TSTP Solution File: ALG264^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ALG264^3 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:09:04 EDT 2023
% Result : Theorem 0.63s 0.83s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15 % Problem : ALG264^3 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.11/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n007.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon Aug 28 05:12:28 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.22/0.53 %----Proving TH0
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 % File : ALG264^3 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.22/0.53 % Domain : Algebra
% 0.22/0.53 % Problem : HOAS induction lemma 2
% 0.22/0.53 % Version : [Bro09] axioms.
% 0.22/0.53 % Theorem formulation : Modified.
% 0.22/0.53 % English :
% 0.22/0.53
% 0.22/0.53 % Refs : [DHK95] Dowek et al. (1995), Higher-order Unification via Expl
% 0.22/0.53 % : [Zha08] Zhang (2008), Using LEO-II to Prove Properties of an E
% 0.22/0.53 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.22/0.53 % : [Bro09] Brown (2009), M-Set Models
% 0.22/0.53 % Source : [Ben09]
% 0.22/0.53 % Names : hoasinduction_lem2v2_gthm [Ben09]
% 0.22/0.53
% 0.22/0.53 % Status : Theorem
% 0.22/0.53 % Rating : 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.57 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0
% 0.22/0.53 % Syntax : Number of formulae : 238 ( 114 unt; 124 typ; 113 def)
% 0.22/0.53 % Number of atoms : 1218 ( 161 equ; 0 cnn)
% 0.22/0.53 % Maximal formula atoms : 1 ( 10 avg)
% 0.22/0.53 % Number of connectives : 1942 ( 6 ~; 0 |; 4 &; 916 @)
% 0.22/0.53 % ( 2 <=>;1014 =>; 0 <=; 0 <~>)
% 0.22/0.53 % Maximal formula depth : 1 ( 1 avg)
% 0.22/0.53 % Number of types : 3 ( 2 usr)
% 0.22/0.53 % Number of type conns : 128 ( 128 >; 0 *; 0 +; 0 <<)
% 0.22/0.53 % Number of symbols : 123 ( 122 usr; 111 con; 0-4 aty)
% 0.22/0.53 % Number of variables : 327 ( 39 ^; 283 !; 5 ?; 327 :)
% 0.22/0.53 % SPC : TH0_THM_EQU_NAR
% 0.22/0.53
% 0.22/0.53 % Comments :
% 0.22/0.53 % Bugfixes : v5.2.0 - Bugfixes in ALG003^0.ax
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 %----Include Untyped Lambda Sigma defs
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 thf(term_type,type,
% 0.22/0.53 term: $tType ).
% 0.22/0.53
% 0.22/0.53 thf(subst_type,type,
% 0.22/0.53 subst: $tType ).
% 0.22/0.53
% 0.22/0.53 thf(one_type,type,
% 0.22/0.53 one: term ).
% 0.22/0.53
% 0.22/0.53 thf(ap_type,type,
% 0.22/0.53 ap: term > term > term ).
% 0.22/0.53
% 0.22/0.53 thf(lam_type,type,
% 0.22/0.53 lam: term > term ).
% 0.22/0.53
% 0.22/0.53 thf(sub_type,type,
% 0.22/0.53 sub: term > subst > term ).
% 0.22/0.53
% 0.22/0.53 thf(id_type,type,
% 0.22/0.53 id: subst ).
% 0.22/0.53
% 0.22/0.53 thf(sh_type,type,
% 0.22/0.53 sh: subst ).
% 0.22/0.53
% 0.22/0.53 thf(push_type,type,
% 0.22/0.53 push: term > subst > subst ).
% 0.22/0.53
% 0.22/0.53 thf(comp_type,type,
% 0.22/0.53 comp: subst > subst > subst ).
% 0.22/0.53
% 0.22/0.53 thf(var_type,type,
% 0.22/0.53 var: term > $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1v2_type,type,
% 0.22/0.53 pushprop_lem1v2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1_gthm_type,type,
% 0.22/0.53 pushprop_lem1_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axmap_type,type,
% 0.22/0.53 axmap: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem0_gthm_type,type,
% 0.22/0.53 pushprop_lem0_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(shinj_type,type,
% 0.22/0.53 shinj: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem1v2_type,type,
% 0.22/0.53 hoasinduction_lem1v2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem1v2_gthm_type,type,
% 0.22/0.53 hoasinduction_lem1v2_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasap_type,type,
% 0.22/0.53 hoasap: subst > term > subst > term > term ).
% 0.22/0.53
% 0.22/0.53 thf(induction2lem_type,type,
% 0.22/0.53 induction2lem: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3v2_f_type,type,
% 0.22/0.53 hoasinduction_lem3v2_f: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axvarshift_type,type,
% 0.22/0.53 axvarshift: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj2_type,type,
% 0.22/0.53 hoasapinj2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapnotvar_gthm_type,type,
% 0.22/0.53 hoasapnotvar_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj1_type,type,
% 0.22/0.53 hoasapinj1: $o ).
% 0.22/0.53
% 0.22/0.53 thf(ulamvar1_type,type,
% 0.22/0.53 ulamvar1: $o ).
% 0.22/0.53
% 0.22/0.53 thf(induction2lem_lthm_type,type,
% 0.22/0.53 induction2lem_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3v2_gthm_type,type,
% 0.22/0.53 hoasinduction_lem3v2_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(apnotvar_type,type,
% 0.22/0.53 apnotvar: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lthm_orig_type,type,
% 0.22/0.53 pushprop_lthm_orig: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3v2_f_lthm_type,type,
% 0.22/0.53 hoasinduction_lem3v2_f_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lthm_type,type,
% 0.22/0.53 hoasinduction_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_no_psi_cond_lthm_type,type,
% 0.22/0.53 hoasinduction_no_psi_cond_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslaminj_type,type,
% 0.22/0.53 hoaslaminj: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3aaa_type,type,
% 0.22/0.53 hoasinduction_lem3aaa: $o ).
% 0.22/0.53
% 0.22/0.53 thf(induction2lem_gthm_type,type,
% 0.22/0.53 induction2lem_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3aa_lthm_type,type,
% 0.22/0.53 hoasinduction_lem3aa_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3_type,type,
% 0.22/0.53 hoasinduction_lem3: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem2_type,type,
% 0.22/0.53 hoasinduction_lem2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(termmset_lthm_type,type,
% 0.22/0.53 termmset_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem1_type,type,
% 0.22/0.53 hoasinduction_lem1: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotap_lthm_type,type,
% 0.22/0.53 hoaslamnotap_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1v2_lthm_type,type,
% 0.22/0.53 pushprop_lem1v2_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapnotvar_type,type,
% 0.22/0.53 hoasapnotvar: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem0_type,type,
% 0.22/0.53 hoasinduction_lem0: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_type,type,
% 0.22/0.53 hoasinduction: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_gthm_type,type,
% 0.22/0.53 hoasinduction_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axapp_type,type,
% 0.22/0.53 axapp: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotvar_lthm_type,type,
% 0.22/0.53 hoaslamnotvar_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem3v2_lthm_type,type,
% 0.22/0.53 pushprop_lem3v2_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3b_lthm_type,type,
% 0.22/0.53 hoasinduction_lem3b_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(ulamvarind_type,type,
% 0.22/0.53 ulamvarind: $o ).
% 0.22/0.53
% 0.22/0.53 thf(induction_type,type,
% 0.22/0.53 induction: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3a_lthm_type,type,
% 0.22/0.53 hoasinduction_lem3a_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(termmset_gthm_type,type,
% 0.22/0.53 termmset_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3aa_type,type,
% 0.22/0.53 hoasinduction_lem3aa: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1v2_gthm_type,type,
% 0.22/0.53 pushprop_lem1v2_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotap_gthm_type,type,
% 0.22/0.53 hoaslamnotap_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotvar_gthm_type,type,
% 0.22/0.53 hoaslamnotvar_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3b_gthm_type,type,
% 0.22/0.53 hoasinduction_lem3b_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem2v2_type,type,
% 0.22/0.53 pushprop_lem2v2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3a_gthm_type,type,
% 0.22/0.53 hoasinduction_lem3a_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axclos_type,type,
% 0.22/0.53 axclos: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axassoc_type,type,
% 0.22/0.53 axassoc: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem2v2_type,type,
% 0.22/0.53 hoasinduction_lem2v2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lthm_type,type,
% 0.22/0.53 pushprop_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(apinj2_type,type,
% 0.22/0.53 apinj2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(apinj1_type,type,
% 0.22/0.53 apinj1: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj2_lthm_type,type,
% 0.22/0.53 hoasapinj2_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3v2a_type,type,
% 0.22/0.53 hoasinduction_lem3v2a: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj1_lthm_type,type,
% 0.22/0.53 hoasapinj1_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslaminj_lthm_type,type,
% 0.22/0.53 hoaslaminj_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axvarcons_type,type,
% 0.22/0.53 axvarcons: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslam_type,type,
% 0.22/0.53 hoaslam: subst > ( subst > term > term ) > term ).
% 0.22/0.53
% 0.22/0.53 thf(axscons_type,type,
% 0.22/0.53 axscons: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem2v2_gthm_type,type,
% 0.22/0.53 hoasinduction_lem2v2_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axidr_type,type,
% 0.22/0.53 axidr: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1_type,type,
% 0.22/0.53 pushprop_lem1: $o ).
% 0.22/0.53
% 0.22/0.53 thf(laminj_type,type,
% 0.22/0.53 laminj: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3_lthm_type,type,
% 0.22/0.53 hoasinduction_lem3_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem0_type,type,
% 0.22/0.53 pushprop_lem0: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_gthm_type,type,
% 0.22/0.53 pushprop_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axabs_type,type,
% 0.22/0.53 axabs: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3v2a_lthm_type,type,
% 0.22/0.53 hoasinduction_lem3v2a_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem2_lthm_type,type,
% 0.22/0.53 hoasinduction_lem2_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj2_gthm_type,type,
% 0.22/0.53 hoasapinj2_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_p_and_p_prime_type,type,
% 0.22/0.53 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem1_lthm_type,type,
% 0.22/0.53 hoasinduction_lem1_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(lamnotap_type,type,
% 0.22/0.53 lamnotap: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj1_gthm_type,type,
% 0.22/0.53 hoasapinj1_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotvar_type,type,
% 0.22/0.53 hoaslamnotvar: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axidl_type,type,
% 0.22/0.53 axidl: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslaminj_gthm_type,type,
% 0.22/0.53 hoaslaminj_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(induction2_lthm_type,type,
% 0.22/0.53 induction2_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem0_lthm_type,type,
% 0.22/0.53 hoasinduction_lem0_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(substmonoid_lthm_type,type,
% 0.22/0.53 substmonoid_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_type,type,
% 0.22/0.53 pushprop: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3_gthm_type,type,
% 0.22/0.53 hoasinduction_lem3_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem2_gthm_type,type,
% 0.22/0.53 hoasinduction_lem2_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3b_type,type,
% 0.22/0.53 hoasinduction_lem3b: $o ).
% 0.22/0.53
% 0.22/0.53 thf(substmonoid_type,type,
% 0.22/0.53 substmonoid: $o ).
% 0.22/0.53
% 0.22/0.53 thf(lamnotvar_type,type,
% 0.22/0.53 lamnotvar: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3a_type,type,
% 0.22/0.53 hoasinduction_lem3a: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem1_gthm_type,type,
% 0.22/0.53 hoasinduction_lem1_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_no_psi_cond_type,type,
% 0.22/0.53 hoasinduction_no_psi_cond: $o ).
% 0.22/0.53
% 0.22/0.53 thf(induction2_gthm_type,type,
% 0.22/0.53 induction2_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem2v2_lthm_type,type,
% 0.22/0.53 pushprop_lem2v2_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasvar_type,type,
% 0.22/0.53 hoasvar: subst > term > subst > $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotap_type,type,
% 0.22/0.53 hoaslamnotap: $o ).
% 0.22/0.53
% 0.22/0.53 thf(substmonoid_gthm_type,type,
% 0.22/0.53 substmonoid_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(ulamvarsh_type,type,
% 0.22/0.53 ulamvarsh: $o ).
% 0.22/0.53
% 0.22/0.53 thf(induction2_type,type,
% 0.22/0.53 induction2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem3v2_type,type,
% 0.22/0.53 pushprop_lem3v2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem2v2_gthm_type,type,
% 0.22/0.53 pushprop_lem2v2_gthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1_lthm_type,type,
% 0.22/0.53 pushprop_lem1_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3v2_type,type,
% 0.22/0.53 hoasinduction_lem3v2: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axshiftcons_type,type,
% 0.22/0.53 axshiftcons: $o ).
% 0.22/0.53
% 0.22/0.53 thf(termmset_type,type,
% 0.22/0.53 termmset: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem0_lthm_type,type,
% 0.22/0.53 pushprop_lem0_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapnotvar_lthm_type,type,
% 0.22/0.53 hoasapnotvar_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lem3v2_lthm_type,type,
% 0.22/0.53 hoasinduction_lem3v2_lthm: $o ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_p_and_p_prime_type,type,
% 0.22/0.53 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(axvarid_type,type,
% 0.22/0.53 axvarid: $o ).
% 0.22/0.53
% 0.22/0.53 thf(hoasinduction_lthm_3_type,type,
% 0.22/0.53 hoasinduction_lthm_3: $o ).
