf(decl_285, type, esk113_1: (term > $o) > term).
% 1.58/0.51 thf(decl_286, type, epred25_0: term > $o).
% 1.58/0.51 thf(decl_287, type, esk114_0: term).
% 1.58/0.51 thf(decl_288, type, esk115_0: term).
% 1.58/0.51 thf(decl_289, type, epred26_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_290, type, esk116_0: term).
% 1.58/0.51 thf(decl_291, type, esk117_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_292, type, esk118_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_293, type, esk119_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_294, type, esk120_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_295, type, esk121_2: (subst > term > subst > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_296, type, esk122_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_297, type, esk123_2: (subst > term > subst > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_298, type, esk124_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_299, type, epred27_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_300, type, esk125_0: term).
% 1.58/0.51 thf(decl_301, type, esk126_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_302, type, esk127_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_303, type, esk128_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_304, type, esk129_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_305, type, esk130_2: (subst > term > subst > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_306, type, esk131_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_307, type, epred28_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_308, type, esk132_0: term).
% 1.58/0.51 thf(decl_309, type, esk133_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_310, type, esk134_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_311, type, esk135_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_312, type, esk136_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_313, type, esk137_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 1.58/0.51 thf(decl_314, type, esk138_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 1.58/0.51 thf(decl_315, type, esk139_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 1.58/0.51 thf(decl_316, type, esk140_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 1.58/0.51 thf(decl_317, type, esk141_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 1.58/0.51 thf(decl_318, type, esk142_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 1.58/0.51 thf(decl_319, type, esk143_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 1.58/0.51 thf(decl_320, type, esk144_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 1.58/0.51 thf(decl_321, type, esk145_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 1.58/0.51 thf(decl_322, type, esk146_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 1.58/0.51 thf(decl_323, type, esk147_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 1.58/0.51 thf(decl_324, type, epred29_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_325, type, epred30_0: term > $o).
% 1.58/0.51 thf(decl_326, type, esk148_0: term).
% 1.58/0.51 thf(decl_327, type, esk149_0: term).
% 1.58/0.51 thf(decl_328, type, esk150_0: term).
% 1.58/0.51 thf(decl_329, type, esk151_0: term).
% 1.58/0.51 thf(decl_330, type, esk152_0: term).
% 1.58/0.51 thf(decl_331, type, esk153_0: term).
% 1.58/0.51 thf(decl_332, type, esk154_0: term).
% 1.58/0.51 thf(decl_333, type, esk155_0: term).
% 1.58/0.51 thf(decl_334, type, esk156_0: term).
% 1.58/0.51 thf(decl_335, type, esk157_0: term).
% 1.58/0.51 thf(decl_336, type, esk158_0: term).
% 1.58/0.51 thf(decl_337, type, esk159_0: term).
% 1.58/0.51 thf(decl_338, type, esk160_0: term).
% 1.58/0.51 thf(decl_339, type, esk161_0: term).
% 1.58/0.51 thf(decl_340, type, esk162_0: term).
% 1.58/0.51 thf(decl_341, type, esk163_0: term).
% 1.58/0.51 thf(decl_342, type, esk164_0: term).
% 1.58/0.51 thf(decl_343, type, esk165_0: term).
% 1.58/0.51 thf(decl_344, type, esk166_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_345, type, esk167_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 1.58/0.51 thf(decl_346, type, esk168_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 1.58/0.51 thf(decl_347, type, epred31_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_348, type, epred32_0: term > $o).
% 1.58/0.51 thf(decl_349, type, esk169_0: term).
% 1.58/0.51 thf(decl_350, type, esk170_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_351, type, esk171_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_352, type, esk172_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_353, type, esk173_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_354, type, esk174_0: term).
% 1.58/0.51 thf(decl_355, type, esk175_0: term).
% 1.58/0.51 thf(decl_356, type, esk176_0: term).
% 1.58/0.51 thf(decl_357, type, esk177_0: term).
% 1.58/0.51 thf(decl_358, type, esk178_0: term).
% 1.58/0.51 thf(decl_359, type, esk179_0: term).
% 1.58/0.51 thf(decl_360, type, esk180_0: term).
% 1.58/0.51 thf(decl_361, type, esk181_0: term).
% 1.58/0.51 thf(decl_362, type, esk182_0: term).
% 1.58/0.51 thf(decl_363, type, esk183_0: term).
% 1.58/0.51 thf(decl_364, type, esk184_0: subst).
% 1.58/0.51 thf(decl_365, type, esk185_0: term).
% 1.58/0.51 thf(decl_366, type, esk186_0: subst).
% 1.58/0.51 thf(decl_367, type, esk187_0: term).
% 1.58/0.51 thf(decl_368, type, esk188_0: term).
% 1.58/0.51 thf(decl_369, type, esk189_2: (subst > term > term) > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_370, type, esk190_2: (subst > term > term) > (subst > term > term) > term).
% 1.58/0.51 thf(decl_371, type, esk191_2: (subst > term > term) > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_372, type, esk192_2: (subst > term > term) > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_373, type, esk193_2: (subst > term > term) > (subst > term > term) > term).
% 1.58/0.51 thf(decl_374, type, esk194_2: (subst > term > term) > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_375, type, esk195_0: subst > term > term).
% 1.58/0.51 thf(decl_376, type, esk196_0: subst > term > term).
% 1.58/0.51 thf(decl_377, type, esk197_0: subst).
% 1.58/0.51 thf(decl_378, type, esk198_0: term).
% 1.58/0.51 thf(decl_379, type, esk199_0: term).
% 1.58/0.51 thf(decl_380, type, esk200_0: subst).
% 1.58/0.51 thf(decl_381, type, esk201_0: subst).
% 1.58/0.51 thf(decl_382, type, esk202_0: subst).
% 1.58/0.51 thf(decl_383, type, epred33_0: term > $o).
% 1.58/0.51 thf(decl_384, type, epred34_0: term > $o).
% 1.58/0.51 thf(decl_385, type, esk203_0: term).
% 1.58/0.51 thf(decl_386, type, esk204_0: subst).
% 1.58/0.51 thf(decl_387, type, esk205_0: term).
% 1.58/0.51 thf(decl_388, type, esk206_0: term).
% 1.58/0.51 thf(decl_389, type, esk207_0: term).
% 1.58/0.51 thf(decl_390, type, esk208_0: term).
% 1.58/0.51 thf(decl_391, type, epred35_3: (term > $o) > term > subst > term > $o).
% 1.58/0.51 thf(decl_392, type, epred36_0: term > $o).
% 1.58/0.51 thf(decl_393, type, esk209_0: term).
% 1.58/0.51 thf(decl_394, type, esk210_0: subst).
% 1.58/0.51 thf(decl_395, type, esk211_1: (term > $o) > term).
% 1.58/0.51 thf(decl_396, type, esk212_0: term).
% 1.58/0.51 thf(decl_397, type, esk213_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_398, type, esk214_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_399, type, esk215_0: term).
% 1.58/0.51 thf(decl_400, type, esk216_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_401, type, esk217_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 1.58/0.51 thf(decl_402, type, esk218_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 1.58/0.51 thf(decl_403, type, esk219_1: term > subst > term > term).
% 1.58/0.51 thf(decl_404, type, epred37_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_405, type, epred38_0: term > $o).
% 1.58/0.51 thf(decl_406, type, esk220_0: term).
% 1.58/0.51 thf(decl_407, type, esk221_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_408, type, esk222_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_409, type, esk223_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_410, type, esk224_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_411, type, esk225_0: subst).
% 1.58/0.51 thf(decl_412, type, esk226_0: term).
% 1.58/0.51 thf(decl_413, type, epred39_1: (subst > term > subst > $o) > term > $o).
% 1.58/0.51 thf(decl_414, type, epred40_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_415, type, esk227_1: (term > $o) > term).
% 1.58/0.51 thf(decl_416, type, esk228_0: subst).
% 1.58/0.51 thf(decl_417, type, esk229_0: subst).
% 1.58/0.51 thf(decl_418, type, esk230_0: subst).
% 1.58/0.51 thf(decl_419, type, esk231_0: subst).
% 1.58/0.51 thf(decl_420, type, esk232_1: term > subst > term > term).
% 1.58/0.51 thf(decl_421, type, esk233_0: term).
% 1.58/0.51 thf(decl_422, type, esk234_0: subst).
% 1.58/0.51 thf(decl_423, type, esk235_0: subst).
% 1.58/0.51 thf(decl_424, type, esk236_2: (subst > term > subst > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_425, type, esk237_2: (subst > term > subst > $o) > term > term).
% 1.58/0.51 thf(decl_426, type, epred41_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_427, type, esk238_0: term).
% 1.58/0.51 thf(decl_428, type, esk239_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_429, type, esk240_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_430, type, esk241_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_431, type, esk242_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_432, type, esk243_1: (subst > term > subst > $o) > term).
% 1.58/0.51 thf(decl_433, type, esk244_1: (subst > term > subst > $o) > term).
% 1.58/0.51 thf(decl_434, type, esk245_1: (subst > term > subst > $o) > subst > term > term).
% 1.58/0.51 thf(decl_435, type, epred42_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_436, type, esk246_0: term).
% 1.58/0.51 thf(decl_437, type, esk247_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_438, type, esk248_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_439, type, esk249_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_440, type, esk250_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_441, type, esk251_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_442, type, esk252_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_443, type, esk253_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_444, type, esk254_0: subst > term > term).
% 1.58/0.51 thf(decl_445, type, esk255_0: term).
% 1.58/0.51 thf(decl_446, type, esk256_0: term).
% 1.58/0.51 thf(decl_447, type, esk257_1: (term > $o) > term).
% 1.58/0.51 thf(decl_448, type, esk258_1: (term > $o) > term).
% 1.58/0.51 thf(decl_449, type, esk259_1: (term > $o) > term).
% 1.58/0.51 thf(decl_450, type, esk260_1: (term > $o) > term).
% 1.58/0.51 thf(decl_451, type, epred43_0: term > $o).
% 1.58/0.51 thf(decl_452, type, esk261_0: term).
% 1.58/0.51 thf(decl_453, type, esk262_1: term > term).
% 1.58/0.51 thf(decl_454, type, esk263_0: term).
% 1.58/0.51 thf(decl_455, type, esk264_0: subst).
% 1.58/0.51 thf(decl_456, type, esk265_0: term).
% 1.58/0.51 thf(decl_457, type, esk266_0: subst).
% 1.58/0.51 thf(decl_458, type, epred44_0: term > $o).
% 1.58/0.51 thf(decl_459, type, epred45_0: term > $o).
% 1.58/0.51 thf(decl_460, type, esk267_0: term).
% 1.58/0.51 thf(decl_461, type, esk268_0: subst).
% 1.58/0.51 thf(decl_462, type, esk269_0: term).
% 1.58/0.51 thf(decl_463, type, epred46_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_464, type, epred47_0: term > $o).
% 1.58/0.51 thf(decl_465, type, esk270_0: term).
% 1.58/0.51 thf(decl_466, type, esk271_0: term).
% 1.58/0.51 thf(decl_467, type, esk272_0: subst).
% 1.58/0.51 thf(decl_468, type, esk273_0: term).
% 1.58/0.51 thf(decl_469, type, epred48_3: (term > $o) > term > subst > term > $o).
% 1.58/0.51 thf(decl_470, type, epred49_0: term > $o).
% 1.58/0.51 thf(decl_471, type, esk274_0: term).
% 1.58/0.51 thf(decl_472, type, esk275_0: subst).
% 1.58/0.51 thf(decl_473, type, esk276_1: (term > $o) > term).
% 1.58/0.51 thf(decl_474, type, esk277_0: term).
% 1.58/0.51 thf(decl_475, type, epred50_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_476, type, epred51_0: term > $o).
% 1.58/0.51 thf(decl_477, type, esk278_0: term).
% 1.58/0.51 thf(decl_478, type, esk279_0: term).
% 1.58/0.51 thf(decl_479, type, epred52_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_480, type, esk280_1: (term > $o) > term).
% 1.58/0.51 thf(decl_481, type, epred53_1: (subst > term > subst > $o) > term > $o).
% 1.58/0.51 thf(decl_482, type, epred54_0: subst > term > subst > $o).
% 1.58/0.51 thf(decl_483, type, epred55_0: term > $o).
% 1.58/0.51 thf(decl_484, type, esk281_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_485, type, esk282_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_486, type, esk283_1: (subst > term > term) > subst).
% 1.58/0.51 thf(decl_487, type, esk284_1: (subst > term > term) > term).
% 1.58/0.51 thf(decl_488, type, esk285_0: term).
% 1.58/0.51 thf(decl_489, type, esk286_1: (subst > term > subst > $o) > subst).
% 1.58/0.51 thf(decl_490, type, esk287_1: (subst > term > subst > $o) > term).
% 1.58/0.51 thf(decl_491, type, esk288_1: (subst > term > subst > $o) > subst).
% 1.58/0.51 thf(decl_492, type, esk289_1: (subst > term > subst > $o) > subst).
% 1.58/0.51 thf(decl_493, type, esk290_1: (subst > term > subst > $o) > subst).
% 1.58/0.51 thf(decl_494, type, esk291_1: (subst > term > subst > $o) > term).
% 1.58/0.51 thf(decl_495, type, esk292_1: (subst > term > subst > $o) > subst).
% 1.58/0.51 thf(decl_496, type, esk293_1: (subst > term > subst > $o) > subst).
% 1.58/0.51 thf(decl_497, type, esk294_1: (subst > term > subst > $o) > subst > term > term).
% 1.58/0.51 thf(decl_498, type, esk295_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 1.58/0.51 thf(decl_625, type, esk409_3: (subst > term > subst > $o) > (term > $o) > term > subst).
% 1.58/0.51 thf(decl_626, type, esk410_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 1.58/0.51 thf(decl_627, type, esk411_3: (subst > term > subst > $o) > (term > $o) > term > subst).
% 1.58/0.51 thf(decl_628, type, esk412_3: (subst > term > subst > $o) > (term > $o) > term > subst).
% 1.58/0.51 thf(decl_629, type, esk413_3: (subst > term > subst > $o) > (term > $o) > term > subst).
