0.00/0.02 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.06 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yHYjoUTaUS true 0.11/0.37 % Computer : n024.cluster.edu 0.11/0.37 % Model : x86_64 x86_64 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.37 % Memory : 8046.5625MB 0.11/0.37 % OS : Linux 6.8.0-71-generic 0.11/0.37 % CPULimit : 1440 0.11/0.37 % WCLimit : 180 0.11/0.37 % DateTime : Mon Jul 27 07:54:00 UTC 2026 0.11/0.37 % CPUTime : 0.11/0.37 % Running portfolio for 1440 s 0.11/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.38 % Number of cores: 8 0.11/0.38 % Python version: Python 3.12.3 0.11/0.38 % Running in HO mode 0.41/0.66 % Total configuration time : 828 0.41/0.66 % Estimated wc time : 1656 0.41/0.66 % Estimated cpu time (8 cpus) : 207.0 0.43/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.43/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.43/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.43/0.79 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.44/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.44/0.85 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.44/0.87 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.45/0.90 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 110.06/18.20 % Solved by lams/40_c.s.sh. 110.06/18.20 % done 309 iterations in 17.253s 110.06/18.20 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 110.06/18.20 % SZS output start Refutation 110.06/18.20 thf(d_term_type, type, d_term: $tType). 110.06/18.20 thf(term_type, type, term: $tType). 110.06/18.20 thf(subst_type, type, subst: $tType). 110.06/18.20 thf(d_subst_type, type, d_subst: $tType). 110.06/18.20 thf(axmap_type, type, axmap: $o). 110.06/18.20 thf(zip_tseitin_34_type, type, zip_tseitin_34: term > term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_2_type, type, zip_tseitin_2: subst > term > (term > $o) > 110.06/18.20 (term > $o) > $o). 110.06/18.20 thf(hoasinduction_lem3a_type, type, hoasinduction_lem3a: $o). 110.06/18.20 thf(hoasapnotvar_gthm_type, type, hoasapnotvar_gthm: $o). 110.06/18.20 thf(zip_tseitin_18_type, type, zip_tseitin_18: $o). 110.06/18.20 thf(zip_tseitin_23_type, type, zip_tseitin_23: term > 110.06/18.20 (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(pushprop_lthm_orig_type, type, pushprop_lthm_orig: $o). 110.06/18.20 thf(termmset_gthm_type, type, termmset_gthm: $o). 110.06/18.20 thf(axclos_type, type, axclos: $o). 110.06/18.20 thf(lam_type, type, lam: term > term). 110.06/18.20 thf(lamnotap_type, type, lamnotap: $o). 110.06/18.20 thf(hoasinduction_lem3aa_type, type, hoasinduction_lem3aa: $o). 110.06/18.20 thf(zip_tseitin_32_type, type, zip_tseitin_32: subst > subst > term > 110.06/18.20 subst > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(hoaslamnotvar_gthm_type, type, hoaslamnotvar_gthm: $o). 110.06/18.20 thf(zip_tseitin_65_type, type, zip_tseitin_65: term > (term > $o) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(axvarcons_type, type, axvarcons: $o). 110.06/18.20 thf(zip_tseitin_28_type, type, zip_tseitin_28: subst > subst > term > 110.06/18.20 subst > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(hoaslamnotvar_lthm_type, type, hoaslamnotvar_lthm: $o). 110.06/18.20 thf(zip_tseitin_13_type, type, zip_tseitin_13: term > (term > $o) > $o). 110.06/18.20 thf(d2term_type, type, d2term: d_term > term). 110.06/18.20 thf(zip_tseitin_71_type, type, zip_tseitin_71: $o). 110.06/18.20 thf(zip_tseitin_110_type, type, zip_tseitin_110: $o). 110.06/18.20 thf(zip_tseitin_12_type, type, zip_tseitin_12: term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_3_type, type, zip_tseitin_3: term > term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_76_type, type, zip_tseitin_76: term > term > 110.06/18.20 (subst > term > term) > $o). 110.06/18.20 thf(hoasinduction_no_psi_cond_lthm_type, type, hoasinduction_no_psi_cond_lthm: 110.06/18.20 $o). 110.06/18.20 thf(zip_tseitin_22_type, type, zip_tseitin_22: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_107_type, type, zip_tseitin_107: term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_29_type, type, zip_tseitin_29: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_58_type, type, zip_tseitin_58: $o). 110.06/18.20 thf(sk__476_type, type, sk__476: (subst > term > term) > term). 110.06/18.20 thf(zip_tseitin_93_type, type, zip_tseitin_93: term > (term > $o) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(substmonoid_type, type, substmonoid: $o). 110.06/18.20 thf(zip_tseitin_53_type, type, zip_tseitin_53: $o). 110.06/18.20 thf(zip_tseitin_100_type, type, zip_tseitin_100: $o). 110.06/18.20 thf(zip_tseitin_102_type, type, zip_tseitin_102: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_31_type, type, zip_tseitin_31: term > term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(hoasinduction_lem3a_gthm_type, type, hoasinduction_lem3a_gthm: $o). 110.06/18.20 thf(substmonoid_gthm_type, type, substmonoid_gthm: $o). 110.06/18.20 thf(d_id_type, type, d_id: d_subst). 110.06/18.20 thf(pushprop_gthm_type, type, pushprop_gthm: $o). 110.06/18.20 thf(zip_tseitin_14_type, type, zip_tseitin_14: subst > term > (term > $o) > $o). 110.06/18.20 thf(sk__475_type, type, sk__475: (subst > term > term) > subst). 110.06/18.20 thf(hoasinduction_lem3v2_type, type, hoasinduction_lem3v2: $o). 110.06/18.20 thf(zip_tseitin_77_type, type, zip_tseitin_77: term > term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_80_type, type, zip_tseitin_80: $o). 110.06/18.20 thf(zip_tseitin_111_type, type, zip_tseitin_111: $o). 110.06/18.20 thf(pushprop_lem1v2_type, type, pushprop_lem1v2: $o). 110.06/18.20 thf(zip_tseitin_66_type, type, zip_tseitin_66: (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(push_type, type, push: term > subst > subst). 110.06/18.20 thf(zip_tseitin_39_type, type, zip_tseitin_39: $o). 110.06/18.20 thf(zip_tseitin_63_type, type, zip_tseitin_63: term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_67_type, type, zip_tseitin_67: term > term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_16_type, type, zip_tseitin_16: $o). 110.06/18.20 thf(hoaslamnotap_lthm_type, type, hoaslamnotap_lthm: $o). 110.06/18.20 thf(axshiftcons_type, type, axshiftcons: $o). 110.06/18.20 thf(zip_tseitin_41_type, type, zip_tseitin_41: term > term > $o). 110.06/18.20 thf(zip_tseitin_10_type, type, zip_tseitin_10: term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_21_type, type, zip_tseitin_21: term > 110.06/18.20 (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_89_type, type, zip_tseitin_89: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_62_type, type, zip_tseitin_62: $o). 110.06/18.20 thf(zip_tseitin_33_type, type, zip_tseitin_33: term > term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_0_type, type, zip_tseitin_0: term > (term > $o) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(sk__44_type, type, sk__44: (subst > term > term) > subst). 110.06/18.20 thf(zip_tseitin_91_type, type, zip_tseitin_91: $o). 110.06/18.20 thf(zip_tseitin_119_type, type, zip_tseitin_119: $o). 110.06/18.20 thf(hoasinduction_lem1v2_type, type, hoasinduction_lem1v2: $o). 110.06/18.20 thf(hoasapinj1_lthm_type, type, hoasapinj1_lthm: $o). 110.06/18.20 thf(sk__434_type, type, sk__434: term). 110.06/18.20 thf(zip_tseitin_83_type, type, zip_tseitin_83: term > (term > $o) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(hoasapinj1_type, type, hoasapinj1: $o). 110.06/18.20 thf(hoasinduction_p_and_p_prime_type, type, hoasinduction_p_and_p_prime: 110.06/18.20 (subst > term > subst > $o) > (term > $o) > $o). 110.06/18.20 thf(axapp_type, type, axapp: $o). 110.06/18.20 thf(hoasinduction_lem3_lthm_type, type, hoasinduction_lem3_lthm: $o). 110.06/18.20 thf(hoasinduction_lem3v2_lthm_type, type, hoasinduction_lem3v2_lthm: $o). 110.06/18.20 thf(pushprop_lem1v2_gthm_type, type, pushprop_lem1v2_gthm: $o). 110.06/18.20 thf(shinj_type, type, shinj: $o). 110.06/18.20 thf(zip_tseitin_120_type, type, zip_tseitin_120: $o). 110.06/18.20 thf(zip_tseitin_85_type, type, zip_tseitin_85: $o). 110.06/18.20 thf(zip_tseitin_6_type, type, zip_tseitin_6: term > (term > $o) > $o). 110.06/18.20 thf(hoasap_type, type, hoasap: subst > term > subst > term > term). 110.06/18.20 thf(hoasinduction_gthm_type, type, hoasinduction_gthm: $o). 110.06/18.20 thf(hoasinduction_lem3b_type, type, hoasinduction_lem3b: $o). 110.06/18.20 thf(hoaslaminj_type, type, hoaslaminj: $o). 110.06/18.20 thf(induction2_lthm_type, type, induction2_lthm: $o). 110.06/18.20 thf(zip_tseitin_44_type, type, zip_tseitin_44: $o). 110.06/18.20 thf(zip_tseitin_19_type, type, zip_tseitin_19: term > term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(sk__478_type, type, sk__478: (subst > term > subst > $o) > 110.06/18.20 (subst > term > term) > term). 110.06/18.20 thf(zip_tseitin_84_type, type, zip_tseitin_84: $o). 110.06/18.20 thf(zip_tseitin_115_type, type, zip_tseitin_115: term > term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_8_type, type, zip_tseitin_8: term > term > term > term > $o). 110.06/18.20 thf(zip_tseitin_87_type, type, zip_tseitin_87: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(sk__387_type, type, sk__387: term). 110.06/18.20 thf(induction2_gthm_type, type, induction2_gthm: $o). 110.06/18.20 thf(hoasinduction_lem2_gthm_type, type, hoasinduction_lem2_gthm: $o). 110.06/18.20 thf(one_type, type, one: term). 110.06/18.20 thf(pushprop_lem2v2_lthm_type, type, pushprop_lem2v2_lthm: $o). 110.06/18.20 thf(zip_tseitin_81_type, type, zip_tseitin_81: $o). 110.06/18.20 thf(id_type, type, id: subst). 110.06/18.20 thf(comp_type, type, comp: subst > subst > subst). 110.06/18.20 thf(hoaslamnotap_type, type, hoaslamnotap: $o). 110.06/18.20 thf(zip_tseitin_48_type, type, zip_tseitin_48: term > term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_97_type, type, zip_tseitin_97: term > term > (term > $o) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_78_type, type, zip_tseitin_78: (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(induction2_type, type, induction2: $o). 110.06/18.20 thf(axvarid_type, type, axvarid: $o). 110.06/18.20 thf(axvarshift_type, type, axvarshift: $o). 110.06/18.20 thf(hoaslamnotap_gthm_type, type, hoaslamnotap_gthm: $o). 110.06/18.20 thf(induction2lem_type, type, induction2lem: $o). 110.06/18.20 thf(hoasinduction_lem1_gthm_type, type, hoasinduction_lem1_gthm: $o). 110.06/18.20 thf(sh_type, type, sh: subst). 110.06/18.20 thf(hoasinduction_lem2v2_type, type, hoasinduction_lem2v2: $o). 110.06/18.20 thf(zip_tseitin_114_type, type, zip_tseitin_114: term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_1_type, type, zip_tseitin_1: term > subst > term > 110.06/18.20 (term > $o) > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_122_type, type, zip_tseitin_122: (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_64_type, type, zip_tseitin_64: term > (term > $o) > $o). 110.06/18.20 thf(laminj_type, type, laminj: $o). 110.06/18.20 thf(sk__42_type, type, sk__42: (subst > term > term) > subst). 110.06/18.20 thf(zip_tseitin_54_type, type, zip_tseitin_54: $o). 110.06/18.20 thf(hoasinduction_lem3aa_lthm_type, type, hoasinduction_lem3aa_lthm: $o). 110.06/18.20 thf(ulamvarind_type, type, ulamvarind: $o). 110.06/18.20 thf(zip_tseitin_121_type, type, zip_tseitin_121: term > term > $o). 110.06/18.20 thf(pushprop_lem2v2_type, type, pushprop_lem2v2: $o). 110.06/18.20 thf(zip_tseitin_56_type, type, zip_tseitin_56: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_74_type, type, zip_tseitin_74: term > (term > $o) > $o). 110.06/18.20 thf(sk__477_type, type, sk__477: (subst > term > term) > subst). 110.06/18.20 thf(zip_tseitin_47_type, type, zip_tseitin_47: term > term > $o). 110.06/18.20 thf(zip_tseitin_70_type, type, zip_tseitin_70: $o). 110.06/18.20 thf(hoasinduction_lthm_3_type, type, hoasinduction_lthm_3: $o). 110.06/18.20 thf(zip_tseitin_9_type, type, zip_tseitin_9: term > term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_106_type, type, zip_tseitin_106: term > subst > 110.06/18.20 (subst > term > term) > 110.06/18.20 (subst > term > term) > $o). 110.06/18.20 thf(zip_tseitin_59_type, type, zip_tseitin_59: term > (term > $o) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(hoasinduction_lem3v2_f_lthm_type, type, hoasinduction_lem3v2_f_lthm: $o). 110.06/18.20 thf(zip_tseitin_109_type, type, zip_tseitin_109: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_55_type, type, zip_tseitin_55: $o). 110.06/18.20 thf(zip_tseitin_96_type, type, zip_tseitin_96: $o). 110.06/18.20 thf(apinj2_type, type, apinj2: $o). 110.06/18.20 thf(hoasapinj2_lthm_type, type, hoasapinj2_lthm: $o). 110.06/18.20 thf(zip_tseitin_24_type, type, zip_tseitin_24: (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(ulamvarsh_type, type, ulamvarsh: $o). 110.06/18.20 thf(zip_tseitin_94_type, type, zip_tseitin_94: term > term > term > term > $o). 110.06/18.20 thf(hoasinduction_lem3v2a_lthm_type, type, hoasinduction_lem3v2a_lthm: $o). 110.06/18.20 thf(hoasinduction_lem3a_lthm_type, type, hoasinduction_lem3a_lthm: $o). 110.06/18.20 thf(pushprop_lthm_type, type, pushprop_lthm: $o). 110.06/18.20 thf(zip_tseitin_42_type, type, zip_tseitin_42: term > subst > 110.06/18.20 (subst > term > term) > 110.06/18.20 (subst > term > term) > $o). 110.06/18.20 thf(hoasapinj1_gthm_type, type, hoasapinj1_gthm: $o). 110.06/18.20 thf(hoasinduction_lem0_lthm_type, type, hoasinduction_lem0_lthm: $o). 110.06/18.20 thf(hoasinduction_lem3b_lthm_type, type, hoasinduction_lem3b_lthm: $o). 110.06/18.20 thf(zip_tseitin_4_type, type, zip_tseitin_4: term > subst > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_52_type, type, zip_tseitin_52: term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_86_type, type, zip_tseitin_86: (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_5_type, type, zip_tseitin_5: term > term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_68_type, type, zip_tseitin_68: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(lamnotvar_type, type, lamnotvar: $o). 110.06/18.20 thf(apnotvar_type, type, apnotvar: $o). 110.06/18.20 thf(zip_tseitin_95_type, type, zip_tseitin_95: term > term > term > term > $o). 110.06/18.20 thf(zip_tseitin_117_type, type, zip_tseitin_117: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_46_type, type, zip_tseitin_46: term > subst > term > 110.06/18.20 (term > $o) > (term > $o) > $o). 110.06/18.20 thf(pushprop_p_and_p_prime_type, type, pushprop_p_and_p_prime: term > 110.06/18.20 subst > 110.06/18.20 (term > $o) > 110.06/18.20 (term > $o) > $o). 110.06/18.20 thf(hoasapinj2_gthm_type, type, hoasapinj2_gthm: $o). 110.06/18.20 thf(zip_tseitin_104_type, type, zip_tseitin_104: $o). 110.06/18.20 thf(zip_tseitin_50_type, type, zip_tseitin_50: subst > term > (term > $o) > $o). 110.06/18.20 thf(d_one_type, type, d_one: d_term). 110.06/18.20 thf(pushprop_lem1_type, type, pushprop_lem1: $o). 110.06/18.20 thf(pushprop_type, type, pushprop: $o). 110.06/18.20 thf(hoasinduction_lem1_lthm_type, type, hoasinduction_lem1_lthm: $o). 110.06/18.20 thf(hoasinduction_lem3_gthm_type, type, hoasinduction_lem3_gthm: $o). 110.06/18.20 thf(sub_type, type, sub: term > subst > term). 