% 0.22/0.53
% 0.22/0.53 thf(axapp,definition,
% 0.22/0.53 ( axapp
% 0.22/0.53 = ( ! [A: term,B: term,M: subst] :
% 0.22/0.53 ( ( sub @ ( ap @ A @ B ) @ M )
% 0.22/0.53 = ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axvarcons,definition,
% 0.22/0.53 ( axvarcons
% 0.22/0.53 = ( ! [A: term,M: subst] :
% 0.22/0.53 ( ( sub @ one @ ( push @ A @ M ) )
% 0.22/0.53 = A ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axvarid,definition,
% 0.22/0.53 ( axvarid
% 0.22/0.53 = ( ! [A: term] :
% 0.22/0.53 ( ( sub @ A @ id )
% 0.22/0.53 = A ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axabs,definition,
% 0.22/0.53 ( axabs
% 0.22/0.53 = ( ! [A: term,M: subst] :
% 0.22/0.53 ( ( sub @ ( lam @ A ) @ M )
% 0.22/0.53 = ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axclos,definition,
% 0.22/0.53 ( axclos
% 0.22/0.53 = ( ! [A: term,M: subst,N: subst] :
% 0.22/0.53 ( ( sub @ ( sub @ A @ M ) @ N )
% 0.22/0.53 = ( sub @ A @ ( comp @ M @ N ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axidl,definition,
% 0.22/0.53 ( axidl
% 0.22/0.53 = ( ! [M: subst] :
% 0.22/0.53 ( ( comp @ id @ M )
% 0.22/0.53 = M ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axshiftcons,definition,
% 0.22/0.53 ( axshiftcons
% 0.22/0.53 = ( ! [A: term,M: subst] :
% 0.22/0.53 ( ( comp @ sh @ ( push @ A @ M ) )
% 0.22/0.53 = M ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axassoc,definition,
% 0.22/0.53 ( axassoc
% 0.22/0.53 = ( ! [M: subst,N: subst,K: subst] :
% 0.22/0.53 ( ( comp @ ( comp @ M @ N ) @ K )
% 0.22/0.53 = ( comp @ M @ ( comp @ N @ K ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axmap,definition,
% 0.22/0.53 ( axmap
% 0.22/0.53 = ( ! [A: term,M: subst,N: subst] :
% 0.22/0.53 ( ( comp @ ( push @ A @ M ) @ N )
% 0.22/0.53 = ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axidr,definition,
% 0.22/0.53 ( axidr
% 0.22/0.53 = ( ! [M: subst] :
% 0.22/0.53 ( ( comp @ M @ id )
% 0.22/0.53 = M ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axvarshift,definition,
% 0.22/0.53 ( axvarshift
% 0.22/0.53 = ( ( push @ one @ sh )
% 0.22/0.53 = id ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(axscons,definition,
% 0.22/0.53 ( axscons
% 0.22/0.53 = ( ! [M: subst] :
% 0.22/0.53 ( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
% 0.22/0.53 = M ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ulamvar1,definition,
% 0.22/0.53 ( ulamvar1
% 0.22/0.53 = ( var @ one ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ulamvarsh,definition,
% 0.22/0.53 ( ulamvarsh
% 0.22/0.53 = ( ! [A: term] :
% 0.22/0.53 ( ( var @ A )
% 0.22/0.53 => ( var @ ( sub @ A @ sh ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ulamvarind,definition,
% 0.22/0.53 ( ulamvarind
% 0.22/0.53 = ( ! [P: term > $o] :
% 0.22/0.53 ( ( P @ one )
% 0.22/0.53 => ( ! [A: term] :
% 0.22/0.53 ( ( var @ A )
% 0.22/0.53 => ( ( P @ A )
% 0.22/0.53 => ( P @ ( sub @ A @ sh ) ) ) )
% 0.22/0.53 => ! [A: term] :
% 0.22/0.53 ( ( var @ A )
% 0.22/0.53 => ( P @ A ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(apinj1,definition,
% 0.22/0.53 ( apinj1
% 0.22/0.53 = ( ! [A: term,B: term,C: term,D: term] :
% 0.22/0.53 ( ( ( ap @ A @ C )
% 0.22/0.53 = ( ap @ B @ D ) )
% 0.22/0.53 => ( A = B ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(apinj2,definition,
% 0.22/0.53 ( apinj2
% 0.22/0.53 = ( ! [A: term,B: term,C: term,D: term] :
% 0.22/0.53 ( ( ( ap @ A @ C )
% 0.22/0.53 = ( ap @ B @ D ) )
% 0.22/0.53 => ( C = D ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(laminj,definition,
% 0.22/0.53 ( laminj
% 0.22/0.53 = ( ! [A: term,B: term] :
% 0.22/0.53 ( ( ( lam @ A )
% 0.22/0.53 = ( lam @ B ) )
% 0.22/0.53 => ( A = B ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(shinj,definition,
% 0.22/0.53 ( shinj
% 0.22/0.53 = ( ! [A: term,B: term] :
% 0.22/0.53 ( ( ( sub @ A @ sh )
% 0.22/0.53 = ( sub @ B @ sh ) )
% 0.22/0.53 => ( A = B ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(lamnotap,definition,
% 0.22/0.53 ( lamnotap
% 0.22/0.53 = ( ! [A: term,B: term,C: term] :
% 0.22/0.53 ( ( lam @ A )
% 0.22/0.53 != ( ap @ B @ C ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(apnotvar,definition,
% 0.22/0.53 ( apnotvar
% 0.22/0.53 = ( ! [A: term,B: term] :
% 0.22/0.53 ~ ( var @ ( ap @ A @ B ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(lamnotvar,definition,
% 0.22/0.53 ( lamnotvar
% 0.22/0.53 = ( ! [A: term] :
% 0.22/0.53 ~ ( var @ ( lam @ A ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(induction,definition,
% 0.22/0.53 ( induction
% 0.22/0.53 = ( ! [P: term > $o] :
% 0.22/0.53 ( ! [A: term] :
% 0.22/0.53 ( ( var @ A )
% 0.22/0.53 => ( P @ A ) )
% 0.22/0.53 => ( ! [A: term,B: term] :
% 0.22/0.53 ( ( P @ A )
% 0.22/0.53 => ( ( P @ B )
% 0.22/0.53 => ( P @ ( ap @ A @ B ) ) ) )
% 0.22/0.53 => ( ! [A: term] :
% 0.22/0.53 ( ( P @ A )
% 0.22/0.53 => ( P @ ( lam @ A ) ) )
% 0.22/0.53 => ! [A: term] : ( P @ A ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_p_and_p_prime,definition,
% 0.22/0.53 ( pushprop_p_and_p_prime
% 0.22/0.53 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.22/0.53 ! [X: term] :
% 0.22/0.53 ( ( Q @ X )
% 0.22/0.53 <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem0,definition,
% 0.22/0.53 ( pushprop_lem0
% 0.22/0.53 = ( ! [P: term > $o,A: term,M: subst] :
% 0.22/0.53 ? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem0_gthm,definition,
% 0.22/0.53 ( pushprop_lem0_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => pushprop_lem0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem0_lthm,definition,
% 0.22/0.53 pushprop_lem0_lthm = pushprop_lem0 ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1,definition,
% 0.22/0.53 ( pushprop_lem1
% 0.22/0.53 = ( ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.22/0.53 ( ( P @ A )
% 0.22/0.53 => ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1_gthm,definition,
% 0.22/0.53 ( pushprop_lem1_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => pushprop_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1_lthm,definition,
% 0.22/0.53 ( pushprop_lem1_lthm
% 0.22/0.53 = ( axvarcons
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => pushprop_lem1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1v2,definition,
% 0.22/0.53 ( pushprop_lem1v2
% 0.22/0.53 = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.22/0.53 ( ( P @ A )
% 0.22/0.53 => ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
% 0.22/0.53 => ( Q @ one ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1v2_gthm,definition,
% 0.22/0.53 ( pushprop_lem1v2_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => pushprop_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem1v2_lthm,definition,
% 0.22/0.53 ( pushprop_lem1v2_lthm
% 0.22/0.53 = ( axvarcons
% 0.22/0.53 => pushprop_lem1v2 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem2v2,definition,
% 0.22/0.53 ( pushprop_lem2v2
% 0.22/0.53 = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.22/0.53 ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
% 0.22/0.53 => ( ! [B: term] :
% 0.22/0.53 ( ( var @ B )
% 0.22/0.53 => ( P @ ( sub @ B @ M ) ) )
% 0.22/0.53 => ! [C: term] :
% 0.22/0.53 ( ( var @ C )
% 0.22/0.53 => ( ( Q @ C )
% 0.22/0.53 => ( Q @ ( sub @ C @ sh ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem2v2_gthm,definition,
% 0.22/0.53 ( pushprop_lem2v2_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => pushprop_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem2v2_lthm,definition,
% 0.22/0.53 ( pushprop_lem2v2_lthm
% 0.22/0.53 = ( axclos
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => pushprop_lem2v2 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem3v2,definition,
% 0.22/0.53 ( pushprop_lem3v2
% 0.22/0.53 = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.22/0.53 ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
% 0.22/0.53 => ( ! [B: term] :
% 0.22/0.53 ( ( var @ B )
% 0.22/0.53 => ( Q @ B ) )
% 0.22/0.53 => ! [B: term] :
% 0.22/0.53 ( ( var @ B )
% 0.22/0.53 => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lem3v2_lthm,definition,
% 0.22/0.53 pushprop_lem3v2_lthm = pushprop_lem3v2 ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop,definition,
% 0.22/0.53 ( pushprop
% 0.22/0.53 = ( ! [P: term > $o,A: term,M: subst] :
% 0.22/0.53 ( ! [B: term] :
% 0.22/0.53 ( ( var @ B )
% 0.22/0.53 => ( P @ ( sub @ B @ M ) ) )
% 0.22/0.53 => ( ( P @ A )
% 0.22/0.53 => ! [B: term] :
% 0.22/0.53 ( ( var @ B )
% 0.22/0.53 => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_gthm,definition,
% 0.22/0.53 ( pushprop_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lthm_orig,definition,
% 0.22/0.53 ( pushprop_lthm_orig
% 0.22/0.53 = ( ulamvar1
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => pushprop ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(pushprop_lthm,definition,
% 0.22/0.53 ( pushprop_lthm
% 0.22/0.53 = ( pushprop_lem0
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => pushprop ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(induction2lem,definition,
% 0.22/0.53 ( induction2lem
% 0.22/0.53 = ( ! [P: term > $o] :
% 0.22/0.53 ( ! [A: term,B: term] :
% 0.22/0.53 ( ( P @ A )
% 0.22/0.53 => ( ( P @ B )
% 0.22/0.53 => ( P @ ( ap @ A @ B ) ) ) )
% 0.22/0.53 => ( ! [A: term] :
% 0.22/0.53 ( ! [B: term] :
% 0.22/0.53 ( ( P @ B )
% 0.22/0.53 => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.22/0.53 => ( P @ ( lam @ A ) ) )
% 0.22/0.53 => ! [A: term,M: subst] :
% 0.22/0.53 ( ! [B: term] :
% 0.22/0.53 ( ( var @ B )
% 0.22/0.53 => ( P @ ( sub @ B @ M ) ) )
% 0.22/0.53 => ( P @ ( sub @ A @ M ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(induction2lem_gthm,definition,
% 0.22/0.53 ( induction2lem_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => induction2lem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(induction2lem_lthm,definition,
% 0.22/0.53 ( induction2lem_lthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => induction2lem ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(induction2,definition,
% 0.22/0.53 ( induction2
% 0.22/0.53 = ( ! [P: term > $o] :
% 0.22/0.53 ( ! [A: term] :
% 0.22/0.53 ( ( var @ A )
% 0.22/0.53 => ( P @ A ) )
% 0.22/0.53 => ( ! [A: term,B: term] :
% 0.22/0.53 ( ( P @ A )
% 0.22/0.53 => ( ( P @ B )
% 0.22/0.53 => ( P @ ( ap @ A @ B ) ) ) )
% 0.22/0.53 => ( ! [A: term] :
% 0.22/0.53 ( ! [B: term] :
% 0.22/0.53 ( ( P @ B )
% 0.22/0.53 => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.22/0.53 => ( P @ ( lam @ A ) ) )
% 0.22/0.53 => ! [A: term] : ( P @ A ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(induction2_gthm,definition,
% 0.22/0.53 ( induction2_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => ( induction2lem
% 0.22/0.53 => induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(induction2_lthm,definition,
% 0.22/0.53 ( induction2_lthm
% 0.22/0.53 = ( axvarid
% 0.22/0.53 => ( induction2lem
% 0.22/0.53 => induction2 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(substmonoid,definition,
% 0.22/0.53 ( substmonoid
% 0.22/0.53 = ( ! [M: subst,N: subst,K: subst] :
% 0.22/0.53 ( ( comp @ ( comp @ M @ N ) @ K )
% 0.22/0.53 = ( comp @ M @ ( comp @ N @ K ) ) )
% 0.22/0.53 & ! [M: subst] :
% 0.22/0.53 ( ( comp @ id @ M )
% 0.22/0.53 = M )
% 0.22/0.53 & ! [M: subst] :
% 0.22/0.53 ( ( comp @ M @ id )
% 0.22/0.53 = M ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(substmonoid_gthm,definition,
% 0.22/0.53 ( substmonoid_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => ( induction2lem
% 0.22/0.53 => ( induction2
% 0.22/0.53 => substmonoid ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(substmonoid_lthm,definition,
% 0.22/0.53 ( substmonoid_lthm
% 0.22/0.53 = ( axidl
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axidr
% 0.22/0.53 => substmonoid ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(termmset,definition,
% 0.22/0.53 ( termmset
% 0.22/0.53 = ( ! [A: term,M: subst,N: subst] :
% 0.22/0.53 ( ( sub @ ( sub @ A @ M ) @ N )
% 0.22/0.53 = ( sub @ A @ ( comp @ M @ N ) ) )
% 0.22/0.53 & ! [A: term] :
% 0.22/0.53 ( ( sub @ A @ id )
% 0.22/0.53 = A ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(termmset_gthm,definition,
% 0.22/0.53 ( termmset_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => ( induction2lem
% 0.22/0.53 => ( induction2
% 0.22/0.53 => ( substmonoid
% 0.22/0.53 => termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(termmset_lthm,definition,
% 0.22/0.53 ( termmset_lthm
% 0.22/0.53 = ( axvarid
% 0.22/0.53 => ( axclos
% 0.22/0.53 => termmset ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasap,definition,
% 0.22/0.53 ( hoasap
% 0.22/0.53 = ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslam,definition,
% 0.22/0.53 ( hoaslam
% 0.22/0.53 = ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasvar,definition,
% 0.22/0.53 ( hoasvar
% 0.22/0.53 = ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj1,definition,
% 0.22/0.53 ( hoasapinj1
% 0.22/0.53 = ( ! [A: term,B: term,C: term,D: term] :
% 0.22/0.53 ( ( ( hoasap @ id @ A @ id @ C )
% 0.22/0.53 = ( hoasap @ id @ B @ id @ D ) )
% 0.22/0.53 => ( A = B ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj1_gthm,definition,
% 0.22/0.53 ( hoasapinj1_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => ( induction2lem
% 0.22/0.53 => ( induction2
% 0.22/0.53 => ( substmonoid
% 0.22/0.53 => ( termmset
% 0.22/0.53 => hoasapinj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj1_lthm,definition,
% 0.22/0.53 ( hoasapinj1_lthm
% 0.22/0.53 = ( axvarid
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => hoasapinj1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj2,definition,
% 0.22/0.53 ( hoasapinj2
% 0.22/0.53 = ( ! [A: term,B: term,C: term,D: term] :
% 0.22/0.53 ( ( ( hoasap @ id @ A @ id @ C )
% 0.22/0.53 = ( hoasap @ id @ B @ id @ D ) )
% 0.22/0.53 => ( C = D ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj2_gthm,definition,
% 0.22/0.53 ( hoasapinj2_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => ( induction2lem
% 0.22/0.53 => ( induction2
% 0.22/0.53 => ( substmonoid
% 0.22/0.53 => ( termmset
% 0.22/0.53 => ( hoasapinj1
% 0.22/0.53 => hoasapinj2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapinj2_lthm,definition,
% 0.22/0.53 ( hoasapinj2_lthm
% 0.22/0.53 = ( apinj2
% 0.22/0.53 => hoasapinj2 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslaminj,definition,
% 0.22/0.53 ( hoaslaminj
% 0.22/0.53 = ( ! [F: subst > term > term] :
% 0.22/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.53 => ! [G: subst > term > term] :
% 0.22/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.53 ( ( sub @ ( G @ M @ A ) @ N )
% 0.22/0.53 = ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.53 => ( ( ( hoaslam @ id
% 0.22/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.53 = ( hoaslam @ id
% 0.22/0.53 @ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
% 0.22/0.53 => ! [M: subst,A: term] :
% 0.22/0.53 ( ( F @ M @ A )
% 0.22/0.53 = ( G @ M @ A ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslaminj_gthm,definition,
% 0.22/0.53 ( hoaslaminj_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => ( induction2lem
% 0.22/0.53 => ( induction2
% 0.22/0.53 => ( substmonoid
% 0.22/0.53 => ( termmset
% 0.22/0.53 => ( hoasapinj1
% 0.22/0.53 => ( hoasapinj2
% 0.22/0.53 => hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslaminj_lthm,definition,
% 0.22/0.53 ( hoaslaminj_lthm
% 0.22/0.53 = ( axvarcons
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( laminj
% 0.22/0.53 => hoaslaminj ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotap,definition,
% 0.22/0.53 ( hoaslamnotap
% 0.22/0.53 = ( ! [F: subst > term > term] :
% 0.22/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.53 => ! [A: term,B: term] :
% 0.22/0.53 ( ( hoaslam @ id
% 0.22/0.53 @ ^ [M: subst,C: term] : ( F @ M @ C ) )
% 0.22/0.53 != ( hoasap @ id @ A @ id @ B ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotap_gthm,definition,
% 0.22/0.53 ( hoaslamnotap_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => ( induction2lem
% 0.22/0.53 => ( induction2
% 0.22/0.53 => ( substmonoid
% 0.22/0.53 => ( termmset
% 0.22/0.53 => ( hoasapinj1
% 0.22/0.53 => ( hoasapinj2
% 0.22/0.53 => ( hoaslaminj
% 0.22/0.53 => hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotap_lthm,definition,
% 0.22/0.53 ( hoaslamnotap_lthm
% 0.22/0.53 = ( lamnotap
% 0.22/0.53 => hoaslamnotap ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotvar,definition,
% 0.22/0.53 ( hoaslamnotvar
% 0.22/0.53 = ( ! [F: subst > term > term] :
% 0.22/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.53 => ~ ( hoasvar @ id
% 0.22/0.53 @ ( hoaslam @ id
% 0.22/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.53 @ id ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotvar_gthm,definition,