% 1.58/0.51 thf(decl_630, type, esk414_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 1.58/0.51 thf(decl_631, type, esk415_3: (subst > term > subst > $o) > (term > $o) > term > subst).
% 1.58/0.51 thf(decl_632, type, esk416_3: (subst > term > subst > $o) > (term > $o) > term > subst).
% 1.58/0.51 thf(decl_633, type, esk417_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
% 1.58/0.51 thf(decl_634, type, esk418_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 1.58/0.51 thf(decl_635, type, esk419_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 1.58/0.51 thf(decl_636, type, esk420_4: (subst > term > subst > $o) > (term > $o) > term > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_637, type, esk421_4: (subst > term > subst > $o) > (term > $o) > term > (subst > term > term) > term).
% 1.58/0.51 thf(decl_638, type, esk422_4: (subst > term > subst > $o) > (term > $o) > term > (subst > term > term) > subst).
% 1.58/0.51 thf(decl_639, type, esk423_4: (subst > term > subst > $o) > (term > $o) > term > (subst > term > term) > term).
% 1.58/0.51 thf(alg444_1, axiom, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X1:term]:(?[X2:d_term]:(((X1)=(d2term @ X2))))&![X2:d_term]:(((X2)=(d_one))))&![X3:d_term, X4:d_term]:((((d2term @ X3)=(d2term @ X4))=>((X3)=(X4)))))&![X5:subst]:(?[X6:d_subst]:(((X5)=(d2subst @ X6)))))&![X6:d_subst]:(((X6)=(d_id))))&![X7:d_subst, X8:d_subst]:((((d2subst @ X7)=(d2subst @ X8))=>((X7)=(X8)))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&((hoaslam)=(^[X9:subst, X10:subst > term > term]:(d2term @ d_one))))&((hoasinduction_p_and_p_prime)=(^[X11:subst > term > subst > $o, X12:term > $o]:(![X13:term]:((((X12 @ X13))<=>((X11 @ id @ X13 @ id))))))))&((pushprop_p_and_p_prime)=(^[X14:term, X15:subst, X16:term > $o, X12:term > $o]:(![X13:term]:((((X12 @ X13))<=>((X16 @ (sub @ X13 @ (push @ X14 @ X15))))))))))&~((var @ (d2term @ d_one))))&((pushprop_lem1v2)<=>![X17:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X17 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X17 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one)))))&(pushprop_lem1_gthm))&(axmap))&(pushprop_lem0_gthm))&((shinj)<=>![X14:term, X18:term]:((((sub @ X14 @ sh)!=(sub @ X18 @ sh))|((X14)=(X18))))))&(hoasinduction_lem1v2))&(hoasinduction_lem1v2_gthm))&((induction2lem)<=>![X19:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X19 @ X14))|~((X19 @ X18))|(X19 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X19 @ X18))|(X19 @ (sub @ X14 @ (push @ X18 @ id))))))|(X19 @ (lam @ X14)))))|~(![X18:term]:((~((var @ X18))|(X19 @ (sub @ X18 @ X21)))))|(X19 @ (sub @ X20 @ X21))))))&((hoasinduction_lem3v2_f)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&(axvarshift))&((hoasapinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24))))))&(hoasapnotvar_gthm))&((hoasapinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))&~((ulamvar1)))&((induction2lem_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(![X25:term > $o, X26:term]:((~(![X14:term]:((~((var @ X14))|(X25 @ X14))))|~(![X14:term, X18:term]:((~((X25 @ X14))|~((X25 @ X18))|(X25 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X25 @ X14))|(X25 @ (lam @ X14)))))|(X25 @ X26)))=>![X27:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X27 @ X14))|~((X27 @ X18))|(X27 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X27 @ X18))|(X27 @ (sub @ X14 @ (push @ X18 @ id))))))|(X27 @ (lam @ X14)))))|~(![X18:term]:((~((var @ X18))|(X27 @ (sub @ X18 @ X21)))))|(X27 @ (sub @ X20 @ X21))))))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((hoasinduction_lem3v2_f_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&((hoasinduction_lthm)<=>(![X28:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X28 @ X14))))|~(![X14:term, X18:term]:((~((X28 @ X14))|~((X28 @ X18))|(X28 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X28 @ X18))|(X28 @ (sub @ X14 @ (push @ X18 @ id))))))|(X28 @ (lam @ X14)))))|(X28 @ X29)))=>(![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))=>(![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~((var @ (sub @ X14 @ id)))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))))&((hoasinduction_no_psi_cond_lthm)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(![X36:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X36 @ X14))))|~(![X14:term, X18:term]:((~((X36 @ X14))|~((X36 @ X18))|(X36 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X36 @ X18))|(X36 @ (sub @ X14 @ (push @ X18 @ id))))))|(X36 @ (lam @ X14)))))|(X36 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id)))))))))&((hoaslaminj)<=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41))))))&((hoasinduction_lem3aaa)<=>![X11:subst > term > subst > $o, X42:term]:((~(![X22:subst > term > term, X43:term]:((~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id)|~(![X44:subst, X45:term, X46:subst]:(((sub @ (X22 @ X44 @ X45) @ X46)=(sub @ (sub @ X43 @ (push @ X45 @ X44)) @ X46))))|~(![X47:subst, X48:term, X49:subst]:(((X22 @ (comp @ X47 @ X49) @ (sub @ X48 @ X49))=(sub @ X43 @ (push @ (sub @ X48 @ X49) @ (comp @ X47 @ X49)))))))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X42 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)))))&(induction2lem_gthm))&((hoasinduction_lem3aa_lthm)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&((hoasinduction_lem3)<=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))))&((hoasinduction_lem2)<=>![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))))&((termmset_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X14:term]:(((X14)=(sub @ X14 @ id))))))&(hoasinduction_lem1))&(hoaslamnotap_lthm))&((pushprop_lem1v2_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>![X51:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X51 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X51 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one))))))&(hoasapnotvar))&((hoasinduction_lem0)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((hoasinduction)<=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~((var @ (sub @ X14 @ id)))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id)))))&(hoasinduction_gthm))&(axapp))&(hoaslamnotvar_lthm))&(pushprop_lem3v2_lthm))&((hoasinduction_lem3b_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&(ulamvarind))&((induction)<=>![X52:term > $o, X26:term]:((~(![X14:term]:((~((var @ X14))|(X52 @ X14))))|~(![X14:term, X18:term]:((~((X52 @ X14))|~((X52 @ X18))|(X52 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X52 @ X14))|(X52 @ (lam @ X14)))))|(X52 @ X26)))))&((hoasinduction_lem3a_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))))&(termmset_gthm))&((hoasinduction_lem3aa)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&(pushprop_lem1v2_gthm))&(hoaslamnotap_gthm))&(hoaslamnotvar_gthm))&(hoasinduction_lem3b_gthm))&(pushprop_lem2v2))&(hoasinduction_lem3a_gthm))&(axclos))&(axassoc))&((hoasinduction_lem2v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X54:term, X55:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~((X12 @ X54))|~((X12 @ X55))|(X12 @ (ap @ X54 @ X55))))))&(pushprop_lthm))&((apinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))))&((apinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))))&((hoasapinj2_lthm)<=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24)))))))&((hoasinduction_lem3v2a)<=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))&((hoasapinj1_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))))&((hoaslaminj_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41)))))))))&((axvarcons)<=>![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))))&((axscons)<=>![X15:subst]:(((X15)=(push @ (sub @ one @ X15) @ (comp @ sh @ X15))))))&(hoasinduction_lem2v2_gthm))&((axidr)<=>![X15:subst]:(((X15)=(comp @ X15 @ id)))))&((pushprop_lem1)<=>![X56:term > $o, X57:term > $o, X14:term, X15:subst, X18:term]:((~((X56 @ X14))|(X57 @ (sub @ X14 @ (push @ X18 @ X15)))))))&((laminj)<=>![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))))&((hoasinduction_lem3_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))))))&((pushprop_lem0)<=>![X58:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X58 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(pushprop_gthm))&(axabs))&((hoasinduction_lem3v2a_lthm)<=>(![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))))&(hoasinduction_lem2_lthm))&(hoasapinj2_gthm))&(hoasinduction_lem1_lthm))&~((lamnotap)))&(hoasapinj1_gthm))&(hoaslamnotvar))&((axidl)<=>![X15:subst]:(((X15)=(comp @ id @ X15)))))&(hoaslaminj_gthm))&((induction2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X59:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X59 @ X14))|~((X59 @ X18))|(X59 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X59 @ X18))|(X59 @ (sub @ X14 @ (push @ X18 @ id))))))|(X59 @ (lam @ X14)))))|~(![X18:term]:((~((var @ X18))|(X59 @ (sub @ X18 @ X21)))))|(X59 @ (sub @ X20 @ X21))))=>![X60:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X60 @ X14))))|~(![X14:term, X18:term]:((~((X60 @ X14))|~((X60 @ X18))|(X60 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X60 @ X18))|(X60 @ (sub @ X14 @ (push @ X18 @ id))))))|(X60 @ (lam @ X14)))))|(X60 @ X29)))))))&((hoasinduction_lem0_lthm)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((substmonoid_lthm)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))))&(pushprop))&(hoasinduction_lem3_gthm))&(hoasinduction_lem2_gthm))&((hoasinduction_lem3b)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&((substmonoid)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))&(lamnotvar))&((hoasinduction_lem3a)<=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))&(hoasinduction_lem1_gthm))&((hoasinduction_no_psi_cond)<=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id)))))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))&((hoaslamnotap)<=>![X22:subst > term > term, X61:term, X62:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(ap @ (sub @ X61 @ id) @ X62))))))&(substmonoid_gthm))&(ulamvarsh))&((induction2)<=>![X63:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X63 @ X14))))|~(![X14:term, X18:term]:((~((X63 @ X14))|~((X63 @ X18))|(X63 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X63 @ X18))|(X63 @ (sub @ X14 @ (push @ X18 @ id))))))|(X63 @ (lam @ X14)))))|(X63 @ X29)))))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((pushprop_lem1_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>![X64:term > $o, X65:term > $o, X14:term, X15:subst, X18:term]:((~((X64 @ X14))|(X65 @ (sub @ X14 @ (push @ X18 @ X15)))))))))&((hoasinduction_lem3v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X66 @ (push @ X18 @ id))))))|(X12 @ (lam @ X66))))))&((axshiftcons)<=>![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))))&((termmset)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((pushprop_lem0_lthm)<=>![X67:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X67 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(hoasapnotvar_lthm))&((hoasinduction_lem3v2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X66 @ (push @ X18 @ id))))))|(X12 @ (lam @ X66)))))))&((axvarid)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((hoasinduction_lthm_3)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(![X68:term > $o, X29:term]:((~(![X14:term]:((~((var @ X14))|(X68 @ X14))))|~(![X14:term, X18:term]:((~((X68 @ X14))|~((X68 @ X18))|(X68 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X68 @ X18))|(X68 @ (sub @ X14 @ (push @ X18 @ id))))))|(X68 @ (lam @ X14)))))|(X68 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~((var @ (sub @ X14 @ id)))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))))), file('/export/starexec/sandbox/tmp/tmp.PxFhX1VfEH/E---3.1_793636.p', alg444_1)).
% 1.58/0.51 thf(hoasinduction_lem3v2, conjecture, ((hoasinduction_lem3v2)<=>![X11:subst > term > subst > $o, X12:term > $o]:((![X15:subst, X14:term, X32:subst, X33:subst]:(((X11 @ X15 @ X14 @ (comp @ X33 @ X32))=>(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32)))=>(![X15:subst, X14:term, X32:subst, X33:subst]:(((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32)=>(X11 @ X15 @ X14 @ (comp @ X33 @ X32))))=>(![X22:subst > term > term]:((![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32))))=>(![X14:term]:(((X11 @ id @ X14 @ id)=>(X11 @ id @ (X22 @ id @ X14) @ id)))=>(X11 @ id @ (hoaslam @ id @ (^[X15:subst, X14:term]:(X22 @ X15 @ X14))) @ id))))=>((hoasinduction_p_and_p_prime @ X11 @ X12)=>![X14:term]:((![X18:term]:(((X12 @ X18)=>(X12 @ (sub @ X14 @ (push @ X18 @ id)))))=>(X12 @ (lam @ X14)))))))))), file('/export/starexec/sandbox/tmp/tmp.PxFhX1VfEH/E---3.1_793636.p', hoasinduction_lem3v2)).
% 1.58/0.51 thf(c_0_2, plain, ((epred1_0)<=>(![X25:term > $o, X26:term]:((~(![X14:term]:((~(var @ X14)|(X25 @ X14))))|~(![X14:term, X18:term]:((~((X25 @ X14))|~((X25 @ X18))|(X25 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X25 @ X14))|(X25 @ (lam @ X14)))))|(X25 @ X26)))=>![X27:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X27 @ X14))|~((X27 @ X18))|(X27 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X27 @ X18))|(X27 @ (sub @ X14 @ (push @ X18 @ id))))))|(X27 @ (lam @ X14)))))|~(![X18:term]:((~(var @ X18)|(X27 @ (sub @ X18 @ X21)))))|(X27 @ (sub @ X20 @ X21)))))), introduced(definition)).
% 1.58/0.51 thf(c_0_3, plain, ((epred4_0)<=>(![X28:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X28 @ X14))))|~(![X14:term, X18:term]:((~((X28 @ X14))|~((X28 @ X18))|(X28 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X28 @ X18))|(X28 @ (sub @ X14 @ (push @ X18 @ id))))))|(X28 @ (lam @ X14)))))|(X28 @ X29)))=>(![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))=>(![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~(var @ (sub @ X14 @ id))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))), introduced(definition)).
% 1.58/0.51 thf(c_0_4, plain, ((epred5_0)<=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id))))), introduced(definition)).
% 1.58/0.51 thf(c_0_5, plain, ![X11:subst > term > subst > $o]:(((epred2_1 @ X11)<=>(~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~(var @ (sub @ X14 @ id))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))))), introduced(definition)).
% 1.58/0.51 thf(c_0_6, plain, ((epred6_0)<=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id))))), introduced(definition)).