110.06/18.20 thf(zip_tseitin_45_type, type, zip_tseitin_45: $o). 110.06/18.20 thf(zip_tseitin_79_type, type, zip_tseitin_79: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_27_type, type, zip_tseitin_27: subst > subst > term > 110.06/18.20 subst > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(apinj1_type, type, apinj1: $o). 110.06/18.20 thf(zip_tseitin_75_type, type, zip_tseitin_75: term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_98_type, type, zip_tseitin_98: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(axidl_type, type, axidl: $o). 110.06/18.20 thf(hoasinduction_type, type, hoasinduction: $o). 110.06/18.20 thf(ap_type, type, ap: term > term > term). 110.06/18.20 thf(termmset_type, type, termmset: $o). 110.06/18.20 thf(zip_tseitin_25_type, type, zip_tseitin_25: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_51_type, type, zip_tseitin_51: term > term > (term > $o) > $o). 110.06/18.20 thf(hoasapinj2_type, type, hoasapinj2: $o). 110.06/18.20 thf(zip_tseitin_26_type, type, zip_tseitin_26: (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(hoasinduction_lem1_type, type, hoasinduction_lem1: $o). 110.06/18.20 thf(pushprop_lem3v2_lthm_type, type, pushprop_lem3v2_lthm: $o). 110.06/18.20 thf(hoasinduction_lem3v2a_type, type, hoasinduction_lem3v2a: $o). 110.06/18.20 thf(hoasapnotvar_type, type, hoasapnotvar: $o). 110.06/18.20 thf(var_type, type, var: term > $o). 110.06/18.20 thf(pushprop_lem1_lthm_type, type, pushprop_lem1_lthm: $o). 110.06/18.20 thf(induction2lem_lthm_type, type, induction2lem_lthm: $o). 110.06/18.20 thf(pushprop_lem0_lthm_type, type, pushprop_lem0_lthm: $o). 110.06/18.20 thf(axassoc_type, type, axassoc: $o). 110.06/18.20 thf(hoaslamnotvar_type, type, hoaslamnotvar: $o). 110.06/18.20 thf(sk__43_type, type, sk__43: (subst > term > term) > term). 110.06/18.20 thf(zip_tseitin_112_type, type, zip_tseitin_112: $o). 110.06/18.20 thf(hoaslam_type, type, hoaslam: subst > (subst > term > term) > term). 110.06/18.20 thf(hoasinduction_lem2_lthm_type, type, hoasinduction_lem2_lthm: $o). 110.06/18.20 thf(zip_tseitin_103_type, type, zip_tseitin_103: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(pushprop_lem3v2_type, type, pushprop_lem3v2: $o). 110.06/18.20 thf(hoasinduction_lem3b_gthm_type, type, hoasinduction_lem3b_gthm: $o). 110.06/18.20 thf(pushprop_lem0_type, type, pushprop_lem0: $o). 110.06/18.20 thf(sk__473_type, type, sk__473: subst > d_subst). 110.06/18.20 thf(hoaslaminj_gthm_type, type, hoaslaminj_gthm: $o). 110.06/18.20 thf(sk__433_type, type, sk__433: term). 110.06/18.20 thf(zip_tseitin_90_type, type, zip_tseitin_90: $o). 110.06/18.20 thf(zip_tseitin_108_type, type, zip_tseitin_108: term > (term > $o) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_113_type, type, zip_tseitin_113: $o). 110.06/18.20 thf(zip_tseitin_61_type, type, zip_tseitin_61: term > (term > $o) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(hoasinduction_lem3_type, type, hoasinduction_lem3: $o). 110.06/18.20 thf(hoasinduction_lem2_type, type, hoasinduction_lem2: $o). 110.06/18.20 thf(hoasinduction_lem0_type, type, hoasinduction_lem0: $o). 110.06/18.20 thf(zip_tseitin_20_type, type, zip_tseitin_20: term > 110.06/18.20 (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(hoaslaminj_lthm_type, type, hoaslaminj_lthm: $o). 110.06/18.20 thf(hoasinduction_lem3aaa_type, type, hoasinduction_lem3aaa: $o). 110.06/18.20 thf(axidr_type, type, axidr: $o). 110.06/18.20 thf(zip_tseitin_57_type, type, zip_tseitin_57: $o). 110.06/18.20 thf(hoasapnotvar_lthm_type, type, hoasapnotvar_lthm: $o). 110.06/18.20 thf(zip_tseitin_40_type, type, zip_tseitin_40: $o). 110.06/18.20 thf(zip_tseitin_92_type, type, zip_tseitin_92: (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_69_type, type, zip_tseitin_69: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_72_type, type, zip_tseitin_72: $o). 110.06/18.20 thf(hoasinduction_lem3v2_f_type, type, hoasinduction_lem3v2_f: $o). 110.06/18.20 thf(sk__479_type, type, sk__479: subst > term > subst > $o). 110.06/18.20 thf(zip_tseitin_30_type, type, zip_tseitin_30: subst > subst > term > 110.06/18.20 subst > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(pushprop_lem2v2_gthm_type, type, pushprop_lem2v2_gthm: $o). 110.06/18.20 thf(substmonoid_lthm_type, type, substmonoid_lthm: $o). 110.06/18.20 thf(axabs_type, type, axabs: $o). 110.06/18.20 thf(hoasinduction_lem3v2_gthm_type, type, hoasinduction_lem3v2_gthm: $o). 110.06/18.20 thf(zip_tseitin_123_type, type, zip_tseitin_123: term > term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_17_type, type, zip_tseitin_17: $o). 110.06/18.20 thf(zip_tseitin_35_type, type, zip_tseitin_35: term > (term > $o) > $o). 110.06/18.20 thf(hoasvar_type, type, hoasvar: subst > term > subst > $o). 110.06/18.20 thf(sk__480_type, type, sk__480: term). 110.06/18.20 thf(zip_tseitin_101_type, type, zip_tseitin_101: $o). 110.06/18.20 thf(hoasinduction_lem2v2_gthm_type, type, hoasinduction_lem2v2_gthm: $o). 110.06/18.20 thf(zip_tseitin_37_type, type, zip_tseitin_37: term > term > term > term > $o). 110.06/18.20 thf(zip_tseitin_116_type, type, zip_tseitin_116: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(ulamvar1_type, type, ulamvar1: $o). 110.06/18.20 thf(sk__386_type, type, sk__386: subst > term > subst > $o). 110.06/18.20 thf(zip_tseitin_11_type, type, zip_tseitin_11: term > (term > $o) > $o). 110.06/18.20 thf(hoasinduction_lem1v2_gthm_type, type, hoasinduction_lem1v2_gthm: $o). 110.06/18.20 thf(induction_type, type, induction: $o). 110.06/18.20 thf(zip_tseitin_99_type, type, zip_tseitin_99: term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_7_type, type, zip_tseitin_7: subst > term > (term > $o) > $o). 110.06/18.20 thf(pushprop_lem1v2_lthm_type, type, pushprop_lem1v2_lthm: $o). 110.06/18.20 thf(axscons_type, type, axscons: $o). 110.06/18.20 thf(zip_tseitin_43_type, type, zip_tseitin_43: $o). 110.06/18.20 thf(zip_tseitin_49_type, type, zip_tseitin_49: term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_105_type, type, zip_tseitin_105: $o). 110.06/18.20 thf(pushprop_lem1_gthm_type, type, pushprop_lem1_gthm: $o). 110.06/18.20 thf(sk__41_type, type, sk__41: (subst > term > subst > $o) > 110.06/18.20 (subst > term > term) > term). 110.06/18.20 thf(zip_tseitin_15_type, type, zip_tseitin_15: $o). 110.06/18.20 thf(zip_tseitin_60_type, type, zip_tseitin_60: (subst > term > term) > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(zip_tseitin_88_type, type, zip_tseitin_88: term > term > 110.06/18.20 (subst > term > subst > $o) > $o). 110.06/18.20 thf(sk__474_type, type, sk__474: term > d_term). 110.06/18.20 thf(induction2lem_gthm_type, type, induction2lem_gthm: $o). 110.06/18.20 thf(pushprop_lem0_gthm_type, type, pushprop_lem0_gthm: $o). 110.06/18.20 thf(termmset_lthm_type, type, termmset_lthm: $o). 110.06/18.20 thf(d2subst_type, type, d2subst: d_subst > subst). 110.06/18.20 thf(hoasinduction_lthm_type, type, hoasinduction_lthm: $o). 110.06/18.20 thf(hoasinduction_no_psi_cond_type, type, hoasinduction_no_psi_cond: $o). 110.06/18.20 thf(zip_tseitin_82_type, type, zip_tseitin_82: $o). 110.06/18.20 thf(zip_tseitin_118_type, type, zip_tseitin_118: $o). 110.06/18.20 thf(zip_tseitin_73_type, type, zip_tseitin_73: $o). 110.06/18.20 thf(zip_tseitin_36_type, type, zip_tseitin_36: term > (term > $o) > $o). 110.06/18.20 thf(zip_tseitin_38_type, type, zip_tseitin_38: term > term > term > term > $o). 110.06/18.20 thf(alg444_1, axiom, 110.06/18.20 (( ![T:term]: ( ?[DT:d_term]: ( ( T ) = ( d2term @ DT ) ) ) ) & 110.06/18.20 ( ![S:subst]: ( ?[DS:d_subst]: ( ( S ) = ( d2subst @ DS ) ) ) ) & 110.06/18.20 ( ![DS:d_subst]: ( ( DS ) = ( d_id ) ) ) & 110.06/18.20 ( ![DS1:d_subst,DS2:d_subst]: 110.06/18.20 ( ( ( d2subst @ DS1 ) = ( d2subst @ DS2 ) ) => ( ( DS1 ) = ( DS2 ) ) ) ) & 110.06/18.20 ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 110.06/18.20 ( ( lam @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 110.06/18.20 ( ( id ) = ( d2subst @ d_id ) ) & 110.06/18.20 ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 110.06/18.20 ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 110.06/18.20 ( ![Bound_variable_4913:subst,Bound_variable_4915:( subst > term > term )]: 110.06/18.20 ( ( hoaslam @ Bound_variable_4913 @ Bound_variable_4915 ) = 110.06/18.20 ( d2term @ d_one ) ) ) & 110.06/18.20 ( ![P:( subst > term > subst > $o ),Q:( term > $o )]: 110.06/18.20 ( ( hoasinduction_p_and_p_prime @ P @ Q ) <=> 110.06/18.20 ( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) & 110.06/18.20 ( ~( var @ ( d2term @ d_one ) ) ) & 110.06/18.20 ( ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]: 110.06/18.20 ( ( ~( ![X:term]: 110.06/18.20 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) | 110.06/18.20 ( Q @ one ) | ( ~( P @ A ) ) ) ) <=> 110.06/18.20 ( pushprop_lem1v2 ) ) & 110.06/18.20 ( pushprop_lem0_gthm ) & ( hoasinduction_lem1v2 ) & 110.06/18.20 ( ( induction2lem ) <=> 110.06/18.20 ( ![P:( term > $o ),Bound_variable_2340:term,Bound_variable_2342:subst]: 110.06/18.20 ( ( ~( ![A:term,B:term]: 110.06/18.20 ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | ( ~( P @ A ) ) ) ) ) | 110.06/18.20 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( var @ B ) ) | ( P @ ( sub @ B @ Bound_variable_2342 ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ B ) ) | 110.06/18.20 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) | 110.06/18.20 ( P @ ( lam @ A ) ) ) ) ) ) ) ) & 110.06/18.20 ( axvarshift ) & ( hoasapnotvar_gthm ) & 110.06/18.20 ( ( hoasapinj1 ) <=> 110.06/18.20 ( ![A:term,B:term,C:term,D:term]: 110.06/18.20 ( ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) | 110.06/18.20 ( ( A ) = ( B ) ) ) ) ) & 110.06/18.20 ( ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 110.06/18.20 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 110.06/18.20 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) => 110.06/18.20 ( ( ![P:( term > $o ),Bound_variable_2140:term]: 110.06/18.20 ( ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ A ) ) | ( ~( P @ B ) ) | 110.06/18.20 ( P @ ( ap @ A @ B ) ) ) ) ) | 110.06/18.20 ( P @ Bound_variable_2140 ) | 110.06/18.20 ( ~( ![A:term]: ( ( ~( P @ A ) ) | ( P @ ( lam @ A ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) ) ) => 110.06/18.20 ( ![P:( term > $o ),Bound_variable_2340:term, 110.06/18.20 Bound_variable_2342:subst]: 110.06/18.20 ( ( ~( ![A:term,B:term]: 110.06/18.20 ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | 110.06/18.20 ( ~( P @ A ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ ( lam @ A ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ B ) ) | 110.06/18.20 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) ) ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( var @ B ) ) | 110.06/18.20 ( P @ ( sub @ B @ Bound_variable_2342 ) ) ) ) ) | 110.06/18.20 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( induction2lem_lthm ) ) & 110.06/18.20 ( hoasinduction_lem3v2_gthm ) & ( apnotvar ) & ( pushprop_lthm_orig ) & 110.06/18.20 ( ( hoasinduction_lem3v2_f_lthm ) <=> 110.06/18.20 ( ![B:term]: 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ~( ![A:term,M:subst]: 110.06/18.20 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) ) & 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3171:term]: 110.06/18.20 ( ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) ) ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ 110.06/18.20 ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) | 110.06/18.20 ( ~( ![F:( subst > term > term ),Bound_variable_3149:term]: 110.06/18.20 ( ( ~( ![A:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 110.06/18.20 ( ~( ![Bound_variable_3090:subst,Bound_variable_3092:term, 110.06/18.20 Bound_variable_3094:subst]: 110.06/18.20 ( ( F @ 110.06/18.20 ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ 110.06/18.20 ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) ) = 110.06/18.20 ( sub @ 110.06/18.20 Bound_variable_3149 @ 110.06/18.20 ( push @ 110.06/18.20 ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ 110.06/18.20 ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) ) ) | 110.06/18.20 ( ~( ![Bound_variable_3072:subst,Bound_variable_3074:term, 110.06/18.20 Bound_variable_3076:subst]: 110.06/18.20 ( ( sub @ 110.06/18.20 ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ 110.06/18.20 Bound_variable_3076 ) = 110.06/18.20 ( sub @ 110.06/18.20 ( sub @ 110.06/18.20 Bound_variable_3149 @ 110.06/18.20 ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ 110.06/18.20 Bound_variable_3076 ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3aaa ) ) & 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 110.06/18.20 ( ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) ) ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ 110.06/18.20 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3aa_lthm ) ) & 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 110.06/18.20 ( ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) ) ) ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 110.06/18.20 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 110.06/18.20 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3 ) ) & 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term, 110.06/18.20 Bound_variable_3001:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 110.06/18.20 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) | 110.06/18.20 ( ~( P @ id @ Bound_variable_3001 @ id ) ) | 110.06/18.20 ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 110.06/18.20 ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.06/18.20 ( ~( P @ id @ B @ id ) ) | ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 110.06/18.20 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem2 ) ) & 110.06/18.20 ( hoasinduction_lem1 ) & ( hoaslamnotap_lthm ) & ( hoasapnotvar ) & 110.06/18.20 ( ( induction ) <=> 110.06/18.20 ( ![P:( term > $o ),Bound_variable_2140:term]: 110.06/18.20 ( ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ A ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: ( ( P @ ( lam @ A ) ) | ( ~( P @ A ) ) ) ) ) | 110.06/18.20 ( P @ Bound_variable_2140 ) | 110.06/18.20 ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) ) ) ) & 110.06/18.20 ( hoaslamnotap_gthm ) & ( hoaslamnotvar_gthm ) & 110.06/18.20 ( hoasinduction_lem3b_gthm ) & ( hoasinduction_lem3a_gthm ) & 110.06/18.20 ( pushprop_lthm ) & 110.06/18.20 ( ( apinj1 ) <=> 110.06/18.20 ( ![A:term,B:term,C:term,D:term]: 110.06/18.20 ( ( ( ap @ A @ C ) != ( ap @ B @ D ) ) | ( ( A ) = ( B ) ) ) ) ) & 110.06/18.20 ( ( hoasapinj1_lthm ) <=> 110.06/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.06/18.20 ( ( ![A:term,B:term,C:term,D:term]: 110.06/18.20 ( ( ( A ) = ( B ) ) | ( ( ap @ A @ C ) != ( ap @ B @ D ) ) ) ) => 110.06/18.20 ( ![A:term,B:term,C:term,D:term]: 110.06/18.20 ( ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) | 110.06/18.20 ( ( A ) = ( B ) ) ) ) ) ) ) & 110.06/18.20 ( ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 110.06/18.20 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 110.06/18.20 ( ( ![A:term,B:term]: 110.06/18.20 ( ( ( A ) = ( B ) ) | ( ( lam @ A ) != ( lam @ B ) ) ) ) => 110.06/18.20 ( ![F:( subst > term > term ), 110.06/18.20 Bound_variable_2547:( subst > term > term ), 110.06/18.20 Bound_variable_2549:subst,Bound_variable_2551:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N ) = 110.06/18.20 ( Bound_variable_2547 @ 110.06/18.20 ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ( lam @ ( F @ sh @ one ) ) != 110.06/18.20 ( lam @ ( Bound_variable_2547 @ sh @ one ) ) ) | 110.06/18.20 ( ( F @ Bound_variable_2549 @ Bound_variable_2551 ) = 110.06/18.20 ( Bound_variable_2547 @ 110.06/18.20 Bound_variable_2549 @ Bound_variable_2551 ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoaslaminj_lthm ) ) & 110.06/18.20 ( ( axscons ) <=> 110.06/18.20 ( ![M:subst]: 110.06/18.20 ( ( M ) = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) ) ) & 110.06/18.20 ( ( axidr ) <=> ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) ) & 110.06/18.20 ( ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]: 110.06/18.20 ( ( ~( P @ A ) ) | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) <=> 110.06/18.20 ( pushprop_lem1 ) ) & 110.06/18.20 ( ( laminj ) <=> 110.06/18.20 ( ![A:term,B:term]: 110.06/18.20 ( ( ( lam @ A ) != ( lam @ B ) ) | ( ( A ) = ( B ) ) ) ) ) & 110.06/18.20 ( ( pushprop_lem0 ) <=> 110.06/18.20 ( ![P:( term > $o ),A:term,M:subst]: 110.06/18.20 ( ~( ![Q:( term > $o )]: 110.06/18.20 ( ~( ![X:term]: 110.06/18.20 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) ) ) ) & 110.06/18.20 ( axabs ) & ( hoasinduction_lem2_lthm ) & ( hoasapinj2_gthm ) & 110.06/18.20 ( hoaslamnotvar ) & 110.06/18.20 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) <=> ( axidl ) ) & 110.06/18.20 ( ( induction2_lthm ) <=> 110.06/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.06/18.20 ( ( ![P:( term > $o ),Bound_variable_2340:term, 110.06/18.20 Bound_variable_2342:subst]: 110.06/18.20 ( ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ A ) ) ) ) ) | 110.06/18.20 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( var @ B ) ) | 110.06/18.20 ( P @ ( sub @ B @ Bound_variable_2342 ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( ![B:term]: 110.06/18.20 ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | 110.06/18.20 ( ~( P @ B ) ) ) ) ) | 110.06/18.20 ( P @ ( lam @ A ) ) ) ) ) ) ) => 110.06/18.20 ( ![P:( term > $o ),Bound_variable_2367:term]: 110.06/18.20 ( ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) ) ) ) | 110.06/18.20 ( P @ Bound_variable_2367 ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ ( lam @ A ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ B ) ) | 110.06/18.20 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) ) ) ) ) ) & 110.06/18.20 ( pushprop ) & ( hoasinduction_lem2_gthm ) & 110.06/18.20 ( ( ![B:term]: 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3b ) ) & 110.06/18.20 ( ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) & 110.06/18.20 ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) ) <=> 110.06/18.20 ( substmonoid ) ) & 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]: 110.06/18.20 ( ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3a ) ) & 110.06/18.20 ( induction2_gthm ) & ( pushprop_lem2v2_lthm ) & ( substmonoid_gthm ) & 110.06/18.20 ( pushprop_lem3v2 ) & ( pushprop_lem2v2_gthm ) & 110.06/18.20 ( ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 110.06/18.20 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 110.06/18.20 ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]: 110.06/18.20 ( ( ~( P @ A ) ) | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) ) <=> 110.06/18.20 ( pushprop_lem1_lthm ) ) & 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.06/18.20 Bound_variable_2910:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 110.06/18.20 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 110.06/18.20 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( Q @ B ) ) | 110.06/18.20 ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) ) ) ) | 110.06/18.20 ( Q @ ( lam @ Bound_variable_2910 ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 110.06/18.20 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3v2 ) ) & 110.06/18.20 ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.06/18.20 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.06/18.20 Bound_variable_2910:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 110.06/18.20 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) | 110.06/18.20 ( ~( Q @ B ) ) ) ) ) | 110.06/18.20 ( Q @ ( lam @ Bound_variable_2910 ) ) | 110.06/18.20 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 110.06/18.20 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3v2_lthm ) ) & 110.06/18.20 ( ( axvarid ) <=> ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) & 110.06/18.20 ( ( ( ![P:( subst > term > subst > $o )]: 110.06/18.20 ( ~( ![Q:( term > $o )]: 110.06/18.20 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) => 110.06/18.20 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 110.06/18.20 ( ( ~( ![A:term]: ( ( ~( var @ A ) ) | ( P @ A ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ B ) ) | 110.06/18.20 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) | 110.06/18.20 ( P @ ( lam @ A ) ) ) ) ) | 110.06/18.20 ( P @ Bound_variable_2367 ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) ) ) ) ) ) => 110.06/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.06/18.20 Bound_variable_2931:term]: 110.06/18.20 ( ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 110.06/18.20 ( Q @ ( lam @ Bound_variable_2931 ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( Q @ B ) ) | 110.06/18.20 ( Q @ 110.06/18.20 ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) ) ) ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) => 110.06/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 110.06/18.20 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 110.06/18.20 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 110.06/18.20 ( P @ id @ Bound_variable_3283 @ id ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.06/18.20 ( ~( P @ id @ B @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( var @ ( sub @ A @ id ) ) ) | ( P @ id @ A @ id ) ) ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lthm_3 ) ) & 110.06/18.20 ( hoasapnotvar_lthm ) & 110.06/18.20 ( ( ![P:( term > $o ),A:term,M:subst]: 110.06/18.20 ( ~( ![Q:( term > $o )]: 110.06/18.20 ( ~( ![X:term]: 110.06/18.20 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( pushprop_lem0_lthm ) ) & 110.06/18.20 ( ( termmset ) <=> ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) & 110.06/18.20 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) <=> 110.06/18.20 ( axshiftcons ) ) & 110.06/18.20 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 110.06/18.20 ( ( P @ Bound_variable_2367 ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ ( lam @ A ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | 110.06/18.20 ( ~( P @ B ) ) ) ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ A ) ) | ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) ) ) <=> 110.06/18.20 ( induction2 ) ) & 110.06/18.20 ( ulamvarsh ) & 110.06/18.20 ( ( ![F:( subst > term > term ),Bound_variable_2603:term, 110.06/18.20 Bound_variable_2605:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ( lam @ ( F @ sh @ one ) ) != 110.06/18.20 ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) ) <=> 110.06/18.20 ( hoaslamnotap ) ) & 110.06/18.20 ( ~( hoasvar @ 110.06/18.20 ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) & 110.06/18.20 ( ( hoasinduction_no_psi_cond ) <=> 110.06/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]: 110.06/18.20 ( ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.06/18.20 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ Bound_variable_3295 @ id ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) ) & 110.06/18.20 ( hoasinduction_lem1_gthm ) & ( lamnotvar ) & 110.06/18.20 ( hoasinduction_lem3_gthm ) & 110.06/18.20 ( ( substmonoid_lthm ) <=> 110.06/18.20 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) => 110.06/18.20 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) => 110.06/18.20 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) & 110.06/18.20 ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) ) ) ) ) & 110.06/18.20 ( ( hoasinduction_lem0_lthm ) <=> 110.06/18.20 ( ![P:( subst > term > subst > $o )]: 110.06/18.20 ( ~( ![Q:( term > $o )]: 110.06/18.20 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) ) & 110.06/18.20 ( hoaslaminj_gthm ) & ( hoasapinj1_gthm ) & ( ~( lamnotap ) ) & 110.06/18.20 ( hoasinduction_lem1_lthm ) & 110.06/18.20 ( ( hoasinduction_lem3v2a_lthm ) <=> 110.06/18.20 ( ( ![B:term]: 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ~( ![A:term,M:subst]: 110.06/18.20 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) => 110.06/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.06/18.20 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.06/18.20 Bound_variable_2931:term]: 110.06/18.20 ( ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 110.06/18.20 ( Q @ ( lam @ Bound_variable_2931 ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( Q @ B ) ) | 110.06/18.20 ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) ) ) ) | 110.06/18.20 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) ) ) & 110.06/18.20 ( pushprop_gthm ) & 110.06/18.20 ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 110.06/18.20 ( ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![A:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ 110.06/18.20 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ 110.06/18.20 id ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ 110.06/18.20 ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) ) ) ) ) ) => 110.06/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 110.06/18.20 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 110.06/18.20 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( P @ 110.06/18.20 id @ 110.06/18.20 ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) | 110.06/18.20 ( ~( P @ id @ B @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3_lthm ) ) & 110.06/18.20 ( hoasinduction_lem2v2_gthm ) & 110.06/18.20 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) <=> 110.06/18.20 ( axvarcons ) ) & 110.06/18.20 ( ( hoasinduction_lem3v2a ) <=> 110.06/18.20 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.06/18.20 Bound_variable_2931:term]: 110.06/18.20 ( ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( Q @ B ) ) | 110.06/18.20 ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) ) ) ) | 110.06/18.20 ( Q @ ( lam @ Bound_variable_2931 ) ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) ) ) ) ) ) ) & 110.06/18.20 ( ( ( ![A:term,B:term,C:term,D:term]: 110.06/18.20 ( ( ( C ) = ( D ) ) | ( ( ap @ A @ C ) != ( ap @ B @ D ) ) ) ) => 110.06/18.20 ( ![A:term,B:term,C:term,D:term]: 110.06/18.20 ( ( ( C ) = ( D ) ) | 110.06/18.20 ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) ) ) ) <=> 110.06/18.20 ( hoasapinj2_lthm ) ) & 110.06/18.20 ( ( ![A:term,B:term,C:term,D:term]: 110.06/18.20 ( ( ( C ) = ( D ) ) | ( ( ap @ A @ C ) != ( ap @ B @ D ) ) ) ) <=> 110.06/18.20 ( apinj2 ) ) & 110.06/18.20 ( ( hoasinduction_lem2v2 ) <=> 110.06/18.20 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.06/18.20 Bound_variable_2820:term,Bound_variable_2822:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 110.06/18.20 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) | 110.06/18.20 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 110.06/18.20 ( ~( Q @ Bound_variable_2822 ) ) | 110.06/18.20 ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) | 110.06/18.20 ( ~( Q @ Bound_variable_2820 ) ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.06/18.20 ( ~( P @ id @ B @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 110.06/18.20 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) & 110.06/18.20 ( axassoc ) & ( axclos ) & ( pushprop_lem2v2 ) & 110.06/18.20 ( pushprop_lem1v2_gthm ) & 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 110.06/18.20 ( ( ~( ![B:term]: 110.06/18.20 ( ( P @ 110.06/18.20 id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) | 110.06/18.20 ( ~( P @ id @ B @ id ) ) ) ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ 110.06/18.20 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3aa ) ) & 110.06/18.20 ( termmset_gthm ) & 110.06/18.20 ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 110.06/18.20 ( ( ~( ![B:term]: 110.06/18.20 ( ( P @ 110.06/18.20 id @ 110.06/18.20 ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) | 110.06/18.20 ( ~( P @ id @ B @ id ) ) ) ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ 110.06/18.20 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ 110.06/18.20 id ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) => 110.06/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]: 110.06/18.20 ( ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ 110.06/18.20 ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3a_lthm ) ) & 110.06/18.20 ( ulamvarind ) & 110.06/18.20 ( ( hoasinduction_lem3b_lthm ) <=> 110.06/18.20 ( ![B:term]: 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) ) & 110.06/18.20 ( pushprop_lem3v2_lthm ) & ( hoaslamnotvar_lthm ) & ( axapp ) & 110.06/18.20 ( hoasinduction_gthm ) & 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 110.06/18.20 ( ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ A @ id ) | ( ~( var @ ( sub @ A @ id ) ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.06/18.20 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) ) ) ) | 110.06/18.20 ( P @ id @ Bound_variable_3283 @ id ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 110.06/18.20 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 110.06/18.20 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction ) ) & 110.06/18.20 ( ( hoasinduction_lem0 ) <=> 110.06/18.20 ( ![P:( subst > term > subst > $o )]: 110.06/18.20 ( ~( ![Q:( term > $o )]: 110.06/18.20 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) ) & 110.06/18.20 ( ( pushprop_lem1v2_lthm ) <=> 110.06/18.20 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 110.06/18.20 ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]: 110.06/18.20 ( ( ~( ![X:term]: 110.06/18.20 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) | 110.06/18.20 ( Q @ one ) | ( ~( P @ A ) ) ) ) ) ) & 110.06/18.20 ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.06/18.20 ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) <=> 110.06/18.20 ( termmset_lthm ) ) & 110.06/18.20 ( induction2lem_gthm ) & 110.06/18.20 ( ( hoaslaminj ) <=> 110.06/18.20 ( ![F:( subst > term > term ), 110.06/18.20 Bound_variable_2547:( subst > term > term ), 110.06/18.20 Bound_variable_2549:subst,Bound_variable_2551:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ( lam @ ( F @ sh @ one ) ) != 110.06/18.20 ( lam @ ( Bound_variable_2547 @ sh @ one ) ) ) | 110.06/18.20 ( ( F @ Bound_variable_2549 @ Bound_variable_2551 ) = 110.06/18.20 ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N ) = 110.06/18.20 ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) & 