% 0.22/0.53 ( hoaslamnotvar_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.53 => ( axmap
% 0.22/0.53 => ( axidr
% 0.22/0.53 => ( axvarshift
% 0.22/0.53 => ( axscons
% 0.22/0.53 => ( ulamvar1
% 0.22/0.53 => ( ulamvarsh
% 0.22/0.53 => ( ulamvarind
% 0.22/0.53 => ( apinj1
% 0.22/0.53 => ( apinj2
% 0.22/0.53 => ( laminj
% 0.22/0.53 => ( shinj
% 0.22/0.53 => ( lamnotap
% 0.22/0.53 => ( apnotvar
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => ( induction
% 0.22/0.53 => ( pushprop
% 0.22/0.53 => ( induction2lem
% 0.22/0.53 => ( induction2
% 0.22/0.53 => ( substmonoid
% 0.22/0.53 => ( termmset
% 0.22/0.53 => ( hoasapinj1
% 0.22/0.53 => ( hoasapinj2
% 0.22/0.53 => ( hoaslaminj
% 0.22/0.53 => ( hoaslamnotap
% 0.22/0.53 => hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoaslamnotvar_lthm,definition,
% 0.22/0.53 ( hoaslamnotvar_lthm
% 0.22/0.53 = ( axvarid
% 0.22/0.53 => ( lamnotvar
% 0.22/0.53 => hoaslamnotvar ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapnotvar,definition,
% 0.22/0.53 ( hoasapnotvar
% 0.22/0.53 = ( ! [A: term,B: term] :
% 0.22/0.53 ~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(hoasapnotvar_gthm,definition,
% 0.22/0.53 ( hoasapnotvar_gthm
% 0.22/0.53 = ( axapp
% 0.22/0.53 => ( axvarcons
% 0.22/0.53 => ( axvarid
% 0.22/0.53 => ( axabs
% 0.22/0.53 => ( axclos
% 0.22/0.53 => ( axidl
% 0.22/0.53 => ( axshiftcons
% 0.22/0.53 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasapnotvar_lthm,definition,
% 0.22/0.54 ( hoasapnotvar_lthm
% 0.22/0.54 = ( axvarid
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => hoasapnotvar ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_p_and_p_prime,definition,
% 0.22/0.54 ( hoasinduction_p_and_p_prime
% 0.22/0.54 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.22/0.54 ! [X: term] :
% 0.22/0.54 ( ( Q @ X )
% 0.22/0.54 <=> ( P @ id @ X @ id ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem0,definition,
% 0.22/0.54 ( hoasinduction_lem0
% 0.22/0.54 = ( ! [P: subst > term > subst > $o] :
% 0.22/0.54 ? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem0_lthm,definition,
% 0.22/0.54 hoasinduction_lem0_lthm = hoasinduction_lem0 ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem1v2,definition,
% 0.22/0.54 ( hoasinduction_lem1v2
% 0.22/0.54 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.22/0.54 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.22/0.54 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.22/0.54 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( hoasvar @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ A @ id ) )
% 0.22/0.54 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.22/0.54 => ! [A: term] :
% 0.22/0.54 ( ( var @ A )
% 0.22/0.54 => ( Q @ A ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem1v2_gthm,definition,
% 0.22/0.54 ( hoasinduction_lem1v2_gthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem2v2,definition,
% 0.22/0.54 ( hoasinduction_lem2v2
% 0.22/0.54 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.22/0.54 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.22/0.54 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.22/0.54 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.22/0.54 => ( ! [A: term,B: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( ( P @ id @ B @ id )
% 0.22/0.54 => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
% 0.22/0.54 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.22/0.54 => ! [A: term,B: term] :
% 0.22/0.54 ( ( Q @ A )
% 0.22/0.54 => ( ( Q @ B )
% 0.22/0.54 => ( Q @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem2v2_gthm,definition,
% 0.22/0.54 ( hoasinduction_lem2v2_gthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3v2_f,definition,
% 0.22/0.54 ( hoasinduction_lem3v2_f
% 0.22/0.54 = ( ! [B: term] :
% 0.22/0.54 ? [F: subst > term > term] :
% 0.22/0.54 ! [A: term,M: subst] :
% 0.22/0.54 ( ( F @ M @ A )
% 0.22/0.54 = ( sub @ B @ ( push @ A @ M ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3v2_f_lthm,definition,
% 0.22/0.54 hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3v2,definition,
% 0.22/0.54 ( hoasinduction_lem3v2
% 0.22/0.54 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.22/0.54 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.22/0.54 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.22/0.54 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.22/0.54 => ( ! [F: subst > term > term] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.22/0.54 => ( P @ id
% 0.22/0.54 @ ( hoaslam @ id
% 0.22/0.54 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.54 @ id ) ) )
% 0.22/0.54 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.22/0.54 => ! [A: term] :
% 0.22/0.54 ( ! [B: term] :
% 0.22/0.54 ( ( Q @ B )
% 0.22/0.54 => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.22/0.54 => ( Q @ ( lam @ A ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3v2_gthm,definition,
% 0.22/0.54 ( hoasinduction_lem3v2_gthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => hoasinduction_lem3v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3v2_lthm,definition,
% 0.22/0.54 ( hoasinduction_lem3v2_lthm
% 0.22/0.54 = ( axvarid
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axmap
% 0.22/0.54 => hoasinduction_lem3v2 ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3v2a,definition,
% 0.22/0.54 ( hoasinduction_lem3v2a
% 0.22/0.54 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.22/0.54 ( ! [F: subst > term > term] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.22/0.54 => ( P @ id
% 0.22/0.54 @ ( hoaslam @ id
% 0.22/0.54 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.54 @ id ) ) )
% 0.22/0.54 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.22/0.54 => ! [A: term] :
% 0.22/0.54 ( ! [B: term] :
% 0.22/0.54 ( ( Q @ B )
% 0.22/0.54 => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.22/0.54 => ( Q @ ( lam @ A ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3v2a_lthm,definition,
% 0.22/0.54 ( hoasinduction_lem3v2a_lthm
% 0.22/0.54 = ( hoasinduction_lem3v2_f
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axmap
% 0.22/0.54 => hoasinduction_lem3v2a ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem1,definition,
% 0.22/0.54 ( hoasinduction_lem1
% 0.22/0.54 = ( ! [P: subst > term > subst > $o] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.22/0.54 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.22/0.54 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.22/0.54 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( hoasvar @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ A @ id ) )
% 0.22/0.54 => ! [A: term] :
% 0.22/0.54 ( ( var @ A )
% 0.22/0.54 => ( P @ id @ A @ id ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem1_gthm,definition,
% 0.22/0.54 ( hoasinduction_lem1_gthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem1_lthm,definition,
% 0.22/0.54 ( hoasinduction_lem1_lthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem2,definition,
% 0.22/0.54 ( hoasinduction_lem2
% 0.22/0.54 = ( ! [P: subst > term > subst > $o] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.22/0.54 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.22/0.54 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.22/0.54 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.22/0.54 => ( ! [A: term,B: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( ( P @ id @ B @ id )
% 0.22/0.54 => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
% 0.22/0.54 => ! [A: term,B: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( ( P @ id @ B @ id )
% 0.22/0.54 => ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem2_gthm,definition,
% 0.22/0.54 ( hoasinduction_lem2_gthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem2_lthm,definition,
% 0.22/0.54 ( hoasinduction_lem2_lthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3aa,definition,
% 0.22/0.54 ( hoasinduction_lem3aa
% 0.22/0.54 = ( ! [P: subst > term > subst > $o] :
% 0.22/0.54 ( ! [F: subst > term > term] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.22/0.54 => ( P @ id
% 0.22/0.54 @ ( hoaslam @ id
% 0.22/0.54 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.54 @ id ) ) )
% 0.22/0.54 => ! [A: term] :
% 0.22/0.54 ( ! [B: term] :
% 0.22/0.54 ( ( P @ id @ B @ id )
% 0.22/0.54 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.22/0.54 => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3aa_lthm,definition,
% 0.22/0.54 ( hoasinduction_lem3aa_lthm
% 0.22/0.54 = ( axclos
% 0.22/0.54 => ( axmap
% 0.22/0.54 => hoasinduction_lem3aa ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3aaa,definition,
% 0.22/0.54 ( hoasinduction_lem3aaa
% 0.22/0.54 = ( ! [P: subst > term > subst > $o] :
% 0.22/0.54 ( ! [F: subst > term > term] :
% 0.22/0.54 ( ? [C: term] :
% 0.22/0.54 ! [M: subst,A: term,N: subst] :
% 0.22/0.54 ( ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.54 = ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
% 0.22/0.54 & ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
% 0.22/0.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.22/0.54 => ( P @ id
% 0.22/0.54 @ ( hoaslam @ id
% 0.22/0.54 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.54 @ id ) ) )
% 0.22/0.54 => ! [A: term] :
% 0.22/0.54 ( ! [B: term] :
% 0.22/0.54 ( ( P @ id @ B @ id )
% 0.22/0.54 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.22/0.54 => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3,definition,
% 0.22/0.54 ( hoasinduction_lem3
% 0.22/0.54 = ( ! [P: subst > term > subst > $o] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.22/0.54 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.22/0.54 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.22/0.54 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.22/0.54 => ( ! [F: subst > term > term] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.22/0.54 => ( P @ id
% 0.22/0.54 @ ( hoaslam @ id
% 0.22/0.54 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.54 @ id ) ) )
% 0.22/0.54 => ! [A: term] :
% 0.22/0.54 ( ! [B: term] :
% 0.22/0.54 ( ( P @ id @ B @ id )
% 0.22/0.54 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.22/0.54 => ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3_gthm,definition,
% 0.22/0.54 ( hoasinduction_lem3_gthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => ( hoasinduction_lem1
% 0.22/0.54 => ( hoasinduction_lem2
% 0.22/0.54 => hoasinduction_lem3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3_lthm,definition,
% 0.22/0.54 ( hoasinduction_lem3_lthm
% 0.22/0.54 = ( axvarid
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( hoasinduction_lem3aa
% 0.22/0.54 => hoasinduction_lem3 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3a,definition,
% 0.22/0.54 ( hoasinduction_lem3a
% 0.22/0.54 = ( ! [P: subst > term > subst > $o] :
% 0.22/0.54 ( ! [F: subst > term > term] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.22/0.54 => ( P @ id
% 0.22/0.54 @ ( hoaslam @ id
% 0.22/0.54 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.54 @ id ) ) )
% 0.22/0.54 => ! [A: term] :
% 0.22/0.54 ( ! [B: term] :
% 0.22/0.54 ( ( P @ id @ B @ id )
% 0.22/0.54 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.22/0.54 => ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3a_gthm,definition,
% 0.22/0.54 ( hoasinduction_lem3a_gthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => ( hoasinduction_lem1
% 0.22/0.54 => ( hoasinduction_lem2
% 0.22/0.54 => hoasinduction_lem3a ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3a_lthm,definition,
% 0.22/0.54 ( hoasinduction_lem3a_lthm
% 0.22/0.54 = ( axvarid
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( hoasinduction_lem3aa
% 0.22/0.54 => hoasinduction_lem3a ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3b,definition,
% 0.22/0.54 ( hoasinduction_lem3b
% 0.22/0.54 = ( ! [B: term] :
% 0.22/0.54 ? [F: subst > term > term] :
% 0.22/0.54 ( ( sub @ B @ ( push @ one @ sh ) )
% 0.22/0.54 = ( F @ sh @ one ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3b_gthm,definition,
% 0.22/0.54 ( hoasinduction_lem3b_gthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => ( hoasinduction_lem1
% 0.22/0.54 => ( hoasinduction_lem2
% 0.22/0.54 => hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lem3b_lthm,definition,
% 0.22/0.54 hoasinduction_lem3b_lthm = hoasinduction_lem3b ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction,definition,
% 0.22/0.54 ( hoasinduction
% 0.22/0.54 = ( ! [P: subst > term > subst > $o] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.22/0.54 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.22/0.54 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.22/0.54 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.22/0.54 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( hoasvar @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ A @ id ) )
% 0.22/0.54 => ( ! [A: term,B: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( ( P @ id @ B @ id )
% 0.22/0.54 => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
% 0.22/0.54 => ( ! [F: subst > term > term] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.22/0.54 => ( P @ id
% 0.22/0.54 @ ( hoaslam @ id
% 0.22/0.54 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.54 @ id ) ) )
% 0.22/0.54 => ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_gthm,definition,
% 0.22/0.54 ( hoasinduction_gthm
% 0.22/0.54 = ( axapp
% 0.22/0.54 => ( axvarcons
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( axabs
% 0.22/0.54 => ( axclos
% 0.22/0.54 => ( axidl
% 0.22/0.54 => ( axshiftcons
% 0.22/0.54 => ( axassoc
% 0.22/0.54 => ( axmap
% 0.22/0.54 => ( axidr
% 0.22/0.54 => ( axvarshift
% 0.22/0.54 => ( axscons
% 0.22/0.54 => ( ulamvar1
% 0.22/0.54 => ( ulamvarsh
% 0.22/0.54 => ( ulamvarind
% 0.22/0.54 => ( apinj1
% 0.22/0.54 => ( apinj2
% 0.22/0.54 => ( laminj
% 0.22/0.54 => ( shinj
% 0.22/0.54 => ( lamnotap
% 0.22/0.54 => ( apnotvar
% 0.22/0.54 => ( lamnotvar
% 0.22/0.54 => ( induction
% 0.22/0.54 => ( pushprop
% 0.22/0.54 => ( induction2lem
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( substmonoid
% 0.22/0.54 => ( termmset
% 0.22/0.54 => ( hoasapinj1
% 0.22/0.54 => ( hoasapinj2
% 0.22/0.54 => ( hoaslaminj
% 0.22/0.54 => ( hoaslamnotap
% 0.22/0.54 => ( hoaslamnotvar
% 0.22/0.54 => ( hoasapnotvar
% 0.22/0.54 => ( hoasinduction_lem1
% 0.22/0.54 => ( hoasinduction_lem2
% 0.22/0.54 => ( hoasinduction_lem3
% 0.22/0.54 => hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lthm,definition,
% 0.22/0.54 ( hoasinduction_lthm
% 0.22/0.54 = ( induction2
% 0.22/0.54 => ( hoasinduction_lem1
% 0.22/0.54 => ( hoasinduction_lem2
% 0.22/0.54 => ( hoasinduction_lem3
% 0.22/0.54 => hoasinduction ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_lthm_3,definition,
% 0.22/0.54 ( hoasinduction_lthm_3
% 0.22/0.54 = ( hoasinduction_lem0
% 0.22/0.54 => ( induction2
% 0.22/0.54 => ( axvarid
% 0.22/0.54 => ( hoasinduction_lem3v2a
% 0.22/0.54 => hoasinduction ) ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 thf(hoasinduction_no_psi_cond,definition,
% 0.22/0.54 ( hoasinduction_no_psi_cond
% 0.22/0.54 = ( ! [P: subst > term > subst > $o] :
% 0.22/0.54 ( ! [A: term,B: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( ( P @ id @ B @ id )
% 0.22/0.54 => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
% 0.22/0.54 => ( ! [F: subst > term > term] :
% 0.22/0.54 ( ! [M: subst,A: term,N: subst] :
% 0.22/0.54 ( ( sub @ ( F @ M @ A ) @ N )
% 0.22/0.54 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.22/0.54 => ( ! [A: term] :
% 0.22/0.54 ( ( P @ id @ A @ id )
% 0.22/0.54 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.22/0.54 => ( P @ id
% 0.22/0.54 @ ( hoaslam @ id
% 0.22/0.58 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.22/0.58 @ id ) ) )
% 0.22/0.58 => ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ).
% 0.22/0.58
% 0.22/0.58 thf(hoasinduction_no_psi_cond_lthm,definition,
% 0.22/0.58 ( hoasinduction_no_psi_cond_lthm
% 0.22/0.58 = ( hoasinduction_lem0
% 0.22/0.58 => ( induction2
% 0.22/0.58 => ( axvarid
% 0.22/0.58 => ( hoasinduction_lem3v2a
% 0.22/0.58 => hoasinduction_no_psi_cond ) ) ) ) ) ).
% 0.22/0.58
% 0.22/0.58 %------------------------------------------------------------------------------
% 0.22/0.58 %------------------------------------------------------------------------------
% 0.22/0.58 thf(thm,conjecture,
% 0.22/0.58 hoasinduction_lem2v2_gthm ).
% 0.22/0.58
% 0.22/0.58 %------------------------------------------------------------------------------
% 0.22/0.58 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.1YFWkpLMSD/cvc5---1.0.5_32091.p...