% 1.58/0.51 thf(c_0_7, plain, ((epred7_0)<=>(![X59:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X59 @ X14))|~((X59 @ X18))|(X59 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X59 @ X18))|(X59 @ (sub @ X14 @ (push @ X18 @ id))))))|(X59 @ (lam @ X14)))))|~(![X18:term]:((~(var @ X18)|(X59 @ (sub @ X18 @ X21)))))|(X59 @ (sub @ X20 @ X21))))=>![X60:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X60 @ X14))))|~(![X14:term, X18:term]:((~((X60 @ X14))|~((X60 @ X18))|(X60 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X60 @ X18))|(X60 @ (sub @ X14 @ (push @ X18 @ id))))))|(X60 @ (lam @ X14)))))|(X60 @ X29))))), introduced(definition)).
% 1.58/0.51 thf(c_0_8, plain, ![X11:subst > term > subst > $o, X12:term > $o, X66:term]:(((epred8_3 @ X66 @ X12 @ X11)<=>(~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X66 @ (push @ X18 @ id))))))))), introduced(definition)).
% 1.58/0.51 thf(c_0_9, plain, ((epred9_0)<=>(![X68:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X68 @ X14))))|~(![X14:term, X18:term]:((~((X68 @ X14))|~((X68 @ X18))|(X68 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X68 @ X18))|(X68 @ (sub @ X14 @ (push @ X18 @ id))))))|(X68 @ (lam @ X14)))))|(X68 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~(var @ (sub @ X14 @ id))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))), introduced(definition)).
% 1.58/0.51 thf(c_0_10, plain, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X1:term]:(?[X2:d_term]:(((X1)=(d2term @ X2))))&![X2:d_term]:(((X2)=(d_one))))&![X3:d_term, X4:d_term]:((((d2term @ X3)=(d2term @ X4))=>((X3)=(X4)))))&![X5:subst]:(?[X6:d_subst]:(((X5)=(d2subst @ X6)))))&![X6:d_subst]:(((X6)=(d_id))))&![X7:d_subst, X8:d_subst]:((((d2subst @ X7)=(d2subst @ X8))=>((X7)=(X8)))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&![X626:subst, X627:subst > term > term]:(((hoaslam @ X626 @ X627)=(d2term @ d_one))))&![X628:subst > term > subst > $o, X629:term > $o]:(((hoasinduction_p_and_p_prime @ X628 @ X629)<=>![X13:term]:(((X629 @ X13)<=>(X628 @ id @ X13 @ id))))))&![X630:term, X631:subst, X632:term > $o, X633:term > $o]:(((pushprop_p_and_p_prime @ X630 @ X631 @ X632 @ X633)<=>![X13:term]:(((X633 @ X13)<=>(X632 @ (sub @ X13 @ (push @ X630 @ X631))))))))&~(var @ (d2term @ d_one)))&((pushprop_lem1v2)<=>![X17:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X17 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X17 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one)))))&(pushprop_lem1_gthm))&(axmap))&(pushprop_lem0_gthm))&((shinj)<=>![X14:term, X18:term]:((((sub @ X14 @ sh)!=(sub @ X18 @ sh))|((X14)=(X18))))))&(hoasinduction_lem1v2))&(hoasinduction_lem1v2_gthm))&((induction2lem)<=>![X19:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X19 @ X14))|~((X19 @ X18))|(X19 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X19 @ X18))|(X19 @ (sub @ X14 @ (push @ X18 @ id))))))|(X19 @ (lam @ X14)))))|~(![X18:term]:((~(var @ X18)|(X19 @ (sub @ X18 @ X21)))))|(X19 @ (sub @ X20 @ X21))))))&((hoasinduction_lem3v2_f)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&(axvarshift))&((hoasapinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24))))))&(hoasapnotvar_gthm))&((hoasapinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))&~(ulamvar1))&((induction2lem_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(epred1_0))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((hoasinduction_lem3v2_f_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&((hoasinduction_lthm)<=>(epred4_0)))&((hoasinduction_no_psi_cond_lthm)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(![X36:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X36 @ X14))))|~(![X14:term, X18:term]:((~((X36 @ X14))|~((X36 @ X18))|(X36 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X36 @ X18))|(X36 @ (sub @ X14 @ (push @ X18 @ id))))))|(X36 @ (lam @ X14)))))|(X36 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(epred5_0))))))&((hoaslaminj)<=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41))))))&((hoasinduction_lem3aaa)<=>![X11:subst > term > subst > $o, X42:term]:((~(![X22:subst > term > term, X43:term]:((~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id)|~(![X44:subst, X45:term, X46:subst]:(((sub @ (X22 @ X44 @ X45) @ X46)=(sub @ (sub @ X43 @ (push @ X45 @ X44)) @ X46))))|~(![X47:subst, X48:term, X49:subst]:(((X22 @ (comp @ X47 @ X49) @ (sub @ X48 @ X49))=(sub @ X43 @ (push @ (sub @ X48 @ X49) @ (comp @ X47 @ X49)))))))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X42 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)))))&(induction2lem_gthm))&((hoasinduction_lem3aa_lthm)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&((hoasinduction_lem3)<=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))))&((hoasinduction_lem2)<=>![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))))&(termmset_lthm))&(hoasinduction_lem1))&(hoaslamnotap_lthm))&((pushprop_lem1v2_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>![X51:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X51 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X51 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one))))))&(hoasapnotvar))&((hoasinduction_lem0)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((hoasinduction)<=>![X11:subst > term > subst > $o, X35:term]:(((epred2_1 @ X11)|(X11 @ id @ X35 @ id)))))&(hoasinduction_gthm))&(axapp))&(hoaslamnotvar_lthm))&(pushprop_lem3v2_lthm))&((hoasinduction_lem3b_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&(ulamvarind))&((induction)<=>![X52:term > $o, X26:term]:((~(![X14:term]:((~(var @ X14)|(X52 @ X14))))|~(![X14:term, X18:term]:((~((X52 @ X14))|~((X52 @ X18))|(X52 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X52 @ X14))|(X52 @ (lam @ X14)))))|(X52 @ X26)))))&((hoasinduction_lem3a_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))))&(termmset_gthm))&((hoasinduction_lem3aa)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&(pushprop_lem1v2_gthm))&(hoaslamnotap_gthm))&(hoaslamnotvar_gthm))&(hoasinduction_lem3b_gthm))&(pushprop_lem2v2))&(hoasinduction_lem3a_gthm))&(axclos))&(axassoc))&((hoasinduction_lem2v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X54:term, X55:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~((X12 @ X54))|~((X12 @ X55))|(X12 @ (ap @ X54 @ X55))))))&(pushprop_lthm))&((apinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))))&((apinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))))&((hoasapinj2_lthm)<=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24)))))))&((hoasinduction_lem3v2a)<=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))&((hoasapinj1_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))))&((hoaslaminj_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41)))))))))&((axvarcons)<=>![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))))&((axscons)<=>![X15:subst]:(((X15)=(push @ (sub @ one @ X15) @ (comp @ sh @ X15))))))&(hoasinduction_lem2v2_gthm))&((axidr)<=>![X15:subst]:(((X15)=(comp @ X15 @ id)))))&((pushprop_lem1)<=>![X56:term > $o, X57:term > $o, X14:term, X15:subst, X18:term]:((~((X56 @ X14))|(X57 @ (sub @ X14 @ (push @ X18 @ X15)))))))&((laminj)<=>![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))))&((hoasinduction_lem3_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(epred6_0))))&((pushprop_lem0)<=>![X58:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X58 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(pushprop_gthm))&(axabs))&((hoasinduction_lem3v2a_lthm)<=>(![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))))&(hoasinduction_lem2_lthm))&(hoasapinj2_gthm))&(hoasinduction_lem1_lthm))&~(lamnotap))&(hoasapinj1_gthm))&(hoaslamnotvar))&((axidl)<=>![X15:subst]:(((X15)=(comp @ id @ X15)))))&(hoaslaminj_gthm))&((induction2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(epred7_0))))&((hoasinduction_lem0_lthm)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((substmonoid_lthm)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))))&(pushprop))&(hoasinduction_lem3_gthm))&(hoasinduction_lem2_gthm))&((hoasinduction_lem3b)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&((substmonoid)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))&(lamnotvar))&((hoasinduction_lem3a)<=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))&(hoasinduction_lem1_gthm))&((hoasinduction_no_psi_cond)<=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id)))))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&((hoaslamnotap)<=>![X22:subst > term > term, X61:term, X62:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(ap @ (sub @ X61 @ id) @ X62))))))&(substmonoid_gthm))&(ulamvarsh))&((induction2)<=>![X63:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X63 @ X14))))|~(![X14:term, X18:term]:((~((X63 @ X14))|~((X63 @ X18))|(X63 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X63 @ X18))|(X63 @ (sub @ X14 @ (push @ X18 @ id))))))|(X63 @ (lam @ X14)))))|(X63 @ X29)))))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((pushprop_lem1_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>![X64:term > $o, X65:term > $o, X14:term, X15:subst, X18:term]:((~((X64 @ X14))|(X65 @ (sub @ X14 @ (push @ X18 @ X15)))))))))&((hoasinduction_lem3v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:(((epred8_3 @ X66 @ X12 @ X11)|(X12 @ (lam @ X66))))))&((axshiftcons)<=>![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))))&((termmset)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((pushprop_lem0_lthm)<=>![X67:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X67 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(hoasapnotvar_lthm))&((hoasinduction_lem3v2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:(((epred8_3 @ X66 @ X12 @ X11)|(X12 @ (lam @ X66)))))))&((axvarid)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((hoasinduction_lthm_3)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(epred9_0)))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[alg444_1])])]), c_0_2]), c_0_3]), c_0_4]), c_0_5]), c_0_6]), c_0_7]), c_0_8]), c_0_8]), c_0_9])).