110.06/18.20 ( ( hoasinduction_no_psi_cond_lthm ) <=> 110.06/18.20 ( ( ![P:( subst > term > subst > $o )]: 110.06/18.20 ( ~( ![Q:( term > $o )]: 110.06/18.20 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) => 110.06/18.20 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 110.06/18.20 ( ( P @ Bound_variable_2367 ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( ![B:term]: 110.06/18.20 ( ( ~( P @ B ) ) | 110.06/18.20 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) | 110.06/18.20 ( P @ ( lam @ A ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | ( ~( P @ A ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) ) ) => 110.06/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.06/18.20 Bound_variable_2931:term]: 110.06/18.20 ( ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( Q @ 110.06/18.20 ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) | 110.06/18.20 ( ~( Q @ B ) ) ) ) ) | 110.06/18.20 ( Q @ ( lam @ Bound_variable_2931 ) ) | 110.06/18.20 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) => 110.06/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]: 110.06/18.20 ( ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.06/18.20 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ Bound_variable_3295 @ id ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) & 110.06/18.20 ( ( ( ![P:( term > $o ),Bound_variable_2367:term]: 110.06/18.20 ( ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) | 110.06/18.20 ( P @ Bound_variable_2367 ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( ![B:term]: 110.06/18.20 ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | 110.06/18.20 ( ~( P @ B ) ) ) ) ) | 110.06/18.20 ( P @ ( lam @ A ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ A ) ) ) ) ) ) ) => 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term, 110.06/18.20 Bound_variable_3001:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 110.06/18.20 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.06/18.20 ( ~( P @ id @ B @ id ) ) | ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 110.06/18.20 ( ~( P @ id @ Bound_variable_3001 @ id ) ) | 110.06/18.20 ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 110.06/18.20 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) => 110.06/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 110.06/18.20 ( ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 110.06/18.20 ( ~( ![B:term]: 110.06/18.20 ( ( P @ 110.06/18.20 id @ 110.06/18.20 ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ 110.06/18.20 id ) | 110.06/18.20 ( ~( P @ id @ B @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 110.06/18.20 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 110.06/18.20 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) => 110.06/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 110.06/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 110.06/18.20 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( ~( var @ ( sub @ A @ id ) ) ) | ( P @ id @ A @ id ) ) ) ) | 110.06/18.20 ( ~( ![A:term,B:term]: 110.06/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.06/18.20 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.06/18.20 ( ~( P @ id @ B @ id ) ) ) ) ) | 110.06/18.20 ( P @ id @ Bound_variable_3283 @ id ) | 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.06/18.20 ( ~( ![A:term]: 110.06/18.20 ( ( P @ id @ ( F @ id @ A ) @ id ) | 110.06/18.20 ( ~( P @ id @ A @ id ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.06/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.06/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 110.06/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.06/18.20 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 110.06/18.20 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lthm ) ) & 110.06/18.20 ( ~( ulamvar1 ) ) & 110.06/18.20 ( ( hoasapinj2 ) <=> 110.06/18.20 ( ![A:term,B:term,C:term,D:term]: 110.06/18.20 ( ( ( C ) = ( D ) ) | 110.06/18.20 ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) ) ) ) & 110.06/18.20 ( ( ![B:term]: 110.06/18.20 ( ~( ![F:( subst > term > term )]: 110.06/18.20 ( ~( ![A:term,M:subst]: 110.06/18.20 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) <=> 110.06/18.20 ( hoasinduction_lem3v2_f ) ) & 110.06/18.20 ( hoasinduction_lem1v2_gthm ) & 110.06/18.20 ( ( ![A:term,B:term]: 110.06/18.20 ( ( ( A ) = ( B ) ) | ( ( sub @ A @ sh ) != ( sub @ B @ sh ) ) ) ) <=> 110.06/18.20 ( shinj ) ) & 110.06/18.20 ( axmap ) & ( pushprop_lem1_gthm ) & 110.06/18.20 ( ![A:term,M:subst,P:( term > $o ),Q:( term > $o )]: 110.06/18.20 ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) <=> 110.06/18.20 ( ![X:term]: ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) & 110.06/18.20 ( ( hoasap @ 110.06/18.20 ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ 110.06/18.20 ( d2term @ d_one ) ) = 110.06/18.20 ( d2term @ d_one ) ) & 110.06/18.20 ( ( sh ) = ( d2subst @ d_id ) ) & 110.06/18.20 ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2term @ d_one ) ) & 110.06/18.20 ( ( one ) = ( d2term @ d_one ) ) & 110.06/18.20 ( ![DT1:d_term,DT2:d_term]: 110.06/18.20 ( ( ( d2term @ DT1 ) = ( d2term @ DT2 ) ) => ( ( DT1 ) = ( DT2 ) ) ) ) & 110.06/18.20 ( ![DT:d_term]: ( ( DT ) = ( d_one ) ) ))). 110.06/18.20 thf(zf_stmt_0, axiom, 110.06/18.20 (![Bound_variable_3046:term,P:( subst > term > subst > $o )]: 110.06/18.20 ( ( zip_tseitin_98 @ Bound_variable_3046 @ P ) <=> 110.06/18.20 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_26 @ F @ P ) ) ) | 110.06/18.20 ( P @ 110.06/18.20 id @ 110.06/18.20 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 110.06/18.20 ( ~( ![B:term]: ( zip_tseitin_88 @ B @ Bound_variable_3046 @ P ) ) ) ) ))). 110.06/18.20 thf(zip_derived_cl370, plain, 110.06/18.20 (![X0 : term, X1 : subst > term > subst > $o, X2 : subst > term > term]: 110.06/18.20 ( (zip_tseitin_98 @ X0 @ X1) | (zip_tseitin_26 @ X2 @ X1))), 110.70/18.20 inference('cnf', [status(esa)], [zf_stmt_0])). 110.70/18.20 thf(zf_stmt_1, axiom, 110.70/18.20 (![A:term,F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_23 @ A @ F @ P ) <=> 110.70/18.20 ( ( ~( P @ id @ A @ id ) ) | ( P @ id @ ( F @ id @ A ) @ id ) ) ))). 110.70/18.20 thf(zip_derived_cl84, plain, 110.70/18.20 (![X0 : term, X1 : subst > term > term, X2 : subst > term > subst > $o]: 110.70/18.20 ( (zip_tseitin_23 @ X0 @ X1 @ X2) | (X2 @ id @ X0 @ id))), 110.70/18.20 inference('cnf', [status(esa)], [zf_stmt_1])). 110.70/18.20 thf(zip_derived_cl371, plain, 110.70/18.20 (![X0 : term, X1 : subst > term > subst > $o]: 110.70/18.20 ( (zip_tseitin_98 @ X0 @ X1) 110.70/18.20 | ~ (X1 @ id @ (lam @ (sub @ X0 @ (push @ one @ sh))) @ id))), 110.70/18.20 inference('cnf', [status(esa)], [zf_stmt_0])). 110.70/18.20 thf(zf_stmt_2, axiom, 110.70/18.20 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_26 @ F @ P ) <=> 110.70/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.70/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.70/18.20 ( ~( ![A:term]: ( zip_tseitin_23 @ A @ F @ P ) ) ) | 110.70/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ))). 110.70/18.20 thf(zip_derived_cl94, plain, 110.70/18.20 (![X0 : subst > term > subst > $o, X1 : subst > term > term]: 110.70/18.20 ( (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) 110.70/18.20 | ~ (zip_tseitin_23 @ (sk__41 @ X0 @ X1) @ X1 @ X0) 110.70/18.20 | ((sub @ (X1 @ (sk__42 @ X1) @ (sk__43 @ X1)) @ (sk__44 @ X1)) 110.70/18.20 != (X1 @ (comp @ (sk__42 @ X1) @ (sk__44 @ X1)) @ 110.70/18.20 (sub @ (sk__43 @ X1) @ (sk__44 @ X1)))) 110.70/18.20 | ~ (zip_tseitin_26 @ X1 @ X0))), 110.70/18.20 inference('cnf', [status(esa)], [zf_stmt_2])). 110.70/18.20 thf(hoasinduction_lem3aa, conjecture, 110.70/18.20 (( hoasinduction_lem3aa ) <=> 110.70/18.20 ( ![P:( subst > term > subst > $o )]: 110.70/18.20 ( ( ![F:( subst > term > term )]: 110.70/18.20 ( ( ![M:subst,A:term,N:subst]: 110.70/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 110.70/18.20 ( ( ![A:term]: 110.70/18.20 ( ( P @ id @ A @ id ) => ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 110.70/18.20 ( P @ 110.70/18.20 id @ 110.70/18.20 ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ id ) ) ) ) => 110.70/18.20 ( ![A:term]: 110.70/18.20 ( ( ![B:term]: 110.70/18.20 ( ( P @ id @ B @ id ) => 110.70/18.20 ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) ) ) => 110.70/18.20 ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_3, type, zip_tseitin_123 : 110.70/18.20 term > term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_4, axiom, 110.70/18.20 (![B:term,A:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_123 @ B @ A @ P ) <=> 110.70/18.20 ( ( P @ id @ B @ id ) => 110.70/18.20 ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) ) ))). 110.70/18.20 thf(zf_stmt_5, type, zip_tseitin_122 : 110.70/18.20 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_6, axiom, 110.70/18.20 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_122 @ F @ P ) <=> 110.70/18.20 ( ( ![M:subst,A:term,N:subst]: 110.70/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 110.70/18.20 ( ( ![A:term]: 110.70/18.20 ( ( P @ id @ A @ id ) => ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 110.70/18.20 ( P @ 110.70/18.20 id @ ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ id ) ) ) ))). 110.70/18.20 thf(zf_stmt_7, conjecture, 110.70/18.20 (( hoasinduction_lem3aa ) <=> 110.70/18.20 ( ![P:( subst > term > subst > $o )]: 110.70/18.20 ( ( ![F:( subst > term > term )]: ( zip_tseitin_122 @ F @ P ) ) => 110.70/18.20 ( ![A:term]: 110.70/18.20 ( ( ![B:term]: ( zip_tseitin_123 @ B @ A @ P ) ) => 110.70/18.20 ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_8, negated_conjecture, 110.70/18.20 (~( ( hoasinduction_lem3aa ) <=> 110.70/18.20 ( ![P:( subst > term > subst > $o )]: 110.70/18.20 ( ( ![F:( subst > term > term )]: ( zip_tseitin_122 @ F @ P ) ) => 110.70/18.20 ( ![A:term]: 110.70/18.20 ( ( ![B:term]: ( zip_tseitin_123 @ B @ A @ P ) ) => 110.70/18.20 ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) )), 110.70/18.20 inference('cnf.neg', [status(esa)], [zf_stmt_7])). 110.70/18.20 thf(zip_derived_cl664, plain, 110.70/18.20 (![X3 : subst > term > term]: 110.70/18.20 ( (zip_tseitin_122 @ X3 @ sk__479) | ~ (hoasinduction_lem3aa))), 110.70/18.20 inference('cnf', [status(esa)], [zf_stmt_8])). 110.70/18.20 thf(zf_stmt_9, type, zip_tseitin_121 : term > term > $o). 110.70/18.20 thf(zf_stmt_10, axiom, 110.70/18.20 (![B:term,A:term]: 110.70/18.20 ( ( zip_tseitin_121 @ B @ A ) <=> 110.70/18.20 ( ( ( sub @ A @ sh ) != ( sub @ B @ sh ) ) | ( ( A ) = ( B ) ) ) ))). 110.70/18.20 thf(zf_stmt_11, type, zip_tseitin_120 : $o). 110.70/18.20 thf(zf_stmt_12, axiom, 110.70/18.20 (( zip_tseitin_120 ) <=> 110.70/18.20 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 110.70/18.20 ( zip_tseitin_114 @ Bound_variable_2367 @ P ) ) => 110.70/18.20 ( zip_tseitin_119 ) ))).thf(zf_stmt_13, type, zip_tseitin_119 : $o). 110.70/18.20 thf(zf_stmt_14, axiom, 110.70/18.20 (( zip_tseitin_119 ) <=> 110.70/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term, 110.70/18.20 Bound_variable_3001:term]: 110.70/18.20 ( zip_tseitin_115 @ Bound_variable_3001 @ Bound_variable_2999 @ P ) ) => 110.70/18.20 ( zip_tseitin_118 ) ))).thf(zf_stmt_15, type, zip_tseitin_118 : $o). 110.70/18.20 thf(zf_stmt_16, axiom, 110.70/18.20 (( zip_tseitin_118 ) <=> 110.70/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 110.70/18.20 ( zip_tseitin_116 @ Bound_variable_3211 @ P ) ) => 110.70/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 110.70/18.20 ( zip_tseitin_117 @ Bound_variable_3283 @ P ) ) ))). 110.70/18.20 thf(zf_stmt_17, type, zip_tseitin_117 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_18, axiom, 110.70/18.20 (![Bound_variable_3283:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_117 @ Bound_variable_3283 @ P ) <=> 110.70/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_30 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.20 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_26 @ F @ P ) ) ) | 110.70/18.20 ( P @ id @ Bound_variable_3283 @ id ) | 110.70/18.20 ( ~( ![A:term,B:term]: ( zip_tseitin_67 @ B @ A @ P ) ) ) | 110.70/18.20 ( ~( ![A:term]: ( zip_tseitin_68 @ A @ P ) ) ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_32 @ K @ N @ A @ M @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_19, type, zip_tseitin_116 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_20, axiom, 110.70/18.20 (![Bound_variable_3211:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_116 @ Bound_variable_3211 @ P ) <=> 110.70/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_30 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.20 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 110.70/18.20 ( ~( ![B:term]: ( zip_tseitin_88 @ B @ Bound_variable_3211 @ P ) ) ) | 110.70/18.20 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_24 @ F @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_21, type, zip_tseitin_115 : 110.70/18.20 term > term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_22, axiom, 110.70/18.20 (![Bound_variable_3001:term,Bound_variable_2999:term, 110.70/18.20 P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_115 @ Bound_variable_3001 @ Bound_variable_2999 @ P ) <=> 110.70/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_30 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.20 ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 110.70/18.20 ( ~( P @ id @ Bound_variable_3001 @ id ) ) | 110.70/18.20 ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 110.70/18.20 ( ~( ![A:term,B:term]: ( zip_tseitin_31 @ B @ A @ P ) ) ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_23, type, zip_tseitin_114 : term > ( term > $o ) > $o). 110.70/18.20 thf(zf_stmt_24, axiom, 110.70/18.20 (![Bound_variable_2367:term,P:( term > $o )]: 110.70/18.20 ( ( zip_tseitin_114 @ Bound_variable_2367 @ P ) <=> 110.70/18.20 ( ( ~( ![A:term,B:term]: ( zip_tseitin_34 @ B @ A @ P ) ) ) | 110.70/18.20 ( ~( ![A:term]: ( zip_tseitin_49 @ A @ P ) ) ) | 110.70/18.20 ( P @ Bound_variable_2367 ) | 110.70/18.20 ( ~( ![A:term]: ( zip_tseitin_11 @ A @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_25, type, zip_tseitin_113 : $o). 110.70/18.20 thf(zf_stmt_26, axiom, 110.70/18.20 (( zip_tseitin_113 ) <=> 110.70/18.20 ( ( ![P:( subst > term > subst > $o )]: 110.70/18.20 ( ~( ![Q:( term > $o )]: 110.70/18.20 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) ) ) ) => 110.70/18.20 ( zip_tseitin_112 ) ))).thf(zf_stmt_27, type, zip_tseitin_112 : $o). 110.70/18.20 thf(zf_stmt_28, axiom, 110.70/18.20 (( zip_tseitin_112 ) <=> 110.70/18.20 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 110.70/18.20 ( zip_tseitin_107 @ Bound_variable_2367 @ P ) ) => 110.70/18.20 ( zip_tseitin_111 ) ))).thf(zf_stmt_29, type, zip_tseitin_111 : $o). 110.70/18.20 thf(zf_stmt_30, axiom, 110.70/18.20 (( zip_tseitin_111 ) <=> 110.70/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_110 ) ))). 110.70/18.20 thf(zf_stmt_31, type, zip_tseitin_110 : $o). 