E---3.5.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SWX161^1 : 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 : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:40:25 AM UTC 2026

% Result   : Theorem 0.57s 0.48s
% Output   : CNFRefutation 0.57s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWX161^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17  % Computer : n009.cluster.edu
% 0.09/0.17  % Model    : x86_64 x86_64
% 0.09/0.17  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17  % Memory   : 8046.5625MB
% 0.09/0.17  % OS       : Linux 6.8.0-71-generic
% 0.09/0.17  % CPULimit : 300
% 0.09/0.17  % WCLimit  : 300
% 0.09/0.17  % DateTime : Tue Sep 29 16:09:15 UTC 2026
% 0.09/0.17  % CPUTime  : 
% 0.09/0.17  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21  Running higher-order theorem proving
% 0.09/0.23  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.W3wP87dhdY/E---3.1_4190328.p
% 0.57/0.48  % Version: 3.5.1-ho
% 0.57/0.48  % partial match(1): HSLMSLSMSSSNHSA
% 0.57/0.48  % Preprocessing class: HSLMSLSSSSSNHSA.
% 0.57/0.48  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.48  % Starting new_ho_10 with 600s (2) cores
% 0.57/0.48  % Starting sh3 with 600s (2) cores
% 0.57/0.48  % Starting ho_unfolding_3 with 600s (2) cores
% 0.57/0.48  % Starting new_ho_10_cnf2 with 600s (2) cores
% 0.57/0.48  % new_ho_10 with pid 4190359 completed with status 0
% 0.57/0.48  % Result found by new_ho_10
% 0.57/0.48  % partial match(1): HSLMSLSMSSSNHSA
% 0.57/0.48  % Preprocessing class: HSLMSLSSSSSNHSA.
% 0.57/0.48  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.48  % Starting new_ho_10 with 600s (2) cores
% 0.57/0.48  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.48  % No SInE strategy applied
% 0.57/0.48  % Search class: HGHSM-SMLM31-MHSFFMBN
% 0.57/0.48  % partial match(1): HGHSM-SMLM31-MHSFFSBN
% 0.57/0.48  % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.57/0.48  % Starting SubtermCWHack with 61s (1) cores
% 0.57/0.48  % Starting new_ho_10 with 361s (1) cores
% 0.57/0.48  % new_ho_10 with pid 4190378 completed with status 0
% 0.57/0.48  % Result found by new_ho_10
% 0.57/0.48  % partial match(1): HSLMSLSMSSSNHSA
% 0.57/0.48  % Preprocessing class: HSLMSLSSSSSNHSA.
% 0.57/0.48  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.48  % Starting new_ho_10 with 600s (2) cores
% 0.57/0.48  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.48  % No SInE strategy applied
% 0.57/0.48  % Search class: HGHSM-SMLM31-MHSFFMBN
% 0.57/0.48  % partial match(1): HGHSM-SMLM31-MHSFFSBN
% 0.57/0.48  % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.57/0.48  % Starting SubtermCWHack with 61s (1) cores
% 0.57/0.48  % Starting new_ho_10 with 361s (1) cores
% 0.57/0.48  % Preprocessing time       : 0.030 s
% 0.57/0.48  % Presaturation interreduction done
% 0.57/0.48  
% 0.57/0.48  % Proof found!
% 0.57/0.48  % SZS status Theorem
% 0.57/0.48  % SZS output start CNFRefutation
% 0.57/0.48  thf(decl_sort1, type, term: $tType).
% 0.57/0.48  thf(decl_sort2, type, subst: $tType).
% 0.57/0.48  thf(decl_sort3, type, d_term: $tType).
% 0.57/0.48  thf(decl_sort4, type, d_subst: $tType).
% 0.57/0.48  thf(decl_23, type, one: term).
% 0.57/0.48  thf(decl_24, type, ap: term > term > term).
% 0.57/0.48  thf(decl_25, type, lam: term > term).
% 0.57/0.48  thf(decl_26, type, sub: term > subst > term).
% 0.57/0.48  thf(decl_27, type, id: subst).
% 0.57/0.48  thf(decl_28, type, sh: subst).
% 0.57/0.48  thf(decl_29, type, push: term > subst > subst).
% 0.57/0.48  thf(decl_30, type, comp: subst > subst > subst).
% 0.57/0.48  thf(decl_31, type, var: term > $o).
% 0.57/0.48  thf(decl_32, type, pushprop_lem1v2: $o).
% 0.57/0.48  thf(decl_33, type, pushprop_lem1_gthm: $o).
% 0.57/0.48  thf(decl_34, type, axmap: $o).
% 0.57/0.48  thf(decl_35, type, pushprop_lem0_gthm: $o).
% 0.57/0.48  thf(decl_36, type, shinj: $o).
% 0.57/0.48  thf(decl_37, type, hoasinduction_lem1v2: $o).
% 0.57/0.48  thf(decl_38, type, hoasinduction_lem1v2_gthm: $o).
% 0.57/0.48  thf(decl_39, type, hoasap: subst > term > subst > term > term).
% 0.57/0.48  thf(decl_40, type, induction2lem: $o).
% 0.57/0.48  thf(decl_41, type, hoasinduction_lem3v2_f: $o).
% 0.57/0.48  thf(decl_42, type, axvarshift: $o).
% 0.57/0.48  thf(decl_43, type, hoasapinj2: $o).
% 0.57/0.48  thf(decl_44, type, hoasapnotvar_gthm: $o).
% 0.57/0.48  thf(decl_45, type, hoasapinj1: $o).
% 0.57/0.48  thf(decl_46, type, ulamvar1: $o).
% 0.57/0.48  thf(decl_47, type, induction2lem_lthm: $o).
% 0.57/0.48  thf(decl_48, type, hoasinduction_lem3v2_gthm: $o).
% 0.57/0.48  thf(decl_49, type, apnotvar: $o).
% 0.57/0.48  thf(decl_50, type, pushprop_lthm_orig: $o).
% 0.57/0.48  thf(decl_51, type, hoasinduction_lem3v2_f_lthm: $o).
% 0.57/0.48  thf(decl_52, type, hoasinduction_lthm: $o).
% 0.57/0.48  thf(decl_53, type, hoasinduction_no_psi_cond_lthm: $o).
% 0.57/0.48  thf(decl_54, type, hoaslaminj: $o).
% 0.57/0.48  thf(decl_55, type, hoasinduction_lem3aaa: $o).
% 0.57/0.48  thf(decl_56, type, induction2lem_gthm: $o).
% 0.57/0.48  thf(decl_57, type, hoasinduction_lem3aa_lthm: $o).
% 0.57/0.48  thf(decl_58, type, hoasinduction_lem3: $o).
% 0.57/0.48  thf(decl_59, type, hoasinduction_lem2: $o).
% 0.57/0.48  thf(decl_60, type, termmset_lthm: $o).
% 0.57/0.48  thf(decl_61, type, hoasinduction_lem1: $o).
% 0.57/0.48  thf(decl_62, type, hoaslamnotap_lthm: $o).
% 0.57/0.48  thf(decl_63, type, pushprop_lem1v2_lthm: $o).
% 0.57/0.48  thf(decl_64, type, hoasapnotvar: $o).
% 0.57/0.48  thf(decl_65, type, hoasinduction_lem0: $o).
% 0.57/0.48  thf(decl_66, type, hoasinduction: $o).
% 0.57/0.48  thf(decl_67, type, hoasinduction_gthm: $o).
% 0.57/0.48  thf(decl_68, type, axapp: $o).
% 0.57/0.48  thf(decl_69, type, hoaslamnotvar_lthm: $o).
% 0.57/0.48  thf(decl_70, type, pushprop_lem3v2_lthm: $o).
% 0.57/0.48  thf(decl_71, type, hoasinduction_lem3b_lthm: $o).
% 0.57/0.48  thf(decl_72, type, ulamvarind: $o).
% 0.57/0.48  thf(decl_73, type, induction: $o).
% 0.57/0.48  thf(decl_74, type, hoasinduction_lem3a_lthm: $o).
% 0.57/0.48  thf(decl_75, type, termmset_gthm: $o).
% 0.57/0.48  thf(decl_76, type, hoasinduction_lem3aa: $o).
% 0.57/0.48  thf(decl_77, type, pushprop_lem1v2_gthm: $o).
% 0.57/0.48  thf(decl_78, type, hoaslamnotap_gthm: $o).
% 0.57/0.48  thf(decl_79, type, hoaslamnotvar_gthm: $o).
% 0.57/0.48  thf(decl_80, type, hoasinduction_lem3b_gthm: $o).
% 0.57/0.48  thf(decl_81, type, pushprop_lem2v2: $o).
% 0.57/0.48  thf(decl_82, type, hoasinduction_lem3a_gthm: $o).
% 0.57/0.48  thf(decl_83, type, axclos: $o).
% 0.57/0.48  thf(decl_84, type, axassoc: $o).
% 0.57/0.48  thf(decl_85, type, hoasinduction_lem2v2: $o).
% 0.57/0.48  thf(decl_86, type, pushprop_lthm: $o).
% 0.57/0.48  thf(decl_87, type, apinj2: $o).
% 0.57/0.48  thf(decl_88, type, apinj1: $o).
% 0.57/0.48  thf(decl_89, type, hoasapinj2_lthm: $o).
% 0.57/0.48  thf(decl_90, type, hoasinduction_lem3v2a: $o).
% 0.57/0.48  thf(decl_91, type, hoasapinj1_lthm: $o).
% 0.57/0.48  thf(decl_92, type, hoaslaminj_lthm: $o).
% 0.57/0.48  thf(decl_93, type, axvarcons: $o).
% 0.57/0.48  thf(decl_94, type, hoaslam: subst > (subst > term > term) > term).
% 0.57/0.48  thf(decl_95, type, axscons: $o).
% 0.57/0.48  thf(decl_96, type, hoasinduction_lem2v2_gthm: $o).
% 0.57/0.48  thf(decl_97, type, axidr: $o).
% 0.57/0.48  thf(decl_98, type, pushprop_lem1: $o).
% 0.57/0.48  thf(decl_99, type, laminj: $o).
% 0.57/0.48  thf(decl_100, type, hoasinduction_lem3_lthm: $o).
% 0.57/0.48  thf(decl_101, type, pushprop_lem0: $o).
% 0.57/0.48  thf(decl_102, type, pushprop_gthm: $o).
% 0.57/0.48  thf(decl_103, type, axabs: $o).
% 0.57/0.48  thf(decl_104, type, hoasinduction_lem3v2a_lthm: $o).
% 0.57/0.48  thf(decl_105, type, hoasinduction_lem2_lthm: $o).
% 0.57/0.48  thf(decl_106, type, hoasapinj2_gthm: $o).
% 0.57/0.48  thf(decl_107, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 0.57/0.48  thf(decl_108, type, hoasinduction_lem1_lthm: $o).
% 0.57/0.48  thf(decl_109, type, lamnotap: $o).
% 0.57/0.48  thf(decl_110, type, hoasapinj1_gthm: $o).
% 0.57/0.48  thf(decl_111, type, hoaslamnotvar: $o).
% 0.57/0.48  thf(decl_112, type, axidl: $o).
% 0.57/0.48  thf(decl_113, type, hoaslaminj_gthm: $o).
% 0.57/0.48  thf(decl_114, type, induction2_lthm: $o).
% 0.57/0.48  thf(decl_115, type, hoasinduction_lem0_lthm: $o).
% 0.57/0.48  thf(decl_116, type, substmonoid_lthm: $o).
% 0.57/0.48  thf(decl_117, type, pushprop: $o).
% 0.57/0.48  thf(decl_118, type, hoasinduction_lem3_gthm: $o).
% 0.57/0.48  thf(decl_119, type, hoasinduction_lem2_gthm: $o).
% 0.57/0.48  thf(decl_120, type, hoasinduction_lem3b: $o).
% 0.57/0.48  thf(decl_121, type, substmonoid: $o).
% 0.57/0.48  thf(decl_122, type, lamnotvar: $o).