% 1.58/0.51 thf(c_0_11, plain, ![X634:term, X636:d_term, X637:d_term, X638:d_term, X639:subst, X641:d_subst, X642:d_subst, X643:d_subst, X644:subst, X645:subst > term > term, X646:subst > term > subst > $o, X647:term > $o, X648:term, X649:term, X650:subst > term > subst > $o, X651:term > $o, X653:term, X654:subst, X655:term > $o, X656:term > $o, X657:term, X658:term, X659:term, X660:subst, X661:term > $o, X662:term > $o, X664:term > $o, X665:term > $o, X666:term, X667:subst, X673:term, X674:term, X675:term, X678:term > $o, X679:term, X680:subst, X684:term, X689:term, X690:term, X691:term, X693:term, X694:term, X696:term, X697:subst, X699:subst > term > term, X702:term, X703:term, X704:term, X705:term, X710:term, X711:term, X712:term, X713:term, X723:term, X724:subst, X725:term, X726:subst, X727:subst, X728:term, X730:term, X731:subst, X733:subst > term > term, X737:term > $o, X741:term, X742:term, X743:term, X744:term, X747:subst > term > subst > $o, X749:term, X750:term, X751:term > $o, X756:term, X757:term, X758:term, X759:subst > term > term, X760:subst > term > term, X767:subst, X768:term, X773:subst, X774:term, X775:subst, X776:subst, X777:term, X778:subst, X779:subst > term > subst > $o, X780:term, X783:term, X784:subst, X785:term, X786:subst, X787:subst, X788:term, X789:subst, X793:subst > term > term, X794:term, X802:term, X803:subst > term > subst > $o, X804:term, X806:subst, X807:term, X808:subst, X809:term, X813:subst > term > term, X818:term, X819:subst > term > subst > $o, X820:term, X830:subst, X831:term, X832:subst, X833:term, X837:subst, X838:term, X839:subst, X840:subst, X841:subst, X842:term, X843:subst, X844:subst, X845:subst > term > term, X850:term, X851:subst > term > subst > $o, X852:term, X853:term, X867:subst, X868:term, X869:subst, X870:subst, X871:subst, X872:term, X873:subst, X874:subst, X875:term, X876:term, X879:term > $o, X880:term > $o, X881:term, X882:subst, X884:term, X885:subst, X890:term, X891:subst > term > subst > $o, X893:term, X894:term, X896:term > $o, X898:subst > term > subst > $o, X899:term, X902:term, X905:subst > term > term, X906:term > $o, X911:term, X914:term, X915:term, X916:term, X917:term, X921:subst > term > term, X926:term, X927:subst > term > subst > $o, X928:term, X930:subst, X931:term, X932:subst, X933:term, X935:term, X936:subst > term > subst > $o, X937:term, X939:subst, X940:term, X941:subst, X942:term, X946:subst > term > term, X951:term, X952:subst > term > subst > $o, X953:term, X955:subst, X956:term, X957:subst, X958:term, X962:subst > term > term, X967:term, X968:subst > term > subst > $o, X969:term > $o, X970:term, X971:term, X987:subst, X988:term, X989:subst, X990:subst, X991:subst, X992:term, X993:subst, X994:subst, X995:term, X996:term, X997:term, X998:term, X999:term, X1000:term, X1001:term, X1006:term, X1007:term, X1008:term, X1009:term, X1018:term, X1019:term, X1020:term, X1021:term, X1022:term, X1023:term, X1024:term, X1025:term, X1030:subst > term > subst > $o, X1031:term > $o, X1032:term, X1034:subst, X1035:term, X1036:subst, X1037:term, X1043:subst > term > term, X1048:term, X1049:term, X1055:term, X1056:term, X1057:term, X1058:term, X1059:term, X1060:term, X1061:term, X1062:term, X1063:term, X1074:subst > term > term, X1075:subst > term > term, X1082:subst, X1083:term, X1084:term, X1085:subst, X1086:term, X1087:subst, X1088:term, X1089:term, X1094:subst, X1095:term, X1096:subst, X1097:subst, X1098:term, X1099:subst, X1100:term, X1101:subst, X1104:subst, X1106:subst, X1108:term > $o, X1109:term > $o, X1110:term, X1111:subst, X1112:term, X1118:term, X1119:term, X1123:term, X1124:term > $o, X1125:term, X1126:subst, X1128:term, X1129:term, X1133:term > $o, X1136:subst > term > term, X1140:subst > term > subst > $o, X1141:term > $o, X1142:term, X1144:subst, X1145:term, X1146:subst, X1147:term, X1150:term, X1152:term, X1153:subst, X1154:term, X1158:subst > term > term, X1163:term, X1164:term, X1165:subst, X1168:term, X1169:subst > term > subst > $o, X1171:term, X1172:term, X1174:term > $o, X1178:subst, X1179:subst, X1180:subst, X1181:subst, X1184:term, X1187:subst > term > term, X1188:subst, X1189:subst, X1192:subst > term > subst > $o, X1193:term, X1195:subst, X1196:term, X1197:subst, X1198:term, X1202:subst > term > term, X1207:term, X1208:subst > term > subst > $o, X1212:subst, X1213:term, X1214:subst, X1215:term, X1216:term, X1219:term, X1220:term, X1221:subst > term > term, X1226:subst > term > term, X1230:term, X1231:term, X1235:subst, X1236:term, X1237:subst, X1238:term > $o, X1243:term, X1244:term, X1247:term, X1248:term, X1249:term, X1250:term, X1256:term > $o, X1257:term > $o, X1258:term, X1259:subst, X1260:term, X1261:term, X1262:subst, X1263:term, X1264:subst, X1270:subst > term > subst > $o, X1271:term > $o, X1272:term, X1276:term, X1277:subst, X1280:term, X1282:term > $o, X1283:term, X1284:subst, X1286:term, X1287:term, X1291:term > $o, X1294:subst > term > subst > $o, X1295:term > $o, X1296:term, X1297:term, X1301:term, X1304:term > $o, X1306:subst > term > subst > $o, X1308:term, X1309:term]:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((X634)=(d2term @ (esk1_1 @ X634)))&((X636)=(d_one)))&(((d2term @ X637)!=(d2term @ X638))|((X637)=(X638))))&((X639)=(d2subst @ (esk2_1 @ X639))))&((X641)=(d_id)))&(((d2subst @ X642)!=(d2subst @ X643))|((X642)=(X643))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&((id)=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&((hoaslam @ X644 @ X645)=(d2term @ d_one)))&(((~(X647 @ X648)|(X646 @ id @ X648 @ id)|~(hoasinduction_p_and_p_prime @ X646 @ X647))&(~(X646 @ id @ X649 @ id)|(X647 @ X649)|~(hoasinduction_p_and_p_prime @ X646 @ X647)))&((~(X651 @ (esk3_2 @ X650 @ X651))|~(X650 @ id @ (esk3_2 @ X650 @ X651) @ id)|(hoasinduction_p_and_p_prime @ X650 @ X651))&((X651 @ (esk3_2 @ X650 @ X651))|(X650 @ id @ (esk3_2 @ X650 @ X651) @ id)|(hoasinduction_p_and_p_prime @ X650 @ X651)))))&(((~(X656 @ X657)|(X655 @ (sub @ X657 @ (push @ X653 @ X654)))|~(pushprop_p_and_p_prime @ X653 @ X654 @ X655 @ X656))&(~(X655 @ (sub @ X658 @ (push @ X653 @ X654)))|(X656 @ X658)|~(pushprop_p_and_p_prime @ X653 @ X654 @ X655 @ X656)))&((~(X662 @ (esk4_4 @ X659 @ X660 @ X661 @ X662))|~(X661 @ (sub @ (esk4_4 @ X659 @ X660 @ X661 @ X662) @ (push @ X659 @ X660)))|(pushprop_p_and_p_prime @ X659 @ X660 @ X661 @ X662))&((X662 @ (esk4_4 @ X659 @ X660 @ X661 @ X662))|(X661 @ (sub @ (esk4_4 @ X659 @ X660 @ X661 @ X662) @ (push @ X659 @ X660)))|(pushprop_p_and_p_prime @ X659 @ X660 @ X661 @ X662)))))&~(var @ (d2term @ d_one)))&(((~(X665 @ (esk5_4 @ X664 @ X665 @ X666 @ X667))|~(X664 @ (sub @ (esk5_4 @ X664 @ X665 @ X666 @ X667) @ (push @ X666 @ X667)))|~(X664 @ X666)|(X665 @ one)|~(pushprop_lem1v2))&((X665 @ (esk5_4 @ X664 @ X665 @ X666 @ X667))|(X664 @ (sub @ (esk5_4 @ X664 @ X665 @ X666 @ X667) @ (push @ X666 @ X667)))|~(X664 @ X666)|(X665 @ one)|~(pushprop_lem1v2)))&((((epred10_0 @ esk6_0)|(pushprop_lem1v2))&((~(epred11_0 @ X673)|(epred10_0 @ (sub @ X673 @ (push @ esk6_0 @ esk7_0)))|(pushprop_lem1v2))&(~(epred10_0 @ (sub @ X673 @ (push @ esk6_0 @ esk7_0)))|(epred11_0 @ X673)|(pushprop_lem1v2))))&(~(epred11_0 @ one)|(pushprop_lem1v2)))))&(pushprop_lem1_gthm))&(axmap))&(pushprop_lem0_gthm))&((~(shinj)|(((sub @ X674 @ sh)!=(sub @ X675 @ sh))|((X674)=(X675))))&((((sub @ esk8_0 @ sh)=(sub @ esk9_0 @ sh))|(shinj))&(((esk8_0)!=(esk9_0))|(shinj)))))&(hoasinduction_lem1v2))&(hoasinduction_lem1v2_gthm))&(((((((var @ (esk13_3 @ X678 @ X679 @ X680))|(~(X678 @ X684)|(X678 @ (sub @ (esk12_3 @ X678 @ X679 @ X680) @ (push @ X684 @ id)))|(X678 @ (esk10_3 @ X678 @ X679 @ X680)))|(X678 @ (sub @ X679 @ X680))|~(induction2lem))&(~(X678 @ (sub @ (esk13_3 @ X678 @ X679 @ X680) @ X680))|(~(X678 @ X684)|(X678 @ (sub @ (esk12_3 @ X678 @ X679 @ X680) @ (push @ X684 @ id)))|(X678 @ (esk10_3 @ X678 @ X679 @ X680)))|(X678 @ (sub @ X679 @ X680))|~(induction2lem)))&(((var @ (esk13_3 @ X678 @ X679 @ X680))|(~(X678 @ (lam @ (esk12_3 @ X678 @ X679 @ X680)))|(X678 @ (esk10_3 @ X678 @ X679 @ X680)))|(X678 @ (sub @ X679 @ X680))|~(induction2lem))&(~(X678 @ (sub @ (esk13_3 @ X678 @ X679 @ X680) @ X680))|(~(X678 @ (lam @ (esk12_3 @ X678 @ X679 @ X680)))|(X678 @ (esk10_3 @ X678 @ X679 @ X680)))|(X678 @ (sub @ X679 @ X680))|~(induction2lem))))&((((var @ (esk13_3 @ X678 @ X679 @ X680))|(~(X678 @ X684)|(X678 @ (sub @ (esk12_3 @ X678 @ X679 @ X680) @ (push @ X684 @ id)))|(X678 @ (esk11_3 @ X678 @ X679 @ X680)))|(X678 @ (sub @ X679 @ X680))|~(induction2lem))&(~(X678 @ (sub @ (esk13_3 @ X678 @ X679 @ X680) @ X680))|(~(X678 @ X684)|(X678 @ (sub @ (esk12_3 @ X678 @ X679 @ X680) @ (push @ X684 @ id)))|(X678 @ (esk11_3 @ X678 @ X679 @ X680)))|(X678 @ (sub @ X679 @ X680))|~(induction2lem)))&(((var @ (esk13_3 @ X678 @ X679 @ X680))|(~(X678 @ (lam @ (esk12_3 @ X678 @ X679 @ X680)))|(X678 @ (esk11_3 @ X678 @ X679 @ X680)))|(X678 @ (sub @ X679 @ X680))|~(induction2lem))&(~(X678 @ (sub @ (esk13_3 @ X678 @ X679 @ X680) @ X680))|(~(X678 @ (lam @ (esk12_3 @ X678 @ X679 @ X680)))|(X678 @ (esk11_3 @ X678 @ X679 @ X680)))|(X678 @ (sub @ X679 @ X680))|~(induction2lem)))))&((((var @ (esk13_3 @ X678 @ X679 @ X680))|(~(X678 @ X684)|(X678 @ (sub @ (esk12_3 @ X678 @ X679 @ X680) @ (push @ X684 @ id)))|~(X678 @ (ap @ (esk10_3 @ X678 @ X679 @ X680) @ (esk11_3 @ X678 @ X679 @ X680))))|(X678 @ (sub @ X679 @ X680))|~(induction2lem))&(~(X678 @ (sub @ (esk13_3 @ X678 @ X679 @ X680) @ X680))|(~(X678 @ X684)|(X678 @ (sub @ (esk12_3 @ X678 @ X679 @ X680) @ (push @ X684 @ id)))|~(X678 @ (ap @ (esk10_3 @ X678 @ X679 @ X680) @ (esk11_3 @ X678 @ X679 @ X680))))|(X678 @ (sub @ X679 @ X680))|~(induction2lem)))&(((var @ (esk13_3 @ X678 @ X679 @ X680))|(~(X678 @ (lam @ (esk12_3 @ X678 @ X679 @ X680)))|~(X678 @ (ap @ (esk10_3 @ X678 @ X679 @ X680) @ (esk11_3 @ X678 @ X679 @ X680))))|(X678 @ (sub @ X679 @ X680))|~(induction2lem))&(~(X678 @ (sub @ (esk13_3 @ X678 @ X679 @ X680) @ X680))|(~(X678 @ (lam @ (esk12_3 @ X678 @ X679 @ X680)))|~(X678 @ (ap @ (esk10_3 @ X678 @ X679 @ X680) @ (esk11_3 @ X678 @ X679 @ X680))))|(X678 @ (sub @ X679 @ X680))|~(induction2lem)))))&((((~(epred12_0 @ X689)|~(epred12_0 @ X690)|(epred12_0 @ (ap @ X689 @ X690))|(induction2lem))&(((epred12_0 @ (esk16_1 @ X691))|(epred12_0 @ (lam @ X691))|(induction2lem))&(~(epred12_0 @ (sub @ X691 @ (push @ (esk16_1 @ X691) @ id)))|(epred12_0 @ (lam @ X691))|(induction2lem))))&(~(var @ X693)|(epred12_0 @ (sub @ X693 @ esk15_0))|(induction2lem)))&(~(epred12_0 @ (sub @ esk14_0 @ esk15_0))|(induction2lem)))))&((~(hoasinduction_lem3v2_f)|((sub @ X694 @ (push @ X696 @ X697))=(esk17_1 @ X694 @ X697 @ X696)))&(((sub @ esk18_0 @ (push @ (esk19_1 @ X699) @ (esk20_1 @ X699)))!=(X699 @ (esk20_1 @ X699) @ (esk19_1 @ X699)))|(hoasinduction_lem3v2_f))))&(axvarshift))&((~(hoasapinj2)|(((ap @ (sub @ X702 @ id) @ X704)!=(ap @ (sub @ X703 @ id) @ X705))|((X704)=(X705))))&((((ap @ (sub @ esk21_0 @ id) @ esk23_0)=(ap @ (sub @ esk22_0 @ id) @ esk24_0))|(hoasapinj2))&(((esk23_0)!=(esk24_0))|(hoasapinj2)))))&(hoasapnotvar_gthm))&((~(hoasapinj1)|(((ap @ (sub @ X710 @ id) @ X712)!=(ap @ (sub @ X711 @ id) @ X713))|((X710)=(X711))))&((((ap @ (sub @ esk25_0 @ id) @ esk27_0)=(ap @ (sub @ esk26_0 @ id) @ esk28_0))|(hoasapinj1))&(((esk25_0)!=(esk26_0))|(hoasapinj1)))))&~(ulamvar1))&((~(induction2lem_lthm)|(((esk29_0)!=(sub @ one @ (push @ esk29_0 @ esk30_0)))|(((esk32_0)!=(comp @ sh @ (push @ esk31_0 @ esk32_0)))|(((esk33_0)!=(comp @ esk33_0 @ id))|(epred1_0)))))&((((X723)=(sub @ one @ (push @ X723 @ X724)))|(induction2lem_lthm))&((((X726)=(comp @ sh @ (push @ X725 @ X726)))|(induction2lem_lthm))&((((X727)=(comp @ X727 @ id))|(induction2lem_lthm))&(~(epred1_0)|(induction2lem_lthm)))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((~(hoasinduction_lem3v2_f_lthm)|((sub @ X728 @ (push @ X730 @ X731))=(esk34_1 @ X728 @ X731 @ X730)))&(((sub @ esk35_0 @ (push @ (esk36_1 @ X733) @ (esk37_1 @ X733)))!=(X733 @ (esk37_1 @ X733) @ (esk36_1 @ X733)))|(hoasinduction_lem3v2_f_lthm))))&((~(hoasinduction_lthm)|(epred4_0))&(~(epred4_0)|(hoasinduction_lthm))))&((((((~(var @ X741)|(epred14_0 @ X741)|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X737 @ (esk38_1 @ X737))|~(epred13_0 @ id @ (esk38_1 @ X737) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ X742)|~(epred14_0 @ X743)|(epred14_0 @ (ap @ X742 @ X743))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X737 @ (esk38_1 @ X737))|~(epred13_0 @ id @ (esk38_1 @ X737) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred14_0 @ (esk40_1 @ X744))|(epred14_0 @ (lam @ 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(esk218_3 @ X1140 @ X1141 @ X1142) @ id)))|((X1141 @ (esk217_3 @ X1140 @ X1141 @ X1142))|(X1140 @ id @ (esk217_3 @ X1140 @ X1141 @ X1142) @ id)|~(X1140 @ id @ (lam @ (esk216_3 @ X1140 @ X1141 @ X1142 @ sh @ one)) @ id))|(X1141 @ (lam @ X1142))|((esk215_0)!