TSTP Solution File: ALG268^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ALG268^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 16:09:06 EDT 2023
% Result : Timeout 299.88s 300.20s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : ALG268^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.16 % Command : do_cvc5 %s %d
% 0.17/0.37 % Computer : n015.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon Aug 28 04:11:55 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.23/0.52 %----Proving TH0
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 % File : ALG268^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.23/0.53 % Domain : Algebra
% 0.23/0.53 % Problem : HOAS induction lemma 3
% 0.23/0.53 % Version : [Bro09] axioms.
% 0.23/0.53 % English :
% 0.23/0.53
% 0.23/0.53 % Refs : [DHK95] Dowek et al. (1995), Higher-order Unification via Expl
% 0.23/0.53 % : [Zha08] Zhang (2008), Using LEO-II to Prove Properties of an E
% 0.23/0.53 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.23/0.53 % : [Bro09] Brown (2009), M-Set Models
% 0.23/0.53 % Source : [Ben09]
% 0.23/0.53 % Names : hoasinduction_lem3_gthm [Ben09]
% 0.23/0.53
% 0.23/0.53 % Status : Theorem
% 0.23/0.53 % Rating : 1.00 v5.2.0
% 0.23/0.53 % Syntax : Number of formulae : 238 ( 114 unt; 124 typ; 113 def)
% 0.23/0.53 % Number of atoms : 1218 ( 161 equ; 0 cnn)
% 0.23/0.53 % Maximal formula atoms : 1 ( 10 avg)
% 0.23/0.53 % Number of connectives : 1942 ( 6 ~; 0 |; 4 &; 916 @)
% 0.23/0.53 % ( 2 <=>;1014 =>; 0 <=; 0 <~>)
% 0.23/0.53 % Maximal formula depth : 1 ( 1 avg)
% 0.23/0.53 % Number of types : 3 ( 2 usr)
% 0.23/0.53 % Number of type conns : 128 ( 128 >; 0 *; 0 +; 0 <<)
% 0.23/0.53 % Number of symbols : 123 ( 122 usr; 111 con; 0-4 aty)
% 0.23/0.53 % Number of variables : 327 ( 39 ^; 283 !; 5 ?; 327 :)
% 0.23/0.53 % SPC : TH0_THM_EQU_NAR
% 0.23/0.53
% 0.23/0.53 % Comments :
% 0.23/0.53 % Bugfixes : v5.2.0 - Bugfixes in ALG003^0.ax
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 %----Include Untyped Lambda Sigma defs
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 thf(term_type,type,
% 0.23/0.53 term: $tType ).
% 0.23/0.53
% 0.23/0.53 thf(subst_type,type,
% 0.23/0.53 subst: $tType ).
% 0.23/0.53
% 0.23/0.53 thf(one_type,type,
% 0.23/0.53 one: term ).
% 0.23/0.53
% 0.23/0.53 thf(ap_type,type,
% 0.23/0.53 ap: term > term > term ).
% 0.23/0.53
% 0.23/0.53 thf(lam_type,type,
% 0.23/0.53 lam: term > term ).
% 0.23/0.53
% 0.23/0.53 thf(sub_type,type,
% 0.23/0.53 sub: term > subst > term ).
% 0.23/0.53
% 0.23/0.53 thf(id_type,type,
% 0.23/0.53 id: subst ).
% 0.23/0.53
% 0.23/0.53 thf(sh_type,type,
% 0.23/0.53 sh: subst ).
% 0.23/0.53
% 0.23/0.53 thf(push_type,type,
% 0.23/0.53 push: term > subst > subst ).
% 0.23/0.53
% 0.23/0.53 thf(comp_type,type,
% 0.23/0.53 comp: subst > subst > subst ).
% 0.23/0.53
% 0.23/0.53 thf(var_type,type,
% 0.23/0.53 var: term > $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1v2_type,type,
% 0.23/0.53 pushprop_lem1v2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1_gthm_type,type,
% 0.23/0.53 pushprop_lem1_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axmap_type,type,
% 0.23/0.53 axmap: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem0_gthm_type,type,
% 0.23/0.53 pushprop_lem0_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(shinj_type,type,
% 0.23/0.53 shinj: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1v2_type,type,
% 0.23/0.53 hoasinduction_lem1v2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1v2_gthm_type,type,
% 0.23/0.53 hoasinduction_lem1v2_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasap_type,type,
% 0.23/0.53 hoasap: subst > term > subst > term > term ).
% 0.23/0.53
% 0.23/0.53 thf(induction2lem_type,type,
% 0.23/0.53 induction2lem: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2_f_type,type,
% 0.23/0.53 hoasinduction_lem3v2_f: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axvarshift_type,type,
% 0.23/0.53 axvarshift: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj2_type,type,
% 0.23/0.53 hoasapinj2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapnotvar_gthm_type,type,
% 0.23/0.53 hoasapnotvar_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj1_type,type,
% 0.23/0.53 hoasapinj1: $o ).