% 0.57/0.48  thf(decl_123, type, hoasinduction_lem3a: $o).
% 0.57/0.48  thf(decl_124, type, hoasinduction_lem1_gthm: $o).
% 0.57/0.48  thf(decl_125, type, hoasinduction_no_psi_cond: $o).
% 0.57/0.48  thf(decl_126, type, induction2_gthm: $o).
% 0.57/0.48  thf(decl_127, type, pushprop_lem2v2_lthm: $o).
% 0.57/0.48  thf(decl_128, type, hoasvar: subst > term > subst > $o).
% 0.57/0.48  thf(decl_129, type, hoaslamnotap: $o).
% 0.57/0.48  thf(decl_130, type, substmonoid_gthm: $o).
% 0.57/0.48  thf(decl_131, type, ulamvarsh: $o).
% 0.57/0.48  thf(decl_132, type, induction2: $o).
% 0.57/0.48  thf(decl_133, type, pushprop_lem3v2: $o).
% 0.57/0.48  thf(decl_134, type, pushprop_lem2v2_gthm: $o).
% 0.57/0.48  thf(decl_135, type, pushprop_lem1_lthm: $o).
% 0.57/0.48  thf(decl_136, type, hoasinduction_lem3v2: $o).
% 0.57/0.48  thf(decl_137, type, axshiftcons: $o).
% 0.57/0.48  thf(decl_138, type, termmset: $o).
% 0.57/0.48  thf(decl_139, type, pushprop_lem0_lthm: $o).
% 0.57/0.48  thf(decl_140, type, hoasapnotvar_lthm: $o).
% 0.57/0.48  thf(decl_141, type, hoasinduction_lem3v2_lthm: $o).
% 0.57/0.48  thf(decl_142, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 0.57/0.48  thf(decl_143, type, axvarid: $o).
% 0.57/0.48  thf(decl_144, type, hoasinduction_lthm_3: $o).
% 0.57/0.48  thf(decl_145, type, d2term: d_term > term).
% 0.57/0.48  thf(decl_146, type, d2subst: d_subst > subst).
% 0.57/0.48  thf(decl_147, type, d_one: d_term).
% 0.57/0.48  thf(decl_148, type, d_id: d_subst).
% 0.57/0.48  thf(decl_149, type, epred1_0: $o).
% 0.57/0.48  thf(decl_150, type, epred2_1: (subst > term > subst > $o) > $o).
% 0.57/0.48  thf(decl_152, type, epred4_0: $o).
% 0.57/0.48  thf(decl_153, type, epred5_0: $o).
% 0.57/0.48  thf(decl_154, type, epred6_0: $o).
% 0.57/0.48  thf(decl_155, type, epred7_0: $o).
% 0.57/0.48  thf(decl_156, type, epred8_3: term > (term > $o) > (subst > term > subst > $o) > $o).
% 0.57/0.48  thf(decl_157, type, epred9_0: $o).
% 0.57/0.48  thf(decl_158, type, esk1_1: term > d_term).
% 0.57/0.48  thf(decl_159, type, esk2_1: subst > d_subst).
% 0.57/0.48  thf(decl_160, type, esk3_2: (subst > term > subst > $o) > (term > $o) > term).
% 0.57/0.48  thf(decl_161, type, esk4_4: term > subst > (term > $o) > (term > $o) > term).
% 0.57/0.48  thf(decl_162, type, esk5_4: (term > $o) > (term > $o) > term > subst > term).
% 0.57/0.48  thf(decl_163, type, epred10_0: term > $o).
% 0.57/0.48  thf(decl_164, type, epred11_0: term > $o).
% 0.57/0.48  thf(decl_165, type, esk6_0: term).
% 0.57/0.48  thf(decl_166, type, esk7_0: subst).
% 0.57/0.48  thf(decl_167, type, esk8_0: term).
% 0.57/0.48  thf(decl_168, type, esk9_0: term).
% 0.57/0.48  thf(decl_169, type, esk10_3: (term > $o) > term > subst > term).
% 0.57/0.48  thf(decl_170, type, esk11_3: (term > $o) > term > subst > term).
% 0.57/0.48  thf(decl_171, type, esk12_3: (term > $o) > term > subst > term).
% 0.57/0.48  thf(decl_172, type, esk13_3: (term > $o) > term > subst > term).
% 0.57/0.48  thf(decl_173, type, epred12_0: term > $o).
% 0.57/0.48  thf(decl_174, type, esk14_0: term).
% 0.57/0.48  thf(decl_175, type, esk15_0: subst).
% 0.57/0.48  thf(decl_176, type, esk16_1: term > term).
% 0.57/0.48  thf(decl_177, type, esk17_1: term > subst > term > term).
% 0.57/0.48  thf(decl_178, type, esk18_0: term).
% 0.57/0.48  thf(decl_179, type, esk19_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_180, type, esk20_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_181, type, esk21_0: term).
% 0.57/0.48  thf(decl_182, type, esk22_0: term).
% 0.57/0.48  thf(decl_183, type, esk23_0: term).
% 0.57/0.48  thf(decl_184, type, esk24_0: term).
% 0.57/0.48  thf(decl_185, type, esk25_0: term).
% 0.57/0.48  thf(decl_186, type, esk26_0: term).
% 0.57/0.48  thf(decl_187, type, esk27_0: term).
% 0.57/0.48  thf(decl_188, type, esk28_0: term).
% 0.57/0.48  thf(decl_189, type, esk29_0: term).
% 0.57/0.48  thf(decl_190, type, esk30_0: subst).
% 0.57/0.48  thf(decl_191, type, esk31_0: term).
% 0.57/0.48  thf(decl_192, type, esk32_0: subst).
% 0.57/0.48  thf(decl_193, type, esk33_0: subst).
% 0.57/0.48  thf(decl_194, type, esk34_1: term > subst > term > term).
% 0.57/0.48  thf(decl_195, type, esk35_0: term).
% 0.57/0.48  thf(decl_196, type, esk36_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_197, type, esk37_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_198, type, epred13_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_199, type, esk38_1: (term > $o) > term).
% 0.57/0.48  thf(decl_200, type, epred14_0: term > $o).
% 0.57/0.48  thf(decl_201, type, esk39_0: term).
% 0.57/0.48  thf(decl_202, type, esk40_1: term > term).
% 0.57/0.48  thf(decl_203, type, esk41_0: term).
% 0.57/0.48  thf(decl_204, type, epred15_1: (subst > term > subst > $o) > term > $o).
% 0.57/0.48  thf(decl_205, type, esk42_1: (term > $o) > term).
% 0.57/0.48  thf(decl_206, type, esk43_1: (term > $o) > term).
% 0.57/0.48  thf(decl_207, type, esk44_1: (term > $o) > term).
% 0.57/0.48  thf(decl_208, type, esk45_1: (term > $o) > term).
% 0.57/0.48  thf(decl_209, type, esk46_2: (subst > term > term) > (subst > term > term) > subst).
% 0.57/0.48  thf(decl_210, type, esk47_2: (subst > term > term) > (subst > term > term) > term).
% 0.57/0.48  thf(decl_211, type, esk48_2: (subst > term > term) > (subst > term > term) > subst).
% 0.57/0.48  thf(decl_212, type, esk49_2: (subst > term > term) > (subst > term > term) > subst).
% 0.57/0.48  thf(decl_213, type, esk50_2: (subst > term > term) > (subst > term > term) > term).
% 0.57/0.48  thf(decl_214, type, esk51_2: (subst > term > term) > (subst > term > term) > subst).
% 0.57/0.48  thf(decl_215, type, esk52_0: subst > term > term).
% 0.57/0.48  thf(decl_216, type, esk53_0: subst > term > term).
% 0.57/0.48  thf(decl_217, type, esk54_0: subst).
% 0.57/0.48  thf(decl_218, type, esk55_0: term).
% 0.57/0.48  thf(decl_219, type, esk56_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.57/0.48  thf(decl_220, type, esk57_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_221, type, esk58_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_222, type, epred16_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_223, type, esk59_0: term).
% 0.57/0.48  thf(decl_224, type, esk60_2: (subst > term > term) > term > term).
% 0.57/0.48  thf(decl_225, type, esk61_2: (subst > term > term) > term > subst).
% 0.57/0.48  thf(decl_226, type, esk62_2: (subst > term > term) > term > term).
% 0.57/0.48  thf(decl_227, type, esk63_2: (subst > term > term) > term > subst).
% 0.57/0.48  thf(decl_228, type, esk64_2: (subst > term > term) > term > subst).
% 0.57/0.48  thf(decl_229, type, esk65_2: (subst > term > term) > term > term).
% 0.57/0.48  thf(decl_230, type, esk66_2: (subst > term > term) > term > subst).
% 0.57/0.48  thf(decl_231, type, esk67_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.57/0.48  thf(decl_232, type, esk68_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_233, type, epred17_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_234, type, esk69_0: term).
% 0.57/0.48  thf(decl_235, type, esk70_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_236, type, esk71_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_237, type, esk72_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_238, type, esk73_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_239, type, esk74_2: (subst > term > subst > $o) > term > subst).
% 0.57/0.48  thf(decl_240, type, esk75_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_241, type, esk76_2: (subst > term > subst > $o) > term > subst).
% 0.57/0.48  thf(decl_242, type, esk77_2: (subst > term > subst > $o) > term > subst).
% 0.57/0.48  thf(decl_243, type, esk78_2: (subst > term > subst > $o) > term > subst).
% 0.57/0.48  thf(decl_244, type, esk79_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_245, type, esk80_2: (subst > term > subst > $o) > term > subst).
% 0.57/0.48  thf(decl_246, type, esk81_2: (subst > term > subst > $o) > term > subst).
% 0.57/0.48  thf(decl_247, type, esk82_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.57/0.48  thf(decl_248, type, esk83_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_249, type, epred18_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_250, type, esk84_0: term).
% 0.57/0.48  thf(decl_251, type, esk85_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_252, type, esk86_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_253, type, esk87_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_254, type, esk88_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_255, type, esk89_3: (subst > term > subst > $o) > term > term > subst).
% 0.57/0.48  thf(decl_256, type, esk90_3: (subst > term > subst > $o) > term > term > term).
% 0.57/0.48  thf(decl_257, type, esk91_3: (subst > term > subst > $o) > term > term > subst).
% 0.57/0.48  thf(decl_258, type, esk92_3: (subst > term > subst > $o) > term > term > subst).
% 0.57/0.48  thf(decl_259, type, esk93_3: (subst > term > subst > $o) > term > term > subst).
% 0.57/0.48  thf(decl_260, type, esk94_3: (subst > term > subst > $o) > term > term > term).
% 0.57/0.48  thf(decl_261, type, esk95_3: (subst > term > subst > $o) > term > term > subst).
% 0.57/0.48  thf(decl_262, type, esk96_3: (subst > term > subst > $o) > term > term > subst).
% 0.57/0.48  thf(decl_263, type, esk97_3: (subst > term > subst > $o) > term > term > term).
% 0.57/0.48  thf(decl_264, type, esk98_3: (subst > term > subst > $o) > term > term > term).
% 0.57/0.48  thf(decl_265, type, epred19_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_266, type, esk99_0: term).
% 0.57/0.48  thf(decl_267, type, esk100_0: term).
% 0.57/0.48  thf(decl_268, type, esk101_0: term).
% 0.57/0.48  thf(decl_269, type, esk102_0: subst).
% 0.57/0.48  thf(decl_270, type, esk103_4: (term > $o) > (term > $o) > term > subst > term).
% 0.57/0.48  thf(decl_271, type, epred20_0: term > $o).
% 0.57/0.48  thf(decl_272, type, epred21_0: term > $o).
% 0.57/0.48  thf(decl_273, type, esk104_0: term).
% 0.57/0.48  thf(decl_274, type, esk105_0: subst).
% 0.57/0.48  thf(decl_275, type, epred22_1: (subst > term > subst > $o) > term > $o).
% 0.57/0.48  thf(decl_276, type, epred23_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_277, type, esk106_1: (term > $o) > term).