=(sub @ esk215_0 @ id))|((sub @ esk212_0 @ (push @ (esk213_1 @ X1136) @ (esk214_1 @ X1136)))!=(X1136 @ (esk214_1 @ X1136) @ (esk213_1 @ X1136)))|~(hoasinduction_lem3v2a_lthm)))))&((((sub @ X1150 @ (push @ X1152 @ X1153))=(esk219_1 @ X1150 @ X1153 @ X1152))|(hoasinduction_lem3v2a_lthm))&((((X1154)=(sub @ X1154 @ id))|(hoasinduction_lem3v2a_lthm))&((((((epred37_0 @ id @ (esk224_1 @ X1158) @ id)|((sub @ (X1158 @ (esk221_1 @ X1158) @ (esk222_1 @ X1158)) @ (esk223_1 @ X1158))!=(X1158 @ (comp @ (esk221_1 @ X1158) @ (esk223_1 @ X1158)) @ (sub @ (esk222_1 @ X1158) @ (esk223_1 @ X1158))))|(epred37_0 @ id @ (lam @ (X1158 @ sh @ one)) @ id)|(hoasinduction_lem3v2a_lthm))&(~(epred37_0 @ id @ (X1158 @ id @ (esk224_1 @ X1158)) @ id)|((sub @ (X1158 @ (esk221_1 @ X1158) @ (esk222_1 @ X1158)) @ (esk223_1 @ X1158))!=(X1158 @ (comp @ (esk221_1 @ X1158) @ (esk223_1 @ X1158)) @ (sub @ (esk222_1 @ X1158) @ (esk223_1 @ X1158))))|(epred37_0 @ id @ (lam @ (X1158 @ sh @ one)) @ id)|(hoasinduction_lem3v2a_lthm)))&((~(epred38_0 @ X1163)|(epred37_0 @ id @ X1163 @ id)|(hoasinduction_lem3v2a_lthm))&(~(epred37_0 @ id @ X1163 @ id)|(epred38_0 @ X1163)|(hoasinduction_lem3v2a_lthm))))&(~(epred38_0 @ X1164)|(epred38_0 @ (sub @ esk220_0 @ (push @ X1164 @ id)))|(hoasinduction_lem3v2a_lthm)))&(~(epred38_0 @ (lam @ esk220_0))|(hoasinduction_lem3v2a_lthm)))))))&(hoasinduction_lem2_lthm))&(hoasapinj2_gthm))&(hoasinduction_lem1_lthm))&~(lamnotap))&(hoasapinj1_gthm))&(hoaslamnotvar))&((~(axidl)|((X1165)=(comp @ id @ X1165)))&(((esk225_0)!=(comp @ id @ esk225_0))|(axidl))))&(hoaslaminj_gthm))&((~(induction2_lthm)|(((esk226_0)!=(sub @ esk226_0 @ id))|(epred7_0)))&((((X1168)=(sub @ X1168 @ id))|(induction2_lthm))&(~(epred7_0)|(induction2_lthm)))))&(((~(epred39_1 @ X1169 @ X1171)|(X1169 @ id @ X1171 @ id)|~(hoasinduction_lem0_lthm))&(~(X1169 @ id @ X1172 @ id)|(epred39_1 @ X1169 @ X1172)|~(hoasinduction_lem0_lthm)))&((~(X1174 @ (esk227_1 @ X1174))|~(epred40_0 @ id @ (esk227_1 @ X1174) @ id)|(hoasinduction_lem0_lthm))&((X1174 @ (esk227_1 @ X1174))|(epred40_0 @ id @ (esk227_1 @ X1174) @ id)|(hoasinduction_lem0_lthm)))))&(((((X1178)=(comp @ id @ X1178))|((esk229_0)!=(comp @ esk229_0 @ id))|((esk228_0)!=(comp @ id @ esk228_0))|~(substmonoid_lthm))&(((X1179)=(comp @ X1179 @ id))|((esk229_0)!=(comp @ esk229_0 @ id))|((esk228_0)!=(comp @ id @ esk228_0))|~(substmonoid_lthm)))&((((X1180)=(comp @ id @ X1180))|(substmonoid_lthm))&((((X1181)=(comp @ X1181 @ id))|(substmonoid_lthm))&(((esk230_0)!=(comp @ id @ esk230_0))|((esk231_0)!=(comp @ esk231_0 @ id))|(substmonoid_lthm))))))&(pushprop))&(hoasinduction_lem3_gthm))&(hoasinduction_lem2_gthm))&((~(hoasinduction_lem3b)|((esk232_1 @ X1184 @ sh @ one)=(sub @ X1184 @ (push @ one @ sh))))&(((X1187 @ sh @ one)!=(sub @ esk233_0 @ (push @ one @ sh)))|(hoasinduction_lem3b))))&(((((X1188)=(comp @ id @ X1188))|~(substmonoid))&(((X1189)=(comp @ X1189 @ id))|~(substmonoid)))&(((esk234_0)!=(comp @ id @ esk234_0))|((esk235_0)!=(comp @ esk235_0 @ id))|(substmonoid))))&(lamnotvar))&((((((X1192 @ id @ (esk237_2 @ X1192 @ X1193) @ id)|((sub @ (esk236_2 @ X1192 @ X1193 @ X1195 @ X1196) @ X1197)=(esk236_2 @ X1192 @ X1193 @ (comp @ X1195 @ X1197) @ (sub @ X1196 @ X1197)))|(X1192 @ id @ (lam @ X1193) @ id)|~(hoasinduction_lem3a))&(~(X1192 @ id @ (sub @ X1193 @ (push @ (esk237_2 @ X1192 @ X1193) @ id)) @ id)|((sub @ (esk236_2 @ X1192 @ X1193 @ X1195 @ X1196) @ X1197)=(esk236_2 @ X1192 @ X1193 @ (comp @ X1195 @ X1197) @ (sub @ X1196 @ X1197)))|(X1192 @ id @ (lam @ X1193) @ id)|~(hoasinduction_lem3a)))&(((X1192 @ id @ (esk237_2 @ X1192 @ X1193) @ id)|(~(X1192 @ id @ X1198 @ id)|(X1192 @ id @ (esk236_2 @ X1192 @ X1193 @ id @ X1198) @ id))|(X1192 @ id @ (lam @ X1193) @ id)|~(hoasinduction_lem3a))&(~(X1192 @ id @ (sub @ X1193 @ (push @ (esk237_2 @ X1192 @ X1193) @ id)) @ id)|(~(X1192 @ id @ X1198 @ id)|(X1192 @ id @ (esk236_2 @ X1192 @ X1193 @ id @ X1198) @ id))|(X1192 @ id @ (lam @ X1193) @ id)|~(hoasinduction_lem3a))))&(((X1192 @ id @ (esk237_2 @ X1192 @ X1193) @ id)|~(X1192 @ id @ (lam @ (esk236_2 @ X1192 @ X1193 @ sh @ one)) @ id)|(X1192 @ id @ (lam @ X1193) @ id)|~(hoasinduction_lem3a))&(~(X1192 @ id @ (sub @ X1193 @ (push @ (esk237_2 @ X1192 @ X1193) @ id)) @ id)|~(X1192 @ id @ (lam @ (esk236_2 @ X1192 @ X1193 @ sh @ one)) @ id)|(X1192 @ id @ (lam @ X1193) @ id)|~(hoasinduction_lem3a))))&(((((epred41_0 @ id @ (esk242_1 @ X1202) @ id)|((sub @ (X1202 @ (esk239_1 @ X1202) @ (esk240_1 @ X1202)) @ (esk241_1 @ X1202))!=(X1202 @ (comp @ (esk239_1 @ X1202) @ (esk241_1 @ X1202)) @ (sub @ (esk240_1 @ X1202) @ (esk241_1 @ X1202))))|(epred41_0 @ id @ (lam @ (X1202 @ sh @ one)) @ id)|(hoasinduction_lem3a))&(~(epred41_0 @ id @ (X1202 @ id @ (esk242_1 @ X1202)) @ id)|((sub @ (X1202 @ (esk239_1 @ X1202) @ (esk240_1 @ X1202)) @ (esk241_1 @ X1202))!=(X1202 @ (comp @ (esk239_1 @ X1202) @ (esk241_1 @ X1202)) @ (sub @ (esk240_1 @ X1202) @ (esk241_1 @ X1202))))|(epred41_0 @ id @ (lam @ (X1202 @ sh @ one)) @ id)|(hoasinduction_lem3a)))&(~(epred41_0 @ id @ X1207 @ id)|(epred41_0 @ id @ (sub @ esk238_0 @ (push @ X1207 @ id)) @ id)|(hoasinduction_lem3a)))&(~(epred41_0 @ id @ (lam @ esk238_0) @ id)|(hoasinduction_lem3a)))))&(hoasinduction_lem1_gthm))&((((((((sub @ (esk245_1 @ X1208 @ X1212 @ X1213) @ X1214)=(esk245_1 @ X1208 @ (comp @ X1212 @ X1214) @ (sub @ X1213 @ X1214)))|(X1208 @ id @ (esk243_1 @ X1208) @ id)|(X1208 @ id @ X1216 @ id)|~(hoasinduction_no_psi_cond))&(~(X1208 @ id @ X1215 @ id)|(X1208 @ id @ (esk245_1 @ X1208 @ id @ X1215) @ id)|(X1208 @ id @ (esk243_1 @ X1208) @ id)|(X1208 @ id @ X1216 @ id)|~(hoasinduction_no_psi_cond)))&(~(X1208 @ id @ (lam @ (esk245_1 @ X1208 @ sh @ one)) @ id)|(X1208 @ id @ (esk243_1 @ X1208) @ id)|(X1208 @ id @ X1216 @ id)|~(hoasinduction_no_psi_cond)))&(((((sub @ (esk245_1 @ X1208 @ X1212 @ X1213) @ X1214)=(esk245_1 @ X1208 @ (comp @ X1212 @ X1214) @ (sub @ X1213 @ X1214)))|(X1208 @ id @ (esk244_1 @ X1208) @ id)|(X1208 @ id @ X1216 @ id)|~(hoasinduction_no_psi_cond))&(~(X1208 @ id @ X1215 @ id)|(X1208 @ id @ (esk245_1 @ X1208 @ id @ X1215) @ id)|(X1208 @ id @ (esk244_1 @ X1208) @ id)|(X1208 @ id @ X1216 @ id)|~(hoasinduction_no_psi_cond)))&(~(X1208 @ id @ (lam @ (esk245_1 @ X1208 @ sh @ one)) @ id)|(X1208 @ id @ (esk244_1 @ X1208) @ id)|(X1208 @ id @ X1216 @ id)|~(hoasinduction_no_psi_cond))))&(((((sub @ (esk245_1 @ X1208 @ X1212 @ X1213) @ X1214)=(esk245_1 @ X1208 @ (comp @ X1212 @ X1214) @ (sub @ X1213 @ X1214)))|~(X1208 @ id @ (ap @ (sub @ (esk243_1 @ X1208) @ id) @ (esk244_1 @ X1208)) @ id)|(X1208 @ id @ X1216 @ id)|~(hoasinduction_no_psi_cond))&(~(X1208 @ id @ X1215 @ id)|(X1208 @ id @ (esk245_1 @ X1208 @ id @ X1215) @ id)|~(X1208 @ id @ (ap @ (sub @ (esk243_1 @ X1208) @ id) @ (esk244_1 @ X1208)) @ id)|(X1208 @ id @ X1216 @ id)|~(hoasinduction_no_psi_cond)))&(~(X1208 @ id @ (lam @ (esk245_1 @ X1208 @ sh @ one)) @ id)|~(X1208 @ id @ (ap @ (sub @ (esk243_1 @ X1208) @ id) @ (esk244_1 @ X1208)) @ id)|(X1208 @ id @ X1216 @ id)|~(hoasinduction_no_psi_cond))))&(((~(epred42_0 @ id @ X1219 @ id)|~(epred42_0 @ id @ X1220 @ id)|(epred42_0 @ id @ (ap @ (sub @ X1219 @ id) @ X1220) @ id)|(hoasinduction_no_psi_cond))&(((epred42_0 @ id @ (esk250_1 @ X1221) @ id)|((sub @ (X1221 @ (esk247_1 @ X1221) @ (esk248_1 @ X1221)) @ (esk249_1 @ X1221))!=(X1221 @ (comp @ (esk247_1 @ X1221) @ (esk249_1 @ X1221)) @ (sub @ (esk248_1 @ X1221) @ (esk249_1 @ X1221))))|(epred42_0 @ id @ (lam @ (X1221 @ sh @ one)) @ id)|(hoasinduction_no_psi_cond))&(~(epred42_0 @ id @ (X1221 @ id @ (esk250_1 @ X1221)) @ id)|((sub @ (X1221 @ (esk247_1 @ X1221) @ (esk248_1 @ X1221)) @ (esk249_1 @ X1221))!=(X1221 @ (comp @ (esk247_1 @ X1221) @ (esk249_1 @ X1221)) @ (sub @ (esk248_1 @ X1221) @ (esk249_1 @ X1221))))|(epred42_0 @ id @ (lam @ (X1221 @ sh @ one)) @ id)|(hoasinduction_no_psi_cond))))&(~(epred42_0 @ id @ esk246_0 @ id)|(hoasinduction_no_psi_cond)))))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&((~(hoaslamnotap)|(((sub @ (X1226 @ (esk251_1 @ X1226) @ (esk252_1 @ X1226)) @ (esk253_1 @ X1226))!=(X1226 @ (comp @ (esk251_1 @ X1226) @ (esk253_1 @ X1226)) @ (sub @ (esk252_1 @ X1226) @ (esk253_1 @ X1226))))|((lam @ (X1226 @ sh @ one))!=(ap @ (sub @ X1230 @ id) @ X1231))))&((((sub @ (esk254_0 @ X1235 @ X1236) @ X1237)=(esk254_0 @ (comp @ X1235 @ X1237) @ (sub @ X1236 @ X1237)))|(hoaslamnotap))&(((lam @ (esk254_0 @ sh @ one))=(ap @ (sub @ esk255_0 @ id) @ esk256_0))|(hoaslamnotap)))))&(substmonoid_gthm))&(ulamvarsh))&((((((~(X1238 @ X1243)|(X1238 @ (sub @ (esk260_1 @ X1238) @ (push @ X1243 @ id)))|((X1238 @ (esk258_1 @ X1238))|(var @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2))&(~(X1238 @ (lam @ (esk260_1 @ X1238)))|((X1238 @ (esk258_1 @ X1238))|(var @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2)))&((~(X1238 @ X1243)|(X1238 @ (sub @ (esk260_1 @ X1238) @ (push @ X1243 @ id)))|((X1238 @ (esk259_1 @ X1238))|(var @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2))&(~(X1238 @ (lam @ (esk260_1 @ X1238)))|((X1238 @ (esk259_1 @ X1238))|(var @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2))))&((~(X1238 @ X1243)|(X1238 @ (sub @ (esk260_1 @ X1238) @ (push @ X1243 @ id)))|(~(X1238 @ (ap @ (esk258_1 @ X1238) @ (esk259_1 @ X1238)))|(var @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2))&(~(X1238 @ (lam @ (esk260_1 @ X1238)))|(~(X1238 @ (ap @ (esk258_1 @ X1238) @ (esk259_1 @ X1238)))|(var @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2))))&((((~(X1238 @ X1243)|(X1238 @ (sub @ (esk260_1 @ X1238) @ (push @ X1243 @ id)))|((X1238 @ (esk258_1 @ X1238))|~(X1238 @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2))&(~(X1238 @ (lam @ (esk260_1 @ X1238)))|((X1238 @ (esk258_1 @ X1238))|~(X1238 @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2)))&((~(X1238 @ X1243)|(X1238 @ (sub @ (esk260_1 @ X1238) @ (push @ X1243 @ id)))|((X1238 @ (esk259_1 @ X1238))|~(X1238 @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2))&(~(X1238 @ (lam @ (esk260_1 @ X1238)))|((X1238 @ (esk259_1 @ X1238))|~(X1238 @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2))))&((~(X1238 @ X1243)|(X1238 @ (sub @ (esk260_1 @ X1238) @ (push @ X1243 @ id)))|(~(X1238 @ (ap @ (esk258_1 @ X1238) @ (esk259_1 @ X1238)))|~(X1238 @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2))&(~(X1238 @ (lam @ (esk260_1 @ X1238)))|(~(X1238 @ (ap @ (esk258_1 @ X1238) @ (esk259_1 @ X1238)))|~(X1238 @ (esk257_1 @ X1238)))|(X1238 @ X1244)|~(induction2)))))&((((~(var @ X1247)|(epred43_0 @ X1247)|(induction2))&(~(epred43_0 @ X1248)|~(epred43_0 @ X1249)|(epred43_0 @ (ap @ X1248 @ X1249))|(induction2)))&(((epred43_0 @ (esk262_1 @ X1250))|(epred43_0 @ (lam @ X1250))|(induction2))&(~(epred43_0 @ (sub @ X1250 @ (push @ (esk262_1 @ X1250) @ id)))|(epred43_0 @ (lam @ X1250))|(induction2))))&(~(epred43_0 @ esk261_0)|(induction2)))))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((~(pushprop_lem1_lthm)|(((esk263_0)!