0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.07 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.IRAI5HfWm9 true 0.13/0.39 % Computer : n026.cluster.edu 0.13/0.39 % Model : x86_64 x86_64 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.39 % Memory : 8046.5625MB 0.13/0.39 % OS : Linux 6.8.0-71-generic 0.13/0.39 % CPULimit : 1440 0.13/0.39 % WCLimit : 180 0.13/0.39 % DateTime : Mon Jul 27 13:25:34 UTC 2026 0.13/0.39 % CPUTime : 0.13/0.39 % Running portfolio for 1440 s 0.13/0.39 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.39 % Number of cores: 8 0.13/0.40 % Python version: Python 3.12.3 0.13/0.40 % Running in HO mode 0.38/0.70 % Total configuration time : 828 0.38/0.70 % Estimated wc time : 1656 0.38/0.70 % Estimated cpu time (8 cpus) : 207.0 0.38/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.39/0.83 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.39/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.39/0.83 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.39/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.39/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.39/0.86 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.39/0.87 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 225.65/30.68 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 289.96/40.93 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 418.54/60.96 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 385.97/70.93 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 533.71/80.88 % /export/starexec/sandbox2/solver/bin/lams/33_shallow_sine.sh running for 66s 485.16/80.94 % /export/starexec/sandbox2/solver/bin/lams/15_lifting1.sh running for 30s 485.16/80.94 % /export/starexec/sandbox2/solver/bin/lams/40_e_lift.sh running for 80s 651.76/88.98 % Solved by lams/40_e_lift.sh. 651.76/88.98 % done 178 iterations in 7.855s 651.76/88.98 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 651.76/88.98 % SZS output start Refutation 651.76/88.98 thf(d_subst_type, type, d_subst: $tType). 651.76/88.98 thf(subst_type, type, subst: $tType). 651.76/88.98 thf(term_type, type, term: $tType). 651.76/88.98 thf(d_term_type, type, d_term: $tType). 651.76/88.98 thf(axmap_type, type, axmap: $o). 651.76/88.98 thf(zip_tseitin_34_type, type, zip_tseitin_34: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(sk__115_type, type, sk__115: (subst > term > term) > subst). 651.76/88.98 thf(zip_tseitin_2_type, type, zip_tseitin_2: term > term > (term > $o) > $o). 651.76/88.98 thf(hoasinduction_lem3a_type, type, hoasinduction_lem3a: $o). 651.76/88.98 thf(hoasapnotvar_gthm_type, type, hoasapnotvar_gthm: $o). 651.76/88.98 thf(zip_tseitin_18_type, type, zip_tseitin_18: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_23_type, type, zip_tseitin_23: term > term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(pushprop_lthm_orig_type, type, pushprop_lthm_orig: $o). 651.76/88.98 thf(termmset_gthm_type, type, termmset_gthm: $o). 651.76/88.98 thf(axclos_type, type, axclos: $o). 651.76/88.98 thf(lam_type, type, lam: term > term). 651.76/88.98 thf(lamnotap_type, type, lamnotap: $o). 651.76/88.98 thf(hoasinduction_lem3aa_type, type, hoasinduction_lem3aa: $o). 651.76/88.98 thf(zip_tseitin_32_type, type, zip_tseitin_32: (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(hoaslamnotvar_gthm_type, type, hoaslamnotvar_gthm: $o). 651.76/88.98 thf(zip_tseitin_65_type, type, zip_tseitin_65: term > term > term > term > $o). 651.76/88.98 thf(axvarcons_type, type, axvarcons: $o). 651.76/88.98 thf(zip_tseitin_28_type, type, zip_tseitin_28: subst > subst > term > 651.76/88.98 subst > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(hoaslamnotvar_lthm_type, type, hoaslamnotvar_lthm: $o). 651.76/88.98 thf(zip_tseitin_13_type, type, zip_tseitin_13: $o). 651.76/88.98 thf(d2term_type, type, d2term: d_term > term). 651.76/88.98 thf(zip_tseitin_71_type, type, zip_tseitin_71: subst > term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_110_type, type, zip_tseitin_110: term > term > term > term > $o). 651.76/88.98 thf(zip_tseitin_12_type, type, zip_tseitin_12: subst > term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_3_type, type, zip_tseitin_3: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_76_type, type, zip_tseitin_76: $o). 651.76/88.98 thf(hoasinduction_no_psi_cond_lthm_type, type, hoasinduction_no_psi_cond_lthm: 651.76/88.98 $o). 651.76/88.98 thf(zip_tseitin_22_type, type, zip_tseitin_22: term > term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_107_type, type, zip_tseitin_107: $o). 651.76/88.98 thf(zip_tseitin_29_type, type, zip_tseitin_29: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_58_type, type, zip_tseitin_58: (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_93_type, type, zip_tseitin_93: term > (term > $o) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(substmonoid_type, type, substmonoid: $o). 651.76/88.98 thf(zip_tseitin_53_type, type, zip_tseitin_53: (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_100_type, type, zip_tseitin_100: $o). 651.76/88.98 thf(zip_tseitin_102_type, type, zip_tseitin_102: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_31_type, type, zip_tseitin_31: term > 651.76/88.98 (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(hoasinduction_lem3a_gthm_type, type, hoasinduction_lem3a_gthm: $o). 651.76/88.98 thf(substmonoid_gthm_type, type, substmonoid_gthm: $o). 651.76/88.98 thf(d_id_type, type, d_id: d_subst). 651.76/88.98 thf(pushprop_gthm_type, type, pushprop_gthm: $o). 651.76/88.98 thf(zip_tseitin_14_type, type, zip_tseitin_14: $o). 651.76/88.98 thf(hoasinduction_lem3v2_type, type, hoasinduction_lem3v2: $o). 651.76/88.98 thf(zip_tseitin_77_type, type, zip_tseitin_77: $o). 651.76/88.98 thf(zip_tseitin_80_type, type, zip_tseitin_80: term > term > 651.76/88.98 (subst > term > term) > $o). 651.76/88.98 thf(zip_tseitin_111_type, type, zip_tseitin_111: $o). 651.76/88.98 thf(sk__481_type, type, sk__481: term). 651.76/88.98 thf(pushprop_lem1v2_type, type, pushprop_lem1v2: $o). 651.76/88.98 thf(zip_tseitin_125_type, type, zip_tseitin_125: (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_66_type, type, zip_tseitin_66: $o). 651.76/88.98 thf(push_type, type, push: term > subst > subst). 651.76/88.98 thf(zip_tseitin_39_type, type, zip_tseitin_39: term > term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_63_type, type, zip_tseitin_63: term > term > term > term > $o). 651.76/88.98 thf(zip_tseitin_67_type, type, zip_tseitin_67: (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_16_type, type, zip_tseitin_16: $o). 651.76/88.98 thf(hoaslamnotap_lthm_type, type, hoaslamnotap_lthm: $o). 651.76/88.98 thf(axshiftcons_type, type, axshiftcons: $o). 651.76/88.98 thf(zip_tseitin_41_type, type, zip_tseitin_41: term > term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_10_type, type, zip_tseitin_10: term > subst > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_21_type, type, zip_tseitin_21: subst > subst > term > 651.76/88.98 subst > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_89_type, type, zip_tseitin_89: $o). 651.76/88.98 thf(zip_tseitin_62_type, type, zip_tseitin_62: $o). 651.76/88.98 thf(zip_tseitin_33_type, type, zip_tseitin_33: term > term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_0_type, type, zip_tseitin_0: term > (term > $o) > 651.76/88.98 (term > $o) > subst > term > $o). 651.76/88.98 thf(zip_tseitin_91_type, type, zip_tseitin_91: $o). 651.76/88.98 thf(zip_tseitin_119_type, type, zip_tseitin_119: $o). 651.76/88.98 thf(hoasinduction_lem1v2_type, type, hoasinduction_lem1v2: $o). 651.76/88.98 thf(sk__407_type, type, sk__407: subst > term > subst > $o). 651.76/88.98 thf(hoasapinj1_lthm_type, type, hoasapinj1_lthm: $o). 651.76/88.98 thf(zip_tseitin_83_type, type, zip_tseitin_83: term > (term > $o) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(hoasapinj1_type, type, hoasapinj1: $o). 651.76/88.98 thf(hoasinduction_p_and_p_prime_type, type, hoasinduction_p_and_p_prime: 651.76/88.98 (subst > term > subst > $o) > (term > $o) > $o). 651.76/88.98 thf(axapp_type, type, axapp: $o). 651.76/88.98 thf(hoasinduction_lem3_lthm_type, type, hoasinduction_lem3_lthm: $o). 651.76/88.98 thf(hoasinduction_lem3v2_lthm_type, type, hoasinduction_lem3v2_lthm: $o). 651.76/88.98 thf(pushprop_lem1v2_gthm_type, type, pushprop_lem1v2_gthm: $o). 651.76/88.98 thf(shinj_type, type, shinj: $o). 651.76/88.98 thf(zip_tseitin_120_type, type, zip_tseitin_120: term > 651.76/88.98 (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_85_type, type, zip_tseitin_85: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_6_type, type, zip_tseitin_6: subst > term > (term > $o) > $o). 651.76/88.98 thf(hoasap_type, type, hoasap: subst > term > subst > term > term). 651.76/88.98 thf(hoasinduction_gthm_type, type, hoasinduction_gthm: $o). 651.76/88.98 thf(hoasinduction_lem3b_type, type, hoasinduction_lem3b: $o). 651.76/88.98 thf(hoaslaminj_type, type, hoaslaminj: $o). 651.76/88.98 thf(induction2_lthm_type, type, induction2_lthm: $o). 651.76/88.98 thf(zip_tseitin_44_type, type, zip_tseitin_44: term > (term > $o) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_19_type, type, zip_tseitin_19: term > (term > $o) > $o). 651.76/88.98 thf(sk__474_type, type, sk__474: subst > d_subst). 651.76/88.98 thf(zip_tseitin_84_type, type, zip_tseitin_84: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_115_type, type, zip_tseitin_115: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_8_type, type, zip_tseitin_8: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_87_type, type, zip_tseitin_87: term > (term > $o) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(induction2_gthm_type, type, induction2_gthm: $o). 651.76/88.98 thf(hoasinduction_lem2_gthm_type, type, hoasinduction_lem2_gthm: $o). 651.76/88.98 thf(one_type, type, one: term). 651.76/88.98 thf(pushprop_lem2v2_lthm_type, type, pushprop_lem2v2_lthm: $o). 651.76/88.98 thf(zip_tseitin_81_type, type, zip_tseitin_81: $o). 651.76/88.98 thf(id_type, type, id: subst). 651.76/88.98 thf(comp_type, type, comp: subst > subst > subst). 651.76/88.98 thf(hoaslamnotap_type, type, hoaslamnotap: $o). 651.76/88.98 thf(zip_tseitin_48_type, type, zip_tseitin_48: $o). 651.76/88.98 thf(zip_tseitin_97_type, type, zip_tseitin_97: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_78_type, type, zip_tseitin_78: $o). 651.76/88.98 thf(induction2_type, type, induction2: $o). 651.76/88.98 thf(axvarid_type, type, axvarid: $o). 651.76/88.98 thf(axvarshift_type, type, axvarshift: $o). 651.76/88.98 thf(hoaslamnotap_gthm_type, type, hoaslamnotap_gthm: $o). 651.76/88.98 thf(induction2lem_type, type, induction2lem: $o). 651.76/88.98 thf(sk__480_type, type, sk__480: subst > term > subst > $o). 651.76/88.98 thf(hoasinduction_lem1_gthm_type, type, hoasinduction_lem1_gthm: $o). 651.76/88.98 thf(sh_type, type, sh: subst). 651.76/88.98 thf(hoasinduction_lem2v2_type, type, hoasinduction_lem2v2: $o). 651.76/88.98 thf(zip_tseitin_114_type, type, zip_tseitin_114: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_1_type, type, zip_tseitin_1: term > term > $o). 651.76/88.98 thf(zip_tseitin_122_type, type, zip_tseitin_122: term > term > term > term > $o). 651.76/88.98 thf(zip_tseitin_64_type, type, zip_tseitin_64: term > term > term > term > $o). 651.76/88.98 thf(sk__477_type, type, sk__477: (subst > term > term) > term). 651.76/88.98 thf(laminj_type, type, laminj: $o). 651.76/88.98 thf(zip_tseitin_54_type, type, zip_tseitin_54: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(hoasinduction_lem3aa_lthm_type, type, hoasinduction_lem3aa_lthm: $o). 651.76/88.98 thf(ulamvarind_type, type, ulamvarind: $o). 651.76/88.98 thf(zip_tseitin_121_type, type, zip_tseitin_121: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(pushprop_lem2v2_type, type, pushprop_lem2v2: $o). 651.76/88.98 thf(zip_tseitin_56_type, type, zip_tseitin_56: term > term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_74_type, type, zip_tseitin_74: $o). 651.76/88.98 thf(zip_tseitin_47_type, type, zip_tseitin_47: $o). 651.76/88.98 thf(zip_tseitin_70_type, type, zip_tseitin_70: term > term > $o). 651.76/88.98 thf(hoasinduction_lthm_3_type, type, hoasinduction_lthm_3: $o). 651.76/88.98 thf(zip_tseitin_9_type, type, zip_tseitin_9: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_106_type, type, zip_tseitin_106: $o). 651.76/88.98 thf(zip_tseitin_59_type, type, zip_tseitin_59: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(hoasinduction_lem3v2_f_lthm_type, type, hoasinduction_lem3v2_f_lthm: $o). 651.76/88.98 thf(zip_tseitin_109_type, type, zip_tseitin_109: term > term > term > term > $o). 651.76/88.98 thf(zip_tseitin_55_type, type, zip_tseitin_55: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(sk__476_type, type, sk__476: (subst > term > term) > subst). 651.76/88.98 thf(zip_tseitin_96_type, type, zip_tseitin_96: term > term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(apinj2_type, type, apinj2: $o). 651.76/88.98 thf(hoasapinj2_lthm_type, type, hoasapinj2_lthm: $o). 651.76/88.98 thf(zip_tseitin_24_type, type, zip_tseitin_24: term > 651.76/88.98 (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(ulamvarsh_type, type, ulamvarsh: $o). 651.76/88.98 thf(zip_tseitin_94_type, type, zip_tseitin_94: $o). 651.76/88.98 thf(hoasinduction_lem3v2a_lthm_type, type, hoasinduction_lem3v2a_lthm: $o). 651.76/88.98 thf(hoasinduction_lem3a_lthm_type, type, hoasinduction_lem3a_lthm: $o). 651.76/88.98 thf(pushprop_lthm_type, type, pushprop_lthm: $o). 651.76/88.98 thf(zip_tseitin_42_type, type, zip_tseitin_42: term > (term > $o) > $o). 651.76/88.98 thf(hoasapinj1_gthm_type, type, hoasapinj1_gthm: $o). 651.76/88.98 thf(hoasinduction_lem0_lthm_type, type, hoasinduction_lem0_lthm: $o). 651.76/88.98 thf(hoasinduction_lem3b_lthm_type, type, hoasinduction_lem3b_lthm: $o). 651.76/88.98 thf(zip_tseitin_4_type, type, zip_tseitin_4: term > subst > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_52_type, type, zip_tseitin_52: term > term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_86_type, type, zip_tseitin_86: (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_5_type, type, zip_tseitin_5: term > term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_68_type, type, zip_tseitin_68: term > (term > $o) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(lamnotvar_type, type, lamnotvar: $o). 651.76/88.98 thf(apnotvar_type, type, apnotvar: $o). 651.76/88.98 thf(zip_tseitin_95_type, type, zip_tseitin_95: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_117_type, type, zip_tseitin_117: subst > term > 651.76/88.98 (term > $o) > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_46_type, type, zip_tseitin_46: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(pushprop_p_and_p_prime_type, type, pushprop_p_and_p_prime: term > 651.76/88.98 subst > 651.76/88.98 (term > $o) > 651.76/88.98 (term > $o) > $o). 651.76/88.98 thf(hoasapinj2_gthm_type, type, hoasapinj2_gthm: $o). 651.76/88.98 thf(zip_tseitin_104_type, type, zip_tseitin_104: $o). 651.76/88.98 thf(zip_tseitin_50_type, type, zip_tseitin_50: $o). 651.76/88.98 thf(zip_tseitin_124_type, type, zip_tseitin_124: subst > term > 651.76/88.98 (term > $o) > (term > $o) > $o). 651.76/88.98 thf(d_one_type, type, d_one: d_term). 651.76/88.98 thf(pushprop_lem1_type, type, pushprop_lem1: $o). 651.76/88.98 thf(pushprop_type, type, pushprop: $o). 651.76/88.98 thf(hoasinduction_lem1_lthm_type, type, hoasinduction_lem1_lthm: $o). 651.76/88.98 thf(hoasinduction_lem3_gthm_type, type, hoasinduction_lem3_gthm: $o). 651.76/88.98 thf(sub_type, type, sub: term > subst > term). 651.76/88.98 thf(zip_tseitin_45_type, type, zip_tseitin_45: (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_79_type, type, zip_tseitin_79: $o). 651.76/88.98 thf(zip_tseitin_27_type, type, zip_tseitin_27: subst > subst > term > 651.76/88.98 subst > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(apinj1_type, type, apinj1: $o). 651.76/88.98 thf(zip_tseitin_75_type, type, zip_tseitin_75: $o). 651.76/88.98 thf(zip_tseitin_98_type, type, zip_tseitin_98: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(axidl_type, type, axidl: $o). 651.76/88.98 thf(hoasinduction_type, type, hoasinduction: $o). 651.76/88.98 thf(ap_type, type, ap: term > term > term). 651.76/88.98 thf(termmset_type, type, termmset: $o). 651.76/88.98 thf(zip_tseitin_25_type, type, zip_tseitin_25: (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_51_type, type, zip_tseitin_51: term > subst > 651.76/88.98 (subst > term > term) > 651.76/88.98 (subst > term > term) > $o). 