% 0.57/0.48  thf(decl_278, type, epred24_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_279, type, esk107_0: term).
% 0.57/0.48  thf(decl_280, type, esk108_1: term > subst > term > term).
% 0.57/0.48  thf(decl_281, type, esk109_0: term).
% 0.57/0.48  thf(decl_282, type, esk110_1: (term > $o) > term).
% 0.57/0.48  thf(decl_283, type, esk111_1: (term > $o) > term).
% 0.57/0.48  thf(decl_284, type, esk112_1: (term > $o) > term).
% 0.57/0.48  thf(decl_285, type, esk113_1: (term > $o) > term).
% 0.57/0.48  thf(decl_286, type, epred25_0: term > $o).
% 0.57/0.48  thf(decl_287, type, esk114_0: term).
% 0.57/0.48  thf(decl_288, type, esk115_0: term).
% 0.57/0.48  thf(decl_289, type, epred26_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_290, type, esk116_0: term).
% 0.57/0.48  thf(decl_291, type, esk117_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_292, type, esk118_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_293, type, esk119_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_294, type, esk120_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_295, type, esk121_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.57/0.48  thf(decl_296, type, esk122_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_297, type, esk123_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.57/0.48  thf(decl_298, type, esk124_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_299, type, epred27_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_300, type, esk125_0: term).
% 0.57/0.48  thf(decl_301, type, esk126_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_302, type, esk127_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_303, type, esk128_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_304, type, esk129_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_305, type, esk130_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.57/0.48  thf(decl_306, type, esk131_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_307, type, epred28_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_308, type, esk132_0: term).
% 0.57/0.48  thf(decl_309, type, esk133_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_310, type, esk134_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_311, type, esk135_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_312, type, esk136_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_313, type, esk137_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.57/0.48  thf(decl_314, type, esk138_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.57/0.48  thf(decl_315, type, esk139_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.57/0.48  thf(decl_316, type, esk140_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.57/0.48  thf(decl_317, type, esk141_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.57/0.48  thf(decl_318, type, esk142_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.57/0.48  thf(decl_319, type, esk143_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.57/0.48  thf(decl_320, type, esk144_4: (subst > term > subst > $o) > (term > $o) > term > term > subst).
% 0.57/0.48  thf(decl_321, type, esk145_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.57/0.48  thf(decl_322, type, esk146_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.57/0.48  thf(decl_323, type, esk147_4: (subst > term > subst > $o) > (term > $o) > term > term > term).
% 0.57/0.48  thf(decl_324, type, epred29_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_325, type, epred30_0: term > $o).
% 0.57/0.48  thf(decl_326, type, esk148_0: term).
% 0.57/0.48  thf(decl_327, type, esk149_0: term).
% 0.57/0.48  thf(decl_328, type, esk150_0: term).
% 0.57/0.48  thf(decl_329, type, esk151_0: term).
% 0.57/0.48  thf(decl_330, type, esk152_0: term).
% 0.57/0.48  thf(decl_331, type, esk153_0: term).
% 0.57/0.48  thf(decl_332, type, esk154_0: term).
% 0.57/0.48  thf(decl_333, type, esk155_0: term).
% 0.57/0.48  thf(decl_334, type, esk156_0: term).
% 0.57/0.48  thf(decl_335, type, esk157_0: term).
% 0.57/0.48  thf(decl_336, type, esk158_0: term).
% 0.57/0.48  thf(decl_337, type, esk159_0: term).
% 0.57/0.48  thf(decl_338, type, esk160_0: term).
% 0.57/0.48  thf(decl_339, type, esk161_0: term).
% 0.57/0.48  thf(decl_340, type, esk162_0: term).
% 0.57/0.48  thf(decl_341, type, esk163_0: term).
% 0.57/0.48  thf(decl_342, type, esk164_0: term).
% 0.57/0.48  thf(decl_343, type, esk165_0: term).
% 0.57/0.48  thf(decl_344, type, esk166_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
% 0.57/0.48  thf(decl_345, type, esk167_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.57/0.48  thf(decl_346, type, esk168_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.57/0.48  thf(decl_347, type, epred31_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_348, type, epred32_0: term > $o).
% 0.57/0.48  thf(decl_349, type, esk169_0: term).
% 0.57/0.48  thf(decl_350, type, esk170_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_351, type, esk171_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_352, type, esk172_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_353, type, esk173_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_354, type, esk174_0: term).
% 0.57/0.48  thf(decl_355, type, esk175_0: term).
% 0.57/0.48  thf(decl_356, type, esk176_0: term).
% 0.57/0.48  thf(decl_357, type, esk177_0: term).
% 0.57/0.48  thf(decl_358, type, esk178_0: term).
% 0.57/0.48  thf(decl_359, type, esk179_0: term).
% 0.57/0.48  thf(decl_360, type, esk180_0: term).
% 0.57/0.48  thf(decl_361, type, esk181_0: term).
% 0.57/0.48  thf(decl_362, type, esk182_0: term).
% 0.57/0.48  thf(decl_363, type, esk183_0: term).
% 0.57/0.48  thf(decl_364, type, esk184_0: subst).
% 0.57/0.48  thf(decl_365, type, esk185_0: term).
% 0.57/0.48  thf(decl_366, type, esk186_0: subst).
% 0.57/0.48  thf(decl_367, type, esk187_0: term).
% 0.57/0.48  thf(decl_368, type, esk188_0: term).
% 0.57/0.48  thf(decl_369, type, esk189_2: (subst > term > term) > (subst > term > term) > subst).
% 0.57/0.48  thf(decl_370, type, esk190_2: (subst > term > term) > (subst > term > term) > term).
% 0.57/0.48  thf(decl_371, type, esk191_2: (subst > term > term) > (subst > term > term) > subst).
% 0.57/0.48  thf(decl_372, type, esk192_2: (subst > term > term) > (subst > term > term) > subst).
% 0.57/0.48  thf(decl_373, type, esk193_2: (subst > term > term) > (subst > term > term) > term).
% 0.57/0.48  thf(decl_374, type, esk194_2: (subst > term > term) > (subst > term > term) > subst).
% 0.57/0.48  thf(decl_375, type, esk195_0: subst > term > term).
% 0.57/0.48  thf(decl_376, type, esk196_0: subst > term > term).
% 0.57/0.48  thf(decl_377, type, esk197_0: subst).
% 0.57/0.48  thf(decl_378, type, esk198_0: term).
% 0.57/0.48  thf(decl_379, type, esk199_0: term).
% 0.57/0.48  thf(decl_380, type, esk200_0: subst).
% 0.57/0.48  thf(decl_381, type, esk201_0: subst).
% 0.57/0.48  thf(decl_382, type, esk202_0: subst).
% 0.57/0.48  thf(decl_383, type, epred33_0: term > $o).
% 0.57/0.48  thf(decl_384, type, epred34_0: term > $o).
% 0.57/0.48  thf(decl_385, type, esk203_0: term).
% 0.57/0.48  thf(decl_386, type, esk204_0: subst).
% 0.57/0.48  thf(decl_387, type, esk205_0: term).
% 0.57/0.48  thf(decl_388, type, esk206_0: term).
% 0.57/0.48  thf(decl_389, type, esk207_0: term).
% 0.57/0.48  thf(decl_390, type, esk208_0: term).
% 0.57/0.48  thf(decl_391, type, epred35_3: (term > $o) > term > subst > term > $o).
% 0.57/0.48  thf(decl_392, type, epred36_0: term > $o).
% 0.57/0.48  thf(decl_393, type, esk209_0: term).
% 0.57/0.48  thf(decl_394, type, esk210_0: subst).
% 0.57/0.48  thf(decl_395, type, esk211_1: (term > $o) > term).
% 0.57/0.48  thf(decl_396, type, esk212_0: term).
% 0.57/0.48  thf(decl_397, type, esk213_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_398, type, esk214_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_399, type, esk215_0: term).
% 0.57/0.48  thf(decl_400, type, esk216_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term).
% 0.57/0.48  thf(decl_401, type, esk217_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.57/0.48  thf(decl_402, type, esk218_3: (subst > term > subst > $o) > (term > $o) > term > term).
% 0.57/0.48  thf(decl_403, type, esk219_1: term > subst > term > term).
% 0.57/0.48  thf(decl_404, type, epred37_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_405, type, epred38_0: term > $o).
% 0.57/0.48  thf(decl_406, type, esk220_0: term).
% 0.57/0.48  thf(decl_407, type, esk221_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_408, type, esk222_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_409, type, esk223_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_410, type, esk224_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_411, type, esk225_0: subst).
% 0.57/0.48  thf(decl_412, type, esk226_0: term).
% 0.57/0.48  thf(decl_413, type, epred39_1: (subst > term > subst > $o) > term > $o).
% 0.57/0.48  thf(decl_414, type, epred40_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_415, type, esk227_1: (term > $o) > term).
% 0.57/0.48  thf(decl_416, type, esk228_0: subst).
% 0.57/0.48  thf(decl_417, type, esk229_0: subst).
% 0.57/0.48  thf(decl_418, type, esk230_0: subst).
% 0.57/0.48  thf(decl_419, type, esk231_0: subst).
% 0.57/0.48  thf(decl_420, type, esk232_1: term > subst > term > term).
% 0.57/0.48  thf(decl_421, type, esk233_0: term).
% 0.57/0.48  thf(decl_422, type, esk234_0: subst).
% 0.57/0.48  thf(decl_423, type, esk235_0: subst).
% 0.57/0.48  thf(decl_424, type, esk236_2: (subst > term > subst > $o) > term > subst > term > term).
% 0.57/0.48  thf(decl_425, type, esk237_2: (subst > term > subst > $o) > term > term).
% 0.57/0.48  thf(decl_426, type, epred41_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_427, type, esk238_0: term).
% 0.57/0.48  thf(decl_428, type, esk239_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_429, type, esk240_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_430, type, esk241_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_431, type, esk242_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_432, type, esk243_1: (subst > term > subst > $o) > term).
% 0.57/0.48  thf(decl_433, type, esk244_1: (subst > term > subst > $o) > term).
% 0.57/0.48  thf(decl_434, type, esk245_1: (subst > term > subst > $o) > subst > term > term).
% 0.57/0.48  thf(decl_435, type, epred42_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_436, type, esk246_0: term).
% 0.57/0.48  thf(decl_437, type, esk247_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_438, type, esk248_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_439, type, esk249_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_440, type, esk250_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_441, type, esk251_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_442, type, esk252_1: (subst > term > term) > term).
% 0.57/0.48  thf(decl_443, type, esk253_1: (subst > term > term) > subst).
% 0.57/0.48  thf(decl_444, type, esk254_0: subst > term > term).
% 0.57/0.48  thf(decl_445, type, esk255_0: term).
% 0.57/0.48  thf(decl_446, type, esk256_0: term).
% 0.57/0.48  thf(decl_447, type, esk257_1: (term > $o) > term).
% 0.57/0.48  thf(decl_448, type, esk258_1: (term > $o) > term).
% 0.57/0.48  thf(decl_449, type, esk259_1: (term > $o) > term).
% 0.57/0.48  thf(decl_450, type, esk260_1: (term > $o) > term).
% 0.57/0.48  thf(decl_451, type, epred43_0: term > $o).
% 0.57/0.48  thf(decl_452, type, esk261_0: term).
% 0.57/0.48  thf(decl_453, type, esk262_1: term > term).
% 0.57/0.48  thf(decl_454, type, esk263_0: term).
% 0.57/0.48  thf(decl_455, type, esk264_0: subst).
% 0.57/0.48  thf(decl_456, type, esk265_0: term).
% 0.57/0.48  thf(decl_457, type, esk266_0: subst).
% 0.57/0.48  thf(decl_458, type, epred44_0: term > $o).
% 0.57/0.48  thf(decl_459, type, epred45_0: term > $o).
% 0.57/0.48  thf(decl_460, type, esk267_0: term).
% 0.57/0.48  thf(decl_461, type, esk268_0: subst).