110.70/18.20 thf(zf_stmt_32, axiom, 110.70/18.20 (( zip_tseitin_110 ) <=> 110.70/18.20 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.70/18.20 Bound_variable_2931:term]: 110.70/18.20 ( zip_tseitin_108 @ Bound_variable_2931 @ Q @ P ) ) => 110.70/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]: 110.70/18.20 ( zip_tseitin_109 @ Bound_variable_3295 @ P ) ) ))). 110.70/18.20 thf(zf_stmt_33, type, zip_tseitin_109 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_34, axiom, 110.70/18.20 (![Bound_variable_3295:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_109 @ Bound_variable_3295 @ P ) <=> 110.70/18.20 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_60 @ F @ P ) ) ) | 110.70/18.20 ( P @ id @ Bound_variable_3295 @ id ) | 110.70/18.20 ( ~( ![A:term,B:term]: ( zip_tseitin_77 @ B @ A @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_35, type, zip_tseitin_108 : 110.70/18.20 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_36, axiom, 110.70/18.20 (![Bound_variable_2931:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_108 @ Bound_variable_2931 @ Q @ P ) <=> 110.70/18.20 ( ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) | 110.70/18.20 ( Q @ ( lam @ Bound_variable_2931 ) ) | 110.70/18.20 ( ~( ![B:term]: ( zip_tseitin_48 @ B @ Bound_variable_2931 @ Q ) ) ) | 110.70/18.20 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_66 @ F @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_37, type, zip_tseitin_107 : term > ( term > $o ) > $o). 110.70/18.20 thf(zf_stmt_38, axiom, 110.70/18.20 (![Bound_variable_2367:term,P:( term > $o )]: 110.70/18.20 ( ( zip_tseitin_107 @ Bound_variable_2367 @ P ) <=> 110.70/18.20 ( ( ~( ![A:term]: ( zip_tseitin_11 @ A @ P ) ) ) | 110.70/18.20 ( ~( ![A:term,B:term]: ( zip_tseitin_3 @ B @ A @ P ) ) ) | 110.70/18.20 ( ~( ![A:term]: ( zip_tseitin_6 @ A @ P ) ) ) | 110.70/18.20 ( P @ Bound_variable_2367 ) ) ))). 110.70/18.20 thf(zf_stmt_39, type, zip_tseitin_106 : 110.70/18.20 term > subst > ( subst > term > term ) > ( subst > term > term ) > $o). 110.70/18.20 thf(zf_stmt_40, axiom, 110.70/18.20 (![Bound_variable_2551:term,Bound_variable_2549:subst, 110.70/18.20 Bound_variable_2547:( subst > term > term ),F:( subst > term > term )]: 110.70/18.20 ( ( zip_tseitin_106 @ 110.70/18.20 Bound_variable_2551 @ Bound_variable_2549 @ Bound_variable_2547 @ F ) <=> 110.70/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.70/18.20 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N ) = 110.70/18.20 ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.70/18.20 ( ( F @ Bound_variable_2549 @ Bound_variable_2551 ) = 110.70/18.20 ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) | 110.70/18.20 ( ( lam @ ( F @ sh @ one ) ) != 110.70/18.20 ( lam @ ( Bound_variable_2547 @ sh @ one ) ) ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.70/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_41, type, zip_tseitin_105 : $o). 110.70/18.20 thf(zf_stmt_42, axiom, 110.70/18.20 (( zip_tseitin_105 ) <=> 110.70/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.70/18.20 ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ))). 110.70/18.20 thf(zf_stmt_43, type, zip_tseitin_104 : $o). 110.70/18.20 thf(zf_stmt_44, axiom, 110.70/18.20 (( zip_tseitin_104 ) <=> 110.70/18.20 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 110.70/18.20 ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]: 110.70/18.20 ( zip_tseitin_2 @ M @ A @ Q @ P ) ) ))). 110.70/18.20 thf(zf_stmt_45, type, zip_tseitin_103 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_46, axiom, 110.70/18.20 (![Bound_variable_3283:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_103 @ Bound_variable_3283 @ P ) <=> 110.70/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_30 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_32 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.20 ( P @ id @ Bound_variable_3283 @ id ) | 110.70/18.20 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_92 @ F @ P ) ) ) | 110.70/18.20 ( ~( ![A:term,B:term]: ( zip_tseitin_77 @ B @ A @ P ) ) ) | 110.70/18.20 ( ~( ![A:term]: ( zip_tseitin_102 @ A @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_47, type, zip_tseitin_102 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_48, axiom, 110.70/18.20 (![A:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_102 @ A @ P ) <=> 110.70/18.20 ( ( ~( var @ ( sub @ A @ id ) ) ) | ( P @ id @ A @ id ) ) ))). 110.70/18.20 thf(zf_stmt_49, type, zip_tseitin_101 : $o). 110.70/18.20 thf(zf_stmt_50, axiom, 110.70/18.20 (( zip_tseitin_101 ) <=> 110.70/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_100 ) ))). 110.70/18.20 thf(zf_stmt_51, type, zip_tseitin_100 : $o). 110.70/18.20 thf(zf_stmt_52, axiom, 110.70/18.20 (( zip_tseitin_100 ) <=> 110.70/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 110.70/18.20 ( zip_tseitin_98 @ Bound_variable_3046 @ P ) ) => 110.70/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]: 110.70/18.20 ( zip_tseitin_99 @ Bound_variable_3232 @ P ) ) ))). 110.70/18.20 thf(zf_stmt_53, type, zip_tseitin_99 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_54, axiom, 110.70/18.20 (![Bound_variable_3232:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_99 @ Bound_variable_3232 @ P ) <=> 110.70/18.20 ( ( ~( ![B:term]: ( zip_tseitin_19 @ B @ Bound_variable_3232 @ P ) ) ) | 110.70/18.20 ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) | 110.70/18.20 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_60 @ F @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_55, type, zip_tseitin_98 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_56, type, zip_tseitin_97 : 110.70/18.20 term > term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_57, axiom, 110.70/18.20 (![Bound_variable_2822:term,Bound_variable_2820:term,Q:( term > $o ), 110.70/18.20 P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_97 @ Bound_variable_2822 @ Bound_variable_2820 @ Q @ P ) <=> 110.70/18.20 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_32 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.20 ( ~( ![A:term,B:term]: ( zip_tseitin_67 @ B @ A @ P ) ) ) | 110.70/18.20 ( ~( Q @ Bound_variable_2820 ) ) | 110.70/18.20 ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) | 110.70/18.20 ( ~( Q @ Bound_variable_2822 ) ) | 110.70/18.20 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_28 @ K @ N @ A @ M @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_58, type, zip_tseitin_96 : $o). 110.70/18.20 thf(zf_stmt_59, axiom, 110.70/18.20 (( zip_tseitin_96 ) <=> 110.70/18.20 ( ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_94 @ D @ C @ B @ A ) ) => 110.70/18.20 ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_95 @ D @ C @ B @ A ) ) ))). 110.70/18.20 thf(zf_stmt_60, type, zip_tseitin_95 : term > term > term > term > $o). 110.70/18.20 thf(zf_stmt_61, axiom, 110.70/18.20 (![D:term,C:term,B:term,A:term]: 110.70/18.20 ( ( zip_tseitin_95 @ D @ C @ B @ A ) <=> 110.70/18.20 ( ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) | 110.70/18.20 ( ( C ) = ( D ) ) ) ))). 110.70/18.20 thf(zf_stmt_62, type, zip_tseitin_94 : term > term > term > term > $o). 110.70/18.20 thf(zf_stmt_63, axiom, 110.70/18.20 (![D:term,C:term,B:term,A:term]: 110.70/18.20 ( ( zip_tseitin_94 @ D @ C @ B @ A ) <=> 110.70/18.20 ( ( ( ap @ A @ C ) != ( ap @ B @ D ) ) | ( ( C ) = ( D ) ) ) ))). 110.70/18.20 thf(zf_stmt_64, type, zip_tseitin_93 : 110.70/18.20 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_65, axiom, 110.70/18.20 (![Bound_variable_2931:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_93 @ Bound_variable_2931 @ Q @ P ) <=> 110.70/18.20 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_92 @ F @ P ) ) ) | 110.70/18.20 ( Q @ ( lam @ Bound_variable_2931 ) ) | 110.70/18.20 ( ~( ![B:term]: ( zip_tseitin_5 @ B @ Bound_variable_2931 @ Q ) ) ) | 110.70/18.20 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_66, type, zip_tseitin_92 : 110.70/18.20 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_67, axiom, 110.70/18.20 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_92 @ F @ P ) <=> 110.70/18.20 ( ( ~( ![A:term]: ( zip_tseitin_20 @ A @ F @ P ) ) ) | 110.70/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.70/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_68, type, zip_tseitin_91 : $o). 110.70/18.20 thf(zf_stmt_69, axiom, 110.70/18.20 (( zip_tseitin_91 ) <=> 110.70/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_90 ) ))). 110.70/18.20 thf(zf_stmt_70, type, zip_tseitin_90 : $o). 110.70/18.20 thf(zf_stmt_71, axiom, 110.70/18.20 (( zip_tseitin_90 ) <=> 110.70/18.20 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 110.70/18.20 ( zip_tseitin_87 @ Bound_variable_3046 @ P ) ) => 110.70/18.20 ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 110.70/18.20 ( zip_tseitin_89 @ Bound_variable_3211 @ P ) ) ))). 110.70/18.20 thf(zf_stmt_72, type, zip_tseitin_89 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_73, axiom, 110.70/18.20 (![Bound_variable_3211:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_89 @ Bound_variable_3211 @ P ) <=> 110.70/18.20 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_60 @ F @ P ) ) ) | 110.70/18.20 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 110.70/18.20 ( ~( ![B:term]: ( zip_tseitin_88 @ B @ Bound_variable_3211 @ P ) ) ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_32 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.20 ( zip_tseitin_28 @ K @ N @ A @ M @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_74, type, zip_tseitin_88 : 110.70/18.20 term > term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_75, axiom, 110.70/18.20 (![B:term,Bound_variable_3211:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_88 @ B @ Bound_variable_3211 @ P ) <=> 110.70/18.20 ( ( ~( P @ id @ B @ id ) ) | 110.70/18.20 ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) ) ))). 110.70/18.20 thf(zf_stmt_76, type, zip_tseitin_87 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_77, axiom, 110.70/18.20 (![Bound_variable_3046:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_87 @ Bound_variable_3046 @ P ) <=> 110.70/18.20 ( ( ~( ![B:term]: ( zip_tseitin_19 @ B @ Bound_variable_3046 @ P ) ) ) | 110.70/18.20 ( P @ 110.70/18.20 id @ 110.70/18.20 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 110.70/18.20 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_86 @ F @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_78, type, zip_tseitin_86 : 110.70/18.20 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_79, axiom, 110.70/18.20 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_86 @ F @ P ) <=> 110.70/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.70/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.70/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.70/18.20 ( ~( ![A:term]: ( zip_tseitin_20 @ A @ F @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_80, type, zip_tseitin_85 : $o). 110.70/18.20 thf(zf_stmt_81, axiom, 110.70/18.20 (( zip_tseitin_85 ) <=> 110.70/18.20 ( ( ![B:term]: 110.70/18.20 ( ~( ![F:( subst > term > term )]: 110.70/18.20 ( ~( ![A:term,M:subst]: 110.70/18.20 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) => 110.70/18.20 ( zip_tseitin_84 ) ))).thf(zf_stmt_82, type, zip_tseitin_84 : $o). 110.70/18.20 thf(zf_stmt_83, axiom, 110.70/18.20 (( zip_tseitin_84 ) <=> 110.70/18.20 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.70/18.20 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.70/18.20 Bound_variable_2931:term]: 110.70/18.20 ( zip_tseitin_83 @ Bound_variable_2931 @ Q @ P ) ) ))). 110.70/18.20 thf(zf_stmt_84, type, zip_tseitin_83 : 110.70/18.20 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_85, axiom, 110.70/18.20 (![Bound_variable_2931:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_83 @ Bound_variable_2931 @ Q @ P ) <=> 110.70/18.20 ( ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) | 110.70/18.20 ( ~( ![B:term]: ( zip_tseitin_5 @ B @ Bound_variable_2931 @ Q ) ) ) | 110.70/18.20 ( Q @ ( lam @ Bound_variable_2931 ) ) | 110.70/18.20 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_24 @ F @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_86, type, zip_tseitin_82 : $o). 110.70/18.20 thf(zf_stmt_87, axiom, 110.70/18.20 (( zip_tseitin_82 ) <=> 110.70/18.20 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) => ( zip_tseitin_81 ) ))). 110.70/18.20 thf(zf_stmt_88, type, zip_tseitin_81 : $o). 110.70/18.20 thf(zf_stmt_89, axiom, 110.70/18.20 (( zip_tseitin_81 ) <=> 110.70/18.20 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) => ( zip_tseitin_80 ) ))). 110.70/18.20 thf(zf_stmt_90, type, zip_tseitin_80 : $o). 110.70/18.20 thf(zf_stmt_91, axiom, 110.70/18.20 (( zip_tseitin_80 ) <=> 110.70/18.20 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) & 110.70/18.20 ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) ))). 110.70/18.20 thf(zf_stmt_92, type, zip_tseitin_79 : 110.70/18.20 term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_93, axiom, 110.70/18.20 (![Bound_variable_3295:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_79 @ Bound_variable_3295 @ P ) <=> 110.70/18.20 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_78 @ F @ P ) ) ) | 110.70/18.20 ( P @ id @ Bound_variable_3295 @ id ) | 110.70/18.20 ( ~( ![A:term,B:term]: ( zip_tseitin_77 @ B @ A @ P ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_94, type, zip_tseitin_78 : 110.70/18.20 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_95, axiom, 110.70/18.20 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_78 @ F @ P ) <=> 110.70/18.20 ( ( ~( ![M:subst,A:term,N:subst]: 110.70/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.70/18.20 ( ~( ![A:term]: ( zip_tseitin_20 @ A @ F @ P ) ) ) | 110.70/18.20 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ))). 110.70/18.20 thf(zf_stmt_96, type, zip_tseitin_77 : 110.70/18.20 term > term > ( subst > term > subst > $o ) > $o). 110.70/18.20 thf(zf_stmt_97, axiom, 110.70/18.20 (![B:term,A:term,P:( subst > term > subst > $o )]: 110.70/18.20 ( ( zip_tseitin_77 @ B @ A @ P ) <=> 110.70/18.20 ( ( ~( P @ id @ A @ id ) ) | 110.70/18.20 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.70/18.20 ( ~( P @ id @ B @ id ) ) ) ))). 110.70/18.20 thf(zf_stmt_98, type, zip_tseitin_76 : 110.70/18.20 term > term > ( subst > term > term ) > $o). 110.70/18.20 thf(zf_stmt_99, axiom, 110.70/18.20 (![Bound_variable_2605:term,Bound_variable_2603:term, 110.70/18.20 F:( subst > term > term )]: 110.70/18.20 ( ( zip_tseitin_76 @ Bound_variable_2605 @ Bound_variable_2603 @ F ) <=> 110.70/18.20 ( ( ( lam @ ( F @ sh @ one ) ) != 110.70/18.20 ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) | 110.70/18.20 ( ~( ![M:subst,A:term,N:subst]: 110.70/18.20 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.20 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 110.70/18.20 thf(zf_stmt_100, type, zip_tseitin_75 : term > ( term > $o ) > $o). 110.70/18.20 thf(zf_stmt_101, axiom, 110.70/18.20 (![Bound_variable_2367:term,P:( term > $o )]: 110.70/18.20 ( ( zip_tseitin_75 @ Bound_variable_2367 @ P ) <=> 110.70/18.21 ( ( ~( ![A:term]: ( zip_tseitin_11 @ A @ P ) ) ) | 110.70/18.21 ( ~( ![A:term,B:term]: ( zip_tseitin_9 @ B @ A @ P ) ) ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_74 @ A @ P ) ) ) | 110.70/18.21 ( P @ Bound_variable_2367 ) ) ))). 