651.76/88.98 thf(hoasapinj2_type, type, hoasapinj2: $o). 651.76/88.98 thf(zip_tseitin_26_type, type, zip_tseitin_26: term > term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(hoasinduction_lem1_type, type, hoasinduction_lem1: $o). 651.76/88.98 thf(pushprop_lem3v2_lthm_type, type, pushprop_lem3v2_lthm: $o). 651.76/88.98 thf(hoasinduction_lem3v2a_type, type, hoasinduction_lem3v2a: $o). 651.76/88.98 thf(hoasapnotvar_type, type, hoasapnotvar: $o). 651.76/88.98 thf(var_type, type, var: term > $o). 651.76/88.98 thf(pushprop_lem1_lthm_type, type, pushprop_lem1_lthm: $o). 651.76/88.98 thf(induction2lem_lthm_type, type, induction2lem_lthm: $o). 651.76/88.98 thf(pushprop_lem0_lthm_type, type, pushprop_lem0_lthm: $o). 651.76/88.98 thf(axassoc_type, type, axassoc: $o). 651.76/88.98 thf(hoaslamnotvar_type, type, hoaslamnotvar: $o). 651.76/88.98 thf(zip_tseitin_112_type, type, zip_tseitin_112: $o). 651.76/88.98 thf(hoaslam_type, type, hoaslam: subst > (subst > term > term) > term). 651.76/88.98 thf(hoasinduction_lem2_lthm_type, type, hoasinduction_lem2_lthm: $o). 651.76/88.98 thf(zip_tseitin_103_type, type, zip_tseitin_103: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(pushprop_lem3v2_type, type, pushprop_lem3v2: $o). 651.76/88.98 thf(hoasinduction_lem3b_gthm_type, type, hoasinduction_lem3b_gthm: $o). 651.76/88.98 thf(sk__113_type, type, sk__113: (subst > term > term) > subst). 651.76/88.98 thf(pushprop_lem0_type, type, pushprop_lem0: $o). 651.76/88.98 thf(hoaslaminj_gthm_type, type, hoaslaminj_gthm: $o). 651.76/88.98 thf(zip_tseitin_90_type, type, zip_tseitin_90: $o). 651.76/88.98 thf(zip_tseitin_108_type, type, zip_tseitin_108: $o). 651.76/88.98 thf(zip_tseitin_113_type, type, zip_tseitin_113: term > term > (term > $o) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_61_type, type, zip_tseitin_61: $o). 651.76/88.98 thf(hoasinduction_lem3_type, type, hoasinduction_lem3: $o). 651.76/88.98 thf(hoasinduction_lem2_type, type, hoasinduction_lem2: $o). 651.76/88.98 thf(hoasinduction_lem0_type, type, hoasinduction_lem0: $o). 651.76/88.98 thf(sk__408_type, type, sk__408: term). 651.76/88.98 thf(zip_tseitin_20_type, type, zip_tseitin_20: subst > subst > term > 651.76/88.98 subst > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(hoaslaminj_lthm_type, type, hoaslaminj_lthm: $o). 651.76/88.98 thf(hoasinduction_lem3aaa_type, type, hoasinduction_lem3aaa: $o). 651.76/88.98 thf(axidr_type, type, axidr: $o). 651.76/88.98 thf(zip_tseitin_126_type, type, zip_tseitin_126: term > term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_57_type, type, zip_tseitin_57: term > term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(hoasapnotvar_lthm_type, type, hoasapnotvar_lthm: $o). 651.76/88.98 thf(sk__479_type, type, sk__479: (subst > term > subst > $o) > 651.76/88.98 (subst > term > term) > term). 651.76/88.98 thf(zip_tseitin_40_type, type, zip_tseitin_40: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_92_type, type, zip_tseitin_92: $o). 651.76/88.98 thf(zip_tseitin_69_type, type, zip_tseitin_69: term > subst > term > 651.76/88.98 (term > $o) > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_72_type, type, zip_tseitin_72: term > (term > $o) > $o). 651.76/88.98 thf(hoasinduction_lem3v2_f_type, type, hoasinduction_lem3v2_f: $o). 651.76/88.98 thf(sk__475_type, type, sk__475: term > d_term). 651.76/88.98 thf(zip_tseitin_30_type, type, zip_tseitin_30: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(sk__114_type, type, sk__114: (subst > term > term) > term). 651.76/88.98 thf(pushprop_lem2v2_gthm_type, type, pushprop_lem2v2_gthm: $o). 651.76/88.98 thf(substmonoid_lthm_type, type, substmonoid_lthm: $o). 651.76/88.98 thf(axabs_type, type, axabs: $o). 651.76/88.98 thf(hoasinduction_lem3v2_gthm_type, type, hoasinduction_lem3v2_gthm: $o). 651.76/88.98 thf(zip_tseitin_123_type, type, zip_tseitin_123: term > term > term > term > $o). 651.76/88.98 thf(zip_tseitin_17_type, type, zip_tseitin_17: term > term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_35_type, type, zip_tseitin_35: $o). 651.76/88.98 thf(hoasvar_type, type, hoasvar: subst > term > subst > $o). 651.76/88.98 thf(zip_tseitin_101_type, type, zip_tseitin_101: $o). 651.76/88.98 thf(hoasinduction_lem2v2_gthm_type, type, hoasinduction_lem2v2_gthm: $o). 651.76/88.98 thf(zip_tseitin_37_type, type, zip_tseitin_37: $o). 651.76/88.98 thf(zip_tseitin_116_type, type, zip_tseitin_116: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(sk__112_type, type, sk__112: (subst > term > subst > $o) > 651.76/88.98 (subst > term > term) > term). 651.76/88.98 thf(ulamvar1_type, type, ulamvar1: $o). 651.76/88.98 thf(zip_tseitin_11_type, type, zip_tseitin_11: term > term > (term > $o) > $o). 651.76/88.98 thf(hoasinduction_lem1v2_gthm_type, type, hoasinduction_lem1v2_gthm: $o). 651.76/88.98 thf(induction_type, type, induction: $o). 651.76/88.98 thf(zip_tseitin_99_type, type, zip_tseitin_99: term > (term > $o) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_7_type, type, zip_tseitin_7: term > (term > $o) > $o). 651.76/88.98 thf(pushprop_lem1v2_lthm_type, type, pushprop_lem1v2_lthm: $o). 651.76/88.98 thf(axscons_type, type, axscons: $o). 651.76/88.98 thf(zip_tseitin_43_type, type, zip_tseitin_43: (subst > term > term) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_49_type, type, zip_tseitin_49: $o). 651.76/88.98 thf(zip_tseitin_105_type, type, zip_tseitin_105: $o). 651.76/88.98 thf(pushprop_lem1_gthm_type, type, pushprop_lem1_gthm: $o). 651.76/88.98 thf(zip_tseitin_15_type, type, zip_tseitin_15: $o). 651.76/88.98 thf(zip_tseitin_60_type, type, zip_tseitin_60: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(zip_tseitin_88_type, type, zip_tseitin_88: term > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(induction2lem_gthm_type, type, induction2lem_gthm: $o). 651.76/88.98 thf(pushprop_lem0_gthm_type, type, pushprop_lem0_gthm: $o). 651.76/88.98 thf(termmset_lthm_type, type, termmset_lthm: $o). 651.76/88.98 thf(d2subst_type, type, d2subst: d_subst > subst). 651.76/88.98 thf(hoasinduction_lthm_type, type, hoasinduction_lthm: $o). 651.76/88.98 thf(hoasinduction_no_psi_cond_type, type, hoasinduction_no_psi_cond: $o). 651.76/88.98 thf(zip_tseitin_82_type, type, zip_tseitin_82: $o). 651.76/88.98 thf(sk__478_type, type, sk__478: (subst > term > term) > subst). 651.76/88.98 thf(zip_tseitin_118_type, type, zip_tseitin_118: $o). 651.76/88.98 thf(zip_tseitin_73_type, type, zip_tseitin_73: term > (term > $o) > $o). 651.76/88.98 thf(zip_tseitin_36_type, type, zip_tseitin_36: $o). 651.76/88.98 thf(zip_tseitin_38_type, type, zip_tseitin_38: term > (term > $o) > 651.76/88.98 (subst > term > subst > $o) > $o). 651.76/88.98 thf(alg444_1, axiom, 651.76/88.98 (( ![T:term]: ( ?[DT:d_term]: ( ( T ) = ( d2term @ DT ) ) ) ) & 651.76/88.98 ( ![DT:d_term]: ( ( DT ) = ( d_one ) ) ) & 651.76/88.98 ( ![DT1:d_term,DT2:d_term]: 651.76/88.98 ( ( ( d2term @ DT1 ) = ( d2term @ DT2 ) ) => ( ( DT1 ) = ( DT2 ) ) ) ) & 651.76/88.98 ( ![S:subst]: ( ?[DS:d_subst]: ( ( S ) = ( d2subst @ DS ) ) ) ) & 651.76/88.98 ( ( one ) = ( d2term @ d_one ) ) & 651.76/88.98 ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2term @ d_one ) ) & 651.76/88.98 ( ( id ) = ( d2subst @ d_id ) ) & ( ( sh ) = ( d2subst @ d_id ) ) & 651.76/88.98 ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 651.76/88.98 ( ( hoasap @ 651.76/88.98 ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ 651.76/88.98 ( d2term @ d_one ) ) = 651.76/88.98 ( d2term @ d_one ) ) & 651.76/88.98 ( ![A:term,M:subst,P:( term > $o ),Q:( term > $o )]: 651.76/88.98 ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) <=> 651.76/88.98 ( ![X:term]: ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) & 651.76/88.98 ( ~( var @ ( d2term @ d_one ) ) ) & ( pushprop_lem1_gthm ) & 651.76/88.98 ( ( shinj ) <=> 651.76/88.98 ( ![A:term,B:term]: 651.76/88.98 ( ( ( A ) = ( B ) ) | ( ( sub @ A @ sh ) != ( sub @ B @ sh ) ) ) ) ) & 651.76/88.98 ( hoasinduction_lem1v2 ) & 651.76/88.98 ( ( ![P:( term > $o ),Bound_variable_2340:term,Bound_variable_2342:subst]: 651.76/88.98 ( ( ~( ![A:term]: 651.76/88.98 ( ( P @ ( lam @ A ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( P @ B ) ) | 651.76/88.98 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) ) ) ) | 651.76/88.98 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( var @ B ) ) | ( P @ ( sub @ B @ Bound_variable_2342 ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ A ) ) | ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) ) ) ) ) ) <=> 651.76/88.98 ( induction2lem ) ) & 651.76/88.98 ( ~( ulamvar1 ) ) & 651.76/88.98 ( ( induction2lem_lthm ) <=> 651.76/88.98 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 651.76/88.98 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 651.76/88.98 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) => 651.76/88.98 ( ( ![P:( term > $o ),Bound_variable_2140:term]: 651.76/88.98 ( ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ A ) ) | ( ~( P @ B ) ) | 651.76/88.98 ( P @ ( ap @ A @ B ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: ( ( ~( P @ A ) ) | ( P @ ( lam @ A ) ) ) ) ) | 651.76/88.98 ( P @ Bound_variable_2140 ) | 651.76/88.98 ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) ) ) => 651.76/88.98 ( ![P:( term > $o ),Bound_variable_2340:term, 651.76/88.98 Bound_variable_2342:subst]: 651.76/88.98 ( ( ~( ![A:term]: 651.76/88.98 ( ( P @ ( lam @ A ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( P @ B ) ) | 651.76/88.98 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) ) ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( P @ ( sub @ B @ Bound_variable_2342 ) ) | 651.76/88.98 ( ~( var @ B ) ) ) ) ) | 651.76/88.98 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) | 651.76/88.98 ( ~( P @ A ) ) ) ) ) ) ) ) ) ) ) ) & 651.76/88.98 ( hoasinduction_lem3v2_gthm ) & ( apnotvar ) & ( pushprop_lthm_orig ) & 651.76/88.98 ( ( hoasinduction_lem3v2_f_lthm ) <=> 651.76/88.98 ( ![B:term]: 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ~( ![A:term,M:subst]: 651.76/88.98 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) ) & 651.76/88.98 ( ( hoasinduction_lthm ) <=> 651.76/88.98 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/88.98 ( ( ~( ![A:term,B:term]: 651.76/88.98 ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | ( ~( P @ A ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ ( lam @ A ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( P @ B ) ) | 651.76/88.98 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) ) ) ) | 651.76/88.98 ( P @ Bound_variable_2367 ) | 651.76/88.98 ( ~( ![A:term]: ( ( ~( var @ A ) ) | ( P @ A ) ) ) ) ) ) => 651.76/88.98 ( ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term, 651.76/88.98 Bound_variable_3001:term]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 651.76/88.98 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 651.76/88.98 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 651.76/88.98 ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 651.76/88.98 ( ~( P @ id @ Bound_variable_3001 @ id ) ) | 651.76/88.98 ( P @ 651.76/88.98 id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | ( ~( P @ id @ B @ id ) ) | 651.76/88.98 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) ) ) ) ) ) => 651.76/88.98 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 651.76/88.98 ( ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( P @ 651.76/88.98 id @ 651.76/88.98 ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ 651.76/88.98 id ) | 651.76/88.98 ( ~( P @ id @ B @ id ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 651.76/88.98 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 651.76/88.98 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) => 651.76/88.98 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 651.76/88.98 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( var @ ( sub @ A @ id ) ) ) | ( P @ id @ A @ id ) ) ) ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.98 ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 651.76/88.98 ( P @ id @ Bound_variable_3283 @ id ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ id @ B @ id ) ) | 651.76/88.98 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 651.76/88.98 ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 651.76/88.98 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) ) ) ) ) & 651.76/88.98 ( ( hoasinduction_no_psi_cond_lthm ) <=> 651.76/88.98 ( ( ![P:( subst > term > subst > $o )]: 651.76/88.98 ( ~( ![Q:( term > $o )]: 651.76/88.98 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) => 651.76/88.98 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/88.98 ( ( P @ Bound_variable_2367 ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( ![B:term]: 651.76/88.98 ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | 651.76/88.98 ( ~( P @ B ) ) ) ) ) | 651.76/88.98 ( P @ ( lam @ A ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) ) ) => 651.76/88.98 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.98 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.98 Bound_variable_2931:term]: 651.76/88.98 ( ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 651.76/88.98 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 651.76/88.98 ( Q @ ( lam @ Bound_variable_2931 ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( Q @ B ) ) | 651.76/88.98 ( Q @ 651.76/88.98 ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) ) ) ) ) ) => 651.76/88.98 ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]: 651.76/88.98 ( ( P @ id @ Bound_variable_3295 @ id ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![A:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( ~( P @ id @ B @ id ) ) | 651.76/88.98 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) ) ) ) ) ) ) ) ) ) ) & 651.76/88.98 ( ( ![F:( subst > term > term ), 651.76/88.98 Bound_variable_2547:( subst > term > term ), 651.76/88.98 Bound_variable_2549:subst,Bound_variable_2551:term]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N ) = 651.76/88.98 ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.98 ( ( F @ Bound_variable_2549 @ Bound_variable_2551 ) = 651.76/88.98 ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) | 651.76/88.98 ( ( lam @ ( F @ sh @ one ) ) != 651.76/88.98 ( lam @ ( Bound_variable_2547 @ sh @ one ) ) ) ) ) <=> 651.76/88.98 ( hoaslaminj ) ) & 651.76/88.98 ( induction2lem_gthm ) & 651.76/88.98 ( ( hoasinduction_lem3aa_lthm ) <=> 651.76/88.98 ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 651.76/88.98 ( ( ~( ![B:term]: 651.76/88.98 ( ( ~( P @ id @ B @ id ) ) | 651.76/88.98 ( P @ 651.76/88.98 id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) ) ) ) | 651.76/88.98 ( P @ 651.76/88.98 id @ 651.76/88.98 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![A:term]: 651.76/88.98 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.98 ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) ) & 651.76/88.98 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 651.76/88.98 ( ( ~( ![B:term]: 651.76/88.98 ( ( P @ 651.76/88.98 id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) | 651.76/88.98 ( ~( P @ id @ B @ id ) ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![A:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 651.76/88.98 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 651.76/88.98 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) ) <=> 651.76/88.98 ( hoasinduction_lem3 ) ) & 651.76/88.98 ( ( hoasinduction_lem2 ) <=> 651.76/88.98 ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term, 651.76/88.98 Bound_variable_3001:term]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 651.76/88.98 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 651.76/88.98 ( ~( P @ id @ B @ id ) ) | ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.98 ( ~( P @ id @ Bound_variable_3001 @ id ) ) | 651.76/88.98 ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 651.76/88.98 ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 651.76/88.98 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) ) & 651.76/88.98 ( hoasinduction_lem1 ) & ( hoasapnotvar ) & 651.76/88.98 ( ( hoasinduction_lem0 ) <=> 651.76/88.98 ( ![P:( subst > term > subst > $o )]: 651.76/88.98 ( ~( ![Q:( term > $o )]: 651.76/88.98 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) ) & 651.76/88.98 ( hoasinduction_gthm ) & ( axapp ) & ( hoaslamnotvar_lthm ) & 651.76/88.98 ( pushprop_lem3v2_lthm ) & ( ulamvarind ) & 651.76/88.98 ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.98 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 651.76/88.98 ( ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) ) ) ) | 