% 0.57/0.48  thf(decl_462, type, esk269_0: term).
% 0.57/0.48  thf(decl_463, type, epred46_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_464, type, epred47_0: term > $o).
% 0.57/0.48  thf(decl_465, type, esk270_0: term).
% 0.57/0.48  thf(decl_466, type, esk271_0: term).
% 0.57/0.48  thf(decl_467, type, esk272_0: subst).
% 0.57/0.48  thf(decl_468, type, esk273_0: term).
% 0.57/0.48  thf(decl_469, type, epred48_3: (term > $o) > term > subst > term > $o).
% 0.57/0.48  thf(decl_470, type, epred49_0: term > $o).
% 0.57/0.48  thf(decl_471, type, esk274_0: term).
% 0.57/0.48  thf(decl_472, type, esk275_0: subst).
% 0.57/0.48  thf(decl_473, type, esk276_1: (term > $o) > term).
% 0.57/0.48  thf(decl_474, type, esk277_0: term).
% 0.57/0.48  thf(decl_475, type, epred50_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_476, type, epred51_0: term > $o).
% 0.57/0.48  thf(decl_477, type, esk278_0: term).
% 0.57/0.48  thf(decl_478, type, esk279_0: term).
% 0.57/0.48  thf(decl_479, type, epred52_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_480, type, esk280_1: (term > $o) > term).
% 0.57/0.48  thf(decl_481, type, epred53_1: (subst > term > subst > $o) > term > $o).
% 0.57/0.48  thf(decl_482, type, epred54_0: subst > term > subst > $o).
% 0.57/0.48  thf(decl_483, type, epred55_1: (subst > term > subst > $o) > term > $o).
% 0.57/0.48  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.W3wP87dhdY/E---3.1_4190328.p', alg444_1)).
% 0.57/0.48  thf(hoasinduction_lem0, conjecture, ((hoasinduction_lem0)<=>![X11:subst > term > subst > $o]:(?[X12:term > $o]:((hoasinduction_p_and_p_prime @ X11 @ X12)))), file('/export/starexec/sandbox/tmp/tmp.W3wP87dhdY/E---3.1_4190328.p', hoasinduction_lem0)).
% 0.57/0.48  thf(c_0_2, plain, ((epred1_0)<=>(![X25:term > $o, X26:term]:((~(![X14:term]:((~(var @ X14)|(X25 @ X14))))|~(![X14:term, X18:term]:((~((X25 @ X14))|~((X25 @ X18))|(X25 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X25 @ X14))|(X25 @ (lam @ X14)))))|(X25 @ X26)))=>![X27:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X27 @ X14))|~((X27 @ X18))|(X27 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X27 @ X18))|(X27 @ (sub @ X14 @ (push @ X18 @ id))))))|(X27 @ (lam @ X14)))))|~(![X18:term]:((~(var @ X18)|(X27 @ (sub @ X18 @ X21)))))|(X27 @ (sub @ X20 @ X21)))))), introduced(definition)).
% 0.57/0.48  thf(c_0_3, plain, ((epred4_0)<=>(![X28:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X28 @ X14))))|~(![X14:term, X18:term]:((~((X28 @ X14))|~((X28 @ X18))|(X28 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X28 @ X18))|(X28 @ (sub @ X14 @ (push @ X18 @ id))))))|(X28 @ (lam @ X14)))))|(X28 @ X29)))=>(![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))=>(![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~(var @ (sub @ X14 @ id))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))), introduced(definition)).
% 0.57/0.48  thf(c_0_4, plain, ((epred5_0)<=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id))))), introduced(definition)).
% 0.57/0.48  thf(c_0_5, plain, ![X11:subst > term > subst > $o]:(((epred2_1 @ X11)<=>(~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~(var @ (sub @ X14 @ id))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))))), introduced(definition)).
% 0.57/0.48  thf(c_0_6, plain, ((epred6_0)<=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id))))), introduced(definition)).
% 0.57/0.48  thf(c_0_7, plain, ((epred7_0)<=>(![X59:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X59 @ X14))|~((X59 @ X18))|(X59 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X59 @ X18))|(X59 @ (sub @ X14 @ (push @ X18 @ id))))))|(X59 @ (lam @ X14)))))|~(![X18:term]:((~(var @ X18)|(X59 @ (sub @ X18 @ X21)))))|(X59 @ (sub @ X20 @ X21))))=>![X60:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X60 @ X14))))|~(![X14:term, X18:term]:((~((X60 @ X14))|~((X60 @ X18))|(X60 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X60 @ X18))|(X60 @ (sub @ X14 @ (push @ X18 @ id))))))|(X60 @ (lam @ X14)))))|(X60 @ X29))))), introduced(definition)).
% 0.57/0.48  thf(c_0_8, plain, ![X11:subst > term > subst > $o, X12:term > $o, X66:term]:(((epred8_3 @ X66 @ X12 @ X11)<=>(~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X66 @ (push @ X18 @ id))))))))), introduced(definition)).
% 0.57/0.48  thf(c_0_9, plain, ((epred9_0)<=>(![X68:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X68 @ X14))))|~(![X14:term, X18:term]:((~((X68 @ X14))|~((X68 @ X18))|(X68 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X68 @ X18))|(X68 @ (sub @ X14 @ (push @ X18 @ id))))))|(X68 @ (lam @ X14)))))|(X68 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))=>![X11:subst > term > subst > $o, X35:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term]:((~(var @ (sub @ X14 @ id))|(X11 @ id @ X14 @ id))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X35 @ id))))))), introduced(definition)).
% 0.57/0.48  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)))&![X611:subst, X612:subst > term > term]:(((hoaslam @ X611 @ X612)=(d2term @ d_one))))&![X613:subst > term > subst > $o, X614:term > $o]:(((hoasinduction_p_and_p_prime @ X613 @ X614)<=>![X13:term]:(((X614 @ X13)<=>(X613 @ id @ X13 @ id))))))&![X615:term, X616:subst, X617:term > $o, X618:term > $o]:(((pushprop_p_and_p_prime @ X615 @ X616 @ X617 @ X618)<=>![X13:term]:(((X618 @ X13)<=>(X617 @ (sub @ X13 @ (push @ X615 @ X616))))))))&~(var @ (d2term @ d_one)))&((pushprop_lem1v2)<=>![X17:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X17 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X17 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one)))))&(pushprop_lem1_gthm))&(axmap))&(pushprop_lem0_gthm))&((shinj)<=>![X14:term, X18:term]:((((sub @ X14 @ sh)!=(sub @ X18 @ sh))|((X14)=(X18))))))&(hoasinduction_lem1v2))&(hoasinduction_lem1v2_gthm))&((induction2lem)<=>![X19:term > $o, X20:term, X21:subst]:((~(![X14:term, X18:term]:((~((X19 @ X14))|~((X19 @ X18))|(X19 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X19 @ X18))|(X19 @ (sub @ X14 @ (push @ X18 @ id))))))|(X19 @ (lam @ X14)))))|~(![X18:term]:((~(var @ X18)|(X19 @ (sub @ X18 @ X21)))))|(X19 @ (sub @ X20 @ X21))))))&((hoasinduction_lem3v2_f)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&(axvarshift))&((hoasapinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24))))))&(hoasapnotvar_gthm))&((hoasapinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))&~(ulamvar1))&((induction2lem_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(epred1_0))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((hoasinduction_lem3v2_f_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))))&((hoasinduction_lthm)<=>(epred4_0)))&((hoasinduction_no_psi_cond_lthm)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(![X36:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X36 @ X14))))|~(![X14:term, X18:term]:((~((X36 @ X14))|~((X36 @ X18))|(X36 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X36 @ X18))|(X36 @ (sub @ X14 @ (push @ X18 @ id))))))|(X36 @ (lam @ X14)))))|(X36 @ X29)))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(epred5_0))))))&((hoaslaminj)<=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41))))))&((hoasinduction_lem3aaa)<=>![X11:subst > term > subst > $o, X42:term]:((~(![X22:subst > term > term, X43:term]:((~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id)|~(![X44:subst, X45:term, X46:subst]:(((sub @ (X22 @ X44 @ X45) @ X46)=(sub @ (sub @ X43 @ (push @ X45 @ X44)) @ X46))))|~(![X47:subst, X48:term, X49:subst]:(((X22 @ (comp @ X47 @ X49) @ (sub @ X48 @ X49))=(sub @ X43 @ (push @ (sub @ X48 @ X49) @ (comp @ X47 @ X49)))))))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X42 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)))))&(induction2lem_gthm))&((hoasinduction_lem3aa_lthm)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&((hoasinduction_lem3)<=>![X11:subst > term > subst > $o, X34:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X34 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X34) @ id)))))&((hoasinduction_lem2)<=>![X11:subst > term > subst > $o, X30:term, X31:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~((X11 @ id @ X30 @ id))|~((X11 @ id @ X31 @ id))|(X11 @ id @ (ap @ X30 @ X31) @ id)))))&(termmset_lthm))&(hoasinduction_lem1))&(hoaslamnotap_lthm))&((pushprop_lem1v2_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>![X51:term > $o, X12:term > $o, X14:term, X15:subst]:((~((X51 @ X14))|~(![X13:term]:(((X12 @ X13)<=>(X51 @ (sub @ X13 @ (push @ X14 @ X15))))))|(X12 @ one))))))&(hoasapnotvar))&((hoasinduction_lem0)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((hoasinduction)<=>![X11:subst > term > subst > $o, X35:term]:(((epred2_1 @ X11)|(X11 @ id @ X35 @ id)))))&(hoasinduction_gthm))&(axapp))&(hoaslamnotvar_lthm))&(pushprop_lem3v2_lthm))&((hoasinduction_lem3b_lthm)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&(ulamvarind))&((induction)<=>![X52:term > $o, X26:term]:((~(![X14:term]:((~(var @ X14)|(X52 @ X14))))|~(![X14:term, X18:term]:((~((X52 @ X14))|~((X52 @ X18))|(X52 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~((X52 @ X14))|(X52 @ (lam @ X14)))))|(X52 @ X26)))))&((hoasinduction_lem3a_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))))&(termmset_gthm))&((hoasinduction_lem3aa)<=>![X11:subst > term > subst > $o, X50:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X50 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ (sub @ X50 @ (push @ one @ sh))) @ id)))))&(pushprop_lem1v2_gthm))&(hoaslamnotap_gthm))&(hoaslamnotvar_gthm))&(hoasinduction_lem3b_gthm))&(pushprop_lem2v2))&(hoasinduction_lem3a_gthm))&(axclos))&(axassoc))&((hoasinduction_lem2v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X54:term, X55:term]:((~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ X15 @ X14 @ (comp @ X33 @ X32)))|(X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))))|~(![X15:subst, X14:term, X32:subst, X33:subst]:((~((X11 @ (comp @ X15 @ X33) @ (sub @ X14 @ X33) @ X32))|(X11 @ X15 @ X14 @ (comp @ X33 @ X32)))))|~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~((X12 @ X54))|~((X12 @ X55))|(X12 @ (ap @ X54 @ X55))))))&(pushprop_lthm))&((apinj2)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))))&((apinj1)<=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))))&((hoasapinj2_lthm)<=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X23)=(X24))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X23)=(X24)))))))&((hoasinduction_lem3v2a)<=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))&((hoasapinj1_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(![X14:term, X18:term, X23:term, X24:term]:((((ap @ X14 @ X23)!