% 0.22/0.58 (declare-sort $$unsorted 0)
% 0.22/0.58 (declare-sort tptp.term 0)
% 0.22/0.58 (declare-sort tptp.subst 0)
% 0.22/0.58 (declare-fun tptp.one () tptp.term)
% 0.22/0.58 (declare-fun tptp.ap (tptp.term tptp.term) tptp.term)
% 0.22/0.58 (declare-fun tptp.lam (tptp.term) tptp.term)
% 0.22/0.58 (declare-fun tptp.sub (tptp.term tptp.subst) tptp.term)
% 0.22/0.58 (declare-fun tptp.id () tptp.subst)
% 0.22/0.58 (declare-fun tptp.sh () tptp.subst)
% 0.22/0.58 (declare-fun tptp.push (tptp.term tptp.subst) tptp.subst)
% 0.22/0.58 (declare-fun tptp.comp (tptp.subst tptp.subst) tptp.subst)
% 0.22/0.58 (declare-fun tptp.var (tptp.term) Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem1v2 () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem1_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.axmap () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem0_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.shinj () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem1v2 () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem1v2_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasap (tptp.subst tptp.term tptp.subst tptp.term) tptp.term)
% 0.22/0.58 (declare-fun tptp.induction2lem () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3v2_f () Bool)
% 0.22/0.58 (declare-fun tptp.axvarshift () Bool)
% 0.22/0.58 (declare-fun tptp.hoasapinj2 () Bool)
% 0.22/0.58 (declare-fun tptp.hoasapnotvar_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasapinj1 () Bool)
% 0.22/0.58 (declare-fun tptp.ulamvar1 () Bool)
% 0.22/0.58 (declare-fun tptp.induction2lem_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3v2_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.apnotvar () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lthm_orig () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3v2_f_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_no_psi_cond_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoaslaminj () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3aaa () Bool)
% 0.22/0.58 (declare-fun tptp.induction2lem_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3aa_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3 () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem2 () Bool)
% 0.22/0.58 (declare-fun tptp.termmset_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem1 () Bool)
% 0.22/0.58 (declare-fun tptp.hoaslamnotap_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem1v2_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasapnotvar () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem0 () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.axapp () Bool)
% 0.22/0.58 (declare-fun tptp.hoaslamnotvar_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem3v2_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3b_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.ulamvarind () Bool)
% 0.22/0.58 (declare-fun tptp.induction () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3a_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.termmset_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3aa () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem1v2_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoaslamnotap_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoaslamnotvar_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3b_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem2v2 () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3a_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.axclos () Bool)
% 0.22/0.58 (declare-fun tptp.axassoc () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem2v2 () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.apinj2 () Bool)
% 0.22/0.58 (declare-fun tptp.apinj1 () Bool)
% 0.22/0.58 (declare-fun tptp.hoasapinj2_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3v2a () Bool)
% 0.22/0.58 (declare-fun tptp.hoasapinj1_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoaslaminj_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.axvarcons () Bool)
% 0.22/0.58 (declare-fun tptp.hoaslam (tptp.subst (-> tptp.subst tptp.term tptp.term)) tptp.term)
% 0.22/0.58 (declare-fun tptp.axscons () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem2v2_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.axidr () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem1 () Bool)
% 0.22/0.58 (declare-fun tptp.laminj () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem0 () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.axabs () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3v2a_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem2_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasapinj2_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_p_and_p_prime ((-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem1_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.lamnotap () Bool)
% 0.22/0.58 (declare-fun tptp.hoasapinj1_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoaslamnotvar () Bool)
% 0.22/0.58 (declare-fun tptp.axidl () Bool)
% 0.22/0.58 (declare-fun tptp.hoaslaminj_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.induction2_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem0_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.substmonoid_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem2_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3b () Bool)
% 0.22/0.58 (declare-fun tptp.substmonoid () Bool)
% 0.22/0.58 (declare-fun tptp.lamnotvar () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3a () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem1_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_no_psi_cond () Bool)
% 0.22/0.58 (declare-fun tptp.induction2_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem2v2_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasvar (tptp.subst tptp.term tptp.subst) Bool)
% 0.22/0.58 (declare-fun tptp.hoaslamnotap () Bool)
% 0.22/0.58 (declare-fun tptp.substmonoid_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.ulamvarsh () Bool)
% 0.22/0.58 (declare-fun tptp.induction2 () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem3v2 () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem2v2_gthm () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem1_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3v2 () Bool)
% 0.22/0.58 (declare-fun tptp.axshiftcons () Bool)
% 0.22/0.58 (declare-fun tptp.termmset () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_lem0_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasapnotvar_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lem3v2_lthm () Bool)
% 0.22/0.58 (declare-fun tptp.pushprop_p_and_p_prime (tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.axvarid () Bool)
% 0.22/0.58 (declare-fun tptp.hoasinduction_lthm_3 () Bool)
% 0.22/0.58 (assert (= tptp.axapp (forall ((A tptp.term) (B tptp.term) (M tptp.subst)) (= (@ (@ tptp.sub (@ (@ tptp.ap A) B)) M) (@ (@ tptp.ap (@ (@ tptp.sub A) M)) (@ (@ tptp.sub B) M))))))
% 0.22/0.58 (assert (= tptp.axvarcons (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ tptp.sub tptp.one) (@ (@ tptp.push A) M)) A))))
% 0.22/0.58 (assert (= tptp.axvarid (forall ((A tptp.term)) (= (@ (@ tptp.sub A) tptp.id) A))))
% 0.22/0.58 (assert (= tptp.axabs (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ tptp.sub (@ tptp.lam A)) M) (@ tptp.lam (@ (@ tptp.sub A) (@ (@ tptp.push tptp.one) (@ (@ tptp.comp M) tptp.sh))))))))
% 0.22/0.58 (assert (= tptp.axclos (forall ((A tptp.term) (M tptp.subst) (N tptp.subst)) (let ((_let_1 (@ tptp.sub A))) (= (@ (@ tptp.sub (@ _let_1 M)) N) (@ _let_1 (@ (@ tptp.comp M) N)))))))
% 0.22/0.58 (assert (= tptp.axidl (forall ((M tptp.subst)) (= (@ (@ tptp.comp tptp.id) M) M))))
% 0.22/0.58 (assert (= tptp.axshiftcons (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ tptp.comp tptp.sh) (@ (@ tptp.push A) M)) M))))
% 0.22/0.58 (assert (= tptp.axassoc (forall ((M tptp.subst) (N tptp.subst) (K tptp.subst)) (let ((_let_1 (@ tptp.comp M))) (= (@ (@ tptp.comp (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.comp N) K)))))))
% 0.22/0.58 (assert (= tptp.axmap (forall ((A tptp.term) (M tptp.subst) (N tptp.subst)) (= (@ (@ tptp.comp (@ (@ tptp.push A) M)) N) (@ (@ tptp.push (@ (@ tptp.sub A) N)) (@ (@ tptp.comp M) N))))))
% 0.22/0.58 (assert (= tptp.axidr (forall ((M tptp.subst)) (= (@ (@ tptp.comp M) tptp.id) M))))
% 0.22/0.58 (assert (= tptp.axvarshift (= (@ (@ tptp.push tptp.one) tptp.sh) tptp.id)))
% 0.22/0.58 (assert (= tptp.axscons (forall ((M tptp.subst)) (= (@ (@ tptp.push (@ (@ tptp.sub tptp.one) M)) (@ (@ tptp.comp tptp.sh) M)) M))))
% 0.22/0.58 (assert (= tptp.ulamvar1 (@ tptp.var tptp.one)))
% 0.22/0.58 (assert (= tptp.ulamvarsh (forall ((A tptp.term)) (=> (@ tptp.var A) (@ tptp.var (@ (@ tptp.sub A) tptp.sh))))))
% 0.22/0.58 (assert (= tptp.ulamvarind (forall ((P (-> tptp.term Bool))) (=> (@ P tptp.one) (=> (forall ((A tptp.term)) (=> (@ tptp.var A) (=> (@ P A) (@ P (@ (@ tptp.sub A) tptp.sh))))) (forall ((A tptp.term)) (=> (@ tptp.var A) (@ P A))))))))
% 0.22/0.58 (assert (= tptp.apinj1 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (=> (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D)) (= A B)))))
% 0.22/0.58 (assert (= tptp.apinj2 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (=> (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D)) (= C D)))))
% 0.22/0.58 (assert (= tptp.laminj (forall ((A tptp.term) (B tptp.term)) (=> (= (@ tptp.lam A) (@ tptp.lam B)) (= A B)))))
% 0.22/0.58 (assert (= tptp.shinj (forall ((A tptp.term) (B tptp.term)) (=> (= (@ (@ tptp.sub A) tptp.sh) (@ (@ tptp.sub B) tptp.sh)) (= A B)))))
% 0.22/0.58 (assert (= tptp.lamnotap (forall ((A tptp.term) (B tptp.term) (C tptp.term)) (not (= (@ tptp.lam A) (@ (@ tptp.ap B) C))))))
% 0.22/0.58 (assert (= tptp.apnotvar (forall ((A tptp.term) (B tptp.term)) (not (@ tptp.var (@ (@ tptp.ap A) B))))))
% 0.22/0.58 (assert (= tptp.lamnotvar (forall ((A tptp.term)) (not (@ tptp.var (@ tptp.lam A))))))
% 0.22/0.58 (assert (= tptp.induction (forall ((P (-> tptp.term Bool))) (=> (forall ((A tptp.term)) (=> (@ tptp.var A) (@ P A))) (=> (forall ((A tptp.term) (B tptp.term)) (=> (@ P A) (=> (@ P B) (@ P (@ (@ tptp.ap A) B))))) (=> (forall ((A tptp.term)) (=> (@ P A) (@ P (@ tptp.lam A)))) (forall ((A tptp.term)) (@ P A))))))))
% 0.22/0.58 (assert (= tptp.pushprop_p_and_p_prime (lambda ((A tptp.term) (M tptp.subst) (P (-> tptp.term Bool)) (Q (-> tptp.term Bool))) (forall ((X tptp.term)) (= (@ Q X) (@ P (@ (@ tptp.sub X) (@ (@ tptp.push A) M))))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem0 (forall ((P (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (exists ((Q (-> tptp.term Bool))) (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q)))))
% 0.22/0.58 (assert (= tptp.pushprop_lem0_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem0)))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0))
% 0.22/0.58 (assert (= tptp.pushprop_lem1 (forall ((P (-> tptp.term Bool)) (K (-> tptp.term Bool)) (A tptp.term) (M tptp.subst) (B tptp.term)) (=> (@ P A) (@ K (@ (@ tptp.sub A) (@ (@ tptp.push B) M)))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1)))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem1v2 (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (=> (@ P A) (=> (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q) (@ Q tptp.one))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1v2)))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2)))
% 0.22/0.58 (assert (= tptp.pushprop_lem2v2 (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (=> (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q) (=> (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) M)))) (forall ((C tptp.term)) (=> (@ tptp.var C) (=> (@ Q C) (@ Q (@ (@ tptp.sub C) tptp.sh))))))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem2v2)))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2))))
% 0.22/0.58 (assert (= tptp.pushprop_lem3v2 (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (=> (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q) (=> (forall ((B tptp.term)) (=> (@ tptp.var B) (@ Q B))) (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) (@ (@ tptp.push A) M))))))))))
% 0.22/0.58 (assert (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2))
% 0.22/0.58 (assert (= tptp.pushprop (forall ((P (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (=> (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) M)))) (=> (@ P A) (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) (@ (@ tptp.push A) M))))))))))
% 0.22/0.58 (assert (= tptp.pushprop_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop)))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.pushprop_lthm_orig (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))))
% 0.22/0.58 (assert (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop))))))))
% 0.22/0.58 (assert (= tptp.induction2lem (forall ((P (-> tptp.term Bool))) (=> (forall ((A tptp.term) (B tptp.term)) (=> (@ P A) (=> (@ P B) (@ P (@ (@ tptp.ap A) B))))) (=> (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (=> (@ P B) (@ P (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))))) (@ P (@ tptp.lam A)))) (forall ((A tptp.term) (M tptp.subst)) (=> (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) M)))) (@ P (@ (@ tptp.sub A) M)))))))))
% 0.22/0.58 (assert (= tptp.induction2lem_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))))))))))))
% 0.22/0.58 (assert (= tptp.induction2 (forall ((P (-> tptp.term Bool))) (=> (forall ((A tptp.term)) (=> (@ tptp.var A) (@ P A))) (=> (forall ((A tptp.term) (B tptp.term)) (=> (@ P A) (=> (@ P B) (@ P (@ (@ tptp.ap A) B))))) (=> (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (=> (@ P B) (@ P (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))))) (@ P (@ tptp.lam A)))) (forall ((A tptp.term)) (@ P A))))))))
% 0.22/0.58 (assert (= tptp.induction2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem tptp.induction2)))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.induction2_lthm (=> tptp.axvarid (=> tptp.induction2lem tptp.induction2))))
% 0.22/0.58 (assert (= tptp.substmonoid (and (forall ((M tptp.subst) (N tptp.subst) (K tptp.subst)) (let ((_let_1 (@ tptp.comp M))) (= (@ (@ tptp.comp (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.comp N) K))))) (forall ((M tptp.subst)) (= (@ (@ tptp.comp tptp.id) M) M)) (forall ((M tptp.subst)) (= (@ (@ tptp.comp M) tptp.id) M)))))
% 0.22/0.58 (assert (= tptp.substmonoid_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 tptp.substmonoid))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid)))))
% 0.22/0.58 (assert (= tptp.termmset (and (forall ((A tptp.term) (M tptp.subst) (N tptp.subst)) (let ((_let_1 (@ tptp.sub A))) (= (@ (@ tptp.sub (@ _let_1 M)) N) (@ _let_1 (@ (@ tptp.comp M) N))))) (forall ((A tptp.term)) (= (@ (@ tptp.sub A) tptp.id) A)))))
% 0.22/0.58 (assert (= tptp.termmset_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid tptp.termmset)))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset))))
% 0.22/0.58 (assert (= tptp.hoasap (lambda ((M tptp.subst) (A tptp.term) (N tptp.subst) (B tptp.term)) (@ (@ tptp.ap (@ (@ tptp.sub A) N)) B))))
% 0.22/0.58 (assert (= tptp.hoaslam (lambda ((M tptp.subst) (F (-> tptp.subst tptp.term tptp.term))) (@ tptp.lam (@ (@ F tptp.sh) tptp.one)))))
% 0.22/0.58 (assert (= tptp.hoasvar (lambda ((M tptp.subst) (A tptp.term) (N tptp.subst)) (@ tptp.var (@ (@ tptp.sub A) N)))))
% 0.22/0.58 (assert (= tptp.hoasapinj1 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (@ tptp.hoasap tptp.id))) (=> (= (@ (@ (@ _let_1 A) tptp.id) C) (@ (@ (@ _let_1 B) tptp.id) D)) (= A B))))))
% 0.22/0.58 (assert (= tptp.hoasapinj1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset tptp.hoasapinj1))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1))))
% 0.22/0.58 (assert (= tptp.hoasapinj2 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (@ tptp.hoasap tptp.id))) (=> (= (@ (@ (@ _let_1 A) tptp.id) C) (@ (@ (@ _let_1 B) tptp.id) D)) (= C D))))))
% 0.22/0.58 (assert (= tptp.hoasapinj2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 tptp.hoasapinj2)))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2)))
% 0.22/0.58 (assert (= tptp.hoaslaminj (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (forall ((G (-> tptp.subst tptp.term tptp.term))) (let ((_let_1 (@ tptp.hoaslam tptp.id))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ G M) A)) N) (@ (@ G (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (= (@ _let_1 (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A))) (@ _let_1 (lambda ((M tptp.subst) (A tptp.term)) (@ (@ G M) A)))) (forall ((M tptp.subst) (A tptp.term)) (= (@ (@ F M) A) (@ (@ G M) A)))))))))))
% 0.22/0.58 (assert (= tptp.hoaslaminj_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 tptp.hoaslaminj))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj)))))
% 0.22/0.58 (assert (= tptp.hoaslamnotap (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (forall ((A tptp.term) (B tptp.term)) (not (= (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (C tptp.term)) (@ (@ F M) C))) (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B))))))))
% 0.22/0.58 (assert (= tptp.hoaslamnotap_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj tptp.hoaslamnotap)))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap)))
% 0.22/0.58 (assert (= tptp.hoaslamnotvar (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (not (@ (@ (@ tptp.hoasvar tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id))))))
% 0.22/0.58 (assert (= tptp.hoaslamnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap tptp.hoaslamnotvar))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar))))
% 0.22/0.58 (assert (= tptp.hoasapnotvar (forall ((A tptp.term) (B tptp.term)) (not (@ (@ (@ tptp.hoasvar tptp.id) (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id)))))
% 0.22/0.58 (assert (= tptp.hoasapnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar tptp.hoasapnotvar)))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar))))
% 0.22/0.58 (assert (= tptp.hoasinduction_p_and_p_prime (lambda ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (forall ((X tptp.term)) (= (@ Q X) (@ (@ (@ P tptp.id) X) tptp.id))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem0 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (exists ((Q (-> tptp.term Bool))) (@ (@ tptp.hoasinduction_p_and_p_prime P) Q)))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem1v2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term)) (=> (@ (@ (@ tptp.hoasvar tptp.id) A) tptp.id) (@ (@ (@ P tptp.id) A) tptp.id))) (=> (@ (@ tptp.hoasinduction_p_and_p_prime P) Q) (forall ((A tptp.term)) (=> (@ tptp.var A) (@ Q A))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1v2))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem2v2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (=> (@ (@ tptp.hoasinduction_p_and_p_prime P) Q) (forall ((A tptp.term) (B tptp.term)) (=> (@ Q A) (=> (@ Q B) (@ Q (@ (@ tptp.ap A) B))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2v2))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3v2_f (forall ((B tptp.term)) (exists ((F (-> tptp.subst tptp.term tptp.term))) (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ F M) A) (@ (@ tptp.sub B) (@ (@ tptp.push A) M))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3v2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (=> (@ (@ tptp.hoasinduction_p_and_p_prime P) Q) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (=> (@ Q B) (@ Q (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))))) (@ Q (@ tptp.lam A)))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem3v2))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3v2a (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (=> (@ (@ tptp.hoasinduction_p_and_p_prime P) Q) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (=> (@ Q B) (@ Q (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))))) (@ Q (@ tptp.lam A)))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a)))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem1 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term)) (=> (@ (@ (@ tptp.hoasvar tptp.id) A) tptp.id) (@ (@ (@ P tptp.id) A) tptp.id))) (forall ((A tptp.term)) (=> (@ tptp.var A) (@ (@ (@ P tptp.id) A) tptp.id)))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem1_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.ap A) B)) tptp.id)))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem2_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3aa (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub A) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id)))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3aaa (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (exists ((C tptp.term)) (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (let ((_let_1 (@ (@ tptp.sub A) N))) (let ((_let_2 (@ (@ tptp.comp M) N))) (let ((_let_3 (@ tptp.sub C))) (and (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ tptp.sub (@ _let_3 (@ (@ tptp.push A) M))) N)) (= (@ _let_3 (@ (@ tptp.push _let_1) _let_2)) (@ (@ F _let_2) _let_1)))))))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub A) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id)))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam A)) tptp.id)))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3))))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3)))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3a (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam A)) tptp.id)))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3a_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3a))))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a)))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3b (forall ((B tptp.term)) (exists ((F (-> tptp.subst tptp.term tptp.term))) (= (@ (@ tptp.sub B) (@ (@ tptp.push tptp.one) tptp.sh)) (@ (@ F tptp.sh) tptp.one))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3b_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3b))))))))))))))))))))))))))))))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b))
% 0.22/0.58 (assert (= tptp.hoasinduction (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term)) (=> (@ (@ (@ tptp.hoasvar tptp.id) A) tptp.id) (@ (@ (@ P tptp.id) A) tptp.id))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (@ (@ (@ P tptp.id) A) tptp.id))))))))))
% 0.22/0.58 (assert (= tptp.hoasinduction_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))))))))))))))))))))))))))))))))))))))
% 0.63/0.83 (assert (= tptp.hoasinduction_lthm (=> tptp.induction2 (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction))))))
% 0.63/0.83 (assert (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction))))))
% 0.63/0.83 (assert (= tptp.hoasinduction_no_psi_cond (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (@ (@ (@ P tptp.id) A) tptp.id)))))))
% 0.63/0.83 (assert (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond))))))
% 0.63/0.83 (assert (not tptp.hoasinduction_lem2v2_gthm))
% 0.63/0.83 (set-info :filename cvc5---1.0.5_32091)
% 0.63/0.83 (check-sat-assuming ( true ))
% 0.63/0.83 ------- get file name : TPTP file name is ALG264^3
% 0.63/0.83 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32091.smt2...