651.76/88.98 ( P @ 651.76/88.98 id @ 651.76/88.98 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ 651.76/88.98 id ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( P @ 651.76/88.98 id @ 651.76/88.98 ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) | 651.76/88.98 ( ~( P @ id @ B @ id ) ) ) ) ) ) ) => 651.76/88.98 ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]: 651.76/88.98 ( ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( P @ id @ B @ id ) ) | 651.76/88.98 ( P @ 651.76/88.98 id @ 651.76/88.98 ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) ) <=> 651.76/88.98 ( hoasinduction_lem3a_lthm ) ) & 651.76/88.98 ( pushprop_lem1v2_gthm ) & ( hoaslamnotap_gthm ) & 651.76/88.98 ( hoasinduction_lem3b_gthm ) & ( pushprop_lem2v2 ) & 651.76/88.98 ( hoasinduction_lem3a_gthm ) & ( axassoc ) & 651.76/88.98 ( ( apinj2 ) <=> 651.76/88.98 ( ![A:term,B:term,C:term,D:term]: 651.76/88.98 ( ( ( C ) = ( D ) ) | ( ( ap @ A @ C ) != ( ap @ B @ D ) ) ) ) ) & 651.76/88.98 ( ( hoasapinj2_lthm ) <=> 651.76/88.98 ( ( ![A:term,B:term,C:term,D:term]: 651.76/88.98 ( ( ( ap @ A @ C ) != ( ap @ B @ D ) ) | ( ( C ) = ( D ) ) ) ) => 651.76/88.98 ( ![A:term,B:term,C:term,D:term]: 651.76/88.98 ( ( ( C ) = ( D ) ) | 651.76/88.98 ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) ) ) ) ) & 651.76/88.98 ( ( hoasinduction_lem3v2a ) <=> 651.76/88.98 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.98 Bound_variable_2931:term]: 651.76/88.98 ( ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 651.76/88.98 ( Q @ ( lam @ Bound_variable_2931 ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( Q @ B ) ) | 651.76/88.98 ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) ) ) ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.98 ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) ) ) ) & 651.76/88.98 ( ( axscons ) <=> 651.76/88.98 ( ![M:subst]: 651.76/88.98 ( ( M ) = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) ) ) & 651.76/88.98 ( hoasinduction_lem2v2_gthm ) & 651.76/88.98 ( ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]: 651.76/88.98 ( ( ~( P @ A ) ) | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) <=> 651.76/88.98 ( pushprop_lem1 ) ) & 651.76/88.98 ( ( ![A:term,B:term]: 651.76/88.98 ( ( ( A ) = ( B ) ) | ( ( lam @ A ) != ( lam @ B ) ) ) ) <=> 651.76/88.98 ( laminj ) ) & 651.76/88.98 ( ( pushprop_lem0 ) <=> 651.76/88.98 ( ![P:( term > $o ),A:term,M:subst]: 651.76/88.98 ( ~( ![Q:( term > $o )]: 651.76/88.98 ( ~( ![X:term]: 651.76/88.98 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) ) ) ) & 651.76/88.98 ( pushprop_gthm ) & ( axabs ) & ( hoasinduction_lem2_lthm ) & 651.76/88.98 ( hoasapinj2_gthm ) & ( ~( lamnotap ) ) & ( hoasapinj1_gthm ) & 651.76/88.98 ( hoaslamnotvar ) & ( hoaslaminj_gthm ) & 651.76/88.98 ( ( induction2_lthm ) <=> 651.76/88.98 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.98 ( ( ![P:( term > $o ),Bound_variable_2340:term, 651.76/88.98 Bound_variable_2342:subst]: 651.76/88.98 ( ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ A ) ) ) ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( var @ B ) ) | 651.76/88.98 ( P @ ( sub @ B @ Bound_variable_2342 ) ) ) ) ) | 651.76/88.98 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ ( lam @ A ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( P @ B ) ) | 651.76/88.98 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) ) ) ) ) ) => 651.76/88.98 ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/88.98 ( ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) | 651.76/88.98 ( P @ Bound_variable_2367 ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( ![B:term]: 651.76/88.98 ( ( ~( P @ B ) ) | 651.76/88.98 ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) | 651.76/88.98 ( P @ ( lam @ A ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ A ) ) | ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) ) & 651.76/88.98 ( ( substmonoid_lthm ) <=> 651.76/88.98 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) => 651.76/88.98 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) => 651.76/88.98 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) & 651.76/88.98 ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) ) ) ) ) & 651.76/88.98 ( hoasinduction_lem3_gthm ) & 651.76/88.98 ( ( ![B:term]: 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) <=> 651.76/88.98 ( hoasinduction_lem3b ) ) & 651.76/88.98 ( ( substmonoid ) <=> 651.76/88.98 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) & 651.76/88.98 ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) ) ) & 651.76/88.98 ( lamnotvar ) & ( induction2_gthm ) & ( pushprop_lem2v2_lthm ) & 651.76/88.98 ( ~( hoasvar @ 651.76/88.98 ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) & 651.76/88.98 ( ( ![F:( subst > term > term ),Bound_variable_2603:term, 651.76/88.98 Bound_variable_2605:term]: 651.76/88.98 ( ( ( lam @ ( F @ sh @ one ) ) != 651.76/88.98 ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) <=> 651.76/88.98 ( hoaslamnotap ) ) & 651.76/88.98 ( substmonoid_gthm ) & ( pushprop_lem2v2_gthm ) & 651.76/88.98 ( ( pushprop_lem1_lthm ) <=> 651.76/88.98 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 651.76/88.98 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 651.76/88.98 ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]: 651.76/88.98 ( ( ~( P @ A ) ) | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) ) ) & 651.76/88.98 ( ( hoasinduction_lem3v2 ) <=> 651.76/88.98 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.98 Bound_variable_2910:term]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 651.76/88.98 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( Q @ B ) ) | 651.76/88.98 ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) ) ) ) | 651.76/88.98 ( Q @ ( lam @ Bound_variable_2910 ) ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 651.76/88.98 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) ) ) & 651.76/88.98 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) <=> 651.76/88.98 ( axshiftcons ) ) & 651.76/88.98 ( ( termmset ) <=> ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) & 651.76/88.98 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) <=> ( axvarid ) ) & 651.76/88.98 ( ( hoasinduction_lthm_3 ) <=> 651.76/88.98 ( ( ![P:( subst > term > subst > $o )]: 651.76/88.98 ( ~( ![Q:( term > $o )]: 651.76/88.98 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) => 651.76/88.98 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/88.98 ( ( P @ Bound_variable_2367 ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ ( lam @ A ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | 651.76/88.98 ( ~( P @ B ) ) ) ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | ( ~( P @ A ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: ( ( ~( var @ A ) ) | ( P @ A ) ) ) ) ) ) => 651.76/88.98 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.98 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.98 Bound_variable_2931:term]: 651.76/88.98 ( ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.98 ( ~( P @ id @ A @ id ) ) ) ) ) ) ) ) | 651.76/88.98 ( Q @ ( lam @ Bound_variable_2931 ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( Q @ 651.76/88.98 ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) | 651.76/88.98 ( ~( Q @ B ) ) ) ) ) | 651.76/88.98 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) => 651.76/88.98 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 651.76/88.98 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( var @ ( sub @ A @ id ) ) ) | ( P @ id @ A @ id ) ) ) ) | 651.76/88.98 ( P @ id @ Bound_variable_3283 @ id ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.98 ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( ~( P @ id @ B @ id ) ) | 651.76/88.98 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 651.76/88.98 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) ) ) ) ) ) & 651.76/88.98 ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.98 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.98 Bound_variable_2910:term]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 651.76/88.98 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) | 651.76/88.98 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) | 651.76/88.98 ( ~( Q @ B ) ) ) ) ) | 651.76/88.98 ( Q @ ( lam @ Bound_variable_2910 ) ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.98 ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 651.76/88.98 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) ) ) ) <=> 651.76/88.98 ( hoasinduction_lem3v2_lthm ) ) & 651.76/88.98 ( hoasapnotvar_lthm ) & 651.76/88.98 ( ( pushprop_lem0_lthm ) <=> 651.76/88.98 ( ![P:( term > $o ),A:term,M:subst]: 651.76/88.98 ( ~( ![Q:( term > $o )]: 651.76/88.98 ( ~( ![X:term]: 651.76/88.98 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) ) ) ) & 651.76/88.98 ( pushprop_lem3v2 ) & 651.76/88.98 ( ( induction2 ) <=> 651.76/88.98 ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/88.98 ( ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ ( lam @ A ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | 651.76/88.98 ( ~( P @ B ) ) ) ) ) ) ) ) | 651.76/88.98 ( P @ Bound_variable_2367 ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ A ) ) ) ) ) ) ) ) & 651.76/88.98 ( ulamvarsh ) & 651.76/88.98 ( ( hoasinduction_no_psi_cond ) <=> 651.76/88.98 ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]: 651.76/88.98 ( ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.98 ( ~( P @ id @ A @ id ) ) ) ) ) ) ) ) | 651.76/88.98 ( P @ id @ Bound_variable_3295 @ id ) | 651.76/88.98 ( ~( ![A:term,B:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 651.76/88.98 ( ~( P @ id @ B @ id ) ) ) ) ) ) ) ) & 651.76/88.98 ( hoasinduction_lem1_gthm ) & 651.76/88.98 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]: 651.76/88.98 ( ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![A:term]: 651.76/88.98 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.98 ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( P @ id @ B @ id ) ) | 651.76/88.98 ( P @ 651.76/88.98 id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) <=> 651.76/88.98 ( hoasinduction_lem3a ) ) & 651.76/88.98 ( hoasinduction_lem2_gthm ) & ( pushprop ) & 651.76/88.98 ( ( hoasinduction_lem0_lthm ) <=> 651.76/88.98 ( ![P:( subst > term > subst > $o )]: 651.76/88.98 ( ~( ![Q:( term > $o )]: 651.76/88.98 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) ) & 651.76/88.98 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) <=> ( axidl ) ) & 651.76/88.98 ( hoasinduction_lem1_lthm ) & 651.76/88.98 ( ( ( ![B:term]: 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ~( ![A:term,M:subst]: 651.76/88.98 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) => 651.76/88.98 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.98 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.98 Bound_variable_2931:term]: 651.76/88.98 ( ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![A:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 651.76/88.98 ( Q @ ( lam @ Bound_variable_2931 ) ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( ~( Q @ B ) ) | 651.76/88.98 ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) ) ) ) | 651.76/88.98 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) ) <=> 651.76/88.98 ( hoasinduction_lem3v2a_lthm ) ) & 651.76/88.98 ( ( hoasinduction_lem3_lthm ) <=> 651.76/88.98 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.98 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 651.76/88.98 ( ( ~( ![B:term]: 651.76/88.98 ( ( P @ 651.76/88.98 id @ 651.76/88.98 ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) | 651.76/88.98 ( ~( P @ id @ B @ id ) ) ) ) ) | 651.76/88.98 ( P @ 651.76/88.98 id @ 651.76/88.98 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ 651.76/88.98 id ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.98 ( ( ~( ![A:term]: 651.76/88.98 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.98 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.98 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.98 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) => 651.76/88.98 ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 651.76/88.98 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 651.76/88.98 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) | 651.76/88.98 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.98 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 651.76/88.98 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 651.76/88.98 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 651.76/88.98 ( ~( ![B:term]: 651.76/88.98 ( ( P @ 651.76/88.98 id @ 651.76/88.98 ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) | 651.76/88.98 ( ~( P @ id @ B @ id ) ) ) ) ) | 651.76/88.98 ( ~( ![F:( subst > term > term )]: 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.99 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.99 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.99 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.99 ( ~( ![A:term]: 651.76/88.99 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.99 ( ~( P @ id @ A @ id ) ) ) ) ) ) ) ) ) ) ) ) ) & 651.76/88.99 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) <=> ( axidr ) ) & 651.76/88.99 ( ( axvarcons ) <=> 651.76/88.99 ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) ) & 651.76/88.99 ( ( hoaslaminj_lthm ) <=> 651.76/88.99 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 651.76/88.99 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 651.76/88.99 ( ( ![A:term,B:term]: 651.76/88.99 ( ( ( A ) = ( B ) ) | ( ( lam @ A ) != ( lam @ B ) ) ) ) => 651.76/88.99 ( ![F:( subst > term > term ), 651.76/88.99 Bound_variable_2547:( subst > term > term ), 651.76/88.99 Bound_variable_2549:subst,Bound_variable_2551:term]: 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.99 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.99 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.99 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N ) = 651.76/88.99 ( Bound_variable_2547 @ 651.76/88.99 ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.99 ( ( F @ Bound_variable_2549 @ Bound_variable_2551 ) = 651.76/88.99 ( Bound_variable_2547 @ 651.76/88.99 Bound_variable_2549 @ Bound_variable_2551 ) ) | 651.76/88.99 ( ( lam @ ( F @ sh @ one ) ) != 651.76/88.99 ( lam @ ( Bound_variable_2547 @ sh @ one ) ) ) ) ) ) ) ) ) & 651.76/88.99 ( ( hoasapinj1_lthm ) <=> 651.76/88.99 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.99 ( ( ![A:term,B:term,C:term,D:term]: 651.76/88.99 ( ( ( A ) = ( B ) ) | ( ( ap @ A @ C ) != ( ap @ B @ D ) ) ) ) => 651.76/88.99 ( ![A:term,B:term,C:term,D:term]: 651.76/88.99 ( ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) | 651.76/88.99 ( ( A ) = ( B ) ) ) ) ) ) ) & 651.76/88.99 ( ( ![A:term,B:term,C:term,D:term]: 651.76/88.99 ( ( ( A ) = ( B ) ) | ( ( ap @ A @ C ) != ( ap @ B @ D ) ) ) ) <=> 651.76/88.99 ( apinj1 ) ) & 651.76/88.99 ( pushprop_lthm ) & 651.76/88.99 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.99 Bound_variable_2820:term,Bound_variable_2822:term]: 651.76/88.99 ( ( ~( ![A:term,B:term]: 651.76/88.99 ( ( ~( P @ id @ A @ id ) ) | ( ~( P @ id @ B @ id ) ) | 651.76/88.99 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) ) ) ) | 651.76/88.99 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 651.76/88.99 ( ~( Q @ Bound_variable_2822 ) ) | 651.76/88.99 ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) | 651.76/88.99 ( ~( Q @ Bound_variable_2820 ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 651.76/88.99 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 651.76/88.99 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) ) <=> 651.76/88.99 ( hoasinduction_lem2v2 ) ) & 651.76/88.99 ( axclos ) & ( hoaslamnotvar_gthm ) & 651.76/88.99 ( ( hoasinduction_lem3aa ) <=> 651.76/88.99 ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 651.76/88.99 ( ( P @ 651.76/88.99 id @ 651.76/88.99 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 651.76/88.99 ( ~( ![B:term]: 651.76/88.99 ( ( P @ 651.76/88.99 id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) | 651.76/88.99 ( ~( P @ id @ B @ id ) ) ) ) ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.99 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.99 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.99 ( ~( ![A:term]: 651.76/88.99 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.99 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 651.76/88.99 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) ) ) ) & 