=(ap @ X18 @ X24))|((X14)=(X18))))=>![X14:term, X18:term, X23:term, X24:term]:((((ap @ (sub @ X14 @ id) @ X23)!=(ap @ (sub @ X18 @ id) @ X24))|((X14)=(X18))))))))&((hoaslaminj_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>(![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))=>![X22:subst > term > term, X39:subst > term > term, X40:subst, X41:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X15:subst, X14:term, X32:subst]:(((sub @ (X39 @ X15 @ X14) @ X32)=(X39 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(lam @ (X39 @ sh @ one)))|((X22 @ X40 @ X41)=(X39 @ X40 @ X41)))))))))&((axvarcons)<=>![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))))&((axscons)<=>![X15:subst]:(((X15)=(push @ (sub @ one @ X15) @ (comp @ sh @ X15))))))&(hoasinduction_lem2v2_gthm))&((axidr)<=>![X15:subst]:(((X15)=(comp @ X15 @ id)))))&((pushprop_lem1)<=>![X56:term > $o, X57:term > $o, X14:term, X15:subst, X18:term]:((~((X56 @ X14))|(X57 @ (sub @ X14 @ (push @ X18 @ X15)))))))&((laminj)<=>![X14:term, X18:term]:((((lam @ X14)!=(lam @ X18))|((X14)=(X18))))))&((hoasinduction_lem3_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(epred6_0))))&((pushprop_lem0)<=>![X58:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X58 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(pushprop_gthm))&(axabs))&((hoasinduction_lem3v2a_lthm)<=>(![X18:term]:(~(![X22:subst > term > term]:(~(![X14:term, X15:subst]:(((sub @ X18 @ (push @ X14 @ X15))=(X22 @ X15 @ X14)))))))=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X37:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id))))|~(![X18:term]:((~((X12 @ X18))|(X12 @ (sub @ X37 @ (push @ X18 @ id))))))|(X12 @ (lam @ X37))))))))&(hoasinduction_lem2_lthm))&(hoasapinj2_gthm))&(hoasinduction_lem1_lthm))&~(lamnotap))&(hoasapinj1_gthm))&(hoaslamnotvar))&((axidl)<=>![X15:subst]:(((X15)=(comp @ id @ X15)))))&(hoaslaminj_gthm))&((induction2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>(epred7_0))))&((hoasinduction_lem0_lthm)<=>![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))))&((substmonoid_lthm)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))=>(![X15:subst]:(((X15)=(comp @ X15 @ id)))=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))))&(pushprop))&(hoasinduction_lem3_gthm))&(hoasinduction_lem2_gthm))&((hoasinduction_lem3b)<=>![X18:term]:(~(![X22:subst > term > term]:(((X22 @ sh @ one)!=(sub @ X18 @ (push @ one @ sh))))))))&((substmonoid)<=>(![X15:subst]:(((X15)=(comp @ id @ X15)))&![X15:subst]:(((X15)=(comp @ X15 @ id))))))&(lamnotvar))&((hoasinduction_lem3a)<=>![X11:subst > term > subst > $o, X53:term]:((~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|~(![X18:term]:((~((X11 @ id @ X18 @ id))|(X11 @ id @ (sub @ X53 @ (push @ X18 @ id)) @ id))))|(X11 @ id @ (lam @ X53) @ id)))))&(hoasinduction_lem1_gthm))&((hoasinduction_no_psi_cond)<=>![X11:subst > term > subst > $o, X38:term]:((~(![X14:term, X18:term]:((~((X11 @ id @ X14 @ id))|~((X11 @ id @ X18 @ id))|(X11 @ id @ (ap @ (sub @ X14 @ id) @ X18) @ id))))|~(![X22:subst > term > term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|~(![X14:term]:((~((X11 @ id @ X14 @ id))|(X11 @ id @ (X22 @ id @ X14) @ id))))|(X11 @ id @ (lam @ (X22 @ sh @ one)) @ id))))|(X11 @ id @ X38 @ id)))))&(induction2_gthm))&(pushprop_lem2v2_lthm))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&((hoaslamnotap)<=>![X22:subst > term > term, X61:term, X62:term]:((~(![X15:subst, X14:term, X32:subst]:(((sub @ (X22 @ X15 @ X14) @ X32)=(X22 @ (comp @ X15 @ X32) @ (sub @ X14 @ X32)))))|((lam @ (X22 @ sh @ one))!=(ap @ (sub @ X61 @ id) @ X62))))))&(substmonoid_gthm))&(ulamvarsh))&((induction2)<=>![X63:term > $o, X29:term]:((~(![X14:term]:((~(var @ X14)|(X63 @ X14))))|~(![X14:term, X18:term]:((~((X63 @ X14))|~((X63 @ X18))|(X63 @ (ap @ X14 @ X18)))))|~(![X14:term]:((~(![X18:term]:((~((X63 @ X18))|(X63 @ (sub @ X14 @ (push @ X18 @ id))))))|(X63 @ (lam @ X14)))))|(X63 @ X29)))))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((pushprop_lem1_lthm)<=>(![X14:term, X15:subst]:(((X14)=(sub @ one @ (push @ X14 @ X15))))=>(![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))=>![X64:term > $o, X65:term > $o, X14:term, X15:subst, X18:term]:((~((X64 @ X14))|(X65 @ (sub @ X14 @ (push @ X18 @ X15)))))))))&((hoasinduction_lem3v2)<=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:(((epred8_3 @ X66 @ X12 @ X11)|(X12 @ (lam @ X66))))))&((axshiftcons)<=>![X14:term, X15:subst]:(((X15)=(comp @ sh @ (push @ X14 @ X15))))))&((termmset)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((pushprop_lem0_lthm)<=>![X67:term > $o, X14:term, X15:subst]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X67 @ (sub @ X13 @ (push @ X14 @ X15)))))))))))&(hoasapnotvar_lthm))&((hoasinduction_lem3v2_lthm)<=>(![X14:term]:(((X14)=(sub @ X14 @ id)))=>![X11:subst > term > subst > $o, X12:term > $o, X66:term]:(((epred8_3 @ X66 @ X12 @ X11)|(X12 @ (lam @ X66)))))))&((axvarid)<=>![X14:term]:(((X14)=(sub @ X14 @ id)))))&((hoasinduction_lthm_3)<=>(![X11:subst > term > subst > $o]:(~(![X12:term > $o]:(~(![X13:term]:(((X12 @ X13)<=>(X11 @ id @ X13 @ id)))))))=>(epred9_0)))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[alg444_1])])]), c_0_2]), c_0_3]), c_0_4]), c_0_5]), c_0_6]), c_0_7]), c_0_8]), c_0_8]), c_0_9])).
% 0.57/0.48  thf(c_0_11, plain, ![X619:term, X621:d_term, X622:d_term, X623:d_term, X624:subst, X626:d_subst, X627:d_subst, X628:d_subst, X629:subst, X630:subst > term > term, X631:subst > term > subst > $o, X632:term > $o, X633:term, X634:term, X635:subst > term > subst > $o, X636:term > $o, X638:term, X639:subst, X640:term > $o, X641:term > $o, X642:term, X643:term, X644:term, X645:subst, X646:term > $o, X647:term > $o, X649:term > $o, X650:term > $o, X651:term, X652:subst, X658:term, X659:term, X660:term, X663:term > $o, X664:term, X665:subst, X669:term, X674:term, X675:term, X676:term, X678:term, X679:term, X681:term, X682:subst, X684:subst > term > term, X687:term, X688:term, X689:term, X690:term, X695:term, X696:term, X697:term, X698:term, X708:term, X709:subst, X710:term, X711:subst, X712:subst, X713:term, X715:term, X716:subst, X718:subst > term > term, X722:term > $o, X726:term, X727:term, X728:term, X729:term, X732:subst > term > subst > $o, X734:term, X735:term, X736:term > $o, X741:term, X742:term, X743:term, X744:subst > term > term, X745:subst > term > term, X752:subst, X753:term, X758:subst, X759:term, X760:subst, X761:subst, X762:term, X763:subst, X764:subst > term > subst > $o, X765:term, X768:term, X769:subst, X770:term, X771:subst, X772:subst, X773:term, X774:subst, X778:subst > term > term, X779:term, X787:term, X788:subst > term > subst > $o, X789:term, X791:subst, X792:term, X793:subst, X794:term, X798:subst > term > term, X803:term, X804:subst > term > subst > $o, X805:term, X815:subst, X816:term, X817:subst, X818:term, X822:subst, X823:term, X824:subst, X825:subst, X826:subst, X827:term, X828:subst, X829:subst, X830:subst > term > term, X835:term, X836:subst > term > subst > $o, X837:term, X838:term, X852:subst, X853:term, X854:subst, X855:subst, X856:subst, X857:term, X858:subst, X859:subst, X860:term, X861:term, X864:term > $o, X865:term > $o, X866:term, X867:subst, X869:term, X870:subst, X875:term, X876:subst > term > subst > $o, X878:term, X879:term, X881:term > $o, X883:subst > term > subst > $o, X884:term, X887:term, X890:subst > term > term, X891:term > $o, X896:term, X899:term, X900:term, X901:term, X902:term, X906:subst > term > term, X911:term, X912:subst > term > subst > $o, X913:term, X915:subst, X916:term, X917:subst, X918:term, X920:term, X921:subst > term > subst > $o, X922:term, X924:subst, X925:term, X926:subst, X927:term, X931:subst > term > term, X936:term, X937:subst > term > subst > $o, X938:term, X940:subst, X941:term, X942:subst, X943:term, X947:subst > term > term, X952:term, X953:subst > term > subst > $o, X954:term > $o, X955:term, X956:term, X972:subst, X973:term, X974:subst, X975:subst, X976:subst, X977:term, X978:subst, X979:subst, X980:term, X981:term, X982:term, X983:term, X984:term, X985:term, X986:term, X991:term, X992:term, X993:term, X994:term, X1003:term, X1004:term, X1005:term, X1006:term, X1007:term, X1008:term, X1009:term, X1010:term, X1015:subst > term > subst > $o, X1016:term > $o, X1017:term, X1019:subst, X1020:term, X1021:subst, X1022:term, X1028:subst > term > term, X1033:term, X1034:term, X1040:term, X1041:term, X1042:term, X1043:term, X1044:term, X1045:term, X1046:term, X1047:term, X1048:term, X1059:subst > term > term, X1060:subst > term > term, X1067:subst, X1068:term, X1069:term, X1070:subst, X1071:term, X1072:subst, X1073:term, X1074:term, X1079:subst, X1080:term, X1081:subst, X1082:subst, X1083:term, X1084:subst, X1085:term, X1086:subst, X1089:subst, X1091:subst, X1093:term > $o, X1094:term > $o, X1095:term, X1096:subst, X1097:term, X1103:term, X1104:term, X1108:term, X1109:term > $o, X1110:term, X1111:subst, X1113:term, X1114:term, X1118:term > $o, X1121:subst > term > term, X1125:subst > term > subst > $o, X1126:term > $o, X1127:term, X1129:subst, X1130:term, X1131:subst, X1132:term, X1135:term, X1137:term, X1138:subst, X1139:term, X1143:subst > term > term, X1148:term, X1149:term, X1150:subst, X1153:term, X1154:subst > term > subst > $o, X1156:term, X1157:term, X1159:term > $o, X1163:subst, X1164:subst, X1165:subst, X1166:subst, X1169:term, X1172:subst > term > term, X1173:subst, X1174:subst, X1177:subst > term > subst > $o, X1178:term, X1180:subst, X1181:term, X1182:subst, X1183:term, X1187:subst > term > term, X1192:term, X1193:subst > term > subst > $o, X1197:subst, X1198:term, X1199:subst, X1200:term, X1201:term, X1204:term, X1205:term, X1206:subst > term > term, X1211:subst > term > term, X1215:term, X1216:term, X1220:subst, X1221:term, X1222:subst, X1223:term > $o, X1228:term, X1229:term, X1232:term, X1233:term, X1234:term, X1235:term, X1241:term > $o, X1242:term > $o, X1243:term, X1244:subst, X1245:term, X1246:term, X1247:subst, X1248:term, X1249:subst, X1255:subst > term > subst > $o, X1256:term > $o, X1257:term, X1261:term, X1262:subst, X1265:term, X1267:term > $o, X1268:term, X1269:subst, X1271:term, X1272:term, X1276:term > $o, X1279:subst > term > subst > $o, X1280:term > $o, X1281:term, X1282:term, X1286:term, X1289:term > $o, X1291:subst > term > subst > $o, X1293:term, X1294:term]:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((X619)=(d2term @ (esk1_1 @ X619)))&((X621)=(d_one)))&(((d2term @ X622)!=(d2term @ X623))|((X622)=(X623))))&((X624)=(d2subst @ (esk2_1 @ X624))))&((X626)=(d_id)))&(((d2subst @ X627)!=(d2subst @ X628))|((X627)=(X628))))&((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 @ X629 @ X630)=(d2term @ d_one)))&(((~(X632 @ X633)|(X631 @ id @ X633 @ id)|~(hoasinduction_p_and_p_prime @ X631 @ X632))&(~(X631 @ id @ X634 @ id)|(X632 @ X634)|~(hoasinduction_p_and_p_prime @ X631 @ X632)))&((~(X636 @ (esk3_2 @ X635 @ X636))|~(X635 @ id @ (esk3_2 @ X635 @ X636) @ id)|(hoasinduction_p_and_p_prime @ X635 @ X636))&((X636 @ (esk3_2 @ X635 @ X636))|(X635 @ id @ (esk3_2 @ X635 @ X636) @ id)|(hoasinduction_p_and_p_prime @ X635 @ X636)))))&(((~(X641 @ X642)|(X640 @ (sub @ X642 @ (push @ X638 @ X639)))|~(pushprop_p_and_p_prime @ X638 @ X639 @ X640 @ X641))&(~(X640 @ (sub @ X643 @ (push @ X638 @ X639)))|(X641 @ X643)|~(pushprop_p_and_p_prime @ X638 @ X639 @ X640 @ X641)))&((~(X647 @ (esk4_4 @ X644 @ X645 @ X646 @ X647))|~(X646 @ (sub @ (esk4_4 @ X644 @ X645 @ X646 @ X647) @ (push @ X644 @ X645)))|(pushprop_p_and_p_prime @ X644 @ X645 @ X646 @ X647))&((X647 @ (esk4_4 @ X644 @ X645 @ X646 @ X647))|(X646 @ (sub @ (esk4_4 @ X644 @ X645 @ X646 @ X647) @ (push @ X644 @ X645)))|(pushprop_p_and_p_prime @ X644 @ X645 @ X646 @ X647)))))&~(var @ (d2term @ d_one)))&(((~(X650 @ (esk5_4 @ X649 @ X650 @ X651 @ X652))|~(X649 @ (sub @ (esk5_4 @ X649 @ X650 @ X651 @ X652) @ (push @ X651 @ X652)))|~(X649 @ X651)|(X650 @ one)|~(pushprop_lem1v2))&((X650 @ (esk5_4 @ X649 @ X650 @ X651 @ X652))|(X649 @ (sub @ (esk5_4 @ X649 @ X650 @ X651 @ X652) @ (push @ X651 @ X652)))|~(X649 @ X651)|(X650 @ one)|~(pushprop_lem1v2)))&((((epred10_0 @ esk6_0)|(pushprop_lem1v2))&((~(epred11_0 @ X658)|(epred10_0 @ (sub @ X658 @ (push @ esk6_0 @ esk7_0)))|(pushprop_lem1v2))&(~(epred10_0 @ (sub @ X658 @ (push @ esk6_0 @ esk7_0)))|(epred11_0 @ X658)|(pushprop_lem1v2))))&(~(epred11_0 @ one)|(pushprop_lem1v2)))))&(pushprop_lem1_gthm))&(axmap))&(pushprop_lem0_gthm))&((~(shinj)|(((sub @ X659 @ sh)!=(sub @ X660 @ sh))|((X659)=(X660))))&((((sub @ esk8_0 @ sh)=(sub @ esk9_0 @ sh))|(shinj))&(((esk8_0)!=(esk9_0))|(shinj)))))&(hoasinduction_lem1v2))&(hoasinduction_lem1v2_gthm))&(((((((var @ (esk13_3 @ X663 @ X664 @ X665))|(~(X663 @ X669)|(X663 @ (sub @ (esk12_3 @ X663 @ X664 @ X665) @ (push @ X669 @ id)))|(X663 @ (esk10_3 @ X663 @ X664 @ X665)))|(X663 @ (sub @ X664 @ X665))|~(induction2lem))&(~(X663 @ (sub @ (esk13_3 @ X663 @ X664 @ X665) @ X665))|(~(X663 @ X669)|(X663 @ (sub @ (esk12_3 @ X663 @ X664 @ X665) @ (push @ X669 @ id)))|(X663 @ (esk10_3 @ X663 @ X664 @ X665)))|(X663 @ (sub @ X664 @ X665))|~(induction2lem)))&(((var @ (esk13_3 @ X663 @ X664 @ X665))|(~(X663 @ (lam @ (esk12_3 @ X663 @ X664 @ X665)))|(X663 @ (esk10_3 @ X663 @ X664 @ X665)))|(X663 @ (sub @ X664 @ X665))|~(induction2lem))&(~(X663 @ (sub @ (esk13_3 @ X663 @ X664 @ X665) @ X665))|(~(X663 @ (lam @ (esk12_3 @ X663 @ X664 @ X665)))|(X663 @ (esk10_3 @ X663 @ X664 @ X665)))|(X663 @ (sub @ X664 @ X665))|~(induction2lem))))&((((var @ (esk13_3 @ X663 @ X664 @ X665))|(~(X663 @ X669)|(X663 @ (sub @ (esk12_3 @ X663 @ X664 @ X665) @ (push @ X669 @ id)))|(X663 @ (esk11_3 @ X663 @ X664 @ X665)))|(X663 @ (sub @ X664 @ X665))|~(induction2lem))&(~(X663 @ (sub @ (esk13_3 @ X663 @ X664 @ X665) @ X665))|(~(X663 @ X669)|(X663 @ (sub @ (esk12_3 @ X663 @ X664 @ X665) @ (push @ X669 @ id)))|(X663 @ (esk11_3 @ X663 @ X664 @ X665)))|(X663 @ (sub @ X664 @ X665))|~(induction2lem)))&(((var @ (esk13_3 @ X663 @ X664 @ X665))|(~(X663 @ (lam @ (esk12_3 @ X663 @ X664 @ X665)))|(X663 @ (esk11_3 @ X663 @ X664 @ X665)))|(X663 @ (sub @ X664 @ X665))|~(induction2lem))&(~(X663 @ (sub @ (esk13_3 @ X663 @ X664 @ X665) @ X665))|(~(X663 @ (lam @ (esk12_3 @ X663 @ X664 @ X665)))|(X663 @ (esk11_3 @ X663 @ X664 @ X665)))|(X663 @ (sub @ X664 @ X665))|~(induction2lem)))))&((((var @ (esk13_3 @ X663 @ X664 @ X665))|(~(X663 @ X669)|(X663 @ (sub @ (esk12_3 @ X663 @ X664 @ X665) @ (push @ X669 @ id)))|~(X663 @ (ap @ (esk10_3 @ X663 @ X664 @ X665) @ (esk11_3 @ X663 @ X664 @ X665))))|(X663 @ (sub @ X664 @ X665))|~(induction2lem))&(~(X663 @ (sub @ (esk13_3 @ X663 @ X664 @ X665) @ X665))|(~(X663 @ X669)|(X663 @ (sub @ (esk12_3 @ X663 @ X664 @ X665) @ (push @ X669 @ id)))|~(X663 @ (ap @ (esk10_3 @ X663 @ X664 @ X665) @ (esk11_3 @ X663 @ X664 @ X665))))|(X663 @ (sub @ X664 @ X665))|~(induction2lem)))&(((var @ (esk13_3 @ X663 @ X664 @ X665))|(~(X663 @ (lam @ (esk12_3 @ X663 @ X664 @ X665)))|~(X663 @ (ap @ (esk10_3 @ X663 @ X664 @ X665) @ (esk11_3 @ X663 @ X664 @ X665))))|(X663 @ (sub @ X664 @ X665))|~(induction2lem))&(~(X663 @ (sub @ (esk13_3 @ X663 @ X664 @ X665) @ X665))|(~(X663 @ (lam @ (esk12_3 @ X663 @ X664 @ X665)))|~(X663 @ (ap @ (esk10_3 @ X663 @ X664 @ X665) @ (esk11_3 @ X663 @ X664 @ X665))))|(X663 @ (sub @ X664 @ X665))|~(induction2lem)))))&((((~(epred12_0 @ X674)|~(epred12_0 @ X675)|(epred12_0 @ (ap @ X674 @ X675))|(induction2lem))&(((epred12_0 @ (esk16_1 @ X676))|(epred12_0 @ (lam @ X676))|(induction2lem))&(~(epred12_0 @ (sub @ X676 @ (push @ (esk16_1 @ X676) @ id)))|(epred12_0 @ (lam @ X676))|(induction2lem))))&(~(var @ X678)|(epred12_0 @ (sub @ X678 @ esk15_0))|(induction2lem)))&(~(epred12_0 @ (sub @ esk14_0 @ esk15_0))|(induction2lem)))))&((~(hoasinduction_lem3v2_f)|((sub @ X679 @ (push @ X681 @ X682))=(esk17_1 @ X679 @ X682 @ X681)))&(((sub @ esk18_0 @ (push @ (esk19_1 @ X684) @ (esk20_1 @ X684)))!=(X684 @ (esk20_1 @ X684) @ (esk19_1 @ X684)))|(hoasinduction_lem3v2_f))))&(axvarshift))&((~(hoasapinj2)|(((ap @ (sub @ X687 @ id) @ X689)!=(ap @ (sub @ X688 @ id) @ X690))|((X689)=(X690))))&((((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 @ X695 @ id) @ X697)!=(ap @ (sub @ X696 @ id) @ X698))|((X695)=(X696))))&((((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)))))&((((X708)=(sub @ one @ (push @ X708 @ X709)))|(induction2lem_lthm))&((((X711)=(comp @ sh @ (push @ X710 @ X711)))|(induction2lem_lthm))&((((X712)=(comp @ X712 @ id))|(induction2lem_lthm))&(~(epred1_0)|(induction2lem_lthm)))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(pushprop_lthm_orig))&((~(hoasinduction_lem3v2_f_lthm)|((sub @ X713 @ (push @ X715 @ X716))=(esk34_1 @ X713 @ X716 @ X715)))&(((sub @ esk35_0 @ (push @ (esk36_1 @ X718) @ (esk37_1 @ X718)))!=(X718 @ (esk37_1 @ X718) @ (esk36_1 @ X718)))|(hoasinduction_lem3v2_f_lthm))))&((~(hoasinduction_lthm)|(epred4_0))&(~(epred4_0)|(hoasinduction_lthm))))&((((((~(var @ X726)|(epred14_0 @ X726)|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X722 @ (esk38_1 @ X722))|~(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ X727)|~(epred14_0 @ X728)|(epred14_0 @ (ap @ X727 @ X728))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X722 @ (esk38_1 @ X722))|~(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred14_0 @ (esk40_1 @ X729))|(epred14_0 @ (lam @ X729))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X722 @ (esk38_1 @ X722))|~(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ (sub @ X729 @ (push @ (esk40_1 @ X729) @ id)))|(epred14_0 @ (lam @ X729))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X722 @ (esk38_1 @ X722))|~(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred14_0 @ esk39_0)|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|(~(X722 @ (esk38_1 @ X722))|~(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm)))&((((~(var @ X726)|(epred14_0 @ X726)|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|((X722 @ (esk38_1 @ X722))|(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ X727)|~(epred14_0 @ X728)|(epred14_0 @ (ap @ X727 @ X728))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|((X722 @ (esk38_1 @ X722))|(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred14_0 @ (esk40_1 @ X729))|(epred14_0 @ (lam @ X729))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|((X722 @ (esk38_1 @ X722))|(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred14_0 @ (sub @ X729 @ (push @ (esk40_1 @ X729) @ id)))|(epred14_0 @ (lam @ X729))|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|((X722 @ (esk38_1 @ X722))|(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(~(epred14_0 @ esk39_0)|(((esk41_0)!