=(sub @ one @ (push @ esk263_0 @ esk264_0)))|(((esk266_0)!=(comp @ sh @ (push @ esk265_0 @ esk266_0)))|(~(X1256 @ X1258)|(X1257 @ (sub @ X1258 @ (push @ X1260 @ X1259)))))))&((((X1261)=(sub @ one @ (push @ X1261 @ X1262)))|(pushprop_lem1_lthm))&((((X1264)=(comp @ sh @ (push @ X1263 @ X1264)))|(pushprop_lem1_lthm))&(((epred44_0 @ esk267_0)|(pushprop_lem1_lthm))&(~(epred45_0 @ (sub @ esk267_0 @ (push @ esk269_0 @ esk268_0)))|(pushprop_lem1_lthm)))))))&((~(hoasinduction_lem3v2)|((epred8_3 @ X1272 @ X1271 @ X1270)|(X1271 @ (lam @ X1272))))&((~(epred8_3 @ esk270_0 @ epred47_0 @ epred46_0)|(hoasinduction_lem3v2))&(~(epred47_0 @ (lam @ esk270_0))|(hoasinduction_lem3v2)))))&((~(axshiftcons)|((X1277)=(comp @ sh @ (push @ X1276 @ X1277))))&(((esk272_0)!=(comp @ sh @ (push @ esk271_0 @ esk272_0)))|(axshiftcons))))&((~(termmset)|((X1280)=(sub @ X1280 @ id)))&(((esk273_0)!=(sub @ esk273_0 @ id))|(termmset))))&(((~(epred48_3 @ X1282 @ X1283 @ X1284 @ X1286)|(X1282 @ (sub @ X1286 @ (push @ X1283 @ X1284)))|~(pushprop_lem0_lthm))&(~(X1282 @ (sub @ X1287 @ (push @ X1283 @ X1284)))|(epred48_3 @ X1282 @ X1283 @ X1284 @ X1287)|~(pushprop_lem0_lthm)))&((~(X1291 @ (esk276_1 @ X1291))|~(epred49_0 @ (sub @ (esk276_1 @ X1291) @ (push @ esk274_0 @ esk275_0)))|(pushprop_lem0_lthm))&((X1291 @ (esk276_1 @ X1291))|(epred49_0 @ (sub @ (esk276_1 @ X1291) @ (push @ esk274_0 @ esk275_0)))|(pushprop_lem0_lthm)))))&(hoasapnotvar_lthm))&((~(hoasinduction_lem3v2_lthm)|(((esk277_0)!=(sub @ esk277_0 @ id))|((epred8_3 @ X1296 @ X1295 @ X1294)|(X1295 @ (lam @ X1296)))))&((((X1297)=(sub @ X1297 @ id))|(hoasinduction_lem3v2_lthm))&((~(epred8_3 @ esk278_0 @ epred51_0 @ epred50_0)|(hoasinduction_lem3v2_lthm))&(~(epred51_0 @ (lam @ esk278_0))|(hoasinduction_lem3v2_lthm))))))&((~(axvarid)|((X1301)=(sub @ X1301 @ id)))&(((esk279_0)!=(sub @ esk279_0 @ id))|(axvarid))))&(((~(X1304 @ (esk280_1 @ X1304))|~(epred52_0 @ id @ (esk280_1 @ X1304) @ id)|(epred9_0)|~(hoasinduction_lthm_3))&((X1304 @ (esk280_1 @ X1304))|(epred52_0 @ id @ (esk280_1 @ X1304) @ id)|(epred9_0)|~(hoasinduction_lthm_3)))&(((~(epred53_1 @ X1306 @ X1308)|(X1306 @ id @ X1308 @ id)|(hoasinduction_lthm_3))&(~(X1306 @ id @ X1309 @ id)|(epred53_1 @ X1306 @ X1309)|(hoasinduction_lthm_3)))&(~(epred9_0)|(hoasinduction_lthm_3)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])])])).
% 1.58/0.51 thf(c_0_12, plain, ![X1:term]:(((X1)=(d2term @ (esk1_1 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_13, plain, ![X2:d_term]:(((X2)=(d_one))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_14, plain, ((one)=(d2term @ d_one)), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_15, negated_conjecture, ~(((hoasinduction_lem3v2)<=>![X11:subst > term > subst > $o, X12:term > $o]:((![X15:subst, X14:term, X32:subst, X33:subst]:(((X11 @ X15 @ X14 @ (comp @ X33 @ X32))=>(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32)))=>(![X15:subst, X14:term, X32:subst, X33:subst]:(((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32)=>(X11 @ X15 @ X14 @ (comp @ X33 @ X32))))=>(![X22:subst > term > term]:((![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32))))=>(![X14:term]:(((X11 @ id @ X14 @ id)=>(X11 @ id @ (X22 @ id @ X14) @ id)))=>(X11 @ id @ (hoaslam @ id @ (^[X15:subst, X14:term]:(X22 @ X15 @ X14))) @ id))))=>((hoasinduction_p_and_p_prime @ X11 @ X12)=>![X14:term]:((![X18:term]:(((X12 @ X18)=>(X12 @ (sub @ X14 @ (push @ X18 @ id)))))=>(X12 @ (lam @ X14))))))))))), inference(assume_negation,[status(cth)],[hoasinduction_lem3v2])).
% 1.58/0.51 thf(c_0_16, plain, ((laminj)|((esk206_0)!=(esk207_0))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_17, plain, ![X1:term]:(((one)=(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13]), c_0_14])).
% 1.58/0.51 thf(c_0_18, negated_conjecture, ~(((hoasinduction_lem3v2)<=>![X11:subst > term > subst > $o, X12:term > $o]:((![X15:subst, X14:term, X32:subst, X33:subst]:(((X11 @ X15 @ X14 @ (comp @ X33 @ X32))=>(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32)))=>(![X15:subst, X14:term, X32:subst, X33:subst]:(((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32)=>(X11 @ X15 @ X14 @ (comp @ X33 @ X32))))=>(![X22:subst > term > term]:((![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32))))=>(![X14:term]:(((X11 @ id @ X14 @ id)=>(X11 @ id @ (X22 @ id @ X14) @ id)))=>(X11 @ id @ (hoaslam @ id @ (^[Z0:subst, Z1:term]:(X22 @ Z0 @ Z1))) @ id))))=>((hoasinduction_p_and_p_prime @ X11 @ X12)=>![X14:term]:((![X18:term]:(((X12 @ X18)=>(X12 @ (sub @ X14 @ (push @ X18 @ id)))))=>(X12 @ (lam @ X14))))))))))), inference(fof_simplification,[status(thm)],[c_0_15])).
% 1.58/0.51 thf(c_0_19, plain, ![X1:term, X13:term]:((((X1)=(X13))|~((laminj))|((lam @ X1)!=(lam @ X13)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 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])])).
% 1.58/0.51 thf(c_0_21, plain, ((induction2)|~((epred43_0 @ esk261_0))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_22, negated_conjecture, ![X1312:subst, X1313:term, X1314:subst, X1315:subst, X1316:subst, X1317:term, X1318:subst, X1319:subst, X1320:subst > term > term, X1326:term, X1327:subst > term > subst > $o, X1337:subst, X1338:term, X1339:subst, X1340:term, X1341:term > $o, X1342:term]:((((~(epred54_0 @ X1312 @ X1313 @ (comp @ X1315 @ X1314))|(epred54_0 @ (comp @ X1312 @ X1315) @ (sub @ X1313 @ X1315) @ X1314)|~(hoasinduction_lem3v2))&((~(epred54_0 @ (comp @ X1316 @ X1319) @ (sub @ X1317 @ X1319) @ X1318)|(epred54_0 @ X1316 @ X1317 @ (comp @ X1319 @ X1318))|~(hoasinduction_lem3v2))&((((epred54_0 @ id @ (esk284_1 @ X1320) @ id)|(epred54_0 @ id @ (hoaslam @ id @ X1320) @ id)|((sub @ (X1320 @ (esk281_1 @ X1320) @ (esk282_1 @ X1320)) @ (esk283_1 @ X1320))!=(X1320 @ (comp @ (esk281_1 @ X1320) @ (esk283_1 @ X1320)) @ (sub @ (esk282_1 @ X1320) @ (esk283_1 @ X1320))))|~(hoasinduction_lem3v2))&(~(epred54_0 @ id @ (X1320 @ id @ (esk284_1 @ X1320)) @ id)|(epred54_0 @ id @ (hoaslam @ id @ X1320) @ id)|((sub @ (X1320 @ (esk281_1 @ X1320) @ (esk282_1 @ X1320)) @ (esk283_1 @ X1320))!=(X1320 @ (comp @ (esk281_1 @ X1320) @ (esk283_1 @ X1320)) @ (sub @ (esk282_1 @ X1320) @ (esk283_1 @ X1320))))|~(hoasinduction_lem3v2)))&(((hoasinduction_p_and_p_prime @ epred54_0 @ epred55_0)|~(hoasinduction_lem3v2))&((~(epred55_0 @ X1326)|(epred55_0 @ (sub @ esk285_0 @ (push @ X1326 @ id)))|~(hoasinduction_lem3v2))&(~(epred55_0 @ (lam @ esk285_0))|~(hoasinduction_lem3v2)))))))&((((((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|((sub @ (esk294_1 @ X1327 @ X1337 @ X1338) @ X1339)=(esk294_1 @ X1327 @ (comp @ X1337 @ X1339) @ (sub @ X1338 @ X1339)))|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|((sub @ (esk294_1 @ X1327 @ X1337 @ X1338) @ X1339)=(esk294_1 @ X1327 @ (comp @ X1337 @ X1339) @ (sub @ X1338 @ X1339)))|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2)))&((((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|(~(X1327 @ id @ X1340 @ id)|(X1327 @ id @ (esk294_1 @ X1327 @ id @ X1340) @ id))|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|(~(X1327 @ id @ X1340 @ id)|(X1327 @ id @ (esk294_1 @ X1327 @ id @ X1340) @ id))|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2)))&(((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|~(X1327 @ id @ (hoaslam @ id @ (esk294_1 @ X1327)) @ id)|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|~(X1327 @ id @ (hoaslam @ id @ (esk294_1 @ X1327)) @ id)|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2)))))&((((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|((sub @ (esk294_1 @ X1327 @ X1337 @ X1338) @ X1339)=(esk294_1 @ X1327 @ (comp @ X1337 @ X1339) @ (sub @ X1338 @ X1339)))|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|((sub @ (esk294_1 @ X1327 @ X1337 @ X1338) @ X1339)=(esk294_1 @ X1327 @ (comp @ X1337 @ X1339) @ (sub @ X1338 @ X1339)))|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2)))&((((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|(~(X1327 @ id @ X1340 @ id)|(X1327 @ id @ (esk294_1 @ X1327 @ id @ X1340) @ id))|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|(~(X1327 @ id @ X1340 @ id)|(X1327 @ id @ (esk294_1 @ X1327 @ id @ X1340) @ id))|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2)))&(((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|~(X1327 @ id @ (hoaslam @ id @ (esk294_1 @ X1327)) @ id)|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|~(X1327 @ id @ (hoaslam @ id @ (esk294_1 @ X1327)) @ id)|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|(X1327 @ (esk286_1 @ X1327) @ (esk287_1 @ X1327) @ (comp @ (esk289_1 @ X1327) @ (esk288_1 @ X1327)))|(hoasinduction_lem3v2))))))&(((((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|((sub @ (esk294_1 @ X1327 @ X1337 @ X1338) @ X1339)=(esk294_1 @ X1327 @ (comp @ X1337 @ X1339) @ (sub @ X1338 @ X1339)))|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|((sub @ (esk294_1 @ X1327 @ X1337 @ X1338) @ X1339)=(esk294_1 @ X1327 @ (comp @ X1337 @ X1339) @ (sub @ X1338 @ X1339)))|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2)))&((((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|(~(X1327 @ id @ X1340 @ id)|(X1327 @ id @ (esk294_1 @ X1327 @ id @ X1340) @ id))|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|(~(X1327 @ id @ X1340 @ id)|(X1327 @ id @ (esk294_1 @ X1327 @ id @ X1340) @ id))|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2)))&(((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|~(X1327 @ id @ (hoaslam @ id @ (esk294_1 @ X1327)) @ id)|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|~(X1327 @ id @ (hoaslam @ id @ (esk294_1 @ X1327)) @ id)|(X1327 @ (comp @ (esk290_1 @ X1327) @ (esk293_1 @ X1327)) @ (sub @ (esk291_1 @ X1327) @ (esk293_1 @ X1327)) @ (esk292_1 @ X1327))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2)))))&((((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|((sub @ (esk294_1 @ X1327 @ X1337 @ X1338) @ X1339)=(esk294_1 @ X1327 @ (comp @ X1337 @ X1339) @ (sub @ X1338 @ X1339)))|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|((sub @ (esk294_1 @ X1327 @ X1337 @ X1338) @ X1339)=(esk294_1 @ X1327 @ (comp @ X1337 @ X1339) @ (sub @ X1338 @ X1339)))|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2)))&((((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|(~(X1327 @ id @ X1340 @ id)|(X1327 @ id @ (esk294_1 @ X1327 @ id @ X1340) @ id))|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|(~(X1327 @ id @ X1340 @ id)|(X1327 @ id @ (esk294_1 @ X1327 @ id @ X1340) @ id))|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2)))&(((X1341 @ (esk295_3 @ X1327 @ X1341 @ X1342))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|~(X1327 @ id @ (hoaslam @ id @ (esk294_1 @ X1327)) @ id)|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(hoasinduction_lem3v2))&(~(X1341 @ (sub @ X1342 @ (push @ (esk295_3 @ X1327 @ X1341 @ X1342) @ id)))|(X1341 @ (lam @ X1342))|~(hoasinduction_p_and_p_prime @ X1327 @ X1341)|~(X1327 @ id @ (hoaslam @ id @ (esk294_1 @ X1327)) @ id)|~(X1327 @ (esk290_1 @ X1327) @ (esk291_1 @ X1327) @ (comp @ (esk293_1 @ X1327) @ (esk292_1 @ X1327)))|~(X1327 @ (comp @ (esk286_1 @ X1327) @ (esk289_1 @ X1327)) @ (sub @ (esk287_1 @ X1327) @ (esk289_1 @ X1327)) @ (esk288_1 @ X1327))|(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_18])])])])])])])).