% 0.63/0.83 --- Run --ho-elim --full-saturate-quant at 10...
% 0.63/0.83 % SZS status Theorem for ALG264^3
% 0.63/0.83 % SZS output start Proof for ALG264^3
% 0.63/0.83 (
% 0.63/0.83 (let ((_let_1 (not tptp.hoasinduction_lem2v2_gthm))) (let ((_let_2 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond))))))) (let ((_let_3 (= tptp.hoasinduction_no_psi_cond (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (@ (@ (@ P tptp.id) A) tptp.id)))))))) (let ((_let_4 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction))))))) (let ((_let_5 (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction))))) (let ((_let_6 (= tptp.hoasinduction_lthm (=> tptp.induction2 _let_5)))) (let ((_let_7 (= tptp.hoasinduction_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar _let_5))))))))))))))))))))))))))))))))))))) (let ((_let_8 (= tptp.hoasinduction (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term)) (=> (@ (@ (@ tptp.hoasvar tptp.id) A) tptp.id) (@ (@ (@ P tptp.id) A) tptp.id))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (@ (@ (@ P tptp.id) A) tptp.id))))))))))) (let ((_let_9 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b))) (let ((_let_10 (= tptp.hoasinduction_lem3b_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3b))))))))))))))))))))))))))))))))))))))) (let ((_let_11 (= tptp.hoasinduction_lem3b (forall ((B tptp.term)) (exists ((F (-> tptp.subst tptp.term tptp.term))) (= (@ (@ tptp.sub B) (@ (@ tptp.push tptp.one) tptp.sh)) (@ (@ F tptp.sh) tptp.one))))))) (let ((_let_12 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a)))))) (let ((_let_13 (= tptp.hoasinduction_lem3a_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3a))))))))))))))))))))))))))))))))))))))) (let ((_let_14 (= tptp.hoasinduction_lem3a (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam A)) tptp.id)))))))) (let ((_let_15 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3)))))) (let ((_let_16 (= tptp.hoasinduction_lem3_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3))))))))))))))))))))))))))))))))))))))) (let ((_let_17 (= tptp.hoasinduction_lem3 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam A)) tptp.id)))))))))) (let ((_let_18 (= tptp.hoasinduction_lem3aaa (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (exists ((C tptp.term)) (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (let ((_let_1 (@ (@ tptp.sub A) N))) (let ((_let_2 (@ (@ tptp.comp M) N))) (let ((_let_3 (@ tptp.sub C))) (and (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ tptp.sub (@ _let_3 (@ (@ tptp.push A) M))) N)) (= (@ _let_3 (@ (@ tptp.push _let_1) _let_2)) (@ (@ F _let_2) _let_1)))))))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub A) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id)))))))) (let ((_let_19 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa))))) (let ((_let_20 (= tptp.hoasinduction_lem3aa (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub A) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id)))))))) (let ((_let_21 (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2)))))))))))))))))))))))))))))))))))) (let ((_let_22 (= tptp.hoasinduction_lem2_lthm _let_21))) (let ((_let_23 (= tptp.hoasinduction_lem2_gthm _let_21))) (let ((_let_24 (= tptp.hoasinduction_lem2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ tptp.ap A) B)) tptp.id)))))))))))) (let ((_let_25 (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1)))))))))))))))))))))))))))))))))))) (let ((_let_26 (= tptp.hoasinduction_lem1_lthm _let_25))) (let ((_let_27 (= tptp.hoasinduction_lem1_gthm _let_25))) (let ((_let_28 (= tptp.hoasinduction_lem1 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term)) (=> (@ (@ (@ tptp.hoasvar tptp.id) A) tptp.id) (@ (@ (@ P tptp.id) A) tptp.id))) (forall ((A tptp.term)) (=> (@ tptp.var A) (@ (@ (@ P tptp.id) A) tptp.id)))))))))) (let ((_let_29 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a)))))))) (let ((_let_30 (= tptp.hoasinduction_lem3v2a (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (=> (@ (@ tptp.hoasinduction_p_and_p_prime P) Q) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (=> (@ Q B) (@ Q (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))))) (@ Q (@ tptp.lam A)))))))))) (let ((_let_31 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2))))))) (let ((_let_32 (= tptp.hoasinduction_lem3v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem3v2))))))))))))))))))))))))))))))))))))) (let ((_let_33 (= tptp.hoasinduction_lem3v2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (=> (@ (@ tptp.hoasinduction_p_and_p_prime P) Q) (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (=> (@ Q B) (@ Q (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))))) (@ Q (@ tptp.lam A)))))))))))) (let ((_let_34 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f))) (let ((_let_35 (= tptp.hoasinduction_lem3v2_f (forall ((B tptp.term)) (exists ((F (-> tptp.subst tptp.term tptp.term))) (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ F M) A) (@ (@ tptp.sub B) (@ (@ tptp.push A) M))))))))) (let ((_let_36 (= tptp.hoasinduction_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2v2))))))))))))))))))))))))))))))))))))) (let ((_let_37 (= tptp.hoasinduction_lem2v2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (=> (@ (@ _let_1 A) tptp.id) (=> (@ (@ _let_1 B) tptp.id) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (=> (@ (@ tptp.hoasinduction_p_and_p_prime P) Q) (forall ((A tptp.term) (B tptp.term)) (=> (@ Q A) (=> (@ Q B) (@ Q (@ (@ tptp.ap A) B))))))))))))) (let ((_let_38 (= tptp.hoasinduction_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1v2))))))))))))))))))))))))))))))))))))) (let ((_let_39 (= tptp.hoasinduction_lem1v2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (=> (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N)))) (=> (forall ((A tptp.term)) (=> (@ (@ (@ tptp.hoasvar tptp.id) A) tptp.id) (@ (@ (@ P tptp.id) A) tptp.id))) (=> (@ (@ tptp.hoasinduction_p_and_p_prime P) Q) (forall ((A tptp.term)) (=> (@ tptp.var A) (@ Q A))))))))))) (let ((_let_40 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0))) (let ((_let_41 (= tptp.hoasinduction_lem0 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (exists ((Q (-> tptp.term Bool))) (@ (@ tptp.hoasinduction_p_and_p_prime P) Q)))))) (let ((_let_42 (= tptp.hoasinduction_p_and_p_prime (lambda ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) (forall ((X tptp.term)) (= (@ Q X) (@ (@ (@ P tptp.id) X) tptp.id))))))) (let ((_let_43 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar))))) (let ((_let_44 (= tptp.hoasapnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar tptp.hoasapnotvar)))))))))))))))))))))))))))))))))))) (let ((_let_45 (= tptp.hoasapnotvar (forall ((A tptp.term) (B tptp.term)) (not (@ (@ (@ tptp.hoasvar tptp.id) (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id)))))) (let ((_let_46 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar))))) (let ((_let_47 (= tptp.hoaslamnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap tptp.hoaslamnotvar))))))))))))))))))))))))))))))))))) (let ((_let_48 (= tptp.hoaslamnotvar (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (not (@ (@ (@ tptp.hoasvar tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id))))))) (let ((_let_49 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap)))) (let ((_let_50 (= tptp.hoaslamnotap_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj tptp.hoaslamnotap)))))))))))))))))))))))))))))))))) (let ((_let_51 (= tptp.hoaslamnotap (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (forall ((A tptp.term) (B tptp.term)) (not (= (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (C tptp.term)) (@ (@ F M) C))) (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B))))))))) (let ((_let_52 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj)))))) (let ((_let_53 (= tptp.hoaslaminj_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 tptp.hoaslaminj))))))))))))))))))))))))))))))))) (let ((_let_54 (= tptp.hoaslaminj (forall ((F (-> tptp.subst tptp.term tptp.term))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (forall ((G (-> tptp.subst tptp.term tptp.term))) (let ((_let_1 (@ tptp.hoaslam tptp.id))) (=> (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ G M) A)) N) (@ (@ G (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N)))) (=> (= (@ _let_1 (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A))) (@ _let_1 (lambda ((M tptp.subst) (A tptp.term)) (@ (@ G M) A)))) (forall ((M tptp.subst) (A tptp.term)) (= (@ (@ F M) A) (@ (@ G M) A)))))))))))) (let ((_let_55 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2)))) (let ((_let_56 (= tptp.hoasapinj2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 tptp.hoasapinj2)))))))))))))))))))))))))))))))) (let ((_let_57 (= tptp.hoasapinj2 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (@ tptp.hoasap tptp.id))) (=> (= (@ (@ (@ _let_1 A) tptp.id) C) (@ (@ (@ _let_1 B) tptp.id) D)) (= C D))))))) (let ((_let_58 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1))))) (let ((_let_59 (= tptp.hoasapinj1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset tptp.hoasapinj1))))))))))))))))))))))))))))))) (let ((_let_60 (= tptp.hoasapinj1 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (@ tptp.hoasap tptp.id))) (=> (= (@ (@ (@ _let_1 A) tptp.id) C) (@ (@ (@ _let_1 B) tptp.id) D)) (= A B))))))) (let ((_let_61 (= tptp.hoasvar (lambda ((M tptp.subst) (A tptp.term) (N tptp.subst)) (@ tptp.var (@ (@ tptp.sub A) N)))))) (let ((_let_62 (= tptp.hoaslam (lambda ((M tptp.subst) (F (-> tptp.subst tptp.term tptp.term))) (@ tptp.lam (@ (@ F tptp.sh) tptp.one)))))) (let ((_let_63 (= tptp.hoasap (lambda ((M tptp.subst) (A tptp.term) (N tptp.subst) (B tptp.term)) (@ (@ tptp.ap (@ (@ tptp.sub A) N)) B))))) (let ((_let_64 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset))))) (let ((_let_65 (= tptp.termmset_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid tptp.termmset)))))))))))))))))))))))))))))) (let ((_let_66 (forall ((A tptp.term) (M tptp.subst) (N tptp.subst)) (let ((_let_1 (@ tptp.sub A))) (= (@ (@ tptp.sub (@ _let_1 M)) N) (@ _let_1 (@ (@ tptp.comp M) N))))))) (let ((_let_67 (= tptp.termmset (and _let_66 (forall ((A tptp.term)) (= (@ (@ tptp.sub A) tptp.id) A)))))) (let ((_let_68 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid)))))) (let ((_let_69 (= tptp.substmonoid_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 tptp.substmonoid))))))))))))))))))))))))))))) (let ((_let_70 (forall ((M tptp.subst) (N tptp.subst) (K tptp.subst)) (let ((_let_1 (@ tptp.comp M))) (= (@ (@ tptp.comp (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.comp N) K))))))) (let ((_let_71 (= tptp.substmonoid (and _let_70 (forall ((M tptp.subst)) (= (@ (@ tptp.comp tptp.id) M) M)) (forall ((M tptp.subst)) (= (@ (@ tptp.comp M) tptp.id) M)))))) (let ((_let_72 (=> tptp.induction2lem tptp.induction2))) (let ((_let_73 (= tptp.induction2_lthm (=> tptp.axvarid _let_72)))) (let ((_let_74 (= tptp.induction2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop _let_72))))))))))))))))))))))))))) (let ((_let_75 (= tptp.induction2 (forall ((P (-> tptp.term Bool))) (=> (forall ((A tptp.term)) (=> (@ tptp.var A) (@ P A))) (=> (forall ((A tptp.term) (B tptp.term)) (=> (@ P A) (=> (@ P B) (@ P (@ (@ tptp.ap A) B))))) (=> (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (=> (@ P B) (@ P (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))))) (@ P (@ tptp.lam A)))) (forall ((A tptp.term)) (@ P A))))))))) (let ((_let_76 (=> tptp.induction (=> tptp.pushprop tptp.induction2lem)))) (let ((_let_77 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr _let_76))))))))))) (let ((_let_78 (= tptp.induction2lem_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar _let_76))))))))))))))))))))))))) (let ((_let_79 (= tptp.induction2lem (forall ((P (-> tptp.term Bool))) (=> (forall ((A tptp.term) (B tptp.term)) (=> (@ P A) (=> (@ P B) (@ P (@ (@ tptp.ap A) B))))) (=> (forall ((A tptp.term)) (=> (forall ((B tptp.term)) (=> (@ P B) (@ P (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id))))) (@ P (@ tptp.lam A)))) (forall ((A tptp.term) (M tptp.subst)) (=> (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) M)))) (@ P (@ (@ tptp.sub A) M)))))))))) (let ((_let_80 (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop))))))) (let ((_let_81 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 _let_80)))) (let ((_let_82 (= tptp.pushprop_lthm_orig _let_80))) (let ((_let_83 (= tptp.pushprop_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop)))))))))))))))))))))))))) (let ((_let_84 (= tptp.pushprop (forall ((P (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (=> (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) M)))) (=> (@ P A) (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) (@ (@ tptp.push A) M))))))))))) (let ((_let_85 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2))) (let ((_let_86 (= tptp.pushprop_lem3v2 (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (=> (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q) (=> (forall ((B tptp.term)) (=> (@ tptp.var B) (@ Q B))) (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) (@ (@ tptp.push A) M))))))))))) (let ((_let_87 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2))))) (let ((_let_88 (= tptp.pushprop_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem2v2)))))))))))))))))))))))))) (let ((_let_89 (= tptp.pushprop_lem2v2 (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (=> (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q) (=> (forall ((B tptp.term)) (=> (@ tptp.var B) (@ P (@ (@ tptp.sub B) M)))) (forall ((C tptp.term)) (=> (@ tptp.var C) (=> (@ Q C) (@ Q (@ (@ tptp.sub C) tptp.sh))))))))))) (let ((_let_90 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2)))) (let ((_let_91 (= tptp.pushprop_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1v2)))))))))))))))))))))))))) (let ((_let_92 (= tptp.pushprop_lem1v2 (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (=> (@ P A) (=> (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q) (@ Q tptp.one))))))) (let ((_let_93 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1))))))) (let ((_let_94 (= tptp.pushprop_lem1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1)))))))))))))))))))))))))) (let ((_let_95 (= tptp.pushprop_lem1 (forall ((P (-> tptp.term Bool)) (K (-> tptp.term Bool)) (A tptp.term) (M tptp.subst) (B tptp.term)) (=> (@ P A) (@ K (@ (@ tptp.sub A) (@ (@ tptp.push B) M)))))))) (let ((_let_96 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0))) (let ((_let_97 (= tptp.pushprop_lem0_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem0)))))))))))))))))))))))))) (let ((_let_98 (= tptp.pushprop_lem0 (forall ((P (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (exists ((Q (-> tptp.term Bool))) (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q)))))) (let ((_let_99 (= tptp.pushprop_p_and_p_prime (lambda ((A tptp.term) (M tptp.subst) (P (-> tptp.term Bool)) (Q (-> tptp.term Bool))) (forall ((X tptp.term)) (= (@ Q X) (@ P (@ (@ tptp.sub X) (@ (@ tptp.push A) M))))))))) (let ((_let_100 (= tptp.induction (forall ((P (-> tptp.term Bool))) (=> (forall ((A tptp.term)) (=> (@ tptp.var A) (@ P A))) (=> (forall ((A tptp.term) (B tptp.term)) (=> (@ P A) (=> (@ P B) (@ P (@ (@ tptp.ap A) B))))) (=> (forall ((A tptp.term)) (=> (@ P A) (@ P (@ tptp.lam A)))) (forall ((A tptp.term)) (@ P A))))))))) (let ((_let_101 (forall ((A tptp.term)) (not (@ tptp.var (@ tptp.lam A)))))) (let ((_let_102 (= tptp.lamnotvar _let_101))) (let ((_let_103 (forall ((A tptp.term) (B tptp.term)) (not (@ tptp.var (@ (@ tptp.ap A) B)))))) (let ((_let_104 (= tptp.apnotvar _let_103))) (let ((_let_105 (forall ((A tptp.term) (B tptp.term) (C tptp.term)) (not (= (@ tptp.lam A) (@ (@ tptp.ap B) C)))))) (let ((_let_106 (= tptp.lamnotap _let_105))) (let ((_let_107 (= tptp.shinj (forall ((A tptp.term) (B tptp.term)) (=> (= (@ (@ tptp.sub A) tptp.sh) (@ (@ tptp.sub B) tptp.sh)) (= A B)))))) (let ((_let_108 (= tptp.laminj (forall ((A tptp.term) (B tptp.term)) (=> (= (@ tptp.lam A) (@ tptp.lam B)) (= A B)))))) (let ((_let_109 (= tptp.apinj2 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (=> (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D)) (= C D)))))) (let ((_let_110 (= tptp.apinj1 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (=> (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D)) (= A B)))))) (let ((_let_111 (= tptp.ulamvarind (forall ((P (-> tptp.term Bool))) (=> (@ P tptp.one) (=> (forall ((A tptp.term)) (=> (@ tptp.var A) (=> (@ P A) (@ P (@ (@ tptp.sub A) tptp.sh))))) (forall ((A tptp.term)) (=> (@ tptp.var A) (@ P A))))))))) (let ((_let_112 (= tptp.ulamvarsh (forall ((A tptp.term)) (=> (@ tptp.var A) (@ tptp.var (@ (@ tptp.sub A) tptp.sh))))))) (let ((_let_113 (@ tptp.var tptp.one))) (let ((_let_114 (= tptp.ulamvar1 _let_113))) (let ((_let_115 (= tptp.axscons (forall ((M tptp.subst)) (= (@ (@ tptp.push (@ (@ tptp.sub tptp.one) M)) (@ (@ tptp.comp tptp.sh) M)) M))))) (let ((_let_116 (= tptp.axvarshift (= (@ (@ tptp.push tptp.one) tptp.sh) tptp.id)))) (let ((_let_117 (= tptp.axidr (forall ((M tptp.subst)) (= (@ (@ tptp.comp M) tptp.id) M))))) (let ((_let_118 (forall ((A tptp.term) (M tptp.subst) (N tptp.subst)) (= (@ (@ tptp.comp (@ (@ tptp.push A) M)) N) (@ (@ tptp.push (@ (@ tptp.sub A) N)) (@ (@ tptp.comp M) N)))))) (let ((_let_119 (= tptp.axmap _let_118))) (let ((_let_120 (forall ((M tptp.subst) (N tptp.subst) (K tptp.subst)) (let ((_let_1 (@ tptp.comp M))) (= (@ (@ tptp.comp (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.comp N) K))))))) (let ((_let_121 (= tptp.axassoc _let_120))) (let ((_let_122 (= tptp.axshiftcons (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ tptp.comp tptp.sh) (@ (@ tptp.push A) M)) M))))) (let ((_let_123 (= tptp.axidl (forall ((M tptp.subst)) (= (@ (@ tptp.comp tptp.id) M) M))))) (let ((_let_124 (forall ((A tptp.term) (M tptp.subst) (N tptp.subst)) (let ((_let_1 (@ tptp.sub A))) (= (@ (@ tptp.sub (@ _let_1 M)) N) (@ _let_1 (@ (@ tptp.comp M) N))))))) (let ((_let_125 (= tptp.axclos _let_124))) (let ((_let_126 (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ tptp.sub (@ tptp.lam A)) M) (@ tptp.lam (@ (@ tptp.sub A) (@ (@ tptp.push tptp.one) (@ (@ tptp.comp M) tptp.sh)))))))) (let ((_let_127 (= tptp.axabs _let_126))) (let ((_let_128 (= tptp.axvarid (forall ((A tptp.term)) (= (@ (@ tptp.sub A) tptp.id) A))))) (let ((_let_129 (= tptp.axvarcons (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ tptp.sub tptp.one) (@ (@ tptp.push A) M)) A))))) (let ((_let_130 (forall ((A tptp.term) (B tptp.term) (M tptp.subst)) (= (@ (@ tptp.sub (@ (@ tptp.ap A) B)) M) (@ (@ tptp.ap (@ (@ tptp.sub A) M)) (@ (@ tptp.sub B) M)))))) (let ((_let_131 (= tptp.axapp _let_130))) (let ((_let_132 (ho_8 (ho_7 k_6 tptp.one) tptp.sh))) (let ((_let_133 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_134 (ho_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_132))) (let ((_let_135 (ho_10 _let_134 _let_133))) (let ((_let_136 (ho_11 _let_135 _let_132))) (let ((_let_137 (= _let_132 (ho_8 (ho_16 k_15 _let_132) _let_132)))) (let ((_let_138 (ho_14 (ho_13 k_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) _let_132))) (let ((_let_139 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_138))) (let ((_let_140 (ho_11 (ho_10 _let_134 (ho_4 (ho_3 k_2 _let_138) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22)) _let_132))) (let ((_let_141 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 _let_133))) (let ((_let_142 (= _let_141 _let_136))) (let ((_let_143 (not _let_136))) (let ((_let_144 (forall ((X tptp.term)) (let ((_let_1 (ho_8 (ho_7 k_6 tptp.one) tptp.sh))) (= (ho_11 (ho_10 (ho_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_1) X) _let_1) (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 X)))))) (let ((_let_145 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_146 (not _let_145))) (let ((_let_147 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_148 (not _let_147))) (let ((_let_149 (not _let_144))) (let ((_let_150 (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (ho_8 (ho_7 k_6 tptp.one) tptp.sh))) (let ((_let_2 (ho_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_1))) (or (not (ho_11 (ho_10 _let_2 A) _let_1)) (not (ho_11 (ho_10 _let_2 B) _let_1)) (ho_11 (ho_10 _let_2 (ho_4 (ho_3 k_2 (ho_14 (ho_13 k_12 A) _let_1)) B)) _let_1))))))) (let ((_let_151 (not _let_150))) (let ((_let_152 (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (ho_11 (ho_10 (ho_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 M) A) (ho_8 (ho_16 k_15 K) N))) (ho_11 (ho_10 (ho_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 (ho_8 (ho_16 k_15 M) K)) (ho_14 (ho_13 k_12 A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (ho_11 (ho_10 (ho_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 (ho_8 (ho_16 k_15 M) K)) (ho_14 (ho_13 k_12 A) K)) N)) (ho_11 (ho_10 (ho_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 M) A) (ho_8 (ho_16 k_15 K) N))))) _let_151 _let_149 _let_148 _let_146 _let_141))) (let ((_let_153 (forall ((BOUND_VARIABLE_9493 |u_(-> tptp.subst tptp.term tptp.subst Bool)|) (BOUND_VARIABLE_9475 |u_(-> tptp.term Bool)|) (BOUND_VARIABLE_3837 tptp.term) (BOUND_VARIABLE_3835 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (ho_11 (ho_10 (ho_9 BOUND_VARIABLE_9493 M) A) (ho_8 (ho_16 k_15 K) N))) (ho_11 (ho_10 (ho_9 BOUND_VARIABLE_9493 (ho_8 (ho_16 k_15 M) K)) (ho_14 (ho_13 k_12 A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (ho_11 (ho_10 (ho_9 BOUND_VARIABLE_9493 (ho_8 (ho_16 k_15 M) K)) (ho_14 (ho_13 k_12 A) K)) N)) (ho_11 (ho_10 (ho_9 BOUND_VARIABLE_9493 M) A) (ho_8 (ho_16 k_15 K) N))))) (not (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (ho_8 (ho_7 k_6 tptp.one) tptp.sh))) (let ((_let_2 (ho_9 BOUND_VARIABLE_9493 _let_1))) (or (not (ho_11 (ho_10 _let_2 A) _let_1)) (not (ho_11 (ho_10 _let_2 B) _let_1)) (ho_11 (ho_10 _let_2 (ho_4 (ho_3 k_2 (ho_14 (ho_13 k_12 A) _let_1)) B)) _let_1)))))) (not (forall ((X tptp.term)) (let ((_let_1 (ho_8 (ho_7 k_6 tptp.one) tptp.sh))) (= (ho_11 (ho_10 (ho_9 BOUND_VARIABLE_9493 _let_1) X) _let_1) (ho_5 BOUND_VARIABLE_9475 X))))) (not (ho_5 BOUND_VARIABLE_9475 BOUND_VARIABLE_3835)) (not (ho_5 BOUND_VARIABLE_9475 BOUND_VARIABLE_3837)) (ho_5 BOUND_VARIABLE_9475 (ho_4 (ho_3 k_2 BOUND_VARIABLE_3835) BOUND_VARIABLE_3837)))))) (let ((_let_154 (not _let_152))) (let ((_let_155 (forall ((M tptp.subst)) (= M (ho_8 (ho_16 k_15 M) (ho_8 (ho_7 k_6 tptp.one) tptp.sh)))))) (let ((_let_156 (forall ((A tptp.term)) (= A (ho_14 (ho_13 k_12 A) (ho_8 (ho_7 k_6 tptp.one) tptp.sh)))))) (let ((_let_157 (ASSUME :args (_let_131)))) (let ((_let_158 (EQ_RESOLVE (ASSUME :args (_let_129)) (MACRO_SR_EQ_INTRO :args (_let_129 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_159 (EQ_RESOLVE (ASSUME :args (_let_128)) (MACRO_SR_EQ_INTRO :args (_let_128 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_160 (ASSUME :args (_let_127)))) (let ((_let_161 (ASSUME :args (_let_125)))) (let ((_let_162 (EQ_RESOLVE (ASSUME :args (_let_123)) (MACRO_SR_EQ_INTRO :args (_let_123 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_163 (EQ_RESOLVE (ASSUME :args (_let_122)) (MACRO_SR_EQ_INTRO :args (_let_122 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_164 (ASSUME :args (_let_121)))) (let ((_let_165 (ASSUME :args (_let_119)))) (let ((_let_166 (EQ_RESOLVE (ASSUME :args (_let_117)) (MACRO_SR_EQ_INTRO :args (_let_117 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_167 (EQ_RESOLVE (ASSUME :args (_let_116)) (MACRO_SR_EQ_INTRO :args (_let_116 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_168 (EQ_RESOLVE (ASSUME :args (_let_115)) (MACRO_SR_EQ_INTRO :args (_let_115 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_169 (ASSUME :args (_let_114)))) (let ((_let_170 (EQ_RESOLVE (ASSUME :args (_let_112)) (MACRO_SR_EQ_INTRO :args (_let_112 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_171 (EQ_RESOLVE (ASSUME :args (_let_111)) (MACRO_SR_EQ_INTRO :args (_let_111 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_172 (EQ_RESOLVE (ASSUME :args (_let_110)) (MACRO_SR_EQ_INTRO :args (_let_110 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_173 (EQ_RESOLVE (ASSUME :args (_let_109)) (MACRO_SR_EQ_INTRO :args (_let_109 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_174 (EQ_RESOLVE (ASSUME :args (_let_108)) (MACRO_SR_EQ_INTRO :args (_let_108 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_175 (EQ_RESOLVE (ASSUME :args (_let_107)) (MACRO_SR_EQ_INTRO :args (_let_107 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_176 (ASSUME :args (_let_106)))) (let ((_let_177 (ASSUME :args (_let_104)))) (let ((_let_178 (ASSUME :args (_let_102)))) (let ((_let_179 (EQ_RESOLVE (ASSUME :args (_let_100)) (MACRO_SR_EQ_INTRO :args (_let_100 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_180 (ASSUME :args (_let_99)))) (let ((_let_181 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_98)) (MACRO_SR_EQ_INTRO :args (_let_98 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.pushprop_lem0 (forall ((P (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (not (forall ((Q (-> tptp.term Bool))) (not (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_182 (EQ_RESOLVE (ASSUME :args (_let_97)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_97 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_183 (EQ_RESOLVE (SYMM (ASSUME :args (_let_96))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.pushprop_lem0 tptp.pushprop_lem0_lthm) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_184 (EQ_RESOLVE (ASSUME :args (_let_95)) (MACRO_SR_EQ_INTRO :args (_let_95 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_185 (EQ_RESOLVE (ASSUME :args (_let_94)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_94 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_186 (EQ_RESOLVE (ASSUME :args (_let_93)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_93 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_187 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_92)) (MACRO_SR_EQ_INTRO :args (_let_92 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.pushprop_lem1v2 (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (or (not (@ P A)) (not (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q)) (@ Q tptp.one)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_188 (EQ_RESOLVE (ASSUME :args (_let_91)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_91 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_189 (EQ_RESOLVE (ASSUME :args (_let_90)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_90 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_190 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_89)) (MACRO_SR_EQ_INTRO :args (_let_89 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.pushprop_lem2v2 (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst) (BOUND_VARIABLE_3476 tptp.term)) (or (not (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q)) (not (forall ((B tptp.term)) (or (not (@ tptp.var B)) (@ P (@ (@ tptp.sub B) M))))) (not (@ tptp.var BOUND_VARIABLE_3476)) (not (@ Q BOUND_VARIABLE_3476)) (@ Q (@ (@ tptp.sub BOUND_VARIABLE_3476) tptp.sh))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_191 (EQ_RESOLVE (ASSUME :args (_let_88)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_88 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_192 (EQ_RESOLVE (ASSUME :args (_let_87)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_87 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_193 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_86)) (MACRO_SR_EQ_INTRO :args (_let_86 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.pushprop_lem3v2 (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst) (BOUND_VARIABLE_3507 tptp.term)) (or (not (@ (@ (@ (@ tptp.pushprop_p_and_p_prime A) M) P) Q)) (not (forall ((B tptp.term)) (or (not (@ tptp.var B)) (@ Q B)))) (not (@ tptp.var BOUND_VARIABLE_3507)) (@ P (@ (@ tptp.sub BOUND_VARIABLE_3507) (@ (@ tptp.push A) M)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_194 (EQ_RESOLVE (ASSUME :args (_let_85)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_85 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_195 (EQ_RESOLVE (ASSUME :args (_let_84)) (MACRO_SR_EQ_INTRO :args (_let_84 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_196 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_197 (EQ_RESOLVE (ASSUME :args (_let_82)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_82 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_198 (EQ_RESOLVE (ASSUME :args (_let_81)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_81 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_199 (EQ_RESOLVE (ASSUME :args (_let_79)) (MACRO_SR_EQ_INTRO :args (_let_79 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_200 (EQ_RESOLVE (ASSUME :args (_let_78)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_78 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_201 (EQ_RESOLVE (ASSUME :args (_let_77)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_77 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_202 (EQ_RESOLVE (ASSUME :args (_let_75)) (MACRO_SR_EQ_INTRO :args (_let_75 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_203 (EQ_RESOLVE (ASSUME :args (_let_74)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_74 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_204 (EQ_RESOLVE (ASSUME :args (_let_73)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_73 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_205 (EQ_RESOLVE (ASSUME :args (_let_71)) (MACRO_SR_EQ_INTRO :args (_let_71 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_206 (EQ_RESOLVE (ASSUME :args (_let_69)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_69 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_207 (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_68 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_208 (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO :args (_let_67 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_209 (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_65 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_210 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_211 (ASSUME :args (_let_63)))) (let ((_let_212 (ASSUME :args (_let_62)))) (let ((_let_213 (ASSUME :args (_let_61)))) (let ((_let_214 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_60)) (MACRO_SR_EQ_INTRO :args (_let_60 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasapinj1 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (@ tptp.hoasap tptp.id))) (or (not (= (@ (@ (@ _let_1 A) tptp.id) C) (@ (@ (@ _let_1 B) tptp.id) D))) (= A B))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_215 (EQ_RESOLVE (ASSUME :args (_let_59)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_59 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_216 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_217 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO :args (_let_57 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasapinj2 (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (@ tptp.hoasap tptp.id))) (or (not (= (@ (@ (@ _let_1 A) tptp.id) C) (@ (@ (@ _let_1 B) tptp.id) D))) (= C D))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_218 