651.76/88.99 ( termmset_gthm ) & 651.76/88.99 ( ( induction ) <=> 651.76/88.99 ( ![P:( term > $o ),Bound_variable_2140:term]: 651.76/88.99 ( ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) | 651.76/88.99 ( ~( ![A:term,B:term]: 651.76/88.99 ( ( ~( P @ A ) ) | ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) ) ) ) | 651.76/88.99 ( P @ Bound_variable_2140 ) | 651.76/88.99 ( ~( ![A:term]: ( ( ~( P @ A ) ) | ( P @ ( lam @ A ) ) ) ) ) ) ) ) & 651.76/88.99 ( ( hoasinduction_lem3b_lthm ) <=> 651.76/88.99 ( ![B:term]: 651.76/88.99 ( ~( ![F:( subst > term > term )]: 651.76/88.99 ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) ) & 651.76/88.99 ( ( hoasinduction ) <=> 651.76/88.99 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 651.76/88.99 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) | 651.76/88.99 ( P @ id @ Bound_variable_3283 @ id ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.99 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.99 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.99 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.99 ( ~( ![A:term]: 651.76/88.99 ( ( ~( P @ id @ A @ id ) ) | 651.76/88.99 ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) ) ) ) | 651.76/88.99 ( ~( ![A:term,B:term]: 651.76/88.99 ( ( ~( P @ id @ B @ id ) ) | 651.76/88.99 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 651.76/88.99 ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.99 ( ~( ![A:term]: 651.76/88.99 ( ( ~( var @ ( sub @ A @ id ) ) ) | ( P @ id @ A @ id ) ) ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 651.76/88.99 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) & 651.76/88.99 ( ( pushprop_lem1v2_lthm ) <=> 651.76/88.99 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 651.76/88.99 ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]: 651.76/88.99 ( ( ~( P @ A ) ) | ( Q @ one ) | 651.76/88.99 ( ~( ![X:term]: 651.76/88.99 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) ) ) ) & 651.76/88.99 ( hoaslamnotap_lthm ) & 651.76/88.99 ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.99 ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) <=> 651.76/88.99 ( termmset_lthm ) ) & 651.76/88.99 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3171:term]: 651.76/88.99 ( ( ~( ![F:( subst > term > term ),Bound_variable_3149:term]: 651.76/88.99 ( ( ~( ![A:term]: 651.76/88.99 ( ( P @ id @ ( F @ id @ A ) @ id ) | 651.76/88.99 ( ~( P @ id @ A @ id ) ) ) ) ) | 651.76/88.99 ( ~( ![Bound_variable_3090:subst,Bound_variable_3092:term, 651.76/88.99 Bound_variable_3094:subst]: 651.76/88.99 ( ( F @ 651.76/88.99 ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ 651.76/88.99 ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) ) = 651.76/88.99 ( sub @ 651.76/88.99 Bound_variable_3149 @ 651.76/88.99 ( push @ 651.76/88.99 ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ 651.76/88.99 ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) ) ) | 651.76/88.99 ( ~( ![Bound_variable_3072:subst,Bound_variable_3074:term, 651.76/88.99 Bound_variable_3076:subst]: 651.76/88.99 ( ( sub @ 651.76/88.99 ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ 651.76/88.99 Bound_variable_3076 ) = 651.76/88.99 ( sub @ 651.76/88.99 ( sub @ 651.76/88.99 Bound_variable_3149 @ 651.76/88.99 ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ 651.76/88.99 Bound_variable_3076 ) ) ) ) | 651.76/88.99 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 651.76/88.99 ( P @ 651.76/88.99 id @ 651.76/88.99 ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) | 651.76/88.99 ( ~( ![B:term]: 651.76/88.99 ( ( P @ 651.76/88.99 id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) | 651.76/88.99 ( ~( P @ id @ B @ id ) ) ) ) ) ) ) <=> 651.76/88.99 ( hoasinduction_lem3aaa ) ) & 651.76/88.99 ( ( ![A:term,B:term,C:term,D:term]: 651.76/88.99 ( ( ( A ) = ( B ) ) | 651.76/88.99 ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) ) ) <=> 651.76/88.99 ( hoasapinj1 ) ) & 651.76/88.99 ( hoasapnotvar_gthm ) & 651.76/88.99 ( ( hoasapinj2 ) <=> 651.76/88.99 ( ![A:term,B:term,C:term,D:term]: 651.76/88.99 ( ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) | 651.76/88.99 ( ( C ) = ( D ) ) ) ) ) & 651.76/88.99 ( axvarshift ) & 651.76/88.99 ( ( ![B:term]: 651.76/88.99 ( ~( ![F:( subst > term > term )]: 651.76/88.99 ( ~( ![A:term,M:subst]: 651.76/88.99 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) <=> 651.76/88.99 ( hoasinduction_lem3v2_f ) ) & 651.76/88.99 ( hoasinduction_lem1v2_gthm ) & ( pushprop_lem0_gthm ) & ( axmap ) & 651.76/88.99 ( ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]: 651.76/88.99 ( ( ~( P @ A ) ) | 651.76/88.99 ( ~( ![X:term]: 651.76/88.99 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) | 651.76/88.99 ( Q @ one ) ) ) <=> 651.76/88.99 ( pushprop_lem1v2 ) ) & 651.76/88.99 ( ![P:( subst > term > subst > $o ),Q:( term > $o )]: 651.76/88.99 ( ( hoasinduction_p_and_p_prime @ P @ Q ) <=> 651.76/88.99 ( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) & 651.76/88.99 ( ![Bound_variable_4913:subst,Bound_variable_4915:( subst > term > term )]: 651.76/88.99 ( ( hoaslam @ Bound_variable_4913 @ Bound_variable_4915 ) = 651.76/88.99 ( d2term @ d_one ) ) ) & 651.76/88.99 ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 651.76/88.99 ( ( lam @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 651.76/88.99 ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 651.76/88.99 ( ![DS1:d_subst,DS2:d_subst]: 651.76/88.99 ( ( ( d2subst @ DS1 ) = ( d2subst @ DS2 ) ) => ( ( DS1 ) = ( DS2 ) ) ) ) & 651.76/88.99 ( ![DS:d_subst]: ( ( DS ) = ( d_id ) ) ))). 651.76/88.99 thf(zf_stmt_0, axiom, 651.76/88.99 (![A:term,F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_31 @ A @ F @ P ) <=> 651.76/88.99 ( ( ~( P @ id @ A @ id ) ) | ( P @ id @ ( F @ id @ A ) @ id ) ) ))). 651.76/88.99 thf(zip_derived_cl115, plain, 651.76/88.99 (![X0 : term, X1 : subst > term > term, X2 : subst > term > subst > $o]: 651.76/88.99 ( (zip_tseitin_31 @ X0 @ X1 @ X2) | (X2 @ id @ X0 @ id))), 651.76/88.99 inference('cnf', [status(esa)], [zf_stmt_0])). 651.76/88.99 thf(zf_stmt_1, type, zip_tseitin_124 : 651.76/88.99 subst > term > ( term > $o ) > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_2, axiom, 651.76/88.99 (![M:subst,A:term,Q:( term > $o ),P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_124 @ M @ A @ Q @ P ) <=> 651.76/88.99 ( ( Q @ one ) | 651.76/88.99 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P @ M @ A ) ) ) | 651.76/88.99 ( ~( P @ A ) ) ) ))). 651.76/88.99 thf(zf_stmt_3, type, zip_tseitin_123 : term > term > term > term > $o). 651.76/88.99 thf(zf_stmt_4, axiom, 651.76/88.99 (![D:term,C:term,B:term,A:term]: 651.76/88.99 ( ( zip_tseitin_123 @ D @ C @ B @ A ) <=> 651.76/88.99 ( ( ( C ) = ( D ) ) | 651.76/88.99 ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) ) ))). 651.76/88.99 thf(zf_stmt_5, type, zip_tseitin_122 : term > term > term > term > $o). 651.76/88.99 thf(zf_stmt_6, axiom, 651.76/88.99 (![D:term,C:term,B:term,A:term]: 651.76/88.99 ( ( zip_tseitin_122 @ D @ C @ B @ A ) <=> 651.76/88.99 ( ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) | 651.76/88.99 ( ( A ) = ( B ) ) ) ))). 651.76/88.99 thf(zf_stmt_7, type, zip_tseitin_121 : 651.76/88.99 term > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_8, axiom, 651.76/88.99 (![Bound_variable_3171:term,P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_121 @ Bound_variable_3171 @ P ) <=> 651.76/88.99 ( ( ~( ![B:term]: ( zip_tseitin_26 @ B @ Bound_variable_3171 @ P ) ) ) | 651.76/88.99 ( P @ 651.76/88.99 id @ 651.76/88.99 ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) | 651.76/88.99 ( ~( ![F:( subst > term > term ),Bound_variable_3149:term]: 651.76/88.99 ( zip_tseitin_120 @ Bound_variable_3149 @ F @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_9, type, zip_tseitin_120 : 651.76/88.99 term > ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_10, axiom, 651.76/88.99 (![Bound_variable_3149:term,F:( subst > term > term ), 651.76/88.99 P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_120 @ Bound_variable_3149 @ F @ P ) <=> 651.76/88.99 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.99 ( ~( ![Bound_variable_3072:subst,Bound_variable_3074:term, 651.76/88.99 Bound_variable_3076:subst]: 651.76/88.99 ( ( sub @ 651.76/88.99 ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ 651.76/88.99 Bound_variable_3076 ) = 651.76/88.99 ( sub @ 651.76/88.99 ( sub @ 651.76/88.99 Bound_variable_3149 @ 651.76/88.99 ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ 651.76/88.99 Bound_variable_3076 ) ) ) ) | 651.76/88.99 ( ~( ![Bound_variable_3090:subst,Bound_variable_3092:term, 651.76/88.99 Bound_variable_3094:subst]: 651.76/88.99 ( ( F @ 651.76/88.99 ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ 651.76/88.99 ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) ) = 651.76/88.99 ( sub @ 651.76/88.99 Bound_variable_3149 @ 651.76/88.99 ( push @ 651.76/88.99 ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ 651.76/88.99 ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) ) ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_31 @ A @ F @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_11, type, zip_tseitin_119 : $o). 651.76/88.99 thf(zf_stmt_12, axiom, 651.76/88.99 (( zip_tseitin_119 ) <=> 651.76/88.99 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.99 ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ))). 651.76/88.99 thf(zf_stmt_13, type, zip_tseitin_118 : $o). 651.76/88.99 thf(zf_stmt_14, axiom, 651.76/88.99 (( zip_tseitin_118 ) <=> 651.76/88.99 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 651.76/88.99 ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]: 651.76/88.99 ( zip_tseitin_117 @ M @ A @ Q @ P ) ) ))). 651.76/88.99 thf(zf_stmt_15, type, zip_tseitin_117 : 651.76/88.99 subst > term > ( term > $o ) > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_16, axiom, 651.76/88.99 (![M:subst,A:term,Q:( term > $o ),P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_117 @ M @ A @ Q @ P ) <=> 651.76/88.99 ( ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P @ M @ A ) ) ) | 651.76/88.99 ( Q @ one ) | ( ~( P @ A ) ) ) ))). 651.76/88.99 thf(zf_stmt_17, type, zip_tseitin_116 : 651.76/88.99 term > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_18, axiom, 651.76/88.99 (![Bound_variable_3283:term,P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_116 @ Bound_variable_3283 @ P ) <=> 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_21 @ K @ N @ A @ M @ P ) ) ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_30 @ A @ P ) ) ) | 651.76/88.99 ( ~( ![A:term,B:term]: ( zip_tseitin_33 @ B @ A @ P ) ) ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_58 @ F @ P ) ) ) | 651.76/88.99 ( P @ id @ Bound_variable_3283 @ id ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_20 @ K @ N @ A @ M @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_19, type, zip_tseitin_115 : term > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_20, axiom, 651.76/88.99 (![Bound_variable_2140:term,P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_115 @ Bound_variable_2140 @ P ) <=> 651.76/88.99 ( ( ~( ![A:term]: ( zip_tseitin_7 @ A @ P ) ) ) | 651.76/88.99 ( P @ Bound_variable_2140 ) | 651.76/88.99 ( ~( ![A:term,B:term]: ( zip_tseitin_5 @ B @ A @ P ) ) ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_8 @ A @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_21, type, zip_tseitin_114 : 651.76/88.99 term > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_22, axiom, 651.76/88.99 (![Bound_variable_3046:term,P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_114 @ Bound_variable_3046 @ P ) <=> 651.76/88.99 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_43 @ F @ P ) ) ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_26 @ B @ Bound_variable_3046 @ P ) ) ) | 651.76/88.99 ( P @ 651.76/88.99 id @ 651.76/88.99 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) ))). 651.76/88.99 thf(zf_stmt_23, type, zip_tseitin_113 : 651.76/88.99 term > term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_24, axiom, 651.76/88.99 (![Bound_variable_2822:term,Bound_variable_2820:term,Q:( term > $o ), 651.76/88.99 P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_113 @ Bound_variable_2822 @ Bound_variable_2820 @ Q @ P ) <=> 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_20 @ K @ N @ A @ M @ P ) ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_21 @ K @ N @ A @ M @ P ) ) ) | 651.76/88.99 ( ~( Q @ Bound_variable_2820 ) ) | 651.76/88.99 ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) | 651.76/88.99 ( ~( Q @ Bound_variable_2822 ) ) | 651.76/88.99 ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) | 651.76/88.99 ( ~( ![A:term,B:term]: ( zip_tseitin_22 @ B @ A @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_25, type, zip_tseitin_112 : $o). 651.76/88.99 thf(zf_stmt_26, axiom, 651.76/88.99 (( zip_tseitin_112 ) <=> 651.76/88.99 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_111 ) ))). 651.76/88.99 thf(zf_stmt_27, type, zip_tseitin_111 : $o). 651.76/88.99 thf(zf_stmt_28, axiom, 651.76/88.99 (( zip_tseitin_111 ) <=> 651.76/88.99 ( ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_109 @ D @ C @ B @ A ) ) => 651.76/88.99 ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_110 @ D @ C @ B @ A ) ) ))). 651.76/88.99 thf(zf_stmt_29, type, zip_tseitin_110 : term > term > term > term > $o). 651.76/88.99 thf(zf_stmt_30, axiom, 651.76/88.99 (![D:term,C:term,B:term,A:term]: 651.76/88.99 ( ( zip_tseitin_110 @ D @ C @ B @ A ) <=> 651.76/88.99 ( ( ( A ) = ( B ) ) | 651.76/88.99 ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) ) ))). 651.76/88.99 thf(zf_stmt_31, type, zip_tseitin_109 : term > term > term > term > $o). 651.76/88.99 thf(zf_stmt_32, axiom, 651.76/88.99 (![D:term,C:term,B:term,A:term]: 651.76/88.99 ( ( zip_tseitin_109 @ D @ C @ B @ A ) <=> 651.76/88.99 ( ( ( ap @ A @ C ) != ( ap @ B @ D ) ) | ( ( A ) = ( B ) ) ) ))). 651.76/88.99 thf(zf_stmt_33, type, zip_tseitin_108 : $o). 651.76/88.99 thf(zf_stmt_34, axiom, 651.76/88.99 (( zip_tseitin_108 ) <=> 651.76/88.99 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 651.76/88.99 ( zip_tseitin_107 ) ))).thf(zf_stmt_35, type, zip_tseitin_107 : $o). 651.76/88.99 thf(zf_stmt_36, axiom, 651.76/88.99 (( zip_tseitin_107 ) <=> 651.76/88.99 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 651.76/88.99 ( zip_tseitin_106 ) ))).thf(zf_stmt_37, type, zip_tseitin_106 : $o). 651.76/88.99 thf(zf_stmt_38, axiom, 651.76/88.99 (( zip_tseitin_106 ) <=> 651.76/88.99 ( ( ![A:term,B:term]: ( zip_tseitin_70 @ B @ A ) ) => 651.76/88.99 ( ![F:( subst > term > term ), 651.76/88.99 Bound_variable_2547:( subst > term > term ), 651.76/88.99 Bound_variable_2549:subst,Bound_variable_2551:term]: 651.76/88.99 ( zip_tseitin_51 @ 651.76/88.99 Bound_variable_2551 @ Bound_variable_2549 @ Bound_variable_2547 @ F ) ) ))). 651.76/88.99 thf(zf_stmt_39, type, zip_tseitin_105 : $o). 651.76/88.99 thf(zf_stmt_40, axiom, 651.76/88.99 (( zip_tseitin_105 ) <=> 651.76/88.99 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_104 ) ))). 651.76/88.99 thf(zf_stmt_41, type, zip_tseitin_104 : $o). 651.76/88.99 thf(zf_stmt_42, axiom, 651.76/88.99 (( zip_tseitin_104 ) <=> 651.76/88.99 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 651.76/88.99 ( zip_tseitin_102 @ Bound_variable_3046 @ P ) ) => 651.76/88.99 ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 651.76/88.99 ( zip_tseitin_103 @ Bound_variable_3211 @ P ) ) ))). 651.76/88.99 thf(zf_stmt_43, type, zip_tseitin_103 : 651.76/88.99 term > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_44, axiom, 651.76/88.99 (![Bound_variable_3211:term,P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_103 @ Bound_variable_3211 @ P ) <=> 651.76/88.99 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_86 @ F @ P ) ) ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_26 @ B @ Bound_variable_3211 @ P ) ) ) | 651.76/88.99 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_21 @ K @ N @ A @ M @ P ) ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_20 @ K @ N @ A @ M @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_45, type, zip_tseitin_102 : 651.76/88.99 term > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_46, axiom, 651.76/88.99 (![Bound_variable_3046:term,P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_102 @ Bound_variable_3046 @ P ) <=> 651.76/88.99 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_45 @ F @ P ) ) ) | 651.76/88.99 ( P @ 651.76/88.99 id @ 651.76/88.99 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_26 @ B @ Bound_variable_3046 @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_47, type, zip_tseitin_101 : $o). 