110.70/18.21 thf(zf_stmt_102, type, zip_tseitin_74 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_103, axiom, 110.70/18.21 (![A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_74 @ A @ P ) <=> 110.70/18.21 ( ( ~( ![B:term]: ( zip_tseitin_48 @ B @ A @ P ) ) ) | 110.70/18.21 ( P @ ( lam @ A ) ) ) ))).thf(zf_stmt_104, type, zip_tseitin_73 : $o). 110.70/18.21 thf(zf_stmt_105, axiom, 110.70/18.21 (( zip_tseitin_73 ) <=> 110.70/18.21 ( ( ![P:( subst > term > subst > $o )]: 110.70/18.21 ( ~( ![Q:( term > $o )]: 110.70/18.21 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) ) ) ) => 110.70/18.21 ( zip_tseitin_72 ) ))).thf(zf_stmt_106, type, zip_tseitin_72 : $o). 110.70/18.21 thf(zf_stmt_107, axiom, 110.70/18.21 (( zip_tseitin_72 ) <=> 110.70/18.21 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 110.70/18.21 ( zip_tseitin_64 @ Bound_variable_2367 @ P ) ) => 110.70/18.21 ( zip_tseitin_71 ) ))).thf(zf_stmt_108, type, zip_tseitin_71 : $o). 110.70/18.21 thf(zf_stmt_109, axiom, 110.70/18.21 (( zip_tseitin_71 ) <=> 110.70/18.21 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_70 ) ))). 110.70/18.21 thf(zf_stmt_110, type, zip_tseitin_70 : $o). 110.70/18.21 thf(zf_stmt_111, axiom, 110.70/18.21 (( zip_tseitin_70 ) <=> 110.70/18.21 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.70/18.21 Bound_variable_2931:term]: 110.70/18.21 ( zip_tseitin_65 @ Bound_variable_2931 @ Q @ P ) ) => 110.70/18.21 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 110.70/18.21 ( zip_tseitin_69 @ Bound_variable_3283 @ P ) ) ))). 110.70/18.21 thf(zf_stmt_112, type, zip_tseitin_69 : 110.70/18.21 term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_113, axiom, 110.70/18.21 (![Bound_variable_3283:term,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_69 @ Bound_variable_3283 @ P ) <=> 110.70/18.21 ( ( ~( ![A:term]: ( zip_tseitin_68 @ A @ P ) ) ) | 110.70/18.21 ( ~( ![A:term,B:term]: ( zip_tseitin_67 @ B @ A @ P ) ) ) | 110.70/18.21 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_66 @ F @ P ) ) ) | 110.70/18.21 ( P @ id @ Bound_variable_3283 @ id ) | 110.70/18.21 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_32 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.21 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_30 @ K @ N @ A @ M @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_114, type, zip_tseitin_68 : 110.70/18.21 term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_115, axiom, 110.70/18.21 (![A:term,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_68 @ A @ P ) <=> 110.70/18.21 ( ( P @ id @ A @ id ) | ( ~( var @ ( sub @ A @ id ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_116, type, zip_tseitin_67 : 110.70/18.21 term > term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_117, axiom, 110.70/18.21 (![B:term,A:term,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_67 @ B @ A @ P ) <=> 110.70/18.21 ( ( ~( P @ id @ B @ id ) ) | 110.70/18.21 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 110.70/18.21 ( ~( P @ id @ A @ id ) ) ) ))). 110.70/18.21 thf(zf_stmt_118, type, zip_tseitin_66 : 110.70/18.21 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_119, axiom, 110.70/18.21 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_66 @ F @ P ) <=> 110.70/18.21 ( ( ~( ![M:subst,A:term,N:subst]: 110.70/18.21 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.21 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.70/18.21 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_23 @ A @ F @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_120, type, zip_tseitin_65 : 110.70/18.21 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_121, axiom, 110.70/18.21 (![Bound_variable_2931:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_65 @ Bound_variable_2931 @ Q @ P ) <=> 110.70/18.21 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_26 @ F @ P ) ) ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_5 @ B @ Bound_variable_2931 @ Q ) ) ) | 110.70/18.21 ( Q @ ( lam @ Bound_variable_2931 ) ) | 110.70/18.21 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_122, type, zip_tseitin_64 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_123, axiom, 110.70/18.21 (![Bound_variable_2367:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_64 @ Bound_variable_2367 @ P ) <=> 110.70/18.21 ( ( ~( ![A:term,B:term]: ( zip_tseitin_51 @ B @ A @ P ) ) ) | 110.70/18.21 ( P @ Bound_variable_2367 ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_6 @ A @ P ) ) ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_63 @ A @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_124, type, zip_tseitin_63 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_125, axiom, 110.70/18.21 (![A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_63 @ A @ P ) <=> ( ( P @ A ) | ( ~( var @ A ) ) ) ))). 110.70/18.21 thf(zf_stmt_126, type, zip_tseitin_62 : $o). 110.70/18.21 thf(zf_stmt_127, axiom, 110.70/18.21 (( zip_tseitin_62 ) <=> 110.70/18.21 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 110.70/18.21 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.70/18.21 Bound_variable_2910:term]: 110.70/18.21 ( zip_tseitin_61 @ Bound_variable_2910 @ Q @ P ) ) ))). 110.70/18.21 thf(zf_stmt_128, type, zip_tseitin_61 : 110.70/18.21 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_129, axiom, 110.70/18.21 (![Bound_variable_2910:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_61 @ Bound_variable_2910 @ Q @ P ) <=> 110.70/18.21 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_32 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.21 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) | 110.70/18.21 ( Q @ ( lam @ Bound_variable_2910 ) ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_48 @ B @ Bound_variable_2910 @ Q ) ) ) | 110.70/18.21 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_60 @ F @ P ) ) ) | 110.70/18.21 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_30 @ K @ N @ A @ M @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_130, type, zip_tseitin_60 : 110.70/18.21 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_131, axiom, 110.70/18.21 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_60 @ F @ P ) <=> 110.70/18.21 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_20 @ A @ F @ P ) ) ) | 110.70/18.21 ( ~( ![M:subst,A:term,N:subst]: 110.70/18.21 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.21 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_132, type, zip_tseitin_59 : 110.70/18.21 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_133, axiom, 110.70/18.21 (![Bound_variable_2910:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_59 @ Bound_variable_2910 @ Q @ P ) <=> 110.70/18.21 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_32 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.21 ( Q @ ( lam @ Bound_variable_2910 ) ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_5 @ B @ Bound_variable_2910 @ Q ) ) ) | 110.70/18.21 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) | 110.70/18.21 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_24 @ F @ P ) ) ) | 110.70/18.21 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_28 @ K @ N @ A @ M @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_134, type, zip_tseitin_58 : $o). 110.70/18.21 thf(zf_stmt_135, axiom, 110.70/18.21 (( zip_tseitin_58 ) <=> 110.70/18.21 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 110.70/18.21 ( zip_tseitin_57 ) ))).thf(zf_stmt_136, type, zip_tseitin_57 : $o). 110.70/18.21 thf(zf_stmt_137, axiom, 110.70/18.21 (( zip_tseitin_57 ) <=> 110.70/18.21 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 110.70/18.21 ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]: 110.70/18.21 ( zip_tseitin_46 @ B @ M @ A @ K @ P ) ) ))). 110.70/18.21 thf(zf_stmt_138, type, zip_tseitin_56 : 110.70/18.21 term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_139, axiom, 110.70/18.21 (![Bound_variable_3232:term,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_56 @ Bound_variable_3232 @ P ) <=> 110.70/18.21 ( ( ~( ![B:term]: ( zip_tseitin_19 @ B @ Bound_variable_3232 @ P ) ) ) | 110.70/18.21 ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) | 110.70/18.21 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_26 @ F @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_140, type, zip_tseitin_55 : $o). 110.70/18.21 thf(zf_stmt_141, axiom, 110.70/18.21 (( zip_tseitin_55 ) <=> 110.70/18.21 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) & 110.70/18.21 ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) ))). 110.70/18.21 thf(zf_stmt_142, type, zip_tseitin_54 : $o). 110.70/18.21 thf(zf_stmt_143, axiom, 110.70/18.21 (( zip_tseitin_54 ) <=> 110.70/18.21 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_53 ) ))). 110.70/18.21 thf(zf_stmt_144, type, zip_tseitin_53 : $o). 110.70/18.21 thf(zf_stmt_145, axiom, 110.70/18.21 (( zip_tseitin_53 ) <=> 110.70/18.21 ( ( ![P:( term > $o ),Bound_variable_2340:term,Bound_variable_2342:subst]: 110.70/18.21 ( zip_tseitin_50 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) ) => 110.70/18.21 ( ![P:( term > $o ),Bound_variable_2367:term]: 110.70/18.21 ( zip_tseitin_52 @ Bound_variable_2367 @ P ) ) ))). 110.70/18.21 thf(zf_stmt_146, type, zip_tseitin_52 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_147, axiom, 110.70/18.21 (![Bound_variable_2367:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_52 @ Bound_variable_2367 @ P ) <=> 110.70/18.21 ( ( ~( ![A:term]: ( zip_tseitin_11 @ A @ P ) ) ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_13 @ A @ P ) ) ) | 110.70/18.21 ( P @ Bound_variable_2367 ) | 110.70/18.21 ( ~( ![A:term,B:term]: ( zip_tseitin_51 @ B @ A @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_148, type, zip_tseitin_51 : term > term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_149, axiom, 110.70/18.21 (![B:term,A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_51 @ B @ A @ P ) <=> 110.70/18.21 ( ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ A ) ) ) ))). 110.70/18.21 thf(zf_stmt_150, type, zip_tseitin_50 : subst > term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_151, axiom, 110.70/18.21 (![Bound_variable_2342:subst,Bound_variable_2340:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_50 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) <=> 110.70/18.21 ( ( ~( ![A:term]: ( zip_tseitin_49 @ A @ P ) ) ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_4 @ B @ Bound_variable_2342 @ P ) ) ) | 110.70/18.21 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 110.70/18.21 ( ~( ![A:term,B:term]: ( zip_tseitin_34 @ B @ A @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_152, type, zip_tseitin_49 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_153, axiom, 110.70/18.21 (![A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_49 @ A @ P ) <=> 110.70/18.21 ( ( P @ ( lam @ A ) ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_48 @ B @ A @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_154, type, zip_tseitin_48 : term > term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_155, axiom, 110.70/18.21 (![B:term,A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_48 @ B @ A @ P ) <=> 110.70/18.21 ( ( ~( P @ B ) ) | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_156, type, zip_tseitin_47 : term > term > $o). 110.70/18.21 thf(zf_stmt_157, axiom, 110.70/18.21 (![B:term,A:term]: 110.70/18.21 ( ( zip_tseitin_47 @ B @ A ) <=> 110.70/18.21 ( ( ( A ) = ( B ) ) | ( ( lam @ A ) != ( lam @ B ) ) ) ))). 110.70/18.21 thf(zf_stmt_158, type, zip_tseitin_46 : 110.70/18.21 term > subst > term > ( term > $o ) > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_159, axiom, 110.70/18.21 (![B:term,M:subst,A:term,K:( term > $o ),P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_46 @ B @ M @ A @ K @ P ) <=> 110.70/18.21 ( ( K @ ( sub @ A @ ( push @ B @ M ) ) ) | ( ~( P @ A ) ) ) ))). 110.70/18.21 thf(zf_stmt_160, type, zip_tseitin_45 : $o). 110.70/18.21 thf(zf_stmt_161, axiom, 110.70/18.21 (( zip_tseitin_45 ) <=> 110.70/18.21 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 110.70/18.21 ( zip_tseitin_44 ) ))).thf(zf_stmt_162, type, zip_tseitin_44 : $o). 110.70/18.21 thf(zf_stmt_163, axiom, 110.70/18.21 (( zip_tseitin_44 ) <=> 110.70/18.21 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 110.70/18.21 ( zip_tseitin_43 ) ))).thf(zf_stmt_164, type, zip_tseitin_43 : $o). 110.70/18.21 thf(zf_stmt_165, axiom, 110.70/18.21 (( zip_tseitin_43 ) <=> 110.70/18.21 ( ( ![A:term,B:term]: ( zip_tseitin_41 @ B @ A ) ) => 110.70/18.21 ( ![F:( subst > term > term ), 110.70/18.21 Bound_variable_2547:( subst > term > term ), 110.70/18.21 Bound_variable_2549:subst,Bound_variable_2551:term]: 110.70/18.21 ( zip_tseitin_42 @ 110.70/18.21 Bound_variable_2551 @ Bound_variable_2549 @ Bound_variable_2547 @ F ) ) ))). 110.70/18.21 thf(zf_stmt_166, type, zip_tseitin_42 : 110.70/18.21 term > subst > ( subst > term > term ) > ( subst > term > term ) > $o). 110.70/18.21 thf(zf_stmt_167, axiom, 110.70/18.21 (![Bound_variable_2551:term,Bound_variable_2549:subst, 110.70/18.21 Bound_variable_2547:( subst > term > term ),F:( subst > term > term )]: 110.70/18.21 ( ( zip_tseitin_42 @ 110.70/18.21 Bound_variable_2551 @ Bound_variable_2549 @ Bound_variable_2547 @ F ) <=> 110.70/18.21 ( ( ~( ![M:subst,A:term,N:subst]: 110.70/18.21 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.21 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 110.70/18.21 ( ( F @ Bound_variable_2549 @ Bound_variable_2551 ) = 110.70/18.21 ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) | 110.70/18.21 ( ( lam @ ( F @ sh @ one ) ) != 110.70/18.21 ( lam @ ( Bound_variable_2547 @ sh @ one ) ) ) | 110.70/18.21 ( ~( ![M:subst,A:term,N:subst]: 110.70/18.21 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N ) = 110.70/18.21 ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_168, type, zip_tseitin_41 : term > term > $o). 110.70/18.21 thf(zf_stmt_169, axiom, 110.70/18.21 (![B:term,A:term]: 110.70/18.21 ( ( zip_tseitin_41 @ B @ A ) <=> 110.70/18.21 ( ( ( lam @ A ) != ( lam @ B ) ) | ( ( A ) = ( B ) ) ) ))). 110.70/18.21 thf(zf_stmt_170, type, zip_tseitin_40 : $o). 110.70/18.21 thf(zf_stmt_171, axiom, 110.70/18.21 (( zip_tseitin_40 ) <=> 110.70/18.21 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_39 ) ))). 110.70/18.21 thf(zf_stmt_172, type, zip_tseitin_39 : $o). 110.70/18.21 thf(zf_stmt_173, axiom, 110.70/18.21 (( zip_tseitin_39 ) <=> 110.70/18.21 ( ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_38 @ D @ C @ B @ A ) ) => 110.70/18.21 ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_8 @ D @ C @ B @ A ) ) ))). 110.70/18.21 thf(zf_stmt_174, type, zip_tseitin_38 : term > term > term > term > $o). 110.70/18.21 thf(zf_stmt_175, axiom, 110.70/18.21 (![D:term,C:term,B:term,A:term]: 110.70/18.21 ( ( zip_tseitin_38 @ D @ C @ B @ A ) <=> 110.70/18.21 ( ( ( ap @ A @ C ) != ( ap @ B @ D ) ) | ( ( A ) = ( B ) ) ) ))). 110.70/18.21 thf(zf_stmt_176, type, zip_tseitin_37 : term > term > term > term > $o). 