=(sub @ esk41_0 @ id))|(epred5_0))|((X722 @ (esk38_1 @ X722))|(epred13_0 @ id @ (esk38_1 @ X722) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(((~(epred15_1 @ X732 @ X734)|(X732 @ id @ X734 @ id)|(hoasinduction_no_psi_cond_lthm))&(~(X732 @ id @ X735 @ id)|(epred15_1 @ X732 @ X735)|(hoasinduction_no_psi_cond_lthm)))&((((((~(X736 @ X741)|(X736 @ (sub @ (esk45_1 @ X736) @ (push @ X741 @ id)))|((X736 @ (esk43_1 @ X736))|(var @ (esk42_1 @ X736)))|(X736 @ 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X1193)) @ id)|(X1193 @ id @ X1201 @ id)|~(hoasinduction_no_psi_cond)))&(~(X1193 @ id @ (lam @ (esk245_1 @ X1193 @ sh @ one)) @ id)|~(X1193 @ id @ (ap @ (sub @ (esk243_1 @ X1193) @ id) @ (esk244_1 @ X1193)) @ id)|(X1193 @ id @ X1201 @ id)|~(hoasinduction_no_psi_cond))))&(((~(epred42_0 @ id @ X1204 @ id)|~(epred42_0 @ id @ X1205 @ id)|(epred42_0 @ id @ (ap @ (sub @ X1204 @ id) @ X1205) @ id)|(hoasinduction_no_psi_cond))&(((epred42_0 @ id @ (esk250_1 @ X1206) @ id)|((sub @ (X1206 @ (esk247_1 @ X1206) @ (esk248_1 @ X1206)) @ (esk249_1 @ X1206))!=(X1206 @ (comp @ (esk247_1 @ X1206) @ (esk249_1 @ X1206)) @ (sub @ (esk248_1 @ X1206) @ (esk249_1 @ X1206))))|(epred42_0 @ id @ (lam @ (X1206 @ sh @ one)) @ id)|(hoasinduction_no_psi_cond))&(~(epred42_0 @ id @ (X1206 @ id @ (esk250_1 @ X1206)) @ id)|((sub @ (X1206 @ (esk247_1 @ X1206) @ (esk248_1 @ X1206)) @ (esk249_1 @ X1206))!=(X1206 @ (comp @ (esk247_1 @ X1206) @ (esk249_1 @ X1206)) @ (sub @ (esk248_1 @ X1206) @ (esk249_1 @ X1206))))|(epred42_0 @ id @ (lam @ (X1206 @ 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 @ (X1211 @ (esk251_1 @ X1211) @ (esk252_1 @ X1211)) @ (esk253_1 @ X1211))!=(X1211 @ (comp @ (esk251_1 @ X1211) @ (esk253_1 @ X1211)) @ (sub @ (esk252_1 @ X1211) @ (esk253_1 @ X1211))))|((lam @ (X1211 @ sh @ one))!=(ap @ (sub @ X1215 @ id) @ X1216))))&((((sub @ (esk254_0 @ X1220 @ X1221) @ X1222)=(esk254_0 @ (comp @ X1220 @ X1222) @ (sub @ X1221 @ X1222)))|(hoaslamnotap))&(((lam @ (esk254_0 @ sh @ one))=(ap @ (sub @ esk255_0 @ id) @ esk256_0))|(hoaslamnotap)))))&(substmonoid_gthm))&(ulamvarsh))&((((((~(X1223 @ X1228)|(X1223 @ (sub @ (esk260_1 @ X1223) @ (push @ X1228 @ id)))|((X1223 @ (esk258_1 @ X1223))|(var @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2))&(~(X1223 @ (lam @ (esk260_1 @ X1223)))|((X1223 @ (esk258_1 @ X1223))|(var @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2)))&((~(X1223 @ X1228)|(X1223 @ (sub @ (esk260_1 @ X1223) @ (push @ X1228 @ id)))|((X1223 @ (esk259_1 @ X1223))|(var @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2))&(~(X1223 @ (lam @ (esk260_1 @ X1223)))|((X1223 @ (esk259_1 @ X1223))|(var @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2))))&((~(X1223 @ X1228)|(X1223 @ (sub @ (esk260_1 @ X1223) @ (push @ X1228 @ id)))|(~(X1223 @ (ap @ (esk258_1 @ X1223) @ (esk259_1 @ X1223)))|(var @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2))&(~(X1223 @ (lam @ (esk260_1 @ X1223)))|(~(X1223 @ (ap @ (esk258_1 @ X1223) @ (esk259_1 @ X1223)))|(var @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2))))&((((~(X1223 @ X1228)|(X1223 @ (sub @ (esk260_1 @ X1223) @ (push @ X1228 @ id)))|((X1223 @ (esk258_1 @ X1223))|~(X1223 @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2))&(~(X1223 @ (lam @ (esk260_1 @ X1223)))|((X1223 @ (esk258_1 @ X1223))|~(X1223 @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2)))&((~(X1223 @ X1228)|(X1223 @ (sub @ (esk260_1 @ X1223) @ (push @ X1228 @ id)))|((X1223 @ (esk259_1 @ X1223))|~(X1223 @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2))&(~(X1223 @ (lam @ (esk260_1 @ X1223)))|((X1223 @ (esk259_1 @ X1223))|~(X1223 @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2))))&((~(X1223 @ X1228)|(X1223 @ (sub @ (esk260_1 @ X1223) @ (push @ X1228 @ id)))|(~(X1223 @ (ap @ (esk258_1 @ X1223) @ (esk259_1 @ X1223)))|~(X1223 @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2))&(~(X1223 @ (lam @ (esk260_1 @ X1223)))|(~(X1223 @ (ap @ (esk258_1 @ X1223) @ (esk259_1 @ X1223)))|~(X1223 @ (esk257_1 @ X1223)))|(X1223 @ X1229)|~(induction2)))))&((((~(var @ X1232)|(epred43_0 @ X1232)|(induction2))&(~(epred43_0 @ X1233)|~(epred43_0 @ X1234)|(epred43_0 @ (ap @ X1233 @ X1234))|(induction2)))&(((epred43_0 @ (esk262_1 @ X1235))|(epred43_0 @ (lam @ X1235))|(induction2))&(~(epred43_0 @ (sub @ X1235 @ (push @ (esk262_1 @ X1235) @ id)))|(epred43_0 @ (lam @ X1235))|(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)))|(~(X1241 @ X1243)|(X1242 @ (sub @ X1243 @ (push @ X1245 @ X1244)))))))&((((X1246)=(sub @ one @ (push @ X1246 @ X1247)))|(pushprop_lem1_lthm))&((((X1249)=(comp @ sh @ (push @ X1248 @ X1249)))|(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 @ X1257 @ X1256 @ X1255)|(X1256 @ (lam @ X1257))))&((~(epred8_3 @ esk270_0 @ epred47_0 @ epred46_0)|(hoasinduction_lem3v2))&(~(epred47_0 @ (lam @ esk270_0))|(hoasinduction_lem3v2)))))&((~(axshiftcons)|((X1262)=(comp @ sh @ (push @ X1261 @ X1262))))&(((esk272_0)!=(comp @ sh @ (push @ esk271_0 @ esk272_0)))|(axshiftcons))))&((~(termmset)|((X1265)=(sub @ X1265 @ id)))&(((esk273_0)!=(sub @ esk273_0 @ id))|(termmset))))&(((~(epred48_3 @ X1267 @ X1268 @ X1269 @ X1271)|(X1267 @ (sub @ X1271 @ (push @ X1268 @ X1269)))|~(pushprop_lem0_lthm))&(~(X1267 @ (sub @ X1272 @ (push @ X1268 @ X1269)))|(epred48_3 @ X1267 @ X1268 @ X1269 @ X1272)|~(pushprop_lem0_lthm)))&((~(X1276 @ (esk276_1 @ X1276))|~(epred49_0 @ (sub @ (esk276_1 @ X1276) @ (push @ esk274_0 @ esk275_0)))|(pushprop_lem0_lthm))&((X1276 @ (esk276_1 @ X1276))|(epred49_0 @ (sub @ (esk276_1 @ X1276) @ (push @ esk274_0 @ esk275_0)))|(pushprop_lem0_lthm)))))&(hoasapnotvar_lthm))&((~(hoasinduction_lem3v2_lthm)|(((esk277_0)!=(sub @ esk277_0 @ id))|((epred8_3 @ X1281 @ X1280 @ X1279)|(X1280 @ (lam @ X1281)))))&((((X1282)=(sub @ X1282 @ id))|(hoasinduction_lem3v2_lthm))&((~(epred8_3 @ esk278_0 @ epred51_0 @ epred50_0)|(hoasinduction_lem3v2_lthm))&(~(epred51_0 @ (lam @ esk278_0))|(hoasinduction_lem3v2_lthm))))))&((~(axvarid)|((X1286)=(sub @ X1286 @ id)))&(((esk279_0)!=(sub @ esk279_0 @ id))|(axvarid))))&(((~(X1289 @ (esk280_1 @ X1289))|~(epred52_0 @ id @ (esk280_1 @ X1289) @ id)|(epred9_0)|~(hoasinduction_lthm_3))&((X1289 @ (esk280_1 @ X1289))|(epred52_0 @ id @ (esk280_1 @ X1289) @ id)|(epred9_0)|~(hoasinduction_lthm_3)))&(((~(epred53_1 @ X1291 @ X1293)|(X1291 @ id @ X1293 @ id)|(hoasinduction_lthm_3))&(~(X1291 @ id @ X1294 @ id)|(epred53_1 @ X1291 @ X1294)|(hoasinduction_lthm_3)))&(~(epred9_0)|(hoasinduction_lthm_3)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])])])).
% 0.57/0.48  thf(c_0_12, plain, ![X1:term]:(((X1)=(d2term @ (esk1_1 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_13, plain, ![X2:d_term]:(((X2)=(d_one))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_14, plain, ((one)=(d2term @ d_one)), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_15, plain, ((laminj)|((esk206_0)!=(esk207_0))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_16, plain, ![X1:term]:(((one)=(X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13]), c_0_14])).
% 0.57/0.48  thf(c_0_17, plain, ![X1:term, X13:term]:((((X1)=(X13))|~((laminj))|((lam @ X1)!=(lam @ X13)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_18, plain, (laminj), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16]), c_0_16])])).
% 0.57/0.48  thf(c_0_19, plain, ((induction2)|~((epred43_0 @ esk261_0))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_20, plain, ![X1:term]:(((epred43_0 @ (esk262_1 @ X1))|(epred43_0 @ (lam @ X1))|(induction2))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_21, 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_17, c_0_16]), c_0_16]), c_0_18])])).
% 0.57/0.48  thf(c_0_22, plain, ((induction2)|~((epred43_0 @ one))), inference(rw,[status(thm)],[c_0_19, c_0_16])).
% 0.57/0.48  thf(c_0_23, plain, ((induction)|~((epred25_0 @ esk114_0))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_24, plain, ~((var @ (d2term @ d_one))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_25, plain, ![X5:subst]:(((X5)=(d2subst @ (esk2_1 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_26, plain, ![X6:d_subst]:(((X6)=(d_id))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_27, plain, ((id)=(d2subst @ d_id)), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_28, 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])).
% 0.57/0.48  thf(c_0_29, plain, (induction2), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_16]), c_0_21])]), c_0_22])).
% 0.57/0.48  thf(c_0_30, plain, ![X1:term]:(((epred25_0 @ (lam @ X1))|(induction)|~((epred25_0 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_31, plain, ((induction)|~((epred25_0 @ one))), inference(rw,[status(thm)],[c_0_23, c_0_16])).
% 0.57/0.48  thf(c_0_32, plain, ![X12:term > $o, X1:term]:(((X12 @ (esk113_1 @ X12))|(X12 @ (esk111_1 @ X12))|(var @ (esk110_1 @ X12))|(X12 @ X1)|~((induction)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_33, plain, ~((var @ one)), inference(rw,[status(thm)],[c_0_24, c_0_14])).
% 0.57/0.48  thf(c_0_34, 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])).