651.76/88.99 thf(zf_stmt_48, axiom, 651.76/88.99 (( zip_tseitin_101 ) <=> 651.76/88.99 ( ( ![B:term]: 651.76/88.99 ( ~( ![F:( subst > term > term )]: 651.76/88.99 ( ~( ![A:term,M:subst]: 651.76/88.99 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) => 651.76/88.99 ( zip_tseitin_100 ) ))).thf(zf_stmt_49, type, zip_tseitin_100 : $o). 651.76/88.99 thf(zf_stmt_50, axiom, 651.76/88.99 (( zip_tseitin_100 ) <=> 651.76/88.99 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.99 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.99 Bound_variable_2931:term]: 651.76/88.99 ( zip_tseitin_99 @ Bound_variable_2931 @ Q @ P ) ) ))). 651.76/88.99 thf(zf_stmt_51, type, zip_tseitin_99 : 651.76/88.99 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_52, axiom, 651.76/88.99 (![Bound_variable_2931:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_99 @ Bound_variable_2931 @ Q @ P ) <=> 651.76/88.99 ( ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_2 @ B @ Bound_variable_2931 @ Q ) ) ) | 651.76/88.99 ( Q @ ( lam @ Bound_variable_2931 ) ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_25 @ F @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_53, type, zip_tseitin_98 : 651.76/88.99 term > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_54, axiom, 651.76/88.99 (![Bound_variable_3232:term,P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_98 @ Bound_variable_3232 @ P ) <=> 651.76/88.99 ( ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_52 @ B @ Bound_variable_3232 @ P ) ) ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_53 @ F @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_55, type, zip_tseitin_97 : 651.76/88.99 term > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_56, axiom, 651.76/88.99 (![Bound_variable_3295:term,P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_97 @ Bound_variable_3295 @ P ) <=> 651.76/88.99 ( ( ~( ![A:term,B:term]: ( zip_tseitin_96 @ B @ A @ P ) ) ) | 651.76/88.99 ( P @ id @ Bound_variable_3295 @ id ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_86 @ F @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_57, type, zip_tseitin_96 : 651.76/88.99 term > term > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_58, axiom, 651.76/88.99 (![B:term,A:term,P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_96 @ B @ A @ P ) <=> 651.76/88.99 ( ( ~( P @ id @ B @ id ) ) | 651.76/88.99 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 651.76/88.99 ( ~( P @ id @ A @ id ) ) ) ))). 651.76/88.99 thf(zf_stmt_59, type, zip_tseitin_95 : term > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_60, axiom, 651.76/88.99 (![Bound_variable_2367:term,P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_95 @ Bound_variable_2367 @ P ) <=> 651.76/88.99 ( ( ~( ![A:term,B:term]: ( zip_tseitin_11 @ B @ A @ P ) ) ) | 651.76/88.99 ( P @ Bound_variable_2367 ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_84 @ A @ P ) ) ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_8 @ A @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_61, type, zip_tseitin_94 : $o). 651.76/88.99 thf(zf_stmt_62, axiom, 651.76/88.99 (( zip_tseitin_94 ) <=> 651.76/88.99 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => 651.76/88.99 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.99 Bound_variable_2910:term]: 651.76/88.99 ( zip_tseitin_93 @ Bound_variable_2910 @ Q @ P ) ) ))). 651.76/88.99 thf(zf_stmt_63, type, zip_tseitin_93 : 651.76/88.99 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_64, axiom, 651.76/88.99 (![Bound_variable_2910:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_93 @ Bound_variable_2910 @ Q @ P ) <=> 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_32 @ F @ P ) ) ) | 651.76/88.99 ( Q @ ( lam @ Bound_variable_2910 ) ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_39 @ B @ Bound_variable_2910 @ Q ) ) ) | 651.76/88.99 ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_28 @ K @ N @ A @ M @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_65, type, zip_tseitin_92 : $o). 651.76/88.99 thf(zf_stmt_66, axiom, 651.76/88.99 (( zip_tseitin_92 ) <=> 651.76/88.99 ( ( ![P:( subst > term > subst > $o )]: 651.76/88.99 ( ~( ![Q:( term > $o )]: 651.76/88.99 ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) ) ) ) => 651.76/88.99 ( zip_tseitin_91 ) ))).thf(zf_stmt_67, type, zip_tseitin_91 : $o). 651.76/88.99 thf(zf_stmt_68, axiom, 651.76/88.99 (( zip_tseitin_91 ) <=> 651.76/88.99 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/88.99 ( zip_tseitin_85 @ Bound_variable_2367 @ P ) ) => 651.76/88.99 ( zip_tseitin_90 ) ))).thf(zf_stmt_69, type, zip_tseitin_90 : $o). 651.76/88.99 thf(zf_stmt_70, axiom, 651.76/88.99 (( zip_tseitin_90 ) <=> 651.76/88.99 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_89 ) ))). 651.76/88.99 thf(zf_stmt_71, type, zip_tseitin_89 : $o). 651.76/88.99 thf(zf_stmt_72, axiom, 651.76/88.99 (( zip_tseitin_89 ) <=> 651.76/88.99 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/88.99 Bound_variable_2931:term]: 651.76/88.99 ( zip_tseitin_87 @ Bound_variable_2931 @ Q @ P ) ) => 651.76/88.99 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 651.76/88.99 ( zip_tseitin_88 @ Bound_variable_3283 @ P ) ) ))). 651.76/88.99 thf(zf_stmt_73, type, zip_tseitin_88 : 651.76/88.99 term > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_74, axiom, 651.76/88.99 (![Bound_variable_3283:term,P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_88 @ Bound_variable_3283 @ P ) <=> 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_28 @ K @ N @ A @ M @ P ) ) ) | 651.76/88.99 ( ~( ![A:term,B:term]: ( zip_tseitin_22 @ B @ A @ P ) ) ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_32 @ F @ P ) ) ) | 651.76/88.99 ( P @ id @ Bound_variable_3283 @ id ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_30 @ A @ P ) ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_75, type, zip_tseitin_87 : 651.76/88.99 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_76, axiom, 651.76/88.99 (![Bound_variable_2931:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_87 @ Bound_variable_2931 @ Q @ P ) <=> 651.76/88.99 ( ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_39 @ B @ Bound_variable_2931 @ Q ) ) ) | 651.76/88.99 ( Q @ ( lam @ Bound_variable_2931 ) ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_86 @ F @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_77, type, zip_tseitin_86 : 651.76/88.99 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_78, axiom, 651.76/88.99 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_86 @ F @ P ) <=> 651.76/88.99 ( ( ~( ![A:term]: ( zip_tseitin_31 @ A @ F @ P ) ) ) | 651.76/88.99 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.99 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.99 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_79, type, zip_tseitin_85 : term > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_80, axiom, 651.76/88.99 (![Bound_variable_2367:term,P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_85 @ Bound_variable_2367 @ P ) <=> 651.76/88.99 ( ( ~( ![A:term]: ( zip_tseitin_18 @ A @ P ) ) ) | 651.76/88.99 ( ~( ![A:term,B:term]: ( zip_tseitin_17 @ B @ A @ P ) ) ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_84 @ A @ P ) ) ) | 651.76/88.99 ( P @ Bound_variable_2367 ) ) ))). 651.76/88.99 thf(zf_stmt_81, type, zip_tseitin_84 : term > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_82, axiom, 651.76/88.99 (![A:term,P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_84 @ A @ P ) <=> 651.76/88.99 ( ( ~( ![B:term]: ( zip_tseitin_39 @ B @ A @ P ) ) ) | 651.76/88.99 ( P @ ( lam @ A ) ) ) ))). 651.76/88.99 thf(zf_stmt_83, type, zip_tseitin_83 : 651.76/88.99 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_84, axiom, 651.76/88.99 (![Bound_variable_2910:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_83 @ Bound_variable_2910 @ Q @ P ) <=> 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_20 @ K @ N @ A @ M @ P ) ) ) | 651.76/88.99 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_25 @ F @ P ) ) ) | 651.76/88.99 ( Q @ ( lam @ Bound_variable_2910 ) ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_2 @ B @ Bound_variable_2910 @ Q ) ) ) | 651.76/88.99 ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/88.99 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_85, type, zip_tseitin_82 : $o). 651.76/88.99 thf(zf_stmt_86, axiom, 651.76/88.99 (( zip_tseitin_82 ) <=> 651.76/88.99 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 651.76/88.99 ( zip_tseitin_81 ) ))).thf(zf_stmt_87, type, zip_tseitin_81 : $o). 651.76/88.99 thf(zf_stmt_88, axiom, 651.76/88.99 (( zip_tseitin_81 ) <=> 651.76/88.99 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 651.76/88.99 ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]: 651.76/88.99 ( zip_tseitin_69 @ B @ M @ A @ K @ P ) ) ))). 651.76/88.99 thf(zf_stmt_89, type, zip_tseitin_80 : 651.76/88.99 term > term > ( subst > term > term ) > $o). 651.76/88.99 thf(zf_stmt_90, axiom, 651.76/88.99 (![Bound_variable_2605:term,Bound_variable_2603:term, 651.76/88.99 F:( subst > term > term )]: 651.76/88.99 ( ( zip_tseitin_80 @ Bound_variable_2605 @ Bound_variable_2603 @ F ) <=> 651.76/88.99 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/88.99 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.99 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/88.99 ( ( lam @ ( F @ sh @ one ) ) != 651.76/88.99 ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) ))). 651.76/88.99 thf(zf_stmt_91, type, zip_tseitin_79 : $o). 651.76/88.99 thf(zf_stmt_92, axiom, 651.76/88.99 (( zip_tseitin_79 ) <=> 651.76/88.99 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) & 651.76/88.99 ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) ))). 651.76/88.99 thf(zf_stmt_93, type, zip_tseitin_78 : $o). 651.76/88.99 thf(zf_stmt_94, axiom, 651.76/88.99 (( zip_tseitin_78 ) <=> 651.76/88.99 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) => ( zip_tseitin_77 ) ))). 651.76/88.99 thf(zf_stmt_95, type, zip_tseitin_77 : $o). 651.76/88.99 thf(zf_stmt_96, axiom, 651.76/88.99 (( zip_tseitin_77 ) <=> 651.76/88.99 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) => ( zip_tseitin_76 ) ))). 651.76/88.99 thf(zf_stmt_97, type, zip_tseitin_76 : $o). 651.76/88.99 thf(zf_stmt_98, axiom, 651.76/88.99 (( zip_tseitin_76 ) <=> 651.76/88.99 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) & 651.76/88.99 ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) ))). 651.76/88.99 thf(zf_stmt_99, type, zip_tseitin_75 : $o). 651.76/88.99 thf(zf_stmt_100, axiom, 651.76/88.99 (( zip_tseitin_75 ) <=> 651.76/88.99 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_74 ) ))). 651.76/88.99 thf(zf_stmt_101, type, zip_tseitin_74 : $o). 651.76/88.99 thf(zf_stmt_102, axiom, 651.76/88.99 (( zip_tseitin_74 ) <=> 651.76/88.99 ( ( ![P:( term > $o ),Bound_variable_2340:term,Bound_variable_2342:subst]: 651.76/88.99 ( zip_tseitin_71 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) ) => 651.76/88.99 ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/88.99 ( zip_tseitin_73 @ Bound_variable_2367 @ P ) ) ))). 651.76/88.99 thf(zf_stmt_103, type, zip_tseitin_73 : term > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_104, axiom, 651.76/88.99 (![Bound_variable_2367:term,P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_73 @ Bound_variable_2367 @ P ) <=> 651.76/88.99 ( ( ~( ![A:term,B:term]: ( zip_tseitin_5 @ B @ A @ P ) ) ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_72 @ A @ P ) ) ) | 651.76/88.99 ( P @ Bound_variable_2367 ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_8 @ A @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_105, type, zip_tseitin_72 : term > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_106, axiom, 651.76/88.99 (![A:term,P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_72 @ A @ P ) <=> 651.76/88.99 ( ( P @ ( lam @ A ) ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_2 @ B @ A @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_107, type, zip_tseitin_71 : subst > term > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_108, axiom, 651.76/88.99 (![Bound_variable_2342:subst,Bound_variable_2340:term,P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_71 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) <=> 651.76/88.99 ( ( ~( ![A:term]: ( zip_tseitin_3 @ A @ P ) ) ) | 651.76/88.99 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_4 @ B @ Bound_variable_2342 @ P ) ) ) | 651.76/88.99 ( ~( ![A:term,B:term]: ( zip_tseitin_11 @ B @ A @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_109, type, zip_tseitin_70 : term > term > $o). 651.76/88.99 thf(zf_stmt_110, axiom, 651.76/88.99 (![B:term,A:term]: 651.76/88.99 ( ( zip_tseitin_70 @ B @ A ) <=> 651.76/88.99 ( ( ( lam @ A ) != ( lam @ B ) ) | ( ( A ) = ( B ) ) ) ))). 651.76/88.99 thf(zf_stmt_111, type, zip_tseitin_69 : 651.76/88.99 term > subst > term > ( term > $o ) > ( term > $o ) > $o). 651.76/88.99 thf(zf_stmt_112, axiom, 651.76/88.99 (![B:term,M:subst,A:term,K:( term > $o ),P:( term > $o )]: 651.76/88.99 ( ( zip_tseitin_69 @ B @ M @ A @ K @ P ) <=> 651.76/88.99 ( ( K @ ( sub @ A @ ( push @ B @ M ) ) ) | ( ~( P @ A ) ) ) ))). 651.76/88.99 thf(zf_stmt_113, type, zip_tseitin_68 : 651.76/88.99 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_114, axiom, 651.76/88.99 (![Bound_variable_2931:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_68 @ Bound_variable_2931 @ Q @ P ) <=> 651.76/88.99 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_67 @ F @ P ) ) ) | 651.76/88.99 ( ~( ![B:term]: ( zip_tseitin_2 @ B @ Bound_variable_2931 @ Q ) ) ) | 651.76/88.99 ( Q @ ( lam @ Bound_variable_2931 ) ) | 651.76/88.99 ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_115, type, zip_tseitin_67 : 651.76/88.99 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/88.99 thf(zf_stmt_116, axiom, 651.76/88.99 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/88.99 ( ( zip_tseitin_67 @ F @ P ) <=> 651.76/88.99 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/88.99 ( ~( ![A:term]: ( zip_tseitin_31 @ A @ F @ P ) ) ) | 651.76/88.99 ( ~( ![M:subst,A:term,N:subst]: 651.76/88.99 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/88.99 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 651.76/88.99 thf(zf_stmt_117, type, zip_tseitin_66 : $o). 651.76/88.99 thf(zf_stmt_118, axiom, 651.76/88.99 (( zip_tseitin_66 ) <=> 651.76/88.99 ( ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_64 @ D @ C @ B @ A ) ) => 651.76/88.99 ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_65 @ D @ C @ B @ A ) ) ))). 651.76/88.99 thf(zf_stmt_119, type, zip_tseitin_65 : term > term > term > term > $o). 651.76/88.99 thf(zf_stmt_120, axiom, 651.76/88.99 (![D:term,C:term,B:term,A:term]: 651.76/88.99 ( ( zip_tseitin_65 @ D @ C @ B @ A ) <=> 651.76/88.99 ( ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) | 651.76/88.99 ( ( C ) = ( D ) ) ) ))). 651.76/88.99 thf(zf_stmt_121, type, zip_tseitin_64 : term > term > term > term > $o). 651.76/88.99 thf(zf_stmt_122, axiom, 651.76/88.99 (![D:term,C:term,B:term,A:term]: 651.76/88.99 ( ( zip_tseitin_64 @ D @ C @ B @ A ) <=> 651.76/88.99 ( ( ( C ) = ( D ) ) | ( ( ap @ A @ C ) != ( ap @ B @ D ) ) ) ))). 651.76/88.99 thf(zf_stmt_123, type, zip_tseitin_63 : term > term > term > term > $o). 651.76/89.00 thf(zf_stmt_124, axiom, 651.76/89.00 (![D:term,C:term,B:term,A:term]: 651.76/89.00 ( ( zip_tseitin_63 @ D @ C @ B @ A ) <=> 651.76/89.00 ( ( ( ap @ A @ C ) != ( ap @ B @ D ) ) | ( ( C ) = ( D ) ) ) ))). 651.76/89.00 thf(zf_stmt_125, type, zip_tseitin_62 : $o). 651.76/89.00 thf(zf_stmt_126, axiom, 651.76/89.00 (( zip_tseitin_62 ) <=> 651.76/89.00 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_61 ) ))). 651.76/89.00 thf(zf_stmt_127, type, zip_tseitin_61 : $o). 651.76/89.00 thf(zf_stmt_128, axiom, 651.76/89.00 (( zip_tseitin_61 ) <=> 651.76/89.00 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 651.76/89.00 ( zip_tseitin_59 @ Bound_variable_3046 @ P ) ) => 651.76/89.00 ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]: 651.76/89.00 ( zip_tseitin_60 @ Bound_variable_3232 @ P ) ) ))). 