110.70/18.21 thf(zf_stmt_177, axiom, 110.70/18.21 (![D:term,C:term,B:term,A:term]: 110.70/18.21 ( ( zip_tseitin_37 @ D @ C @ B @ A ) <=> 110.70/18.21 ( ( ( A ) = ( B ) ) | ( ( ap @ A @ C ) != ( ap @ B @ D ) ) ) ))). 110.70/18.21 thf(zf_stmt_178, type, zip_tseitin_36 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_179, axiom, 110.70/18.21 (![Bound_variable_2140:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_36 @ Bound_variable_2140 @ P ) <=> 110.70/18.21 ( ( ~( ![A:term]: ( zip_tseitin_11 @ A @ P ) ) ) | 110.70/18.21 ( P @ Bound_variable_2140 ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_35 @ A @ P ) ) ) | 110.70/18.21 ( ~( ![A:term,B:term]: ( zip_tseitin_34 @ B @ A @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_180, type, zip_tseitin_35 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_181, axiom, 110.70/18.21 (![A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_35 @ A @ P ) <=> ( ( ~( P @ A ) ) | ( P @ ( lam @ A ) ) ) ))). 110.70/18.21 thf(zf_stmt_182, type, zip_tseitin_34 : term > term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_183, axiom, 110.70/18.21 (![B:term,A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_34 @ B @ A @ P ) <=> 110.70/18.21 ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) ) ))). 110.70/18.21 thf(zf_stmt_184, type, zip_tseitin_33 : 110.70/18.21 term > term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_185, axiom, 110.70/18.21 (![Bound_variable_3001:term,Bound_variable_2999:term, 110.70/18.21 P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_33 @ Bound_variable_3001 @ Bound_variable_2999 @ P ) <=> 110.70/18.21 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_32 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.21 ( ~( ![A:term,B:term]: ( zip_tseitin_31 @ B @ A @ P ) ) ) | 110.70/18.21 ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 110.70/18.21 ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 110.70/18.21 ( ~( P @ id @ Bound_variable_3001 @ id ) ) | 110.70/18.21 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_30 @ K @ N @ A @ M @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_186, type, zip_tseitin_32 : 110.70/18.21 subst > subst > term > subst > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_187, axiom, 110.70/18.21 (![K:subst,N:subst,A:term,M:subst,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_32 @ K @ N @ A @ M @ P ) <=> 110.70/18.21 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 110.70/18.21 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ))). 110.70/18.21 thf(zf_stmt_188, type, zip_tseitin_31 : 110.70/18.21 term > term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_189, axiom, 110.70/18.21 (![B:term,A:term,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_31 @ B @ A @ P ) <=> 110.70/18.21 ( ( ~( P @ id @ A @ id ) ) | ( ~( P @ id @ B @ id ) ) | 110.70/18.21 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) ) ))). 110.70/18.21 thf(zf_stmt_190, type, zip_tseitin_30 : 110.70/18.21 subst > subst > term > subst > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_191, axiom, 110.70/18.21 (![K:subst,N:subst,A:term,M:subst,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_30 @ K @ N @ A @ M @ P ) <=> 110.70/18.21 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 110.70/18.21 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ))). 110.70/18.21 thf(zf_stmt_192, type, zip_tseitin_29 : 110.70/18.21 term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_193, axiom, 110.70/18.21 (![Bound_variable_3211:term,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_29 @ Bound_variable_3211 @ P ) <=> 110.70/18.21 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_28 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.21 ( ~( ![M:subst,A:term,N:subst,K:subst]: 110.70/18.21 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) | 110.70/18.21 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_26 @ F @ P ) ) ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_19 @ B @ Bound_variable_3211 @ P ) ) ) | 110.70/18.21 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ))). 110.70/18.21 thf(zf_stmt_194, type, zip_tseitin_28 : 110.70/18.21 subst > subst > term > subst > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_195, axiom, 110.70/18.21 (![K:subst,N:subst,A:term,M:subst,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_28 @ K @ N @ A @ M @ P ) <=> 110.70/18.21 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 110.70/18.21 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_196, type, zip_tseitin_27 : 110.70/18.21 subst > subst > term > subst > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_197, axiom, 110.70/18.21 (![K:subst,N:subst,A:term,M:subst,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_27 @ K @ N @ A @ M @ P ) <=> 110.70/18.21 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 110.70/18.21 ( P @ M @ A @ ( comp @ K @ N ) ) ) ))). 110.70/18.21 thf(zf_stmt_198, type, zip_tseitin_26 : 110.70/18.21 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_199, type, zip_tseitin_25 : 110.70/18.21 term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_200, axiom, 110.70/18.21 (![Bound_variable_3046:term,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_25 @ Bound_variable_3046 @ P ) <=> 110.70/18.21 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_24 @ F @ P ) ) ) | 110.70/18.21 ( P @ 110.70/18.21 id @ 110.70/18.21 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_19 @ B @ Bound_variable_3046 @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_201, type, zip_tseitin_24 : 110.70/18.21 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_202, axiom, 110.70/18.21 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_24 @ F @ P ) <=> 110.70/18.21 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_23 @ A @ F @ P ) ) ) | 110.70/18.21 ( ~( ![M:subst,A:term,N:subst]: 110.70/18.21 ( ( sub @ ( F @ M @ A ) @ N ) = 110.70/18.21 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_203, type, zip_tseitin_23 : 110.70/18.21 term > ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_204, type, zip_tseitin_22 : 110.70/18.21 term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_205, axiom, 110.70/18.21 (![Bound_variable_3171:term,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_22 @ Bound_variable_3171 @ P ) <=> 110.70/18.21 ( ( ~( ![F:( subst > term > term ),Bound_variable_3149:term]: 110.70/18.21 ( zip_tseitin_21 @ Bound_variable_3149 @ F @ P ) ) ) | 110.70/18.21 ( P @ 110.70/18.21 id @ 110.70/18.21 ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_19 @ B @ Bound_variable_3171 @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_206, type, zip_tseitin_21 : 110.70/18.21 term > ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_207, axiom, 110.70/18.21 (![Bound_variable_3149:term,F:( subst > term > term ), 110.70/18.21 P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_21 @ Bound_variable_3149 @ F @ P ) <=> 110.70/18.21 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 110.70/18.21 ( ~( ![Bound_variable_3072:subst,Bound_variable_3074:term, 110.70/18.21 Bound_variable_3076:subst]: 110.70/18.21 ( ( sub @ 110.70/18.21 ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ 110.70/18.21 Bound_variable_3076 ) = 110.70/18.21 ( sub @ 110.70/18.21 ( sub @ 110.70/18.21 Bound_variable_3149 @ 110.70/18.21 ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ 110.70/18.21 Bound_variable_3076 ) ) ) ) | 110.70/18.21 ( ~( ![Bound_variable_3090:subst,Bound_variable_3092:term, 110.70/18.21 Bound_variable_3094:subst]: 110.70/18.21 ( ( F @ 110.70/18.21 ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ 110.70/18.21 ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) ) = 110.70/18.21 ( sub @ 110.70/18.21 Bound_variable_3149 @ 110.70/18.21 ( push @ 110.70/18.21 ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ 110.70/18.21 ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) ) ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_20 @ A @ F @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_208, type, zip_tseitin_20 : 110.70/18.21 term > ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_209, axiom, 110.70/18.21 (![A:term,F:( subst > term > term ),P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_20 @ A @ F @ P ) <=> 110.70/18.21 ( ( P @ id @ ( F @ id @ A ) @ id ) | ( ~( P @ id @ A @ id ) ) ) ))). 110.70/18.21 thf(zf_stmt_210, type, zip_tseitin_19 : 110.70/18.21 term > term > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_211, axiom, 110.70/18.21 (![B:term,Bound_variable_3171:term,P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_19 @ B @ Bound_variable_3171 @ P ) <=> 110.70/18.21 ( ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) | 110.70/18.21 ( ~( P @ id @ B @ id ) ) ) ))). 110.70/18.21 thf(zf_stmt_212, type, zip_tseitin_18 : $o). 110.70/18.21 thf(zf_stmt_213, axiom, 110.70/18.21 (( zip_tseitin_18 ) <=> 110.70/18.21 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 110.70/18.21 ( zip_tseitin_17 ) ))).thf(zf_stmt_214, type, zip_tseitin_17 : $o). 110.70/18.21 thf(zf_stmt_215, axiom, 110.70/18.21 (( zip_tseitin_17 ) <=> 110.70/18.21 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 110.70/18.21 ( zip_tseitin_16 ) ))).thf(zf_stmt_216, type, zip_tseitin_16 : $o). 110.70/18.21 thf(zf_stmt_217, axiom, 110.70/18.21 (( zip_tseitin_16 ) <=> 110.70/18.21 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) => ( zip_tseitin_15 ) ))). 110.70/18.21 thf(zf_stmt_218, type, zip_tseitin_15 : $o). 110.70/18.21 thf(zf_stmt_219, axiom, 110.70/18.21 (( zip_tseitin_15 ) <=> 110.70/18.21 ( ( ![P:( term > $o ),Bound_variable_2140:term]: 110.70/18.21 ( zip_tseitin_12 @ Bound_variable_2140 @ P ) ) => 110.70/18.21 ( ![P:( term > $o ),Bound_variable_2340:term,Bound_variable_2342:subst]: 110.70/18.21 ( zip_tseitin_14 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) ) ))). 110.70/18.21 thf(zf_stmt_220, type, zip_tseitin_14 : subst > term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_221, axiom, 110.70/18.21 (![Bound_variable_2342:subst,Bound_variable_2340:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_14 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) <=> 110.70/18.21 ( ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_4 @ B @ Bound_variable_2342 @ P ) ) ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_13 @ A @ P ) ) ) | 110.70/18.21 ( ~( ![A:term,B:term]: ( zip_tseitin_3 @ B @ A @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_222, type, zip_tseitin_13 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_223, axiom, 110.70/18.21 (![A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_13 @ A @ P ) <=> 110.70/18.21 ( ( ~( ![B:term]: ( zip_tseitin_5 @ B @ A @ P ) ) ) | 110.70/18.21 ( P @ ( lam @ A ) ) ) ))). 110.70/18.21 thf(zf_stmt_224, type, zip_tseitin_12 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_225, axiom, 110.70/18.21 (![Bound_variable_2140:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_12 @ Bound_variable_2140 @ P ) <=> 110.70/18.21 ( ( ~( ![A:term]: ( zip_tseitin_11 @ A @ P ) ) ) | 110.70/18.21 ( ~( ![A:term]: ( zip_tseitin_10 @ A @ P ) ) ) | 110.70/18.21 ( P @ Bound_variable_2140 ) | 110.70/18.21 ( ~( ![A:term,B:term]: ( zip_tseitin_9 @ B @ A @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_226, type, zip_tseitin_11 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_227, axiom, 110.70/18.21 (![A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_11 @ A @ P ) <=> ( ( ~( var @ A ) ) | ( P @ A ) ) ))). 110.70/18.21 thf(zf_stmt_228, type, zip_tseitin_10 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_229, axiom, 110.70/18.21 (![A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_10 @ A @ P ) <=> ( ( P @ ( lam @ A ) ) | ( ~( P @ A ) ) ) ))). 110.70/18.21 thf(zf_stmt_230, type, zip_tseitin_9 : term > term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_231, axiom, 110.70/18.21 (![B:term,A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_9 @ B @ A @ P ) <=> 110.70/18.21 ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | ( ~( P @ A ) ) ) ))). 110.70/18.21 thf(zf_stmt_232, type, zip_tseitin_8 : term > term > term > term > $o). 110.70/18.21 thf(zf_stmt_233, axiom, 110.70/18.21 (![D:term,C:term,B:term,A:term]: 110.70/18.21 ( ( zip_tseitin_8 @ D @ C @ B @ A ) <=> 110.70/18.21 ( ( ( A ) = ( B ) ) | 110.70/18.21 ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) ) ))). 110.70/18.21 thf(zf_stmt_234, type, zip_tseitin_7 : subst > term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_235, axiom, 110.70/18.21 (![Bound_variable_2342:subst,Bound_variable_2340:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_7 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) <=> 110.70/18.21 ( ( ~( ![A:term]: ( zip_tseitin_6 @ A @ P ) ) ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_4 @ B @ Bound_variable_2342 @ P ) ) ) | 110.70/18.21 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 110.70/18.21 ( ~( ![A:term,B:term]: ( zip_tseitin_3 @ B @ A @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_236, type, zip_tseitin_6 : term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_237, axiom, 110.70/18.21 (![A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_6 @ A @ P ) <=> 110.70/18.21 ( ( P @ ( lam @ A ) ) | 110.70/18.21 ( ~( ![B:term]: ( zip_tseitin_5 @ B @ A @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_238, type, zip_tseitin_5 : term > term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_239, axiom, 110.70/18.21 (![B:term,A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_5 @ B @ A @ P ) <=> 110.70/18.21 ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | ( ~( P @ B ) ) ) ))). 110.70/18.21 thf(zf_stmt_240, type, zip_tseitin_4 : term > subst > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_241, axiom, 110.70/18.21 (![B:term,Bound_variable_2342:subst,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_4 @ B @ Bound_variable_2342 @ P ) <=> 110.70/18.21 ( ( P @ ( sub @ B @ Bound_variable_2342 ) ) | ( ~( var @ B ) ) ) ))). 110.70/18.21 thf(zf_stmt_242, type, zip_tseitin_3 : term > term > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_243, axiom, 110.70/18.21 (![B:term,A:term,P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_3 @ B @ A @ P ) <=> 110.70/18.21 ( ( ~( P @ A ) ) | ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) ) ))). 110.70/18.21 thf(zf_stmt_244, type, zip_tseitin_2 : 110.70/18.21 subst > term > ( term > $o ) > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_245, axiom, 110.70/18.21 (![M:subst,A:term,Q:( term > $o ),P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_2 @ M @ A @ Q @ P ) <=> 110.70/18.21 ( ( ~( P @ A ) ) | ( Q @ one ) | 110.70/18.21 ( ~( ![X:term]: ( zip_tseitin_1 @ X @ M @ A @ Q @ P ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_246, type, zip_tseitin_1 : 110.70/18.21 term > subst > term > ( term > $o ) > ( term > $o ) > $o). 110.70/18.21 thf(zf_stmt_247, axiom, 110.70/18.21 (![X:term,M:subst,A:term,Q:( term > $o ),P:( term > $o )]: 110.70/18.21 ( ( zip_tseitin_1 @ X @ M @ A @ Q @ P ) <=> 110.70/18.21 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ))). 