% 0.57/0.48  thf(c_0_35, plain, ![X5:subst]:(((id)=(X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26]), c_0_27])).
% 0.57/0.48  thf(c_0_36, 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_28, c_0_29]), c_0_21]), c_0_21]), c_0_16]), c_0_21]), c_0_21]), c_0_16])])).
% 0.57/0.48  thf(c_0_37, plain, ![X12:term > $o]:(((X12 @ (esk106_1 @ X12))|(epred23_0 @ id @ (esk106_1 @ X12) @ id)|(hoasinduction_lem0))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_38, plain, ![X12:term > $o]:(((hoasinduction_lem0)|~((X12 @ (esk106_1 @ X12)))|~((epred23_0 @ id @ (esk106_1 @ X12) @ id)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_39, plain, ![X1:term]:(((induction)|~((epred25_0 @ X1)))), inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_16]), c_0_31])).
% 0.57/0.48  thf(c_0_40, plain, ~((induction)), inference(sr,[status(thm)],[inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_21]), c_0_21]), c_0_21])])]), c_0_33])).
% 0.57/0.48  thf(c_0_41, 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_34, c_0_21]), c_0_21]), c_0_21]), c_0_35]), c_0_16]), c_0_29])]), c_0_33]), c_0_36])).
% 0.57/0.48  thf(c_0_42, plain, ![X12:term > $o]:(((epred23_0 @ id @ one @ id)|(X12 @ one)|(hoasinduction_lem0))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_21]), c_0_21])).
% 0.57/0.48  thf(c_0_43, negated_conjecture, ~(((hoasinduction_lem0)<=>![X11:subst > term > subst > $o]:(?[X12:term > $o]:((hoasinduction_p_and_p_prime @ X11 @ X12))))), inference(assume_negation,[status(cth)],[hoasinduction_lem0])).
% 0.57/0.48  thf(c_0_44, plain, ![X12:term > $o]:(((hoasinduction_lem0)|~((epred23_0 @ id @ one @ id))|~((X12 @ one)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_21]), c_0_21])).
% 0.57/0.48  thf(c_0_45, plain, ![X5:subst, X9:subst]:(((X5)=(X9))), inference(spm,[status(thm)],[c_0_35, c_0_35])).
% 0.57/0.48  thf(c_0_46, plain, ![X1:term]:(~((epred25_0 @ X1))), inference(sr,[status(thm)],[c_0_39, c_0_40])).
% 0.57/0.48  thf(c_0_47, plain, ![X12:term > $o, X1:term]:(((epred23_0 @ id @ one @ id)|(hoasinduction_lem0)|(X12 @ X1))), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 0.57/0.48  thf(c_0_48, negated_conjecture, ![X1296:term > $o, X1297:subst > term > subst > $o]:(((~(hoasinduction_lem0)|~(hoasinduction_p_and_p_prime @ epred54_0 @ X1296))&((hoasinduction_lem0)|(hoasinduction_p_and_p_prime @ X1297 @ (epred55_1 @ X1297))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])])).
% 0.57/0.48  thf(c_0_49, plain, ![X11:subst > term > subst > $o, X12:term > $o]:(((hoasinduction_p_and_p_prime @ X11 @ X12)|~((X12 @ (esk3_2 @ X11 @ X12)))|~((X11 @ id @ (esk3_2 @ X11 @ X12) @ id)))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.48  thf(c_0_50, plain, ![X5:subst, X12:term > $o]:(((hoasinduction_lem0)|~((epred23_0 @ X5 @ one @ X5))|~((X12 @ one)))), inference(spm,[status(thm)],[c_0_44, c_0_45])).
% 0.57/0.48  thf(c_0_51, plain, ((epred23_0 @ id @ one @ id)|(hoasinduction_lem0)), inference(spm,[status(thm)],[c_0_46, c_0_47])).
% 0.57/0.48  thf(c_0_52, negated_conjecture, ![X12:term > $o]:((~((hoasinduction_lem0))|~((hoasinduction_p_and_p_prime @ epred54_0 @ X12)))), inference(split_conjunct,[status(thm)],[c_0_48])).
% 0.57/0.48  thf(c_0_53, plain, ![X11:subst > term > subst > $o, X12:term > $o]:(((hoasinduction_p_and_p_prime @ X11 @ X12)|~((X11 @ id @ one @ id))|~((X12 @ one)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_21]), c_0_21])).
% 0.57/0.48  thf(c_0_54, 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])).
% 0.57/0.48  thf(c_0_55, negated_conjecture, ![X11:subst > term > subst > $o]:(((hoasinduction_lem0)|(hoasinduction_p_and_p_prime @ X11 @ (epred55_1 @ X11)))), inference(split_conjunct,[status(thm)],[c_0_48])).
% 0.57/0.48  thf(c_0_56, plain, ![X12:term > $o]:(((hoasinduction_lem0)|~((X12 @ one)))), inference(spm,[status(thm)],[c_0_50, c_0_51])).
% 0.57/0.48  thf(c_0_57, negated_conjecture, ![X12:term > $o]:((~((epred54_0 @ id @ one @ id))|~((X12 @ one))|~((hoasinduction_lem0)))), inference(spm,[status(thm)],[c_0_52, c_0_53])).
% 0.57/0.48  thf(c_0_58, negated_conjecture, ![X11:subst > term > subst > $o, X1:term]:(((epred55_1 @ X11 @ X1)|(hoasinduction_lem0)|~((X11 @ id @ X1 @ id)))), inference(spm,[status(thm)],[c_0_54, c_0_55])).
% 0.57/0.48  thf(c_0_59, plain, ![X12:term > $o, X1:term]:(((hoasinduction_lem0)|~((X12 @ X1)))), inference(spm,[status(thm)],[c_0_56, c_0_21])).
% 0.57/0.48  thf(c_0_60, 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])).
% 0.57/0.48  thf(c_0_61, negated_conjecture, ![X5:subst, X12:term > $o]:((~((epred54_0 @ X5 @ one @ X5))|~((X12 @ one))|~((hoasinduction_lem0)))), inference(spm,[status(thm)],[c_0_57, c_0_45])).
% 0.57/0.48  thf(c_0_62, negated_conjecture, ![X11:subst > term > subst > $o, X1:term]:(((hoasinduction_lem0)|~((X11 @ id @ X1 @ id)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_58]), c_0_59])).
% 0.57/0.48  thf(c_0_63, 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_60, c_0_21]), c_0_21])).
% 0.57/0.48  thf(c_0_64, negated_conjecture, ![X12:term > $o, X5:subst, X1:term]:((~((epred54_0 @ X5 @ X1 @ X5))|~((X12 @ X1))|~((hoasinduction_lem0)))), inference(spm,[status(thm)],[c_0_61, c_0_21])).
% 0.57/0.48  thf(c_0_65, negated_conjecture, (hoasinduction_lem0), inference(spm,[status(thm)],[c_0_62, c_0_51])).
% 0.57/0.48  thf(c_0_66, negated_conjecture, ![X12:term > $o]:(((epred54_0 @ id @ one @ id)|(X12 @ one)|~((hoasinduction_lem0)))), inference(spm,[status(thm)],[c_0_52, c_0_63])).
% 0.57/0.48  thf(c_0_67, negated_conjecture, ![X12:term > $o, X5:subst, X1:term]:((~((epred54_0 @ X5 @ X1 @ X5))|~((X12 @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64, c_0_65])])).
% 0.57/0.48  thf(c_0_68, negated_conjecture, ![X12:term > $o]:(((epred54_0 @ id @ one @ id)|(X12 @ one))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66, c_0_65])])).
% 0.57/0.48  thf(c_0_69, negated_conjecture, ($false), inference(flex_resolve,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68])]), ['proof']).
% 0.57/0.48  % SZS output end CNFRefutation
% 0.57/0.48  % Parsed axioms                        : 132
% 0.57/0.48  % Removed by relevancy pruning/SinE    : 0
% 0.57/0.48  % Initial clauses                      : 1233
% 0.57/0.48  % Removed in clause preprocessing      : 130
% 0.57/0.48  % Initial clauses in saturation        : 1103
% 0.57/0.48  % Processed clauses                    : 1511
% 0.57/0.48  % ...of these trivial                  : 690
% 0.57/0.48  % ...subsumed                          : 207
% 0.57/0.48  % ...remaining for further processing  : 613
% 0.57/0.48  % Other redundant clauses eliminated   : 0
% 0.57/0.48  % Clauses deleted for lack of memory   : 0
% 0.57/0.48  % Backward-subsumed                    : 113
% 0.57/0.48  % Backward-rewritten                   : 138
% 0.57/0.48  % Generated clauses                    : 965
% 0.57/0.48  % ...of the previous two non-redundant : 938
% 0.57/0.48  % ...aggressively subsumed             : 0
% 0.57/0.48  % Contextual simplify-reflections      : 65
% 0.57/0.48  % Paramodulations                      : 965
% 0.57/0.48  % Factorizations                       : 0
% 0.57/0.48  % NegExts                              : 0
% 0.57/0.48  % Equation resolutions                 : 0
% 0.57/0.48  % Disequality decompositions           : 0
% 0.57/0.48  % Total rewrite steps                  : 11467
% 0.57/0.48  % ...of those cached                   : 10878
% 0.57/0.48  % Propositional unsat checks           : 0
% 0.57/0.48  %    Propositional check models        : 0
% 0.57/0.48  %    Propositional check unsatisfiable : 0
% 0.57/0.48  %    Propositional clauses             : 0
% 0.57/0.48  %    Propositional clauses after purity: 0
% 0.57/0.48  %    Propositional unsat core size     : 0
% 0.57/0.48  %    Propositional preprocessing time  : 0.000
% 0.57/0.48  %    Propositional encoding time       : 0.000
% 0.57/0.48  %    Propositional solver time         : 0.000
% 0.57/0.48  %    Success case prop preproc time    : 0.000
% 0.57/0.48  %    Success case prop encoding time   : 0.000
% 0.57/0.48  %    Success case prop solver time     : 0.000
% 0.57/0.48  % Current number of processed clauses  : 175
% 0.57/0.48  %    Positive orientable unit clauses  : 108
% 0.57/0.48  %    Positive unorientable unit clauses: 4
% 0.57/0.48  %    Negative unit clauses             : 8
% 0.57/0.48  %    Non-unit-clauses                  : 55
% 0.57/0.48  % Current number of unprocessed clauses: 404
% 0.57/0.48  % ...number of literals in the above   : 1269
% 0.57/0.48  % Current number of archived formulas  : 0
% 0.57/0.48  % Current number of archived clauses   : 438
% 0.57/0.48  % Clause-clause subsumption calls (NU) : 23486
% 0.57/0.48  % Rec. Clause-clause subsumption calls : 14654
% 0.57/0.48  % Non-unit clause-clause subsumptions  : 473
% 0.57/0.48  % Unit Clause-clause subsumption calls : 2847
% 0.57/0.48  % Rewrite failures with RHS unbound    : 0
% 0.57/0.48  % BW rewrite match attempts            : 2608
% 0.57/0.48  % BW rewrite match successes           : 112
% 0.57/0.48  % Condensation attempts                : 1517
% 0.57/0.48  % Condensation successes               : 132
% 0.57/0.48  % Termbank termtop insertions          : 140284
% 0.57/0.48  % Search garbage collected termcells   : 22386
% 0.57/0.48  
% 0.57/0.48  % -------------------------------------------------
% 0.57/0.48  % User time                : 0.198 s
% 0.57/0.48  % System time              : 0.012 s
% 0.57/0.48  % Total time               : 0.210 s
% 0.57/0.48  % Maximum resident set size: 8000 pages
% 0.57/0.48  
% 0.57/0.48  % -------------------------------------------------
% 0.57/0.48  % User time                : 0.307 s
% 0.57/0.48  % System time              : 0.033 s
% 0.57/0.48  % Total time               : 0.340 s
% 0.57/0.48  % Maximum resident set size: 5376 pages
% 0.57/0.48  % E exiting
%------------------------------------------------------------------------------