651.76/89.00 thf(zf_stmt_129, type, zip_tseitin_60 : 651.76/89.00 term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_130, axiom, 651.76/89.00 (![Bound_variable_3232:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_60 @ Bound_variable_3232 @ P ) <=> 651.76/89.00 ( ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) | 651.76/89.00 ( ~( ![B:term]: ( zip_tseitin_52 @ B @ Bound_variable_3232 @ P ) ) ) | 651.76/89.00 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_43 @ F @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_131, type, zip_tseitin_59 : 651.76/89.00 term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_132, axiom, 651.76/89.00 (![Bound_variable_3046:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_59 @ Bound_variable_3046 @ P ) <=> 651.76/89.00 ( ( ~( ![B:term]: ( zip_tseitin_26 @ B @ Bound_variable_3046 @ P ) ) ) | 651.76/89.00 ( P @ 651.76/89.00 id @ 651.76/89.00 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 651.76/89.00 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_58 @ F @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_133, type, zip_tseitin_58 : 651.76/89.00 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_134, axiom, 651.76/89.00 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_58 @ F @ P ) <=> 651.76/89.00 ( ( ~( ![A:term]: ( zip_tseitin_24 @ A @ F @ P ) ) ) | 651.76/89.00 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst]: 651.76/89.00 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/89.00 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_135, type, zip_tseitin_57 : 651.76/89.00 term > term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_136, axiom, 651.76/89.00 (![Bound_variable_3001:term,Bound_variable_2999:term, 651.76/89.00 P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_57 @ Bound_variable_3001 @ Bound_variable_2999 @ P ) <=> 651.76/89.00 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_28 @ K @ N @ A @ M @ P ) ) ) | 651.76/89.00 ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 651.76/89.00 ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 651.76/89.00 ( ~( P @ id @ Bound_variable_3001 @ id ) ) | 651.76/89.00 ( ~( ![A:term,B:term]: ( zip_tseitin_56 @ B @ A @ P ) ) ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_137, type, zip_tseitin_56 : 651.76/89.00 term > term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_138, axiom, 651.76/89.00 (![B:term,A:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_56 @ B @ A @ P ) <=> 651.76/89.00 ( ( ~( P @ id @ A @ id ) ) | ( ~( P @ id @ B @ id ) ) | 651.76/89.00 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) ) ))). 651.76/89.00 thf(zf_stmt_139, type, zip_tseitin_55 : 651.76/89.00 term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_140, axiom, 651.76/89.00 (![Bound_variable_3211:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_55 @ Bound_variable_3211 @ P ) <=> 651.76/89.00 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_20 @ K @ N @ A @ M @ P ) ) ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) | 651.76/89.00 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_45 @ F @ P ) ) ) | 651.76/89.00 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 651.76/89.00 ( ~( ![B:term]: ( zip_tseitin_26 @ B @ Bound_variable_3211 @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_141, type, zip_tseitin_54 : 651.76/89.00 term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_142, axiom, 651.76/89.00 (![Bound_variable_3046:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_54 @ Bound_variable_3046 @ P ) <=> 651.76/89.00 ( ( ~( ![F:( subst > term > term )]: ( zip_tseitin_53 @ F @ P ) ) ) | 651.76/89.00 ( P @ 651.76/89.00 id @ 651.76/89.00 ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 651.76/89.00 ( ~( ![B:term]: ( zip_tseitin_52 @ B @ Bound_variable_3046 @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_143, type, zip_tseitin_53 : 651.76/89.00 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_144, axiom, 651.76/89.00 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_53 @ F @ P ) <=> 651.76/89.00 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/89.00 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/89.00 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/89.00 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_31 @ A @ F @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_145, type, zip_tseitin_52 : 651.76/89.00 term > term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_146, axiom, 651.76/89.00 (![B:term,Bound_variable_3046:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_52 @ B @ Bound_variable_3046 @ P ) <=> 651.76/89.00 ( ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) | 651.76/89.00 ( ~( P @ id @ B @ id ) ) ) ))). 651.76/89.00 thf(zf_stmt_147, type, zip_tseitin_51 : 651.76/89.00 term > subst > ( subst > term > term ) > ( subst > term > term ) > $o). 651.76/89.00 thf(zf_stmt_148, axiom, 651.76/89.00 (![Bound_variable_2551:term,Bound_variable_2549:subst, 651.76/89.00 Bound_variable_2547:( subst > term > term ),F:( subst > term > term )]: 651.76/89.00 ( ( zip_tseitin_51 @ 651.76/89.00 Bound_variable_2551 @ Bound_variable_2549 @ Bound_variable_2547 @ F ) <=> 651.76/89.00 ( ( ( lam @ ( F @ sh @ one ) ) != 651.76/89.00 ( lam @ ( Bound_variable_2547 @ sh @ one ) ) ) | 651.76/89.00 ( ( F @ Bound_variable_2549 @ Bound_variable_2551 ) = 651.76/89.00 ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst]: 651.76/89.00 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N ) = 651.76/89.00 ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst]: 651.76/89.00 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/89.00 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_149, type, zip_tseitin_50 : $o). 651.76/89.00 thf(zf_stmt_150, axiom, 651.76/89.00 (( zip_tseitin_50 ) <=> 651.76/89.00 ( ( ![P:( subst > term > subst > $o )]: 651.76/89.00 ( ~( ![Q:( term > $o )]: 651.76/89.00 ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) ) ) ) => 651.76/89.00 ( zip_tseitin_49 ) ))).thf(zf_stmt_151, type, zip_tseitin_49 : $o). 651.76/89.00 thf(zf_stmt_152, axiom, 651.76/89.00 (( zip_tseitin_49 ) <=> 651.76/89.00 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/89.00 ( zip_tseitin_42 @ Bound_variable_2367 @ P ) ) => 651.76/89.00 ( zip_tseitin_48 ) ))).thf(zf_stmt_153, type, zip_tseitin_48 : $o). 651.76/89.00 thf(zf_stmt_154, axiom, 651.76/89.00 (( zip_tseitin_48 ) <=> 651.76/89.00 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) => ( zip_tseitin_47 ) ))). 651.76/89.00 thf(zf_stmt_155, type, zip_tseitin_47 : $o). 651.76/89.00 thf(zf_stmt_156, axiom, 651.76/89.00 (( zip_tseitin_47 ) <=> 651.76/89.00 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/89.00 Bound_variable_2931:term]: 651.76/89.00 ( zip_tseitin_44 @ Bound_variable_2931 @ Q @ P ) ) => 651.76/89.00 ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]: 651.76/89.00 ( zip_tseitin_46 @ Bound_variable_3295 @ P ) ) ))). 651.76/89.00 thf(zf_stmt_157, type, zip_tseitin_46 : 651.76/89.00 term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_158, axiom, 651.76/89.00 (![Bound_variable_3295:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_46 @ Bound_variable_3295 @ P ) <=> 651.76/89.00 ( ( ~( ![A:term,B:term]: ( zip_tseitin_22 @ B @ A @ P ) ) ) | 651.76/89.00 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_45 @ F @ P ) ) ) | 651.76/89.00 ( P @ id @ Bound_variable_3295 @ id ) ) ))). 651.76/89.00 thf(zf_stmt_159, type, zip_tseitin_45 : 651.76/89.00 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_160, axiom, 651.76/89.00 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_45 @ F @ P ) <=> 651.76/89.00 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/89.00 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/89.00 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/89.00 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_24 @ A @ F @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_161, type, zip_tseitin_44 : 651.76/89.00 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_162, axiom, 651.76/89.00 (![Bound_variable_2931:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_44 @ Bound_variable_2931 @ Q @ P ) <=> 651.76/89.00 ( ( ~( ![B:term]: ( zip_tseitin_2 @ B @ Bound_variable_2931 @ Q ) ) ) | 651.76/89.00 ( Q @ ( lam @ Bound_variable_2931 ) ) | 651.76/89.00 ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) | 651.76/89.00 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_43 @ F @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_163, type, zip_tseitin_43 : 651.76/89.00 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_164, axiom, 651.76/89.00 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_43 @ F @ P ) <=> 651.76/89.00 ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_24 @ A @ F @ P ) ) ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst]: 651.76/89.00 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/89.00 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_165, type, zip_tseitin_42 : term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_166, axiom, 651.76/89.00 (![Bound_variable_2367:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_42 @ Bound_variable_2367 @ P ) <=> 651.76/89.00 ( ( ~( ![A:term]: ( zip_tseitin_8 @ A @ P ) ) ) | 651.76/89.00 ( ~( ![A:term,B:term]: ( zip_tseitin_41 @ B @ A @ P ) ) ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_40 @ A @ P ) ) ) | 651.76/89.00 ( P @ Bound_variable_2367 ) ) ))). 651.76/89.00 thf(zf_stmt_167, type, zip_tseitin_41 : term > term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_168, axiom, 651.76/89.00 (![B:term,A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_41 @ B @ A @ P ) <=> 651.76/89.00 ( ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ A ) ) ) ))). 651.76/89.00 thf(zf_stmt_169, type, zip_tseitin_40 : term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_170, axiom, 651.76/89.00 (![A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_40 @ A @ P ) <=> 651.76/89.00 ( ( P @ ( lam @ A ) ) | 651.76/89.00 ( ~( ![B:term]: ( zip_tseitin_39 @ B @ A @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_171, type, zip_tseitin_39 : term > term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_172, axiom, 651.76/89.00 (![B:term,A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_39 @ B @ A @ P ) <=> 651.76/89.00 ( ( ~( P @ B ) ) | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_173, type, zip_tseitin_38 : 651.76/89.00 term > ( term > $o ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_174, axiom, 651.76/89.00 (![X:term,Q:( term > $o ),P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_38 @ X @ Q @ P ) <=> ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ))). 651.76/89.00 thf(zf_stmt_175, type, zip_tseitin_37 : $o). 651.76/89.00 thf(zf_stmt_176, axiom, 651.76/89.00 (( zip_tseitin_37 ) <=> 651.76/89.00 ( ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/89.00 ( zip_tseitin_19 @ Bound_variable_2367 @ P ) ) => 651.76/89.00 ( zip_tseitin_36 ) ))).thf(zf_stmt_177, type, zip_tseitin_36 : $o). 651.76/89.00 thf(zf_stmt_178, axiom, 651.76/89.00 (( zip_tseitin_36 ) <=> 651.76/89.00 ( ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term, 651.76/89.00 Bound_variable_3001:term]: 651.76/89.00 ( zip_tseitin_23 @ Bound_variable_3001 @ Bound_variable_2999 @ P ) ) => 651.76/89.00 ( zip_tseitin_35 ) ))).thf(zf_stmt_179, type, zip_tseitin_35 : $o). 651.76/89.00 thf(zf_stmt_180, axiom, 651.76/89.00 (( zip_tseitin_35 ) <=> 651.76/89.00 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 651.76/89.00 ( zip_tseitin_29 @ Bound_variable_3211 @ P ) ) => 651.76/89.00 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 651.76/89.00 ( zip_tseitin_34 @ Bound_variable_3283 @ P ) ) ))). 651.76/89.00 thf(zf_stmt_181, type, zip_tseitin_34 : 651.76/89.00 term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_182, axiom, 651.76/89.00 (![Bound_variable_3283:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_34 @ Bound_variable_3283 @ P ) <=> 651.76/89.00 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_28 @ K @ N @ A @ M @ P ) ) ) | 651.76/89.00 ( ~( ![A:term,B:term]: ( zip_tseitin_33 @ B @ A @ P ) ) ) | 651.76/89.00 ( P @ id @ Bound_variable_3283 @ id ) | 651.76/89.00 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_32 @ F @ P ) ) ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_30 @ A @ P ) ) ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_183, type, zip_tseitin_33 : 651.76/89.00 term > term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_184, axiom, 651.76/89.00 (![B:term,A:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_33 @ B @ A @ P ) <=> 651.76/89.00 ( ( ~( P @ id @ A @ id ) ) | 651.76/89.00 ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 651.76/89.00 ( ~( P @ id @ B @ id ) ) ) ))). 651.76/89.00 thf(zf_stmt_185, type, zip_tseitin_32 : 651.76/89.00 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_186, axiom, 651.76/89.00 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_32 @ F @ P ) <=> 651.76/89.00 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/89.00 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/89.00 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_31 @ A @ F @ P ) ) ) | 651.76/89.00 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ))). 651.76/89.00 thf(zf_stmt_187, type, zip_tseitin_31 : 651.76/89.00 term > ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_188, type, zip_tseitin_30 : 651.76/89.00 term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_189, axiom, 651.76/89.00 (![A:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_30 @ A @ P ) <=> 651.76/89.00 ( ( P @ id @ A @ id ) | ( ~( var @ ( sub @ A @ id ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_190, type, zip_tseitin_29 : 651.76/89.00 term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_191, axiom, 651.76/89.00 (![Bound_variable_3211:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_29 @ Bound_variable_3211 @ P ) <=> 651.76/89.00 ( ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_28 @ K @ N @ A @ M @ P ) ) ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_27 @ K @ N @ A @ M @ P ) ) ) | 651.76/89.00 ( ~( ![B:term]: ( zip_tseitin_26 @ B @ Bound_variable_3211 @ P ) ) ) | 651.76/89.00 ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 651.76/89.00 ( ~( ![F:( subst > term > term )]: ( zip_tseitin_25 @ F @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_192, type, zip_tseitin_28 : 651.76/89.00 subst > subst > term > subst > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_193, axiom, 651.76/89.00 (![K:subst,N:subst,A:term,M:subst,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_28 @ K @ N @ A @ M @ P ) <=> 651.76/89.00 ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 651.76/89.00 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ))). 651.76/89.00 thf(zf_stmt_194, type, zip_tseitin_27 : 651.76/89.00 subst > subst > term > subst > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_195, axiom, 651.76/89.00 (![K:subst,N:subst,A:term,M:subst,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_27 @ K @ N @ A @ M @ P ) <=> 651.76/89.00 ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 651.76/89.00 ( P @ M @ A @ ( comp @ K @ N ) ) ) ))). 651.76/89.00 thf(zf_stmt_196, type, zip_tseitin_26 : 651.76/89.00 term > term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_197, axiom, 651.76/89.00 (![B:term,Bound_variable_3211:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_26 @ B @ Bound_variable_3211 @ P ) <=> 651.76/89.00 ( ( ~( P @ id @ B @ id ) ) | 651.76/89.00 ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) ) ))). 651.76/89.00 thf(zf_stmt_198, type, zip_tseitin_25 : 651.76/89.00 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_199, axiom, 651.76/89.00 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_25 @ F @ P ) <=> 651.76/89.00 ( ( ~( ![M:subst,A:term,N:subst]: 651.76/89.00 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/89.00 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_24 @ A @ F @ P ) ) ) | 651.76/89.00 ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ))). 651.76/89.00 thf(zf_stmt_200, type, zip_tseitin_24 : 651.76/89.00 term > ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_201, axiom, 651.76/89.00 (![A:term,F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_24 @ A @ F @ P ) <=> 651.76/89.00 ( ( P @ id @ ( F @ id @ A ) @ id ) | ( ~( P @ id @ A @ id ) ) ) ))). 