% 1.58/0.51 thf(c_0_23, plain, ![X5:subst]:(((X5)=(d2subst @ (esk2_1 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_24, plain, ![X6:d_subst]:(((X6)=(d_id))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_25, plain, ((id)=(d2subst @ d_id)), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_26, plain, ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_27, plain, ![X1:term]:(((epred43_0 @ (esk262_1 @ X1))|(epred43_0 @ (lam @ X1))|(induction2))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_28, plain, ![X1:term, X13:term]:(((X1)=(X13))), 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])])).
% 1.58/0.51 thf(c_0_29, plain, ((induction2)|~((epred43_0 @ one))), inference(rw,[status(thm)],[c_0_21, c_0_17])).
% 1.58/0.51 thf(c_0_30, negated_conjecture, ![X10:subst > term > term]:(((epred54_0 @ id @ (esk284_1 @ X10) @ id)|(epred54_0 @ id @ (hoaslam @ id @ X10) @ id)|((sub @ (X10 @ (esk281_1 @ X10) @ (esk282_1 @ X10)) @ (esk283_1 @ X10))!=(X10 @ (comp @ (esk281_1 @ X10) @ (esk283_1 @ X10)) @ (sub @ (esk282_1 @ X10) @ (esk283_1 @ X10))))|~((hoasinduction_lem3v2)))), inference(split_conjunct,[status(thm)],[c_0_22])).
% 1.58/0.51 thf(c_0_31, plain, ![X5:subst]:(((id)=(X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24]), c_0_25])).
% 1.58/0.51 thf(c_0_32, plain, ~((hoasvar @ id @ (d2term @ d_one) @ id)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_25]), c_0_25])).
% 1.58/0.51 thf(c_0_33, plain, ~((var @ (d2term @ d_one))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_34, plain, ![X1:term, X12:term > $o]:(((X12 @ X1)|~((X12 @ (lam @ (esk260_1 @ X12))))|~((X12 @ (ap @ (esk258_1 @ X12) @ (esk259_1 @ X12))))|~((X12 @ (esk257_1 @ X12)))|~((induction2)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_35, plain, (induction2), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_17]), c_0_28])]), c_0_29])).
% 1.58/0.51 thf(c_0_36, plain, ![X11:subst > term > subst > $o, X12:term > $o]:(((X12 @ (esk3_2 @ X11 @ X12))|(X11 @ id @ (esk3_2 @ X11 @ X12) @ id)|(hoasinduction_p_and_p_prime @ X11 @ X12))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_37, negated_conjecture, ![X1:term, X5:subst, X9:subst, X15:subst]:(((epred54_0 @ (comp @ X5 @ X9) @ (sub @ X1 @ X9) @ X15)|~((epred54_0 @ X5 @ X1 @ (comp @ X9 @ X15)))|~((hoasinduction_lem3v2)))), inference(split_conjunct,[status(thm)],[c_0_22])).
% 1.58/0.51 thf(c_0_38, negated_conjecture, ((epred54_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_30, c_0_28]), c_0_28]), c_0_31]), c_0_31]), c_0_31]), c_0_28]), c_0_31]), c_0_17]), c_0_28]), c_0_31]), c_0_28]), c_0_28]), c_0_31]), c_0_17])])).
% 1.58/0.51 thf(c_0_39, plain, ![X1598:subst > term > subst > $o, X1599:term > $o, X1600:term, X1610:subst, X1611:term, X1612:subst, X1613:term, X1616:subst > term > subst > $o, X1617:term > $o, X1618:term, X1619:subst, X1620:term, X1621:subst, X1622:subst, X1623:subst, X1624:term, X1625:subst, X1626:subst, X1627:subst > term > term, X1632:term, X1633:term, X1634:term]:((((((((((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(((sub @ (esk417_3 @ X1598 @ X1599 @ X1600 @ X1610 @ X1611) @ X1612)=(esk417_3 @ X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(((sub @ (esk417_3 @ X1598 @ X1599 @ X1600 @ X1610 @ X1611) @ X1612)=(esk417_3 @ X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))&(((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(((sub @ (esk417_3 @ X1598 @ X1599 @ X1600 @ X1610 @ X1611) @ X1612)=(esk417_3 @ X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(((sub @ (esk417_3 @ X1598 @ X1599 @ X1600 @ X1610 @ X1611) @ X1612)=(esk417_3 @ X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))))&((((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))&(((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))))&((((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ (lam @ (esk417_3 @ X1598 @ X1599 @ X1600 @ sh @ one)) @ id)|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ (lam @ (esk417_3 @ X1598 @ X1599 @ X1600 @ sh @ one)) @ id)|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))&(((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ (lam @ (esk417_3 @ X1598 @ X1599 @ X1600 @ sh @ one)) @ id)|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ (lam @ (esk417_3 @ X1598 @ X1599 @ X1600 @ sh @ one)) @ id)|((X1598 @ (comp @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (esk416_3 @ X1598 @ X1599 @ X1600)) @ (esk415_3 @ X1598 @ X1599 @ X1600))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))))&((((((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(((sub @ (esk417_3 @ X1598 @ X1599 @ X1600 @ X1610 @ X1611) @ X1612)=(esk417_3 @ X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(((sub @ (esk417_3 @ X1598 @ X1599 @ X1600 @ X1610 @ X1611) @ X1612)=(esk417_3 @ X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))&(((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(((sub @ (esk417_3 @ X1598 @ X1599 @ X1600 @ X1610 @ X1611) @ X1612)=(esk417_3 @ X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(((sub @ (esk417_3 @ X1598 @ X1599 @ X1600 @ X1610 @ X1611) @ X1612)=(esk417_3 @ X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))))&((((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|(X1598 @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk412_3 @ X1598 @ X1599 @ X1600) @ (esk411_3 @ X1598 @ X1599 @ X1600))))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))&(((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ 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X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(((sub @ (esk417_3 @ X1598 @ X1599 @ X1600 @ X1610 @ X1611) @ X1612)=(esk417_3 @ X1598 @ X1599 @ X1600 @ (comp @ X1610 @ X1612) @ (sub @ X1611 @ X1612)))|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598))))&((((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))&(((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ X1613 @ id)|(X1598 @ id @ (esk417_3 @ X1598 @ X1599 @ X1600 @ id @ X1613) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))))&((((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ (lam @ (esk417_3 @ X1598 @ X1599 @ X1600 @ sh @ one)) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|(~(X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|~(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ (lam @ (esk417_3 @ X1598 @ X1599 @ X1600 @ sh @ one)) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))&(((X1599 @ (esk419_3 @ X1598 @ X1599 @ X1600))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ (lam @ (esk417_3 @ X1598 @ X1599 @ X1600 @ sh @ one)) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598))&(~(X1599 @ (sub @ X1600 @ (push @ (esk419_3 @ X1598 @ X1599 @ X1600) @ id)))|((X1599 @ (esk418_3 @ X1598 @ X1599 @ X1600))|(X1598 @ id @ (esk418_3 @ X1598 @ X1599 @ X1600) @ id)|(~(X1598 @ id @ (lam @ (esk417_3 @ X1598 @ X1599 @ X1600 @ sh @ one)) @ id)|(~(X1598 @ (esk413_3 @ X1598 @ X1599 @ X1600) @ (esk414_3 @ X1598 @ X1599 @ X1600) @ (comp @ (esk416_3 @ X1598 @ X1599 @ X1600) @ (esk415_3 @ X1598 @ X1599 @ X1600)))|~(X1598 @ (comp @ (esk409_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (sub @ (esk410_3 @ X1598 @ X1599 @ X1600) @ (esk412_3 @ X1598 @ X1599 @ X1600)) @ (esk411_3 @ X1598 @ X1599 @ X1600)))))|~(epred8_3 @ X1600 @ X1599 @ X1598)))))))&(((((~(X1616 @ X1619 @ X1620 @ (comp @ X1622 @ X1621))|(X1616 @ (comp @ X1619 @ X1622) @ (sub @ X1620 @ X1622) @ X1621)|(epred8_3 @ X1618 @ X1617 @ X1616))&(~(X1616 @ (comp @ X1623 @ X1626) @ (sub @ X1624 @ X1626) @ X1625)|(X1616 @ X1623 @ X1624 @ (comp @ X1626 @ X1625))|(epred8_3 @ X1618 @ X1617 @ X1616)))&(((X1616 @ id @ (esk423_4 @ X1616 @ X1617 @ X1618 @ X1627) @ id)|((sub @ (X1627 @ (esk420_4 @ X1616 @ X1617 @ X1618 @ X1627) @ (esk421_4 @ X1616 @ X1617 @ X1618 @ X1627)) @ (esk422_4 @ X1616 @ X1617 @ X1618 @ X1627))!=(X1627 @ (comp @ (esk420_4 @ X1616 @ X1617 @ X1618 @ X1627) @ (esk422_4 @ X1616 @ X1617 @ X1618 @ X1627)) @ (sub @ (esk421_4 @ X1616 @ X1617 @ X1618 @ X1627) @ (esk422_4 @ X1616 @ X1617 @ X1618 @ X1627))))|(X1616 @ id @ (lam @ (X1627 @ sh @ one)) @ id)|(epred8_3 @ X1618 @ X1617 @ X1616))&(~(X1616 @ id @ (X1627 @ id @ (esk423_4 @ X1616 @ X1617 @ X1618 @ X1627)) @ id)|((sub @ (X1627 @ (esk420_4 @ X1616 @ X1617 @ X1618 @ X1627) @ (esk421_4 @ X1616 @ X1617 @ X1618 @ X1627)) @ (esk422_4 @ X1616 @ X1617 @ X1618 @ X1627))!=(X1627 @ (comp @ (esk420_4 @ X1616 @ X1617 @ X1618 @ X1627) @ (esk422_4 @ X1616 @ X1617 @ X1618 @ X1627)) @ (sub @ (esk421_4 @ X1616 @ X1617 @ X1618 @ X1627) @ (esk422_4 @ X1616 @ X1617 @ X1618 @ X1627))))|(X1616 @ id @ (lam @ (X1627 @ sh @ one)) @ id)|(epred8_3 @ X1618 @ X1617 @ X1616))))&((~(X1617 @ X1632)|(X1616 @ id @ X1632 @ id)|(epred8_3 @ X1618 @ X1617 @ X1616))&(~(X1616 @ id @ X1633 @ id)|(X1617 @ X1633)|(epred8_3 @ X1618 @ X1617 @ X1616))))&(~(X1617 @ X1634)|(X1617 @ (sub @ X1618 @ (push @ X1634 @ id)))|(epred8_3 @ X1618 @ X1617 @ X1616))))), 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_8])])])])])])])).
% 1.58/0.51 thf(c_0_40, plain, ~((hoasvar @ id @ one @ id)), inference(rw,[status(thm)],[c_0_32, c_0_14])).
% 1.58/0.51 thf(c_0_41, plain, ![X13:term, X12:term > $o, X1:term]:(((X12 @ (sub @ (esk260_1 @ X12) @ (push @ X1 @ id)))|(X12 @ (esk258_1 @ X12))|(var @ (esk257_1 @ X12))|(X12 @ X13)|~((X12 @ X1))|~((induction2)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_42, plain, ~((var @ one)), inference(rw,[status(thm)],[c_0_33, c_0_14])).