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_219 (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_55 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_220 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_54)) (MACRO_SR_EQ_INTRO :args (_let_54 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoaslaminj (forall ((F (-> tptp.subst tptp.term tptp.term)) (BOUND_VARIABLE_3699 tptp.subst) (BOUND_VARIABLE_3697 tptp.term) (BOUND_VARIABLE_3695 (-> tptp.subst tptp.term tptp.term))) (let ((_let_1 (@ tptp.hoaslam tptp.id))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ BOUND_VARIABLE_3695 M) A)) N) (@ (@ BOUND_VARIABLE_3695 (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (= (@ _let_1 (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A))) (@ _let_1 (lambda ((M tptp.subst) (A tptp.term)) (@ (@ BOUND_VARIABLE_3695 M) A))))) (= (@ (@ F BOUND_VARIABLE_3699) BOUND_VARIABLE_3697) (@ (@ BOUND_VARIABLE_3695 BOUND_VARIABLE_3699) BOUND_VARIABLE_3697)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_221 (EQ_RESOLVE (ASSUME :args (_let_53)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_53 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_222 (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_52 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_223 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO :args (_let_51 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoaslamnotap (forall ((F (-> tptp.subst tptp.term tptp.term)) (BOUND_VARIABLE_3737 tptp.term) (BOUND_VARIABLE_3735 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (= (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (C tptp.term)) (@ (@ F M) C))) (@ (@ (@ (@ tptp.hoasap tptp.id) BOUND_VARIABLE_3735) tptp.id) BOUND_VARIABLE_3737)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_224 (EQ_RESOLVE (ASSUME :args (_let_50)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_50 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_225 (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_49 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_226 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO :args (_let_48 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoaslamnotvar (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (@ (@ (@ tptp.hoasvar tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_227 (EQ_RESOLVE (ASSUME :args (_let_47)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_47 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_228 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_229 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_230 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_231 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_232 (ASSUME :args (_let_42)))) (let ((_let_233 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem0 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool))) (not (forall ((Q (-> tptp.term Bool))) (not (@ (@ tptp.hoasinduction_p_and_p_prime P) Q)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_234 (EQ_RESOLVE (SYMM (ASSUME :args (_let_40))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem0 tptp.hoasinduction_lem0_lthm) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_235 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem1v2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool)) (BOUND_VARIABLE_3792 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ tptp.hoasvar tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) A) tptp.id)))) (not (@ (@ tptp.hoasinduction_p_and_p_prime P) Q)) (not (@ tptp.var BOUND_VARIABLE_3792)) (@ Q BOUND_VARIABLE_3792)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_236 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_237 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem2v2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool)) (BOUND_VARIABLE_3837 tptp.term) (BOUND_VARIABLE_3835 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (not (@ (@ _let_1 B) tptp.id)) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (not (@ (@ tptp.hoasinduction_p_and_p_prime P) Q)) (not (@ Q BOUND_VARIABLE_3835)) (not (@ Q BOUND_VARIABLE_3837)) (@ Q (@ (@ tptp.ap BOUND_VARIABLE_3835) BOUND_VARIABLE_3837))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_238 (ASSUME :args (_let_36)))) (let ((_let_239 (EQ_RESOLVE _let_238 (MACRO_SR_EQ_INTRO (AND_INTRO _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_240 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_241 (EQ_RESOLVE (SYMM (ASSUME :args (_let_34))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem3v2_f tptp.hoasinduction_lem3v2_f_lthm) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_242 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem3v2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool)) (BOUND_VARIABLE_3903 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id))))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (not (@ (@ tptp.hoasinduction_p_and_p_prime P) Q)) (not (forall ((B tptp.term)) (or (not (@ Q B)) (@ Q (@ (@ tptp.sub BOUND_VARIABLE_3903) (@ (@ tptp.push B) tptp.id)))))) (@ Q (@ tptp.lam BOUND_VARIABLE_3903))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_243 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_244 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_245 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem3v2a (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool)) (BOUND_VARIABLE_3950 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id))))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (not (@ (@ tptp.hoasinduction_p_and_p_prime P) Q)) (not (forall ((B tptp.term)) (or (not (@ Q B)) (@ Q (@ (@ tptp.sub BOUND_VARIABLE_3950) (@ (@ tptp.push B) tptp.id)))))) (@ Q (@ tptp.lam BOUND_VARIABLE_3950))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_246 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_247 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem1 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_3991 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ tptp.hoasvar tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) A) tptp.id)))) (not (@ tptp.var BOUND_VARIABLE_3991)) (@ (@ (@ P tptp.id) BOUND_VARIABLE_3991) tptp.id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_248 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_249 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_250 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem2 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4034 tptp.term) (BOUND_VARIABLE_4032 tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (not (@ (@ _let_1 B) tptp.id)) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (not (@ (@ _let_1 BOUND_VARIABLE_4032) tptp.id)) (not (@ (@ _let_1 BOUND_VARIABLE_4034) tptp.id)) (@ (@ _let_1 (@ (@ tptp.ap BOUND_VARIABLE_4032) BOUND_VARIABLE_4034)) tptp.id))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_251 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_252 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_253 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem3aa (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4080 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id))))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (not (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 B) tptp.id)) (@ (@ _let_1 (@ (@ tptp.sub BOUND_VARIABLE_4080) (@ (@ tptp.push B) tptp.id))) tptp.id))))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub BOUND_VARIABLE_4080) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_254 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_255 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem3aaa (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4195 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term)) (BOUND_VARIABLE_4159 tptp.term)) (or (not (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id))))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id) (not (forall ((BOUND_VARIABLE_4101 tptp.subst) (BOUND_VARIABLE_4103 tptp.term) (BOUND_VARIABLE_4105 tptp.subst)) (= (@ (@ tptp.sub (@ (@ F BOUND_VARIABLE_4101) BOUND_VARIABLE_4103)) BOUND_VARIABLE_4105) (@ (@ tptp.sub (@ (@ tptp.sub BOUND_VARIABLE_4159) (@ (@ tptp.push BOUND_VARIABLE_4103) BOUND_VARIABLE_4101))) BOUND_VARIABLE_4105)))) (not (forall ((BOUND_VARIABLE_4119 tptp.subst) (BOUND_VARIABLE_4121 tptp.term) (BOUND_VARIABLE_4123 tptp.subst)) (let ((_let_1 (@ (@ tptp.comp BOUND_VARIABLE_4119) BOUND_VARIABLE_4123))) (let ((_let_2 (@ (@ tptp.sub BOUND_VARIABLE_4121) BOUND_VARIABLE_4123))) (= (@ (@ F _let_1) _let_2) (@ (@ tptp.sub BOUND_VARIABLE_4159) (@ (@ tptp.push _let_2) _let_1)))))))))) (not (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 B) tptp.id)) (@ (@ _let_1 (@ (@ tptp.sub BOUND_VARIABLE_4195) (@ (@ tptp.push B) tptp.id))) tptp.id))))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub BOUND_VARIABLE_4195) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_256 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem3 (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4254 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id))))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (not (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 B) tptp.id)) (@ (@ _let_1 (@ (@ tptp.sub BOUND_VARIABLE_4254) (@ (@ tptp.push B) tptp.id))) tptp.id))))) (@ (@ (@ P tptp.id) (@ tptp.lam BOUND_VARIABLE_4254)) tptp.id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_257 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_258 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_259 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_lem3a (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4300 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id))))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (not (forall ((B tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 B) tptp.id)) (@ (@ _let_1 (@ (@ tptp.sub BOUND_VARIABLE_4300) (@ (@ tptp.push B) tptp.id))) tptp.id))))) (@ (@ (@ P tptp.id) (@ tptp.lam BOUND_VARIABLE_4300)) tptp.id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_260 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_261 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_262 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_263 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_264 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_265 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4370 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ tptp.hoasvar tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) A) tptp.id)))) (not (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (not (@ (@ _let_1 B) tptp.id)) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id))))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (@ (@ (@ P tptp.id) BOUND_VARIABLE_4370) tptp.id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_266 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_267 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_268 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_269 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args ((= tptp.hoasinduction_no_psi_cond (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4405 tptp.term)) (or (not (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (not (@ (@ _let_1 B) tptp.id)) (@ (@ _let_1 (@ (@ (@ (@ tptp.hoasap tptp.id) A) tptp.id) B)) tptp.id))))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (let ((_let_1 (@ P tptp.id))) (or (not (@ (@ _let_1 A) tptp.id)) (@ (@ _let_1 (@ (@ F tptp.id) A)) tptp.id))))) (@ (@ (@ P tptp.id) (@ (@ tptp.hoaslam tptp.id) (lambda ((M tptp.subst) (A tptp.term)) (@ (@ F M) A)))) tptp.id)))) (@ (@ (@ P tptp.id) BOUND_VARIABLE_4405) tptp.id)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_270 (ASSUME :args (_let_1)))) (let ((_let_271 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE _let_270 (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (NOT_IMPLIES_ELIM1 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (RESOLUTION (EQUIV_ELIM2 _let_238) _let_270 :args (true tptp.hoasinduction_lem2v2_gthm))))))))))))) _let_167) (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157) :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> _let_130 (=> (forall ((A tptp.term) (M tptp.subst)) (= A (@ (@ tptp.sub tptp.one) (@ (@ tptp.push A) M)))) (=> (forall ((A tptp.term)) (= A (@ (@ tptp.sub A) (@ (@ tptp.push tptp.one) tptp.sh)))) (=> _let_126 (=> _let_124 (=> (forall ((M tptp.subst)) (= M (@ (@ tptp.comp (@ (@ tptp.push tptp.one) tptp.sh)) M))) (=> (forall ((A tptp.term) (M tptp.subst)) (= M (@ (@ tptp.comp tptp.sh) (@ (@ tptp.push A) M)))) (=> _let_120 (=> _let_118 (=> (forall ((M tptp.subst)) (= M (@ (@ tptp.comp M) (@ (@ tptp.push tptp.one) tptp.sh)))) (=> (forall ((M tptp.subst)) (= M (@ (@ tptp.push (@ (@ tptp.sub tptp.one) M)) (@ (@ tptp.comp tptp.sh) M)))) (=> _let_113 (=> (forall ((A tptp.term)) (or (not (@ tptp.var A)) (@ tptp.var (@ (@ tptp.sub A) tptp.sh)))) (=> (forall ((P (-> tptp.term Bool)) (BOUND_VARIABLE_3371 tptp.term)) (or (not (@ P tptp.one)) (not (forall ((A tptp.term)) (or (not (@ tptp.var A)) (not (@ P A)) (@ P (@ (@ tptp.sub A) tptp.sh))))) (not (@ tptp.var BOUND_VARIABLE_3371)) (@ P BOUND_VARIABLE_3371))) (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D))) (= A B))) (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D))) (= C D))) (=> (forall ((A tptp.term) (B tptp.term)) (or (not (= (@ tptp.lam A) (@ tptp.lam B))) (= A B))) (=> (forall ((A tptp.term) (B tptp.term)) (or (not (= (@ (@ tptp.sub A) tptp.sh) (@ (@ tptp.sub B) tptp.sh))) (= A B))) (=> _let_105 (=> _let_103 (=> _let_101 (=> (forall ((P (-> tptp.term Bool)) (BOUND_VARIABLE_3426 tptp.term)) (or (not (forall ((A tptp.term)) (or (not (@ tptp.var A)) (@ P A)))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ tptp.ap A) B))))) (not (forall ((A tptp.term)) (or (not (@ P A)) (@ P (@ tptp.lam A))))) (@ P BOUND_VARIABLE_3426))) (=> (forall ((P (-> tptp.term Bool)) (A tptp.term) (M tptp.subst) (BOUND_VARIABLE_3536 tptp.term)) (or (not (forall ((B tptp.term)) (or (not (@ tptp.var B)) (@ P (@ (@ tptp.sub B) M))))) (not (@ P A)) (not (@ tptp.var BOUND_VARIABLE_3536)) (@ P (@ (@ tptp.sub BOUND_VARIABLE_3536) (@ (@ tptp.push A) M))))) (=> (forall ((P (-> tptp.term Bool)) (BOUND_VARIABLE_3582 tptp.subst) (BOUND_VARIABLE_3580 tptp.term)) (or (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ tptp.ap A) B))))) (not (forall ((A tptp.term)) (or (not (forall ((B tptp.term)) (or (not (@ P B)) (@ P (@ (@ tptp.sub A) (@ (@ tptp.push B) (@ (@ tptp.push tptp.one) tptp.sh))))))) (@ P (@ tptp.lam A))))) (not (forall ((B tptp.term)) (or (not (@ tptp.var B)) (@ P (@ (@ tptp.sub B) BOUND_VARIABLE_3582))))) (@ P (@ (@ tptp.sub BOUND_VARIABLE_3580) BOUND_VARIABLE_3582)))) (=> (forall ((P (-> tptp.term Bool)) (BOUND_VARIABLE_3627 tptp.term)) (or (not (forall ((A tptp.term)) (or (not (@ tptp.var A)) (@ P A)))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ tptp.ap A) B))))) (not (forall ((A tptp.term)) (or (not (forall ((B tptp.term)) (or (not (@ P B)) (@ P (@ (@ tptp.sub A) (@ (@ tptp.push B) (@ (@ tptp.push tptp.one) tptp.sh))))))) (@ P (@ tptp.lam A))))) (@ P BOUND_VARIABLE_3627))) (=> (and _let_70 (forall ((M tptp.subst)) (= M (@ (@ tptp.comp (@ (@ tptp.push tptp.one) tptp.sh)) M))) (forall ((M tptp.subst)) (= M (@ (@ tptp.comp M) (@ (@ tptp.push tptp.one) tptp.sh))))) (=> (and _let_66 (forall ((A tptp.term)) (= A (@ (@ tptp.sub A) (@ (@ tptp.push tptp.one) tptp.sh))))) (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (@ (@ tptp.push tptp.one) tptp.sh))) (or (not (= (@ (@ tptp.ap (@ (@ tptp.sub B) _let_1)) D) (@ (@ tptp.ap (@ (@ tptp.sub