651.76/89.00 thf(zf_stmt_202, type, zip_tseitin_23 : 651.76/89.00 term > term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_203, axiom, 651.76/89.00 (![Bound_variable_3001:term,Bound_variable_2999:term, 651.76/89.00 P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_23 @ Bound_variable_3001 @ Bound_variable_2999 @ P ) <=> 651.76/89.00 ( ( ~( ![A:term,B:term]: ( zip_tseitin_22 @ B @ A @ P ) ) ) | 651.76/89.00 ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 651.76/89.00 ( ~( P @ id @ Bound_variable_3001 @ id ) ) | 651.76/89.00 ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_21 @ K @ N @ A @ M @ P ) ) ) | 651.76/89.00 ( ~( ![M:subst,A:term,N:subst,K:subst]: 651.76/89.00 ( zip_tseitin_20 @ K @ N @ A @ M @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_204, type, zip_tseitin_22 : 651.76/89.00 term > term > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_205, axiom, 651.76/89.00 (![B:term,A:term,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_22 @ B @ A @ P ) <=> 651.76/89.00 ( ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 651.76/89.00 ( ~( P @ id @ B @ id ) ) | ( ~( P @ id @ A @ id ) ) ) ))). 651.76/89.00 thf(zf_stmt_206, type, zip_tseitin_21 : 651.76/89.00 subst > subst > term > subst > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_207, axiom, 651.76/89.00 (![K:subst,N:subst,A:term,M:subst,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_21 @ K @ N @ A @ M @ P ) <=> 651.76/89.00 ( ( P @ M @ A @ ( comp @ K @ N ) ) | 651.76/89.00 ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ))). 651.76/89.00 thf(zf_stmt_208, type, zip_tseitin_20 : 651.76/89.00 subst > subst > term > subst > ( subst > term > subst > $o ) > $o). 651.76/89.00 thf(zf_stmt_209, axiom, 651.76/89.00 (![K:subst,N:subst,A:term,M:subst,P:( subst > term > subst > $o )]: 651.76/89.00 ( ( zip_tseitin_20 @ K @ N @ A @ M @ P ) <=> 651.76/89.00 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 651.76/89.00 ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_210, type, zip_tseitin_19 : term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_211, axiom, 651.76/89.00 (![Bound_variable_2367:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_19 @ Bound_variable_2367 @ P ) <=> 651.76/89.00 ( ( ~( ![A:term]: ( zip_tseitin_18 @ A @ P ) ) ) | 651.76/89.00 ( P @ Bound_variable_2367 ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_3 @ A @ P ) ) ) | 651.76/89.00 ( ~( ![A:term,B:term]: ( zip_tseitin_17 @ B @ A @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_212, type, zip_tseitin_18 : term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_213, axiom, 651.76/89.00 (![A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_18 @ A @ P ) <=> ( ( P @ A ) | ( ~( var @ A ) ) ) ))). 651.76/89.00 thf(zf_stmt_214, type, zip_tseitin_17 : term > term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_215, axiom, 651.76/89.00 (![B:term,A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_17 @ B @ A @ P ) <=> 651.76/89.00 ( ( ~( P @ A ) ) | ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) ) ))). 651.76/89.00 thf(zf_stmt_216, type, zip_tseitin_16 : $o). 651.76/89.00 thf(zf_stmt_217, axiom, 651.76/89.00 (( zip_tseitin_16 ) <=> 651.76/89.00 ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) => 651.76/89.00 ( zip_tseitin_15 ) ))).thf(zf_stmt_218, type, zip_tseitin_15 : $o). 651.76/89.00 thf(zf_stmt_219, axiom, 651.76/89.00 (( zip_tseitin_15 ) <=> 651.76/89.00 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) => 651.76/89.00 ( zip_tseitin_14 ) ))).thf(zf_stmt_220, type, zip_tseitin_14 : $o). 651.76/89.00 thf(zf_stmt_221, axiom, 651.76/89.00 (( zip_tseitin_14 ) <=> 651.76/89.00 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) => ( zip_tseitin_13 ) ))). 651.76/89.00 thf(zf_stmt_222, type, zip_tseitin_13 : $o). 651.76/89.00 thf(zf_stmt_223, axiom, 651.76/89.00 (( zip_tseitin_13 ) <=> 651.76/89.00 ( ( ![P:( term > $o ),Bound_variable_2140:term]: 651.76/89.00 ( zip_tseitin_9 @ Bound_variable_2140 @ P ) ) => 651.76/89.00 ( ![P:( term > $o ),Bound_variable_2340:term,Bound_variable_2342:subst]: 651.76/89.00 ( zip_tseitin_12 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) ) ))). 651.76/89.00 thf(zf_stmt_224, type, zip_tseitin_12 : subst > term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_225, axiom, 651.76/89.00 (![Bound_variable_2342:subst,Bound_variable_2340:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_12 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) <=> 651.76/89.00 ( ( ~( ![A:term,B:term]: ( zip_tseitin_11 @ B @ A @ P ) ) ) | 651.76/89.00 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 651.76/89.00 ( ~( ![B:term]: ( zip_tseitin_10 @ B @ Bound_variable_2342 @ P ) ) ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_3 @ A @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_226, type, zip_tseitin_11 : term > term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_227, axiom, 651.76/89.00 (![B:term,A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_11 @ B @ A @ P ) <=> 651.76/89.00 ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) ) ))). 651.76/89.00 thf(zf_stmt_228, type, zip_tseitin_10 : term > subst > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_229, axiom, 651.76/89.00 (![B:term,Bound_variable_2342:subst,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_10 @ B @ Bound_variable_2342 @ P ) <=> 651.76/89.00 ( ( ~( var @ B ) ) | ( P @ ( sub @ B @ Bound_variable_2342 ) ) ) ))). 651.76/89.00 thf(zf_stmt_230, type, zip_tseitin_9 : term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_231, axiom, 651.76/89.00 (![Bound_variable_2140:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_9 @ Bound_variable_2140 @ P ) <=> 651.76/89.00 ( ( ~( ![A:term]: ( zip_tseitin_8 @ A @ P ) ) ) | 651.76/89.00 ( P @ Bound_variable_2140 ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_7 @ A @ P ) ) ) | 651.76/89.00 ( ~( ![A:term,B:term]: ( zip_tseitin_5 @ B @ A @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_232, type, zip_tseitin_8 : term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_233, axiom, 651.76/89.00 (![A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_8 @ A @ P ) <=> ( ( ~( var @ A ) ) | ( P @ A ) ) ))). 651.76/89.00 thf(zf_stmt_234, type, zip_tseitin_7 : term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_235, axiom, 651.76/89.00 (![A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_7 @ A @ P ) <=> ( ( P @ ( lam @ A ) ) | ( ~( P @ A ) ) ) ))). 651.76/89.00 thf(zf_stmt_236, type, zip_tseitin_6 : subst > term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_237, axiom, 651.76/89.00 (![Bound_variable_2342:subst,Bound_variable_2340:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_6 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) <=> 651.76/89.00 ( ( ~( ![A:term,B:term]: ( zip_tseitin_5 @ B @ A @ P ) ) ) | 651.76/89.00 ( ~( ![B:term]: ( zip_tseitin_4 @ B @ Bound_variable_2342 @ P ) ) ) | 651.76/89.00 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 651.76/89.00 ( ~( ![A:term]: ( zip_tseitin_3 @ A @ P ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_238, type, zip_tseitin_5 : term > term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_239, axiom, 651.76/89.00 (![B:term,A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_5 @ B @ A @ P ) <=> 651.76/89.00 ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | ( ~( P @ A ) ) ) ))). 651.76/89.00 thf(zf_stmt_240, type, zip_tseitin_4 : term > subst > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_241, axiom, 651.76/89.00 (![B:term,Bound_variable_2342:subst,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_4 @ B @ Bound_variable_2342 @ P ) <=> 651.76/89.00 ( ( P @ ( sub @ B @ Bound_variable_2342 ) ) | ( ~( var @ B ) ) ) ))). 651.76/89.00 thf(zf_stmt_242, type, zip_tseitin_3 : term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_243, axiom, 651.76/89.00 (![A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_3 @ A @ P ) <=> 651.76/89.00 ( ( ~( ![B:term]: ( zip_tseitin_2 @ B @ A @ P ) ) ) | 651.76/89.00 ( P @ ( lam @ A ) ) ) ))). 651.76/89.00 thf(zf_stmt_244, type, zip_tseitin_2 : term > term > ( term > $o ) > $o). 651.76/89.00 thf(zf_stmt_245, axiom, 651.76/89.00 (![B:term,A:term,P:( term > $o )]: 651.76/89.00 ( ( zip_tseitin_2 @ B @ A @ P ) <=> 651.76/89.00 ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | ( ~( P @ B ) ) ) ))). 651.76/89.00 thf(zf_stmt_246, type, zip_tseitin_1 : term > term > $o). 651.76/89.00 thf(zf_stmt_247, axiom, 651.76/89.00 (![B:term,A:term]: 651.76/89.00 ( ( zip_tseitin_1 @ B @ A ) <=> 651.76/89.00 ( ( ( sub @ A @ sh ) != ( sub @ B @ sh ) ) | ( ( A ) = ( B ) ) ) ))). 651.76/89.00 thf(zf_stmt_248, type, zip_tseitin_0 : 651.76/89.00 term > ( term > $o ) > ( term > $o ) > subst > term > $o). 651.76/89.00 thf(zf_stmt_249, axiom, 651.76/89.00 (![X:term,Q:( term > $o ),P:( term > $o ),M:subst,A:term]: 651.76/89.00 ( ( zip_tseitin_0 @ X @ Q @ P @ M @ A ) <=> 651.76/89.00 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ))). 651.76/89.00 thf(zf_stmt_250, axiom, 651.76/89.00 (( ![DS:d_subst]: ( ( DS ) = ( d_id ) ) ) & 651.76/89.00 ( ![DS1:d_subst,DS2:d_subst]: 651.76/89.00 ( ( ( d2subst @ DS1 ) = ( d2subst @ DS2 ) ) => ( ( DS1 ) = ( DS2 ) ) ) ) & 651.76/89.00 ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 651.76/89.00 ( ( lam @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 651.76/89.00 ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 651.76/89.00 ( ![Bound_variable_4913:subst,Bound_variable_4915:( subst > term > term )]: 651.76/89.00 ( ( hoaslam @ Bound_variable_4913 @ Bound_variable_4915 ) = 651.76/89.00 ( d2term @ d_one ) ) ) & 651.76/89.00 ( ![P:( subst > term > subst > $o ),Q:( term > $o )]: 651.76/89.00 ( ( hoasinduction_p_and_p_prime @ P @ Q ) <=> 651.76/89.00 ( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) ) & 651.76/89.00 ( ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]: 651.76/89.00 ( zip_tseitin_124 @ M @ A @ Q @ P ) ) <=> 651.76/89.00 ( pushprop_lem1v2 ) ) & 651.76/89.00 ( axmap ) & ( pushprop_lem0_gthm ) & ( hoasinduction_lem1v2_gthm ) & 651.76/89.00 ( ( ![B:term]: 651.76/89.00 ( ~( ![F:( subst > term > term )]: 651.76/89.00 ( ~( ![A:term,M:subst]: 651.76/89.00 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) <=> 651.76/89.00 ( hoasinduction_lem3v2_f ) ) & 651.76/89.00 ( axvarshift ) & 651.76/89.00 ( ( hoasapinj2 ) <=> 651.76/89.00 ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_123 @ D @ C @ B @ A ) ) ) & 651.76/89.00 ( hoasapnotvar_gthm ) & 651.76/89.00 ( ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_122 @ D @ C @ B @ A ) ) <=> 651.76/89.00 ( hoasapinj1 ) ) & 651.76/89.00 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3171:term]: 651.76/89.00 ( zip_tseitin_121 @ Bound_variable_3171 @ P ) ) <=> 651.76/89.00 ( hoasinduction_lem3aaa ) ) & 651.76/89.00 ( ( zip_tseitin_119 ) <=> ( termmset_lthm ) ) & ( hoaslamnotap_lthm ) & 651.76/89.00 ( ( pushprop_lem1v2_lthm ) <=> ( zip_tseitin_118 ) ) & 651.76/89.00 ( ( hoasinduction ) <=> 651.76/89.00 ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]: 651.76/89.00 ( zip_tseitin_116 @ Bound_variable_3283 @ P ) ) ) & 651.76/89.00 ( ( hoasinduction_lem3b_lthm ) <=> 651.76/89.00 ( ![B:term]: 651.76/89.00 ( ~( ![F:( subst > term > term )]: 651.76/89.00 ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) ) & 651.76/89.00 ( ( induction ) <=> 651.76/89.00 ( ![P:( term > $o ),Bound_variable_2140:term]: 651.76/89.00 ( zip_tseitin_115 @ Bound_variable_2140 @ P ) ) ) & 651.76/89.00 ( termmset_gthm ) & 651.76/89.00 ( ( hoasinduction_lem3aa ) <=> 651.76/89.00 ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 651.76/89.00 ( zip_tseitin_114 @ Bound_variable_3046 @ P ) ) ) & 651.76/89.00 ( hoaslamnotvar_gthm ) & ( axclos ) & 651.76/89.00 ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/89.00 Bound_variable_2820:term,Bound_variable_2822:term]: 651.76/89.00 ( zip_tseitin_113 @ Bound_variable_2822 @ Bound_variable_2820 @ Q @ P ) ) <=> 651.76/89.00 ( hoasinduction_lem2v2 ) ) & 651.76/89.00 ( pushprop_lthm ) & 651.76/89.00 ( ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_109 @ D @ C @ B @ A ) ) <=> 651.76/89.00 ( apinj1 ) ) & 651.76/89.00 ( ( hoasapinj1_lthm ) <=> ( zip_tseitin_112 ) ) & 651.76/89.00 ( ( hoaslaminj_lthm ) <=> ( zip_tseitin_108 ) ) & 651.76/89.00 ( ( axvarcons ) <=> 651.76/89.00 ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) ) & 651.76/89.00 ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) <=> ( axidr ) ) & 651.76/89.00 ( ( hoasinduction_lem3_lthm ) <=> ( zip_tseitin_105 ) ) & 651.76/89.00 ( ( zip_tseitin_101 ) <=> ( hoasinduction_lem3v2a_lthm ) ) & 651.76/89.00 ( hoasinduction_lem1_lthm ) & 651.76/89.00 ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) <=> ( axidl ) ) & 651.76/89.00 ( ( hoasinduction_lem0_lthm ) <=> 651.76/89.00 ( ![P:( subst > term > subst > $o )]: 651.76/89.00 ( ~( ![Q:( term > $o )]: 651.76/89.00 ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) ) ) ) ) & 651.76/89.00 ( pushprop ) & ( hoasinduction_lem2_gthm ) & 651.76/89.00 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]: 651.76/89.00 ( zip_tseitin_98 @ Bound_variable_3232 @ P ) ) <=> 651.76/89.00 ( hoasinduction_lem3a ) ) & 651.76/89.00 ( hoasinduction_lem1_gthm ) & 651.76/89.00 ( ( hoasinduction_no_psi_cond ) <=> 651.76/89.00 ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]: 651.76/89.00 ( zip_tseitin_97 @ Bound_variable_3295 @ P ) ) ) & 651.76/89.00 ( ulamvarsh ) & 651.76/89.00 ( ( induction2 ) <=> 651.76/89.00 ( ![P:( term > $o ),Bound_variable_2367:term]: 651.76/89.00 ( zip_tseitin_95 @ Bound_variable_2367 @ P ) ) ) & 651.76/89.00 ( pushprop_lem3v2 ) & 651.76/89.00 ( ( pushprop_lem0_lthm ) <=> 651.76/89.00 ( ![P:( term > $o ),A:term,M:subst]: 651.76/89.00 ( ~( ![Q:( term > $o )]: 651.76/89.00 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P @ M @ A ) ) ) ) ) ) ) & 651.76/89.00 ( hoasapnotvar_lthm ) & 651.76/89.00 ( ( zip_tseitin_94 ) <=> ( hoasinduction_lem3v2_lthm ) ) & 651.76/89.00 ( ( hoasinduction_lthm_3 ) <=> ( zip_tseitin_92 ) ) & 651.76/89.00 ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) <=> ( axvarid ) ) & 651.76/89.00 ( ( termmset ) <=> ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) & 651.76/89.00 ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) <=> 651.76/89.00 ( axshiftcons ) ) & 651.76/89.00 ( ( hoasinduction_lem3v2 ) <=> 651.76/89.00 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/89.00 Bound_variable_2910:term]: 651.76/89.00 ( zip_tseitin_83 @ Bound_variable_2910 @ Q @ P ) ) ) & 651.76/89.00 ( ( pushprop_lem1_lthm ) <=> ( zip_tseitin_82 ) ) & 651.76/89.00 ( pushprop_lem2v2_gthm ) & ( substmonoid_gthm ) & 651.76/89.00 ( ( ![F:( subst > term > term ),Bound_variable_2603:term, 651.76/89.00 Bound_variable_2605:term]: 651.76/89.00 ( zip_tseitin_80 @ Bound_variable_2605 @ Bound_variable_2603 @ F ) ) <=> 651.76/89.00 ( hoaslamnotap ) ) & 651.76/89.00 ( ~( hoasvar @ 651.76/89.00 ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) & 651.76/89.00 ( pushprop_lem2v2_lthm ) & ( induction2_gthm ) & ( lamnotvar ) & 651.76/89.00 ( ( substmonoid ) <=> ( zip_tseitin_79 ) ) & 651.76/89.00 ( ( ![B:term]: 651.76/89.00 ( ~( ![F:( subst > term > term )]: 651.76/89.00 ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) <=> 651.76/89.00 ( hoasinduction_lem3b ) ) & 651.76/89.00 ( hoasinduction_lem3_gthm ) & 651.76/89.00 ( ( substmonoid_lthm ) <=> ( zip_tseitin_78 ) ) & 651.76/89.00 ( ( induction2_lthm ) <=> ( zip_tseitin_75 ) ) & ( hoaslaminj_gthm ) & 651.76/89.00 ( hoaslamnotvar ) & ( hoasapinj1_gthm ) & ( ~( lamnotap ) ) & 651.76/89.00 ( hoasapinj2_gthm ) & ( hoasinduction_lem2_lthm ) & ( axabs ) & 651.76/89.00 ( pushprop_gthm ) & 651.76/89.00 ( ( pushprop_lem0 ) <=> 651.76/89.00 ( ![P:( term > $o ),A:term,M:subst]: 651.76/89.00 ( ~( ![Q:( term > $o )]: 651.76/89.00 ( ~( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P @ M @ A ) ) ) ) ) ) ) & 651.76/89.00 ( ( ![A:term,B:term]: ( zip_tseitin_70 @ B @ A ) ) <=> ( laminj ) ) & 651.76/89.00 ( ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]: 651.76/89.00 ( zip_tseitin_69 @ B @ M @ A @ K @ P ) ) <=> 651.76/89.00 ( pushprop_lem1 ) ) & 651.76/89.00 ( hoasinduction_lem2v2_gthm ) & 651.76/89.00 ( ( axscons ) <=> 651.76/89.00 ( ![M:subst]: 651.76/89.00 ( ( M ) = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) ) ) & 651.76/89.00 ( ( hoasinduction_lem3v2a ) <=> 651.76/89.00 ( ![P:( subst > term > subst > $o ),Q:( term > $o ), 651.76/89.00 Bound_variable_2931:term]: 651.76/89.00 ( zip_tseitin_68 @ Bound_variable_2931 @ Q @ P ) ) ) & 651.76/89.00 ( ( hoasapinj2_lthm ) <=> ( zip_tseitin_66 ) ) & 651.76/89.00 ( ( apinj2 ) <=> 651.76/89.00 ( ![A:term,B:term,C:term,D:term]: ( zip_tseitin_63 @ D @ C @ B @ A ) ) ) & 651.76/89.00 ( axassoc ) & ( hoasinduction_lem3a_gthm ) & ( pushprop_lem2v2 ) & 651.76/89.00 ( hoasinduction_lem3b_gthm ) & ( hoaslamnotap_gthm ) & 651.76/89.00 ( pushprop_lem1v2_gthm ) & 651.76/89.00 ( ( zip_tseitin_62 ) <=> ( hoasinduction_lem3a_lthm ) ) & 651.76/89.00 ( ulamvarind ) & ( pushprop_lem3v2_lthm ) & ( hoaslamnotvar_lthm ) & 651.76/89.00 ( axapp ) & ( hoasinduction_gthm ) & 651.76/89.00 ( ( hoasinduction_lem0 ) <=> 651.76/89.00 ( ![P:( subst > term > subst > $o )]: 651.76/89.00 ( ~( ![Q:( term > $o )]: 651.76/89.00 ( ~( ![X:term]: ( zip_tseitin_38 @ X @ Q @ P ) ) ) ) ) ) ) & 651.76/89.00 ( hoasapnotvar ) & ( hoasinduction_lem1 ) & 651.76/89.00 ( ( hoasinduction_lem2 ) <=> 651.76/89.00 ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term, 651.76/89.00 Bound_variable_3001:term]: 651.76/89.00 ( zip_tseitin_57 @ Bound_variable_3001 @ Bound_variable_2999 @ P ) ) ) & 651.76/89.00 ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]: 651.76/89.00 ( zip_tseitin_55 @ Bound_variable_3211 @ P ) ) <=> 651.76/89.00 ( hoasinduction_lem3 ) ) & 651.76/89.00 ( ( hoasinduction_lem3aa_lthm ) <=> 651.76/89.00 ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]: 651.76/89.00 ( zip_tseitin_54 @ Bound_variable_3046 @ P ) ) ) & 651.76/89.00 ( induction2lem_gthm ) & 651.76/89.00 ( ( ![F:( subst > term > term ), 651.76/89.00 Bound_variable_2547:( subst > term > term ), 651.76/89.00 Bound_variable_2549:subst,Bound_variable_2551:term]: 651.76/89.00 ( zip_tseitin_51 @ 651.76/89.00 Bound_variable_2551 @ Bound_variable_2549 @ Bound_variable_2547 @ F ) ) <=> 651.76/89.01 ( hoaslaminj ) ) & 651.76/89.01 ( ( hoasinduction_no_psi_cond_lthm ) <=> ( zip_tseitin_50 ) ) & 651.76/89.01 ( ( hoasinduction_lthm ) <=> ( zip_tseitin_37 ) ) & 651.76/89.01 ( ( hoasinduction_lem3v2_f_lthm ) <=> 651.76/89.01 ( ![B:term]: 651.76/89.01 ( ~( ![F:( subst > term > term )]: 651.76/89.01 ( ~( ![A:term,M:subst]: 651.76/89.01 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) ) & 651.76/89.01 ( pushprop_lthm_orig ) & ( apnotvar ) & ( hoasinduction_lem3v2_gthm ) & 651.76/89.01 ( ( induction2lem_lthm ) <=> ( zip_tseitin_16 ) ) & ( ~( ulamvar1 ) ) & 651.76/89.01 ( ( ![P:( term > $o ),Bound_variable_2340:term,Bound_variable_2342:subst]: 651.76/89.01 ( zip_tseitin_6 @ Bound_variable_2342 @ Bound_variable_2340 @ P ) ) <=> 651.76/89.01 ( induction2lem ) ) & 651.76/89.01 ( hoasinduction_lem1v2 ) & 651.76/89.01 ( ( shinj ) <=> ( ![A:term,B:term]: ( zip_tseitin_1 @ B @ A ) ) ) & 651.76/89.01 ( pushprop_lem1_gthm ) & ( ~( var @ ( d2term @ d_one ) ) ) & 651.76/89.01 ( ![A:term,M:subst,P:( term > $o ),Q:( term > $o )]: 651.76/89.01 ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) <=> 651.76/89.01 ( ![X:term]: ( zip_tseitin_0 @ X @ Q @ P @ M @ A ) ) ) ) & 651.76/89.01 ( ( hoasap @ 651.76/89.01 ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ 651.76/89.01 ( d2term @ d_one ) ) = 651.76/89.01 ( d2term @ d_one ) ) & 651.76/89.01 ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 651.76/89.01 ( ( sh ) = ( d2subst @ d_id ) ) & ( ( id ) = ( d2subst @ d_id ) ) & 651.76/89.01 ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2term @ d_one ) ) & 651.76/89.01 ( ( one ) = ( d2term @ d_one ) ) & 651.76/89.01 ( ![S:subst]: ( ?[DS:d_subst]: ( ( S ) = ( d2subst @ DS ) ) ) ) & 651.76/89.01 ( ![DT1:d_term,DT2:d_term]: 651.76/89.01 ( ( ( d2term @ DT1 ) = ( d2term @ DT2 ) ) => ( ( DT1 ) = ( DT2 ) ) ) ) & 651.76/89.01 ( ![DT:d_term]: ( ( DT ) = ( d_one ) ) ) & 651.76/89.01 ( ![T:term]: ( ?[DT:d_term]: ( ( T ) = ( d2term @ DT ) ) ) ))). 651.76/89.01 thf(zip_derived_cl600, plain, 651.76/89.01 (( (hoasinduction_lem3a) | ~ (zip_tseitin_98 @ sk__408 @ sk__407))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_250])). 651.76/89.01 thf(zip_derived_cl478, plain, 651.76/89.01 (![X0 : term]: ((X0) = (d2term @ (sk__475 @ X0)))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_250])). 651.76/89.01 thf(zip_derived_cl479, plain, (![X0 : d_term]: ((X0) = (d_one))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_250])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl756, plain, 651.76/89.01 (( (hoasinduction_lem3a) 651.76/89.01 | ~ (zip_tseitin_98 @ (d2term @ d_one) @ sk__407))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl600, zip_derived_cl721])). 651.76/89.01 thf(hoasinduction_lem3a, conjecture, 651.76/89.01 (( hoasinduction_lem3a ) <=> 651.76/89.01 ( ![P:( subst > term > subst > $o )]: 651.76/89.01 ( ( ![F:( subst > term > term )]: 651.76/89.01 ( ( ![M:subst,A:term,N:subst]: 651.76/89.01 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/89.01 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 651.76/89.01 ( ( ![A:term]: 651.76/89.01 ( ( P @ id @ A @ id ) => ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 651.76/89.01 ( P @ 651.76/89.01 id @ 651.76/89.01 ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ id ) ) ) ) => 651.76/89.01 ( ![A:term]: 651.76/89.01 ( ( ![B:term]: 651.76/89.01 ( ( P @ id @ B @ id ) => 651.76/89.01 ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) ) ) => 651.76/89.01 ( P @ id @ ( lam @ A ) @ id ) ) ) ) ))). 651.76/89.01 thf(zf_stmt_251, type, zip_tseitin_126 : 651.76/89.01 term > term > ( subst > term > subst > $o ) > $o). 651.76/89.01 thf(zf_stmt_252, axiom, 651.76/89.01 (![B:term,A:term,P:( subst > term > subst > $o )]: 651.76/89.01 ( ( zip_tseitin_126 @ B @ A @ P ) <=> 651.76/89.01 ( ( P @ id @ B @ id ) => 651.76/89.01 ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) ) ))). 651.76/89.01 thf(zf_stmt_253, type, zip_tseitin_125 : 651.76/89.01 ( subst > term > term ) > ( subst > term > subst > $o ) > $o). 651.76/89.01 thf(zf_stmt_254, axiom, 651.76/89.01 (![F:( subst > term > term ),P:( subst > term > subst > $o )]: 651.76/89.01 ( ( zip_tseitin_125 @ F @ P ) <=> 651.76/89.01 ( ( ![M:subst,A:term,N:subst]: 651.76/89.01 ( ( sub @ ( F @ M @ A ) @ N ) = 651.76/89.01 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 651.76/89.01 ( ( ![A:term]: 651.76/89.01 ( ( P @ id @ A @ id ) => ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 651.76/89.01 ( P @ 651.76/89.01 id @ ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ id ) ) ) ))). 651.76/89.01 thf(zf_stmt_255, conjecture, 651.76/89.01 (( hoasinduction_lem3a ) <=> 651.76/89.01 ( ![P:( subst > term > subst > $o )]: 651.76/89.01 ( ( ![F:( subst > term > term )]: ( zip_tseitin_125 @ F @ P ) ) => 651.76/89.01 ( ![A:term]: 651.76/89.01 ( ( ![B:term]: ( zip_tseitin_126 @ B @ A @ P ) ) => 651.76/89.01 ( P @ id @ ( lam @ A ) @ id ) ) ) ) ))). 651.76/89.01 thf(zf_stmt_256, negated_conjecture, 651.76/89.01 (~( ( hoasinduction_lem3a ) <=> 651.76/89.01 ( ![P:( subst > term > subst > $o )]: 651.76/89.01 ( ( ![F:( subst > term > term )]: ( zip_tseitin_125 @ F @ P ) ) => 651.76/89.01 ( ![A:term]: 651.76/89.01 ( ( ![B:term]: ( zip_tseitin_126 @ B @ A @ P ) ) => 651.76/89.01 ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) )), 651.76/89.01 inference('cnf.neg', [status(esa)], [zf_stmt_255])). 651.76/89.01 thf(zip_derived_cl675, plain, 651.76/89.01 (![X3 : subst > term > term]: 651.76/89.01 ( (zip_tseitin_125 @ X3 @ sk__480) | ~ (hoasinduction_lem3a))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_256])). 651.76/89.01 thf(zip_derived_cl376, plain, 651.76/89.01 (![X0 : term, X1 : subst > term > subst > $o, X2 : subst > term > term]: 651.76/89.01 ( (zip_tseitin_98 @ X0 @ X1) | (zip_tseitin_53 @ X2 @ X1))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_54])). 651.76/89.01 thf(zip_derived_cl665, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 (((sub @ (X0 @ (sk__476 @ X0) @ (sk__477 @ X0)) @ (sk__478 @ X0)) 651.76/89.01 != (X0 @ (comp @ (sk__476 @ X0) @ (sk__478 @ X0)) @ 651.76/89.01 (sub @ (sk__477 @ X0) @ (sk__478 @ X0)))) 651.76/89.01 | (X1 @ id @ 651.76/89.01 (hoaslam @ id @ (^[Y0 : subst,Y1 : term]: (X0 @ Y0 @ Y1))) @ id) 651.76/89.01 | (X1 @ id @ (sk__479 @ X1 @ X0) @ id) 651.76/89.01 | ~ (zip_tseitin_125 @ X0 @ X1))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_254])). 651.76/89.01 thf(zip_derived_cl1005, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 (((sub @ (X0 @ (sk__476 @ X0) @ (sk__477 @ X0)) @ (sk__478 @ X0)) 651.76/89.01 != (X0 @ (comp @ (sk__476 @ X0) @ (sk__478 @ X0)) @ 651.76/89.01 (sub @ (sk__477 @ X0) @ (sk__478 @ X0)))) 651.76/89.01 | (X1 @ id @ (hoaslam @ id @ X0) @ id) 651.76/89.01 | (X1 @ id @ (sk__479 @ X1 @ X0) @ id) 651.76/89.01 | ~ (zip_tseitin_125 @ X0 @ X1))), 651.76/89.01 inference('ho_norm', [status(thm)], [zip_derived_cl665])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl1006, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 (((d2term @ d_one) 651.76/89.01 != (X0 @ (comp @ (sk__476 @ X0) @ (sk__478 @ X0)) @ 651.76/89.01 (sub @ (sk__477 @ X0) @ (sk__478 @ X0)))) 651.76/89.01 | (X1 @ id @ (hoaslam @ id @ X0) @ id) 651.76/89.01 | (X1 @ id @ (sk__479 @ X1 @ X0) @ id) 651.76/89.01 | ~ (zip_tseitin_125 @ X0 @ X1))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl1005, zip_derived_cl721])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl1007, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 (~ (zip_tseitin_125 @ X0 @ X1) 651.76/89.01 | (X1 @ id @ (sk__479 @ X1 @ X0) @ id) 651.76/89.01 | (X1 @ id @ (hoaslam @ id @ X0) @ id))), 651.76/89.01 inference('simplify_reflect+', [status(thm)], 651.76/89.01 [zip_derived_cl1006, zip_derived_cl721])). 651.76/89.01 thf(zip_derived_cl481, plain, 651.76/89.01 (![X0 : subst]: ((X0) = (d2subst @ (sk__474 @ X0)))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_250])). 651.76/89.01 thf(zip_derived_cl663, plain, (![X0 : d_subst]: ((X0) = (d_id))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_250])). 651.76/89.01 thf(zip_derived_cl796, plain, (![X0 : subst]: ((X0) = (d2subst @ d_id))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl481, zip_derived_cl663])). 651.76/89.01 thf(zip_derived_cl796, plain, (![X0 : subst]: ((X0) = (d2subst @ d_id))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl481, zip_derived_cl663])). 651.76/89.01 thf(zip_derived_cl2321, plain, (![X0 : subst, X1 : subst]: ((X1) = (X0))), 651.76/89.01 inference('sup+', [status(thm)], [zip_derived_cl796, zip_derived_cl796])). 651.76/89.01 thf(zip_derived_cl197, plain, 651.76/89.01 (![X0 : subst > term > subst > $o, X1 : subst > term > term]: 651.76/89.01 (~ (zip_tseitin_31 @ (sk__112 @ X0 @ X1) @ X1 @ X0) 651.76/89.01 | (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) 651.76/89.01 | ((sub @ (X1 @ (sk__113 @ X1) @ (sk__114 @ X1)) @ (sk__115 @ X1)) 651.76/89.01 != (X1 @ (comp @ (sk__113 @ X1) @ (sk__115 @ X1)) @ 651.76/89.01 (sub @ (sk__114 @ X1) @ (sk__115 @ X1)))) 651.76/89.01 | ~ (zip_tseitin_53 @ X1 @ X0))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_144])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl991, plain, 651.76/89.01 (![X0 : subst > term > subst > $o, X1 : subst > term > term]: 651.76/89.01 (~ (zip_tseitin_31 @ (d2term @ d_one) @ X1 @ X0) 651.76/89.01 | (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) 651.76/89.01 | ((d2term @ d_one) 651.76/89.01 != (X1 @ (comp @ (sk__113 @ X1) @ (sk__115 @ X1)) @ 651.76/89.01 (sub @ (sk__114 @ X1) @ (sk__115 @ X1)))) 651.76/89.01 | ~ (zip_tseitin_53 @ X1 @ X0))), 651.76/89.01 inference('demod', [status(thm)], 651.76/89.01 [zip_derived_cl197, zip_derived_cl721, zip_derived_cl721])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl992, plain, 651.76/89.01 (![X0 : subst > term > subst > $o, X1 : subst > term > term]: 651.76/89.01 (~ (zip_tseitin_53 @ X1 @ X0) 651.76/89.01 | (X0 @ id @ (lam @ (X1 @ sh @ one)) @ id) 651.76/89.01 | ~ (zip_tseitin_31 @ (d2term @ d_one) @ X1 @ X0))), 651.76/89.01 inference('simplify_reflect+', [status(thm)], 651.76/89.01 [zip_derived_cl991, zip_derived_cl721])). 651.76/89.01 thf(zip_derived_cl479, plain, (![X0 : d_term]: ((X0) = (d_one))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_250])). 651.76/89.01 thf(zip_derived_cl479, plain, (![X0 : d_term]: ((X0) = (d_one))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_250])). 651.76/89.01 thf(zip_derived_cl2031, plain, (![X0 : d_term, X1 : d_term]: ((X1) = (X0))), 651.76/89.01 inference('sup+', [status(thm)], [zip_derived_cl479, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl674, plain, 651.76/89.01 ((~ (sk__480 @ id @ (lam @ sk__481) @ id) | ~ (hoasinduction_lem3a))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_256])). 651.76/89.01 thf(zip_derived_cl484, plain, (((id) = (d2subst @ d_id))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_250])). 651.76/89.01 thf(zip_derived_cl484, plain, (((id) = (d2subst @ d_id))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_250])). 651.76/89.01 thf(zip_derived_cl677, plain, 651.76/89.01 ((~ (sk__480 @ (d2subst @ d_id) @ (lam @ sk__481) @ (d2subst @ d_id)) 651.76/89.01 | ~ (hoasinduction_lem3a))), 651.76/89.01 inference('demod', [status(thm)], 651.76/89.01 [zip_derived_cl674, zip_derived_cl484, zip_derived_cl484])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl843, plain, 651.76/89.01 ((~ (sk__480 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) 651.76/89.01 | ~ (hoasinduction_lem3a))), 651.76/89.01 inference('demod', [status(thm)], 651.76/89.01 [zip_derived_cl677, zip_derived_cl721, zip_derived_cl721])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl2199, plain, (![X0 : term, X1 : term]: ((X1) = (X0))), 651.76/89.01 inference('sup+', [status(thm)], [zip_derived_cl721, zip_derived_cl721])). 651.76/89.01 thf(zip_derived_cl664, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 (((sub @ (X0 @ (sk__476 @ X0) @ (sk__477 @ X0)) @ (sk__478 @ X0)) 651.76/89.01 != (X0 @ (comp @ (sk__476 @ X0) @ (sk__478 @ X0)) @ 651.76/89.01 (sub @ (sk__477 @ X0) @ (sk__478 @ X0)))) 651.76/89.01 | (X1 @ id @ 651.76/89.01 (hoaslam @ id @ (^[Y0 : subst,Y1 : term]: (X0 @ Y0 @ Y1))) @ id) 651.76/89.01 | ~ (X1 @ id @ (X0 @ id @ (sk__479 @ X1 @ X0)) @ id) 651.76/89.01 | ~ (zip_tseitin_125 @ X0 @ X1))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_254])). 651.76/89.01 thf(zip_derived_cl1002, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 (((sub @ (X0 @ (sk__476 @ X0) @ (sk__477 @ X0)) @ (sk__478 @ X0)) 651.76/89.01 != (X0 @ (comp @ (sk__476 @ X0) @ (sk__478 @ X0)) @ 651.76/89.01 (sub @ (sk__477 @ X0) @ (sk__478 @ X0)))) 651.76/89.01 | (X1 @ id @ (hoaslam @ id @ X0) @ id) 651.76/89.01 | ~ (X1 @ id @ (X0 @ id @ (sk__479 @ X1 @ X0)) @ id) 651.76/89.01 | ~ (zip_tseitin_125 @ X0 @ X1))), 651.76/89.01 inference('ho_norm', [status(thm)], [zip_derived_cl664])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl1003, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 (((d2term @ d_one) 651.76/89.01 != (X0 @ (comp @ (sk__476 @ X0) @ (sk__478 @ X0)) @ 651.76/89.01 (sub @ (sk__477 @ X0) @ (sk__478 @ X0)))) 651.76/89.01 | (X1 @ id @ (hoaslam @ id @ X0) @ id) 651.76/89.01 | ~ (X1 @ id @ (X0 @ id @ (sk__479 @ X1 @ X0)) @ id) 651.76/89.01 | ~ (zip_tseitin_125 @ X0 @ X1))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl1002, zip_derived_cl721])). 651.76/89.01 thf(zip_derived_cl721, plain, (![X0 : term]: ((X0) = (d2term @ d_one))), 651.76/89.01 inference('demod', [status(thm)], [zip_derived_cl478, zip_derived_cl479])). 651.76/89.01 thf(zip_derived_cl1004, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 (~ (zip_tseitin_125 @ X0 @ X1) 651.76/89.01 | ~ (X1 @ id @ (X0 @ id @ (sk__479 @ X1 @ X0)) @ id) 651.76/89.01 | (X1 @ id @ (hoaslam @ id @ X0) @ id))), 651.76/89.01 inference('simplify_reflect+', [status(thm)], 651.76/89.01 [zip_derived_cl1003, zip_derived_cl721])). 651.76/89.01 thf(zip_derived_cl374, plain, 651.76/89.01 (![X0 : term, X1 : subst > term > subst > $o]: 651.76/89.01 ( (zip_tseitin_98 @ X0 @ X1) | ~ (X1 @ id @ (lam @ X0) @ id))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_54])). 651.76/89.01 thf(zip_derived_cl667, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 ( (zip_tseitin_125 @ X0 @ X1) 651.76/89.01 | ~ (X1 @ id @ 651.76/89.01 (hoaslam @ id @ (^[Y0 : subst,Y1 : term]: (X0 @ Y0 @ Y1))) @ id))), 651.76/89.01 inference('cnf', [status(esa)], [zf_stmt_254])). 651.76/89.01 thf(zip_derived_cl907, plain, 651.76/89.01 (![X0 : subst > term > term, X1 : subst > term > subst > $o]: 651.76/89.01 ( (zip_tseitin_125 @ X0 @ X1) | ~ (X1 @ id @ (hoaslam @ id @ X0) @ id))), 651.76/89.01 inference('ho_norm', [status(thm)], [zip_derived_cl667])). 651.76/89.01 thf(zip_derived_cl2474, plain, ($false), 651.76/89.01 inference('eprover', [status(thm)], 651.76/89.01 [zip_derived_cl115, zip_derived_cl756, zip_derived_cl675, 651.76/89.01 zip_derived_cl376, zip_derived_cl1007, zip_derived_cl2321, 651.76/89.01 zip_derived_cl992, zip_derived_cl2031, zip_derived_cl843, 651.76/89.01 zip_derived_cl2199, zip_derived_cl1004, zip_derived_cl374, 651.76/89.01 zip_derived_cl907])). 651.76/89.01 651.76/89.01 % SZS output end Refutation 651.76/89.01 651.76/89.01 651.76/89.01 % Terminating... 651.76/89.01 % /export/starexec/sandbox2/solver/bin/lams/8_new_cnf.sh running for 16s 444.15/89.11 % Runner terminated. 444.15/89.18 % Zipperpin 1.5 exiting 444.15/89.21 EOF