% 1.58/0.51 thf(c_0_43, plain, ![X1:term, X12:term > $o]:(((X12 @ X1)|~((X12 @ one)))), 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_34, c_0_35]), c_0_28]), c_0_28]), c_0_17]), c_0_28]), c_0_28]), c_0_17])])).
% 1.58/0.51 thf(c_0_44, plain, ![X11:subst > term > subst > $o, X12:term > $o]:(((X11 @ id @ one @ id)|(hoasinduction_p_and_p_prime @ X11 @ X12)|(X12 @ one))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_28]), c_0_28])).
% 1.58/0.51 thf(c_0_45, negated_conjecture, ![X9:subst, X5:subst, X1:term]:(((epred54_0 @ id @ one @ X5)|~((epred54_0 @ X9 @ X1 @ id))|~((hoasinduction_lem3v2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_31]), c_0_28]), c_0_31])).
% 1.58/0.51 thf(c_0_46, negated_conjecture, ![X1:term]:(((epred54_0 @ id @ X1 @ id)|~((hoasinduction_lem3v2)))), inference(spm,[status(thm)],[c_0_38, c_0_28])).
% 1.58/0.51 thf(c_0_47, negated_conjecture, (~((epred55_0 @ (lam @ esk285_0)))|~((hoasinduction_lem3v2))), inference(split_conjunct,[status(thm)],[c_0_22])).
% 1.58/0.51 thf(c_0_48, plain, ![X1:term, X12:term > $o, X11:subst > term > subst > $o, X10:subst > term > term]:(((X11 @ id @ (esk423_4 @ X11 @ X12 @ X1 @ X10) @ id)|(X11 @ id @ (lam @ (X10 @ sh @ one)) @ id)|(epred8_3 @ X1 @ X12 @ X11)|((sub @ (X10 @ (esk420_4 @ X11 @ X12 @ X1 @ X10) @ (esk421_4 @ X11 @ X12 @ X1 @ X10)) @ (esk422_4 @ X11 @ X12 @ X1 @ X10))!=(X10 @ (comp @ (esk420_4 @ X11 @ X12 @ X1 @ X10) @ (esk422_4 @ X11 @ X12 @ X1 @ X10)) @ (sub @ (esk421_4 @ X11 @ X12 @ X1 @ X10) @ (esk422_4 @ X11 @ X12 @ X1 @ X10)))))), inference(split_conjunct,[status(thm)],[c_0_39])).
% 1.58/0.51 thf(c_0_49, plain, ((hoasinduction_lem3v2)|~((epred47_0 @ (lam @ esk270_0)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_50, plain, ![X5:subst]:(~((hoasvar @ X5 @ one @ X5))), inference(spm,[status(thm)],[c_0_40, c_0_31])).
% 1.58/0.51 thf(c_0_51, plain, ![X1:term, X12:term > $o, X13:term]:(((X12 @ X1)|~((X12 @ X13)))), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_28]), c_0_28]), c_0_28]), c_0_31]), c_0_17]), c_0_35])]), c_0_42]), c_0_43])).
% 1.58/0.51 thf(c_0_52, plain, ![X12:term > $o, X11:subst > term > subst > $o, X1:term]:(((X11 @ id @ X1 @ id)|(hoasinduction_p_and_p_prime @ X11 @ X12)|(X12 @ X1))), inference(spm,[status(thm)],[c_0_44, c_0_28])).
% 1.58/0.51 thf(c_0_53, negated_conjecture, ![X5:subst]:(((epred54_0 @ id @ one @ X5)|~((hoasinduction_lem3v2)))), inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 1.58/0.51 thf(c_0_54, negated_conjecture, ![X1:term]:(((epred55_0 @ (sub @ esk285_0 @ (push @ X1 @ id)))|~((epred55_0 @ X1))|~((hoasinduction_lem3v2)))), inference(split_conjunct,[status(thm)],[c_0_22])).
% 1.58/0.51 thf(c_0_55, negated_conjecture, (~((epred55_0 @ one))|~((hoasinduction_lem3v2))), inference(rw,[status(thm)],[c_0_47, c_0_17])).
% 1.58/0.51 thf(c_0_56, plain, ![X1:term, X12:term > $o, X11:subst > term > subst > $o]:(((X11 @ id @ one @ id)|(epred8_3 @ X1 @ X12 @ X11))), 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_48, c_0_28]), c_0_17]), c_0_31]), c_0_31]), c_0_31]), c_0_28]), c_0_31]), c_0_17]), c_0_28]), c_0_31]), c_0_28]), c_0_28]), c_0_31]), c_0_17])])).
% 1.58/0.51 thf(c_0_57, plain, ((hoasinduction_lem3v2)|~((epred47_0 @ one))), inference(rw,[status(thm)],[c_0_49, c_0_17])).
% 1.58/0.51 thf(c_0_58, plain, ![X1:term, X5:subst]:(~((hoasvar @ X5 @ X1 @ X5))), inference(spm,[status(thm)],[c_0_50, c_0_28])).
% 1.58/0.51 thf(c_0_59, plain, ![X1:term, X11:subst > term > subst > $o, X12:term > $o, X13:term]:(((X11 @ id @ X1 @ id)|(hoasinduction_p_and_p_prime @ X11 @ X12)|(X12 @ X13))), inference(spm,[status(thm)],[c_0_51, c_0_52])).
% 1.58/0.51 thf(c_0_60, plain, ![X1:term, X11:subst > term > subst > $o, X12:term > $o]:(((X12 @ X1)|~((X11 @ id @ X1 @ id))|~((hoasinduction_p_and_p_prime @ X11 @ X12)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_61, negated_conjecture, ((hoasinduction_p_and_p_prime @ epred54_0 @ epred55_0)|~((hoasinduction_lem3v2))), inference(split_conjunct,[status(thm)],[c_0_22])).
% 1.58/0.51 thf(c_0_62, negated_conjecture, ![X1:term, X5:subst]:(((epred54_0 @ id @ X1 @ X5)|~((hoasinduction_lem3v2)))), inference(spm,[status(thm)],[c_0_53, c_0_28])).
% 1.58/0.51 thf(c_0_63, negated_conjecture, ![X1:term]:((~((epred55_0 @ X1))|~((hoasinduction_lem3v2)))), inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_17]), c_0_55])).
% 1.58/0.51 thf(c_0_64, plain, ((hoasinduction_lem3v2)|~((epred8_3 @ esk270_0 @ epred47_0 @ epred46_0))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_65, plain, ![X13:term, X12:term > $o, X11:subst > term > subst > $o, X1:term]:(((X12 @ X1)|(epred8_3 @ X13 @ X12 @ X11)|~((X11 @ id @ X1 @ id)))), inference(split_conjunct,[status(thm)],[c_0_39])).
% 1.58/0.51 thf(c_0_66, plain, ![X5:subst, X9:subst]:(((X5)=(X9))), inference(spm,[status(thm)],[c_0_31, c_0_31])).
% 1.58/0.51 thf(c_0_67, plain, ![X1:term, X13:term, X12:term > $o, X11:subst > term > subst > $o]:(((X11 @ id @ X1 @ id)|(epred8_3 @ X13 @ X12 @ X11))), inference(spm,[status(thm)],[c_0_56, c_0_28])).
% 1.58/0.51 thf(c_0_68, plain, ![X1:term]:(((hoasinduction_lem3v2)|~((epred47_0 @ X1)))), inference(spm,[status(thm)],[c_0_57, c_0_28])).
% 1.58/0.51 thf(c_0_69, plain, ![X12:term > $o, X1:term]:(((hoasinduction_p_and_p_prime @ hoasvar @ X12)|(X12 @ X1))), inference(spm,[status(thm)],[c_0_58, c_0_59])).
% 1.58/0.51 thf(c_0_70, negated_conjecture, ~((hoasinduction_lem3v2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61]), c_0_62]), c_0_63])).
% 1.58/0.51 thf(c_0_71, plain, ((hoasinduction_lem3v2)|~((epred8_3 @ one @ epred47_0 @ epred46_0))), inference(rw,[status(thm)],[c_0_64, c_0_17])).
% 1.58/0.51 thf(c_0_72, plain, ![X1:term, X12:term > $o, X13:term, X11:subst > term > subst > $o, X5:subst]:(((epred8_3 @ X1 @ X12 @ X11)|(X12 @ X13)|~((X11 @ X5 @ X13 @ X5)))), inference(spm,[status(thm)],[c_0_65, c_0_66])).
% 1.58/0.51 thf(c_0_73, plain, ![X1:term, X11:subst > term > subst > $o, X13:term, X12:term > $o, X5:subst]:(((epred8_3 @ X1 @ X12 @ X11)|(X11 @ X5 @ X13 @ X5))), inference(spm,[status(thm)],[c_0_67, c_0_66])).
% 1.58/0.51 thf(c_0_74, plain, ![X1:term, X11:subst > term > subst > $o, X12:term > $o]:(((X11 @ id @ X1 @ id)|~((X12 @ X1))|~((hoasinduction_p_and_p_prime @ X11 @ X12)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 1.58/0.51 thf(c_0_75, plain, (hoasinduction_p_and_p_prime @ hoasvar @ epred47_0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_70])).
% 1.58/0.51 thf(c_0_76, plain, ![X1:term]:(((hoasinduction_lem3v2)|~((epred8_3 @ X1 @ epred47_0 @ epred46_0)))), inference(spm,[status(thm)],[c_0_71, c_0_28])).
% 1.58/0.51 thf(c_0_77, plain, ![X1:term, X11:subst > term > subst > $o, X12:term > $o, X13:term]:(((epred8_3 @ X1 @ X12 @ X11)|(X12 @ X13))), inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])).
% 1.58/0.51 thf(c_0_78, plain, ![X1:term]:(~((epred47_0 @ X1))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75]), c_0_58])).
% 1.58/0.51 thf(c_0_79, plain, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77]), c_0_70]), c_0_78]), ['proof']).
% 1.58/0.51 % SZS output end CNFRefutation
% 1.58/0.51 % Parsed axioms : 132
% 1.58/0.51 % Removed by relevancy pruning/SinE : 0
% 1.58/0.51 % Initial clauses : 1262
% 1.58/0.51 % Removed in clause preprocessing : 130
% 1.58/0.51 % Initial clauses in saturation : 1132
% 1.58/0.51 % Processed clauses : 1602
% 1.58/0.51 % ...of these trivial : 718
% 1.58/0.51 % ...subsumed : 217
% 1.58/0.51 % ...remaining for further processing : 667
% 1.58/0.51 % Other redundant clauses eliminated : 0
% 1.58/0.51 % Clauses deleted for lack of memory : 0
% 1.58/0.51 % Backward-subsumed : 149
% 1.58/0.51 % Backward-rewritten : 118
% 1.58/0.51 % Generated clauses : 1396
% 1.58/0.51 % ...of the previous two non-redundant : 1368
% 1.58/0.51 % ...aggressively subsumed : 0
% 1.58/0.51 % Contextual simplify-reflections : 69
% 1.58/0.51 % Paramodulations : 1393
% 1.58/0.51 % Factorizations : 2
% 1.58/0.51 % NegExts : 0
% 1.58/0.51 % Equation resolutions : 0
% 1.58/0.51 % Disequality decompositions : 0
% 1.58/0.51 % Total rewrite steps : 11893
% 1.58/0.51 % ...of those cached : 11271
% 1.58/0.51 % Propositional unsat checks : 0
% 1.58/0.51 % Propositional check models : 0
% 1.58/0.51 % Propositional check unsatisfiable : 0
% 1.58/0.51 % Propositional clauses : 0
% 1.58/0.51 % Propositional clauses after purity: 0
% 1.58/0.51 % Propositional unsat core size : 0
% 1.58/0.51 % Propositional preprocessing time : 0.000
% 1.58/0.51 % Propositional encoding time : 0.000
% 1.58/0.51 % Propositional solver time : 0.000
% 1.58/0.51 % Success case prop preproc time : 0.000
% 1.58/0.51 % Success case prop encoding time : 0.000
% 1.58/0.51 % Success case prop solver time : 0.000
% 1.58/0.51 % Current number of processed clauses : 208
% 1.58/0.51 % Positive orientable unit clauses : 111
% 1.58/0.51 % Positive unorientable unit clauses: 4
% 1.58/0.51 % Negative unit clauses : 10
% 1.58/0.51 % Non-unit-clauses : 83
% 1.58/0.51 % Current number of unprocessed clauses: 352
% 1.58/0.51 % ...number of literals in the above : 1093
% 1.58/0.51 % Current number of archived formulas : 0
% 1.58/0.51 % Current number of archived clauses : 459
% 1.58/0.51 % Clause-clause subsumption calls (NU) : 23007
% 1.58/0.51 % Rec. Clause-clause subsumption calls : 13735
% 1.58/0.51 % Non-unit clause-clause subsumptions : 502
% 1.58/0.51 % Unit Clause-clause subsumption calls : 3192
% 1.58/0.51 % Rewrite failures with RHS unbound : 0
% 1.58/0.51 % BW rewrite match attempts : 2674
% 1.58/0.51 % BW rewrite match successes : 127
% 1.58/0.51 % Condensation attempts : 1610
% 1.58/0.51 % Condensation successes : 128
% 1.58/0.51 % Termbank termtop insertions : 148209
% 1.58/0.51 % Search garbage collected termcells : 23031
% 1.58/0.51
% 1.58/0.51 % -------------------------------------------------
% 1.58/0.51 % User time : 0.207 s
% 1.58/0.51 % System time : 0.019 s
% 1.58/0.51 % Total time : 0.226 s
% 1.58/0.51 % Maximum resident set size: 8004 pages
% 1.58/0.51
% 1.58/0.51 % -------------------------------------------------
% 1.58/0.51 % User time : 0.754 s
% 1.58/0.51 % System time : 0.056 s
% 1.58/0.51 % Total time : 0.810 s
% 1.58/0.51 % Maximum resident set size: 5376 pages
% 1.58/0.51 % E exiting
%------------------------------------------------------------------------------