A) _let_1)) C))) (= A B)))) (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (@ (@ tptp.push tptp.one) tptp.sh))) (or (not (= (@ (@ tptp.ap (@ (@ tptp.sub B) _let_1)) D) (@ (@ tptp.ap (@ (@ tptp.sub A) _let_1)) C))) (= C D)))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term)) (BOUND_VARIABLE_3699 tptp.subst) (BOUND_VARIABLE_3697 tptp.term) (BOUND_VARIABLE_3695 (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ BOUND_VARIABLE_3695 M) A)) N) (@ (@ BOUND_VARIABLE_3695 (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (= (@ tptp.lam (@ (@ F tptp.sh) tptp.one)) (@ tptp.lam (@ (@ BOUND_VARIABLE_3695 tptp.sh) tptp.one)))) (= (@ (@ F BOUND_VARIABLE_3699) BOUND_VARIABLE_3697) (@ (@ BOUND_VARIABLE_3695 BOUND_VARIABLE_3699) BOUND_VARIABLE_3697)))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term)) (BOUND_VARIABLE_3737 tptp.term) (BOUND_VARIABLE_3735 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (= (@ tptp.lam (@ (@ F tptp.sh) tptp.one)) (@ (@ tptp.ap (@ (@ tptp.sub BOUND_VARIABLE_3735) (@ (@ tptp.push tptp.one) tptp.sh))) BOUND_VARIABLE_3737))))) (=> (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (@ tptp.var (@ (@ tptp.sub (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) (@ (@ tptp.push tptp.one) tptp.sh)))))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ (@ tptp.push tptp.one) tptp.sh))) (not (@ tptp.var (@ (@ tptp.sub (@ (@ tptp.ap (@ (@ tptp.sub A) _let_1)) B)) _let_1))))) (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool)) (BOUND_VARIABLE_3837 tptp.term) (BOUND_VARIABLE_3835 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (@ (@ tptp.push tptp.one) tptp.sh))) (let ((_let_2 (@ P _let_1))) (or (not (@ (@ _let_2 A) _let_1)) (not (@ (@ _let_2 B) _let_1)) (@ (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.sub A) _let_1)) B)) _let_1)))))) (not (forall ((X tptp.term)) (let ((_let_1 (@ (@ tptp.push tptp.one) tptp.sh))) (= (@ Q X) (@ (@ (@ P _let_1) X) _let_1))))) (not (@ Q BOUND_VARIABLE_3835)) (not (@ Q BOUND_VARIABLE_3837)) (@ Q (@ (@ tptp.ap BOUND_VARIABLE_3835) BOUND_VARIABLE_3837)))))))))))))))))))))))))))))))))))))) (not (=> (forall ((A tptp.term) (B tptp.term) (M tptp.subst)) (= (ho_4 (ho_3 k_2 (ho_14 (ho_13 k_12 A) M)) (ho_14 (ho_13 k_12 B) M)) (ho_14 (ho_13 k_12 (ho_4 (ho_3 k_2 A) B)) M))) (=> (forall ((A tptp.term) (M tptp.subst)) (= A (ho_14 (ho_13 k_12 tptp.one) (ho_8 (ho_7 k_6 A) M)))) (=> _let_156 (=> (forall ((A tptp.term) (M tptp.subst)) (= (ho_4 k_19 (ho_14 (ho_13 k_12 A) (ho_8 (ho_7 k_6 tptp.one) (ho_8 (ho_16 k_15 M) tptp.sh)))) (ho_14 (ho_13 k_12 (ho_4 k_19 A)) M))) (=> (forall ((A tptp.term) (M tptp.subst) (N tptp.subst)) (let ((_let_1 (ho_13 k_12 A))) (= (ho_14 _let_1 (ho_8 (ho_16 k_15 M) N)) (ho_14 (ho_13 k_12 (ho_14 _let_1 M)) N)))) (=> (forall ((M tptp.subst)) (= M (ho_8 (ho_16 k_15 (ho_8 (ho_7 k_6 tptp.one) tptp.sh)) M))) (=> (forall ((A tptp.term) (M tptp.subst)) (= M (ho_8 (ho_16 k_15 tptp.sh) (ho_8 (ho_7 k_6 A) M)))) (=> (forall ((M tptp.subst) (N tptp.subst) (K tptp.subst)) (let ((_let_1 (ho_16 k_15 M))) (= (ho_8 _let_1 (ho_8 (ho_16 k_15 N) K)) (ho_8 (ho_16 k_15 (ho_8 _let_1 N)) K)))) (=> (forall ((A tptp.term) (M tptp.subst) (N tptp.subst)) (= (ho_8 (ho_7 k_6 (ho_14 (ho_13 k_12 A) N)) (ho_8 (ho_16 k_15 M) N)) (ho_8 (ho_16 k_15 (ho_8 (ho_7 k_6 A) M)) N))) (=> _let_155 (=> (forall ((M tptp.subst)) (= M (ho_8 (ho_7 k_6 (ho_14 (ho_13 k_12 tptp.one) M)) (ho_8 (ho_16 k_15 tptp.sh) M)))) (=> (ho_5 k_17 tptp.one) (=> (forall ((A tptp.term)) (or (not (ho_5 k_17 A)) (ho_5 k_17 (ho_14 (ho_13 k_12 A) tptp.sh)))) (=> (forall ((BOUND_VARIABLE_9923 |u_(-> tptp.term Bool)|) (BOUND_VARIABLE_3371 tptp.term)) (or (not (ho_5 BOUND_VARIABLE_9923 tptp.one)) (not (forall ((A tptp.term)) (or (not (ho_5 k_17 A)) (not (ho_5 BOUND_VARIABLE_9923 A)) (ho_5 BOUND_VARIABLE_9923 (ho_14 (ho_13 k_12 A) tptp.sh))))) (not (ho_5 k_17 BOUND_VARIABLE_3371)) (ho_5 BOUND_VARIABLE_9923 BOUND_VARIABLE_3371))) (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (ho_4 (ho_3 k_2 B) D) (ho_4 (ho_3 k_2 A) C))) (= A B))) (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (ho_4 (ho_3 k_2 B) D) (ho_4 (ho_3 k_2 A) C))) (= C D))) (=> (forall ((A tptp.term) (B tptp.term)) (or (not (= (ho_4 k_19 B) (ho_4 k_19 A))) (= A B))) (=> (forall ((A tptp.term) (B tptp.term)) (or (not (= (ho_14 (ho_13 k_12 B) tptp.sh) (ho_14 (ho_13 k_12 A) tptp.sh))) (= A B))) (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term)) (not (= (ho_4 (ho_3 k_2 B) C) (ho_4 k_19 A)))) (=> (forall ((A tptp.term) (B tptp.term)) (not (ho_5 k_17 (ho_4 (ho_3 k_2 A) B)))) (=> (forall ((A tptp.term)) (not (ho_5 k_17 (ho_4 k_19 A)))) (=> (forall ((BOUND_VARIABLE_9842 |u_(-> tptp.term Bool)|) (BOUND_VARIABLE_3426 tptp.term)) (or (not (forall ((A tptp.term)) (or (not (ho_5 k_17 A)) (ho_5 BOUND_VARIABLE_9842 A)))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (ho_5 BOUND_VARIABLE_9842 A)) (not (ho_5 BOUND_VARIABLE_9842 B)) (ho_5 BOUND_VARIABLE_9842 (ho_4 (ho_3 k_2 A) B))))) (not (forall ((A tptp.term)) (or (not (ho_5 BOUND_VARIABLE_9842 A)) (ho_5 BOUND_VARIABLE_9842 (ho_4 k_19 A))))) (ho_5 BOUND_VARIABLE_9842 BOUND_VARIABLE_3426))) (=> (forall ((BOUND_VARIABLE_9824 |u_(-> tptp.term Bool)|) (A tptp.term) (M tptp.subst) (BOUND_VARIABLE_3536 tptp.term)) (or (not (forall ((B tptp.term)) (or (not (ho_5 k_17 B)) (ho_5 BOUND_VARIABLE_9824 (ho_14 (ho_13 k_12 B) M))))) (not (ho_5 BOUND_VARIABLE_9824 A)) (not (ho_5 k_17 BOUND_VARIABLE_3536)) (ho_5 BOUND_VARIABLE_9824 (ho_14 (ho_13 k_12 BOUND_VARIABLE_3536) (ho_8 (ho_7 k_6 A) M))))) (=> (forall ((BOUND_VARIABLE_9781 |u_(-> tptp.term Bool)|) (BOUND_VARIABLE_3582 tptp.subst) (BOUND_VARIABLE_3580 tptp.term)) (or (not (forall ((A tptp.term) (B tptp.term)) (or (not (ho_5 BOUND_VARIABLE_9781 A)) (not (ho_5 BOUND_VARIABLE_9781 B)) (ho_5 BOUND_VARIABLE_9781 (ho_4 (ho_3 k_2 A) B))))) (not (forall ((A tptp.term)) (or (not (forall ((B tptp.term)) (or (not (ho_5 BOUND_VARIABLE_9781 B)) (ho_5 BOUND_VARIABLE_9781 (ho_14 (ho_13 k_12 A) (ho_8 (ho_7 k_6 B) (ho_8 (ho_7 k_6 tptp.one) tptp.sh))))))) (ho_5 BOUND_VARIABLE_9781 (ho_4 k_19 A))))) (not (forall ((B tptp.term)) (or (not (ho_5 k_17 B)) (ho_5 BOUND_VARIABLE_9781 (ho_14 (ho_13 k_12 B) BOUND_VARIABLE_3582))))) (ho_5 BOUND_VARIABLE_9781 (ho_14 (ho_13 k_12 BOUND_VARIABLE_3580) BOUND_VARIABLE_3582)))) (=> (forall ((BOUND_VARIABLE_9742 |u_(-> tptp.term Bool)|) (BOUND_VARIABLE_3627 tptp.term)) (or (not (forall ((A tptp.term)) (or (not (ho_5 k_17 A)) (ho_5 BOUND_VARIABLE_9742 A)))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (ho_5 BOUND_VARIABLE_9742 A)) (not (ho_5 BOUND_VARIABLE_9742 B)) (ho_5 BOUND_VARIABLE_9742 (ho_4 (ho_3 k_2 A) B))))) (not (forall ((A tptp.term)) (or (not (forall ((B tptp.term)) (or (not (ho_5 BOUND_VARIABLE_9742 B)) (ho_5 BOUND_VARIABLE_9742 (ho_14 (ho_13 k_12 A) (ho_8 (ho_7 k_6 B) (ho_8 (ho_7 k_6 tptp.one) tptp.sh))))))) (ho_5 BOUND_VARIABLE_9742 (ho_4 k_19 A))))) (ho_5 BOUND_VARIABLE_9742 BOUND_VARIABLE_3627))) (=> (and (forall ((M tptp.subst) (N tptp.subst) (K tptp.subst)) (let ((_let_1 (ho_16 k_15 M))) (= (ho_8 _let_1 (ho_8 (ho_16 k_15 N) K)) (ho_8 (ho_16 k_15 (ho_8 _let_1 N)) K)))) (forall ((M tptp.subst)) (= M (ho_8 (ho_16 k_15 (ho_8 (ho_7 k_6 tptp.one) tptp.sh)) M))) (forall ((M tptp.subst)) (= M (ho_8 (ho_16 k_15 M) (ho_8 (ho_7 k_6 tptp.one) tptp.sh))))) (=> (and (forall ((A tptp.term) (M tptp.subst) (N tptp.subst)) (let ((_let_1 (ho_13 k_12 A))) (= (ho_14 _let_1 (ho_8 (ho_16 k_15 M) N)) (ho_14 (ho_13 k_12 (ho_14 _let_1 M)) N)))) (forall ((A tptp.term)) (= A (ho_14 (ho_13 k_12 A) (ho_8 (ho_7 k_6 tptp.one) tptp.sh))))) (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (ho_8 (ho_7 k_6 tptp.one) tptp.sh))) (or (not (= (ho_4 (ho_3 k_2 (ho_14 (ho_13 k_12 A) _let_1)) C) (ho_4 (ho_3 k_2 (ho_14 (ho_13 k_12 B) _let_1)) D))) (= A B)))) (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (let ((_let_1 (ho_8 (ho_7 k_6 tptp.one) tptp.sh))) (or (not (= (ho_4 (ho_3 k_2 (ho_14 (ho_13 k_12 A) _let_1)) C) (ho_4 (ho_3 k_2 (ho_14 (ho_13 k_12 B) _let_1)) D))) (= C D)))) (=> (forall ((BOUND_VARIABLE_9640 |u_(-> tptp.subst tptp.term tptp.term)|) (BOUND_VARIABLE_3699 tptp.subst) (BOUND_VARIABLE_3697 tptp.term) (BOUND_VARIABLE_9637 |u_(-> tptp.subst tptp.term tptp.term)|)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (ho_4 (ho_18 BOUND_VARIABLE_9640 (ho_8 (ho_16 k_15 M) N)) (ho_14 (ho_13 k_12 A) N)) (ho_14 (ho_13 k_12 (ho_4 (ho_18 BOUND_VARIABLE_9640 M) A)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (ho_4 (ho_18 BOUND_VARIABLE_9637 (ho_8 (ho_16 k_15 M) N)) (ho_14 (ho_13 k_12 A) N)) (ho_14 (ho_13 k_12 (ho_4 (ho_18 BOUND_VARIABLE_9637 M) A)) N)))) (not (= (ho_4 k_19 (ho_4 (ho_18 BOUND_VARIABLE_9637 tptp.sh) tptp.one)) (ho_4 k_19 (ho_4 (ho_18 BOUND_VARIABLE_9640 tptp.sh) tptp.one)))) (= (ho_4 (ho_18 BOUND_VARIABLE_9637 BOUND_VARIABLE_3699) BOUND_VARIABLE_3697) (ho_4 (ho_18 BOUND_VARIABLE_9640 BOUND_VARIABLE_3699) BOUND_VARIABLE_3697)))) (=> (forall ((BOUND_VARIABLE_9614 |u_(-> tptp.subst tptp.term tptp.term)|) (BOUND_VARIABLE_3737 tptp.term) (BOUND_VARIABLE_3735 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (ho_4 (ho_18 BOUND_VARIABLE_9614 (ho_8 (ho_16 k_15 M) N)) (ho_14 (ho_13 k_12 A) N)) (ho_14 (ho_13 k_12 (ho_4 (ho_18 BOUND_VARIABLE_9614 M) A)) N)))) (not (= (ho_4 (ho_3 k_2 (ho_14 (ho_13 k_12 BOUND_VARIABLE_3735) (ho_8 (ho_7 k_6 tptp.one) tptp.sh))) BOUND_VARIABLE_3737) (ho_4 k_19 (ho_4 (ho_18 BOUND_VARIABLE_9614 tptp.sh) tptp.one)))))) (=> (forall ((BOUND_VARIABLE_9582 |u_(-> tptp.subst tptp.term tptp.term)|)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (ho_4 (ho_18 BOUND_VARIABLE_9582 (ho_8 (ho_16 k_15 M) N)) (ho_14 (ho_13 k_12 A) N)) (ho_14 (ho_13 k_12 (ho_4 (ho_18 BOUND_VARIABLE_9582 M) A)) N)))) (not (ho_5 k_17 (ho_14 (ho_13 k_12 (ho_4 k_19 (ho_4 (ho_18 BOUND_VARIABLE_9582 tptp.sh) tptp.one))) (ho_8 (ho_7 k_6 tptp.one) tptp.sh)))))) (=> (forall ((A tptp.term) (B tptp.term)) (let ((_let_1 (ho_8 (ho_7 k_6 tptp.one) tptp.sh))) (not (ho_5 k_17 (ho_14 (ho_13 k_12 (ho_4 (ho_3 k_2 (ho_14 (ho_13 k_12 A) _let_1)) B)) _let_1))))) _let_153))))))))))))))))))))))))))))))))))))))))))) (let ((_let_272 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_271))))))))) (let ((_let_273 (or))) (let ((_let_274 (not _let_153))) (let ((_let_275 (_let_274))) (let ((_let_276 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_275)) :args _let_275)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_274) _let_153))) (REFL :args (_let_154)) :args _let_273)) (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_272)))))))))))))))))))))))) :args (_let_154 true _let_153)))) (let ((_let_277 (REFL :args (_let_152)))) (let ((_let_278 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_152 3)) (CONG _let_277 (MACRO_SR_PRED_INTRO :args ((= (not _let_149) _let_144))) :args _let_273)) :args ((or _let_144 _let_152))) _let_276 :args (_let_144 true _let_152)))) (let ((_let_279 (_let_144))) (let ((_let_280 ((ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 X)))) (let ((_let_281 (ASSUME :args _let_279))) (let ((_let_282 (_let_155))) (let ((_let_283 (_let_156))) (let ((_let_284 (ho_11 (ho_10 _let_134 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22) _let_132))) (let ((_let_285 (not _let_284))) (let ((_let_286 (ho_11 (ho_10 _let_134 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) _let_132))) (let ((_let_287 (not _let_286))) (let ((_let_288 (or _let_287 _let_285 _let_140))) (let ((_let_289 (_let_150))) (let ((_let_290 (= _let_147 _let_286))) (let ((_let_291 (= _let_145 _let_284))) (let ((_let_292 (ASSUME :args (_let_140)))) (let ((_let_293 (APPLY_UF ho_11))) (let ((_let_294 (ASSUME :args (_let_137)))) (let ((_let_295 (ASSUME :args (_let_139)))) (let ((_let_296 (ASSUME :args (_let_143)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_292 _let_295 _let_294 _let_296) :args (_let_143 _let_137 _let_139 _let_140)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_296)) (CONG (REFL :args (_let_135)) _let_294 :args _let_293) (CONG (CONG (REFL :args (_let_134)) (CONG (CONG (REFL :args (k_2)) (SYMM (SYMM _let_295)) :args (APPLY_UF ho_3)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22)) :args (APPLY_UF ho_4)) :args (APPLY_UF ho_10)) (SYMM _let_294) :args _let_293) (TRUE_INTRO _let_292))) :args (_let_140 _let_139 _let_137 _let_143)) :args ((not (and _let_143 _let_137 _let_139 _let_140)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_143) _let_136))) (REFL :args ((not _let_137))) (REFL :args ((not _let_139))) (REFL :args ((not _let_140))) :args _let_273)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_288)) :args ((or _let_285 _let_287 _let_140 (not _let_288)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_291)) :args ((or _let_146 _let_284 (not _let_291)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_152 5)) (CONG _let_277 (MACRO_SR_PRED_INTRO :args ((= (not _let_146) _let_145))) :args _let_273)) :args ((or _let_145 _let_152))) _let_276 :args (_let_145 true _let_152)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_281 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_280)) :args _let_279))) _let_278 :args (_let_291 false _let_144)) :args (_let_284 false _let_145 false _let_291)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_290)) :args ((or _let_148 _let_286 (not _let_290)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_152 4)) (CONG _let_277 (MACRO_SR_PRED_INTRO :args ((= (not _let_148) _let_147))) :args _let_273)) :args ((or _let_147 _let_152))) _let_276 :args (_let_147 true _let_152)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_281 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_280)) :args _let_279))) _let_278 :args (_let_290 false _let_144)) :args (_let_286 false _let_147 false _let_290)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_289) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_289)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_152 2)) (CONG _let_277 (MACRO_SR_PRED_INTRO :args ((= (not _let_151) _let_150))) :args _let_273)) :args ((or _let_150 _let_152))) _let_276 :args (_let_150 true _let_152)) :args (_let_288 false _let_150)) :args (_let_140 false _let_284 false _let_286 false _let_288)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_283) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_CBQI_PROP)) :args _let_283)) (NOT_IMPLIES_ELIM1 _let_271) :args (_let_139 false _let_156)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_282) :args (_let_132 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_16 k_15 M)))) :args _let_282)) (NOT_IMPLIES_ELIM1 _let_272) :args (_let_137 false _let_155)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_142)) :args ((or _let_141 _let_143 (not _let_142)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_152 6)) _let_276 :args ((not _let_141) true _let_152)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_281 :args (_let_133 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_280)) :args _let_279))) _let_278 :args (_let_142 false _let_144)) :args (_let_143 true _let_141 false _let_142)) :args (false false _let_140 false _let_139 false _let_137 true _let_136)) :args (_let_131 _let_129 _let_128 _let_127 _let_125 _let_123 _let_122 _let_121 _let_119 _let_117 _let_116 _let_115 _let_114 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_104 _let_102 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_79 _let_78 _let_77 _let_75 _let_74 _let_73 _let_71 _let_69 _let_68 _let_67 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_24 _let_23 _let_22 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.63/0.83 )
% 0.63/0.83 % SZS output end Proof for ALG264^3
% 0.63/0.83 % cvc5---1.0.5 exiting
% 0.63/0.83 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------