110.70/18.21 thf(zf_stmt_248, type, zip_tseitin_0 : 110.70/18.21 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 110.70/18.21 thf(zf_stmt_249, axiom, 110.70/18.21 (![X:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 110.70/18.21 ( ( zip_tseitin_0 @ X @ Q @ P ) <=> ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ))). 110.70/18.21 thf(zf_stmt_250, axiom, 110.70/18.21 (( ![DT:d_term]: ( ( DT ) = ( d_one ) ) ) & 110.70/18.21 ( ![DT1:d_term,DT2:d_term]: 110.70/18.21 ( ( ( d2term @ DT1 ) = ( d2term @ DT2 ) ) => ( ( DT1 ) = ( DT2 ) ) ) ) & 110.70/18.21 ( ( one ) = ( d2term @ d_one ) ) & 110.70/18.21 ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2term @ d_one ) ) & 110.70/18.21 ( ( sh ) = ( d2subst @ d_id ) ) & 110.70/18.21 ( ( hoasap @ 110.70/18.21 ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ 110.70/18.21 ( d2term @ d_one ) ) = 110.70/18.21 ( d2term @ d_one ) ) & 110.70/18.21 ( ![A:term,M:subst,P:( term > $o ),Q:( term > $o )]: 110.70/18.21 ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) <=> 110.70/18.21 ( ![X:term]: ( zip_tseitin_1 @ X @ M @ A @ Q @ P ) ) ) ) & 110.70/18.21 ( pushprop_lem1_gthm ) & ( axmap ) & 110.70/18.21 ( ( ![A:term,B:term]: ( zip_tseitin_121 @ B @ A ) ) <=> ( shinj ) ) & 110.70/18.21 ( hoasinduction_lem1v2_gthm ) & 110.70/18.21 ( ( ![B:term]: 110.70/18.21 ( ~( ![F:( subst > term > term )]: 110.70/18.21 ( ~( ![A:term,M:subst]: 110.70/18.21 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) <=> 110.70/18.21 ( hoasinduction_lem3v2_f ) ) & 110.70/18.21 ( ( hoasapinj2 ) <=> 110.70/18.21 ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_95 @ D @ C @ B @ A ) ) ) & 110.70/18.21 ( ~( ulamvar1 ) ) & ( ( zip_tseitin_120 ) <=> ( hoasinduction_lthm ) ) & 110.70/18.21 ( ( hoasinduction_no_psi_cond_lthm ) <=> ( zip_tseitin_113 ) ) & 110.70/18.21 ( ( hoaslaminj ) <=> 110.70/18.21 ( ![F:( subst > term > term ), 110.70/18.21 Bound_variable_2547:( subst > term > term ), 110.70/18.21 Bound_variable_2549:subst,Bound_variable_2551:term]: 110.70/18.21 ( zip_tseitin_106 @ 110.70/18.21 Bound_variable_2551 @ Bound_variable_2549 @ Bound_variable_2547 @ F ) ) ) & 110.70/18.21 ( induction2lem_gthm ) & ( ( zip_tseitin_105 ) <=> ( termmset_lthm ) ) & 110.70/18.21 ( ( pushprop_lem1v2_lthm ) <=> ( zip_tseitin_104 ) ) & 110.70/18.21 ( ( hoasinduction_lem0 ) <=> 110.70/18.21 ( ![P:( subst > term > subst > $o )]: 110.70/18.21 ( ~( ![Q:( term > $o )]: 110.70/18.21 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) ) ) ) ) & 110.70/18.21 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 110.70/18.21 ( zip_tseitin_103 @ Bound_variable_3283 @ P ) ) <=> 110.70/18.21 ( hoasinduction ) ) & 110.70/18.21 ( hoasinduction_gthm ) & ( axapp ) & ( hoaslamnotvar_lthm ) & 110.70/18.21 ( pushprop_lem3v2_lthm ) & 110.70/18.21 ( ( hoasinduction_lem3b_lthm ) <=> 110.70/18.21 ( ![B:term]: 110.70/18.21 ( ~( ![F:( subst > term > term )]: 110.70/18.21 ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) ) & 110.70/18.21 ( ulamvarind ) & 110.70/18.21 ( ( zip_tseitin_101 ) <=> ( hoasinduction_lem3a_lthm ) ) & 110.70/18.21 ( termmset_gthm ) & 110.70/18.21 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 110.70/18.21 ( zip_tseitin_98 @ Bound_variable_3046 @ P ) ) <=> 110.70/18.21 ( hoasinduction_lem3aa ) ) & 110.70/18.21 ( pushprop_lem1v2_gthm ) & ( pushprop_lem2v2 ) & ( axclos ) & 110.70/18.21 ( axassoc ) & 110.70/18.21 ( ( hoasinduction_lem2v2 ) <=> 110.70/18.21 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.70/18.21 Bound_variable_2820:term,Bound_variable_2822:term]: 110.70/18.21 ( zip_tseitin_97 @ Bound_variable_2822 @ Bound_variable_2820 @ Q @ P ) ) ) & 110.70/18.21 ( ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_94 @ D @ C @ B @ A ) ) <=> 110.70/18.21 ( apinj2 ) ) & 110.70/18.21 ( ( zip_tseitin_96 ) <=> ( hoasapinj2_lthm ) ) & 110.70/18.21 ( ( hoasinduction_lem3v2a ) <=> 110.70/18.21 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.70/18.21 Bound_variable_2931:term]: 110.70/18.21 ( zip_tseitin_93 @ Bound_variable_2931 @ Q @ P ) ) ) & 110.70/18.21 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) <=> 110.70/18.21 ( axvarcons ) ) & 110.70/18.21 ( hoasinduction_lem2v2_gthm ) & 110.70/18.21 ( ( zip_tseitin_91 ) <=> ( hoasinduction_lem3_lthm ) ) & 110.70/18.21 ( pushprop_gthm ) & 110.70/18.21 ( ( hoasinduction_lem3v2a_lthm ) <=> ( zip_tseitin_85 ) ) & 110.70/18.21 ( hoasinduction_lem1_lthm ) & ( ~( lamnotap ) ) & ( hoasapinj1_gthm ) & 110.70/18.21 ( hoaslaminj_gthm ) & 110.70/18.21 ( ( hoasinduction_lem0_lthm ) <=> 110.70/18.21 ( ![P:( subst > term > subst > $o )]: 110.70/18.21 ( ~( ![Q:( term > $o )]: 110.70/18.21 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) ) ) ) ) & 110.70/18.21 ( ( substmonoid_lthm ) <=> ( zip_tseitin_82 ) ) & 110.70/18.21 ( hoasinduction_lem3_gthm ) & ( lamnotvar ) & 110.70/18.21 ( hoasinduction_lem1_gthm ) & 110.70/18.21 ( ( hoasinduction_no_psi_cond ) <=> 110.70/18.21 ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]: 110.70/18.21 ( zip_tseitin_79 @ Bound_variable_3295 @ P ) ) ) & 110.70/18.21 ( ~( hoasvar @ 110.70/18.21 ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) & 110.70/18.21 ( ( ![F:( subst > term > term ),Bound_variable_2603:term, 110.70/18.21 Bound_variable_2605:term]: 110.70/18.21 ( zip_tseitin_76 @ Bound_variable_2605 @ Bound_variable_2603 @ F ) ) <=> 110.70/18.21 ( hoaslamnotap ) ) & 110.70/18.21 ( ulamvarsh ) & 110.70/18.21 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 110.70/18.21 ( zip_tseitin_75 @ Bound_variable_2367 @ P ) ) <=> 110.70/18.21 ( induction2 ) ) & 110.70/18.21 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) <=> 110.70/18.21 ( axshiftcons ) ) & 110.70/18.21 ( ( termmset ) <=> ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) & 110.70/18.21 ( ( ![P:( term > $o ),A:term,M:subst]: 110.70/18.21 ( ~( ![Q:( term > $o )]: 110.70/18.21 ( ~( ![X:term]: ( zip_tseitin_1 @ X @ M @ A @ Q @ P ) ) ) ) ) ) <=> 110.70/18.21 ( pushprop_lem0_lthm ) ) & 110.70/18.21 ( hoasapnotvar_lthm ) & 110.70/18.21 ( ( zip_tseitin_73 ) <=> ( hoasinduction_lthm_3 ) ) & 110.70/18.21 ( ( axvarid ) <=> ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) & 110.70/18.21 ( ( zip_tseitin_62 ) <=> ( hoasinduction_lem3v2_lthm ) ) & 110.70/18.21 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 110.70/18.21 Bound_variable_2910:term]: 110.70/18.21 ( zip_tseitin_59 @ Bound_variable_2910 @ Q @ P ) ) <=> 110.70/18.21 ( hoasinduction_lem3v2 ) ) & 110.70/18.21 ( ( zip_tseitin_58 ) <=> ( pushprop_lem1_lthm ) ) & 110.70/18.21 ( pushprop_lem2v2_gthm ) & ( pushprop_lem3v2 ) & ( substmonoid_gthm ) & 110.70/18.21 ( pushprop_lem2v2_lthm ) & ( induction2_gthm ) & 110.70/18.21 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]: 110.70/18.21 ( zip_tseitin_56 @ Bound_variable_3232 @ P ) ) <=> 110.70/18.21 ( hoasinduction_lem3a ) ) & 110.70/18.21 ( ( zip_tseitin_55 ) <=> ( substmonoid ) ) & 110.70/18.21 ( ( ![B:term]: 110.70/18.21 ( ~( ![F:( subst > term > term )]: 110.70/18.21 ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) <=> 110.70/18.21 ( hoasinduction_lem3b ) ) & 110.70/18.21 ( hoasinduction_lem2_gthm ) & ( pushprop ) & 110.70/18.21 ( ( induction2_lthm ) <=> ( zip_tseitin_54 ) ) & 110.70/18.21 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) <=> ( axidl ) ) & 110.70/18.21 ( hoaslamnotvar ) & ( hoasapinj2_gthm ) & ( hoasinduction_lem2_lthm ) & 110.70/18.21 ( axabs ) & 110.70/18.21 ( ( pushprop_lem0 ) <=> 110.70/18.21 ( ![P:( term > $o ),A:term,M:subst]: 110.70/18.21 ( ~( ![Q:( term > $o )]: 110.70/18.21 ( ~( ![X:term]: ( zip_tseitin_1 @ X @ M @ A @ Q @ P ) ) ) ) ) ) ) & 110.70/18.21 ( ( laminj ) <=> ( ![A:term,B:term]: ( zip_tseitin_47 @ B @ A ) ) ) & 110.70/18.21 ( ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]: 110.70/18.21 ( zip_tseitin_46 @ B @ M @ A @ K @ P ) ) <=> 110.70/18.21 ( pushprop_lem1 ) ) & 110.70/18.21 ( ( axidr ) <=> ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) ) & 110.70/18.21 ( ( axscons ) <=> 110.70/18.21 ( ![M:subst]: 110.70/18.21 ( ( M ) = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) ) ) & 110.70/18.21 ( ( zip_tseitin_45 ) <=> ( hoaslaminj_lthm ) ) & 110.70/18.21 ( ( hoasapinj1_lthm ) <=> ( zip_tseitin_40 ) ) & 110.70/18.21 ( ( apinj1 ) <=> 110.70/18.21 ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_37 @ D @ C @ B @ A ) ) ) & 110.70/18.21 ( pushprop_lthm ) & ( hoasinduction_lem3a_gthm ) & 110.70/18.21 ( hoasinduction_lem3b_gthm ) & ( hoaslamnotvar_gthm ) & 110.70/18.21 ( hoaslamnotap_gthm ) & 110.70/18.21 ( ( induction ) <=> 110.70/18.21 ( ![P:( term > $o ),Bound_variable_2140:term]: 110.70/18.21 ( zip_tseitin_36 @ Bound_variable_2140 @ P ) ) ) & 110.70/18.21 ( hoasapnotvar ) & ( hoaslamnotap_lthm ) & ( hoasinduction_lem1 ) & 110.70/18.21 ( ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term, 110.70/18.21 Bound_variable_3001:term]: 110.70/18.21 ( zip_tseitin_33 @ Bound_variable_3001 @ Bound_variable_2999 @ P ) ) <=> 110.70/18.21 ( hoasinduction_lem2 ) ) & 110.70/18.21 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 110.70/18.21 ( zip_tseitin_29 @ Bound_variable_3211 @ P ) ) <=> 110.70/18.21 ( hoasinduction_lem3 ) ) & 110.70/18.21 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 110.70/18.21 ( zip_tseitin_25 @ Bound_variable_3046 @ P ) ) <=> 110.70/18.21 ( hoasinduction_lem3aa_lthm ) ) & 110.70/18.21 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3171:term]: 110.70/18.21 ( zip_tseitin_22 @ Bound_variable_3171 @ P ) ) <=> 110.70/18.21 ( hoasinduction_lem3aaa ) ) & 110.70/18.21 ( ( hoasinduction_lem3v2_f_lthm ) <=> 110.70/18.21 ( ![B:term]: 110.70/18.21 ( ~( ![F:( subst > term > term )]: 110.70/18.21 ( ~( ![A:term,M:subst]: 110.70/18.21 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) ) & 110.70/18.21 ( pushprop_lthm_orig ) & ( apnotvar ) & ( hoasinduction_lem3v2_gthm ) & 110.70/18.21 ( ( zip_tseitin_18 ) <=> ( induction2lem_lthm ) ) & 110.70/18.21 ( ( hoasapinj1 ) <=> 110.70/18.21 ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_8 @ D @ C @ B @ A ) ) ) & 110.70/18.21 ( hoasapnotvar_gthm ) & ( axvarshift ) & 110.70/18.21 ( ( induction2lem ) <=> 110.70/18.21 ( ![P:( term > $o ),Bound_variable_2340:term,Bound_variable_2342:subst]: 110.70/18.21 ( zip_tseitin_7 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) ) ) & 110.70/18.21 ( hoasinduction_lem1v2 ) & ( pushprop_lem0_gthm ) & 110.70/18.21 ( ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]: 110.70/18.21 ( zip_tseitin_2 @ M @ A @ Q @ P ) ) <=> 110.70/18.21 ( pushprop_lem1v2 ) ) & 110.70/18.21 ( ~( var @ ( d2term @ d_one ) ) ) & 110.70/18.21 ( ![P:( subst > term > subst > $o ),Q:( term > $o )]: 110.70/18.21 ( ( hoasinduction_p_and_p_prime @ P @ Q ) <=> 110.70/18.21 ( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P ) ) ) ) & 110.70/18.21 ( ![Bound_variable_4913:subst,Bound_variable_4915:( subst > term > term )]: 110.70/18.21 ( ( hoaslam @ Bound_variable_4913 @ Bound_variable_4915 ) = 110.70/18.21 ( d2term @ d_one ) ) ) & 110.70/18.21 ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 110.70/18.21 ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 110.70/18.21 ( ( id ) = ( d2subst @ d_id ) ) & 110.70/18.21 ( ( lam @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 110.70/18.21 ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 110.70/18.21 ( ![DS1:d_subst,DS2:d_subst]: 110.70/18.21 ( ( ( d2subst @ DS1 ) = ( d2subst @ DS2 ) ) => ( ( DS1 ) = ( DS2 ) ) ) ) & 110.70/18.21 ( ![DS:d_subst]: ( ( DS ) = ( d_id ) ) ) & 110.70/18.21 ( ![S:subst]: ( ?[DS:d_subst]: ( ( S ) = ( d2subst @ DS ) ) ) ) & 110.70/18.21 ( ![T:term]: ( ?[DT:d_term]: ( ( T ) = ( d2term @ DT ) ) ) ))). 110.70/18.21 thf(zip_derived_cl609, plain, 110.70/18.21 (( (hoasinduction_lem3aa) | ~ (zip_tseitin_98 @ sk__387 @ sk__386))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl473, plain, (((id) = (d2subst @ d_id))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl3088, plain, 110.70/18.21 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 110.70/18.21 (((sub @ (X0 @ (sk__475 @ X0) @ (sk__476 @ X0)) @ (sk__477 @ X0)) 110.70/18.21 != (X0 @ (comp @ (sk__475 @ X0) @ (sk__477 @ X0)) @ 110.70/18.21 (sub @ (sk__476 @ X0) @ (sk__477 @ X0)))) 110.70/18.21 | (X1 @ id @ (hoaslam @ id @ X0) @ id) 110.70/18.21 | (X1 @ id @ (sk__478 @ X1 @ X0) @ id) 110.70/18.21 | ~ (zip_tseitin_122 @ X0 @ X1))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_6])). 110.70/18.21 thf(zip_derived_cl469, plain, (![X0 : d_subst]: ((X0) = (d_id))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl469, plain, (![X0 : d_subst]: ((X0) = (d_id))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl936, plain, (![X0 : d_subst, X1 : d_subst]: ((X1) = (X0))), 110.70/18.21 inference('sup+', [status(thm)], [zip_derived_cl469, zip_derived_cl469])). 110.70/18.21 thf(zip_derived_cl468, plain, 110.70/18.21 (![X0 : subst]: ((X0) = (d2subst @ (sk__473 @ X0)))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl663, plain, 110.70/18.21 ((~ (sk__479 @ id @ (lam @ (sub @ sk__480 @ (push @ one @ sh))) @ id) 110.70/18.21 | ~ (hoasinduction_lem3aa))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_8])). 110.70/18.21 thf(zip_derived_cl171, plain, 110.70/18.21 (![X0 : term, X1 : term]: 110.70/18.21 (((lam @ X1) != (lam @ X0)) 110.70/18.21 | ((X1) = (X0)) 110.70/18.21 | ~ (zip_tseitin_47 @ X0 @ X1))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_157])). 110.70/18.21 thf(zip_derived_cl528, plain, 110.70/18.21 (![X0 : term, X1 : term]: ( (zip_tseitin_47 @ X0 @ X1) | ~ (laminj))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl172, plain, 110.70/18.21 (![X0 : term, X1 : term]: ( (zip_tseitin_47 @ X0 @ X1) | ((X1) != (X0)))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_157])). 110.70/18.21 thf(zip_derived_cl650, plain, (((one) = (d2term @ d_one))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl527, plain, 110.70/18.21 (( (laminj) | ~ (zip_tseitin_47 @ sk__434 @ sk__433))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl652, plain, (![X0 : d_term]: ((X0) = (d_one))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl652, plain, (![X0 : d_term]: ((X0) = (d_one))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl940, plain, (![X0 : d_term, X1 : d_term]: ((X1) = (X0))), 110.70/18.21 inference('sup+', [status(thm)], [zip_derived_cl652, zip_derived_cl652])). 110.70/18.21 thf(zip_derived_cl467, plain, 110.70/18.21 (![X0 : term]: ((X0) = (d2term @ (sk__474 @ X0)))), 110.70/18.21 inference('cnf', [status(esa)], [zf_stmt_250])). 110.70/18.21 thf(zip_derived_cl3128, plain, ($false), 110.70/18.21 inference('eprover', [status(thm)], 110.70/18.21 [zip_derived_cl370, zip_derived_cl84, zip_derived_cl371, 110.70/18.21 zip_derived_cl94, zip_derived_cl664, zip_derived_cl609, 110.70/18.21 zip_derived_cl473, zip_derived_cl3088, zip_derived_cl936, 110.70/18.21 zip_derived_cl468, zip_derived_cl663, zip_derived_cl171, 110.70/18.21 zip_derived_cl528, zip_derived_cl172, zip_derived_cl650, 110.70/18.21 zip_derived_cl527, zip_derived_cl940, zip_derived_cl467])). 110.70/18.21 110.70/18.21 % SZS output end Refutation 110.70/18.21 110.70/18.21 110.70/18.21 % Terminating... 110.70/18.28 % Runner terminated. 0.54/18.31 % Zipperpin 1.5 exiting 0.54/18.31 EOF