% 0.23/0.53
% 0.23/0.53 thf(ulamvar1_type,type,
% 0.23/0.53 ulamvar1: $o ).
% 0.23/0.53
% 0.23/0.53 thf(induction2lem_lthm_type,type,
% 0.23/0.53 induction2lem_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2_gthm_type,type,
% 0.23/0.53 hoasinduction_lem3v2_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(apnotvar_type,type,
% 0.23/0.53 apnotvar: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lthm_orig_type,type,
% 0.23/0.53 pushprop_lthm_orig: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2_f_lthm_type,type,
% 0.23/0.53 hoasinduction_lem3v2_f_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lthm_type,type,
% 0.23/0.53 hoasinduction_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_no_psi_cond_lthm_type,type,
% 0.23/0.53 hoasinduction_no_psi_cond_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslaminj_type,type,
% 0.23/0.53 hoaslaminj: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3aaa_type,type,
% 0.23/0.53 hoasinduction_lem3aaa: $o ).
% 0.23/0.53
% 0.23/0.53 thf(induction2lem_gthm_type,type,
% 0.23/0.53 induction2lem_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3aa_lthm_type,type,
% 0.23/0.53 hoasinduction_lem3aa_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3_type,type,
% 0.23/0.53 hoasinduction_lem3: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2_type,type,
% 0.23/0.53 hoasinduction_lem2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(termmset_lthm_type,type,
% 0.23/0.53 termmset_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1_type,type,
% 0.23/0.53 hoasinduction_lem1: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotap_lthm_type,type,
% 0.23/0.53 hoaslamnotap_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1v2_lthm_type,type,
% 0.23/0.53 pushprop_lem1v2_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapnotvar_type,type,
% 0.23/0.53 hoasapnotvar: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem0_type,type,
% 0.23/0.53 hoasinduction_lem0: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_type,type,
% 0.23/0.53 hoasinduction: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_gthm_type,type,
% 0.23/0.53 hoasinduction_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axapp_type,type,
% 0.23/0.53 axapp: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotvar_lthm_type,type,
% 0.23/0.53 hoaslamnotvar_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem3v2_lthm_type,type,
% 0.23/0.53 pushprop_lem3v2_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3b_lthm_type,type,
% 0.23/0.53 hoasinduction_lem3b_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(ulamvarind_type,type,
% 0.23/0.53 ulamvarind: $o ).
% 0.23/0.53
% 0.23/0.53 thf(induction_type,type,
% 0.23/0.53 induction: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3a_lthm_type,type,
% 0.23/0.53 hoasinduction_lem3a_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(termmset_gthm_type,type,
% 0.23/0.53 termmset_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3aa_type,type,
% 0.23/0.53 hoasinduction_lem3aa: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1v2_gthm_type,type,
% 0.23/0.53 pushprop_lem1v2_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotap_gthm_type,type,
% 0.23/0.53 hoaslamnotap_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotvar_gthm_type,type,
% 0.23/0.53 hoaslamnotvar_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3b_gthm_type,type,
% 0.23/0.53 hoasinduction_lem3b_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem2v2_type,type,
% 0.23/0.53 pushprop_lem2v2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3a_gthm_type,type,
% 0.23/0.53 hoasinduction_lem3a_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axclos_type,type,
% 0.23/0.53 axclos: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axassoc_type,type,
% 0.23/0.53 axassoc: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2v2_type,type,
% 0.23/0.53 hoasinduction_lem2v2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lthm_type,type,
% 0.23/0.53 pushprop_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(apinj2_type,type,
% 0.23/0.53 apinj2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(apinj1_type,type,
% 0.23/0.53 apinj1: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj2_lthm_type,type,
% 0.23/0.53 hoasapinj2_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2a_type,type,
% 0.23/0.53 hoasinduction_lem3v2a: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj1_lthm_type,type,
% 0.23/0.53 hoasapinj1_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslaminj_lthm_type,type,
% 0.23/0.53 hoaslaminj_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axvarcons_type,type,
% 0.23/0.53 axvarcons: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslam_type,type,
% 0.23/0.53 hoaslam: subst > ( subst > term > term ) > term ).
% 0.23/0.53
% 0.23/0.53 thf(axscons_type,type,
% 0.23/0.53 axscons: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2v2_gthm_type,type,
% 0.23/0.53 hoasinduction_lem2v2_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axidr_type,type,
% 0.23/0.53 axidr: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1_type,type,
% 0.23/0.53 pushprop_lem1: $o ).
% 0.23/0.53
% 0.23/0.53 thf(laminj_type,type,
% 0.23/0.53 laminj: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3_lthm_type,type,
% 0.23/0.53 hoasinduction_lem3_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem0_type,type,
% 0.23/0.53 pushprop_lem0: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_gthm_type,type,
% 0.23/0.53 pushprop_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axabs_type,type,
% 0.23/0.53 axabs: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2a_lthm_type,type,
% 0.23/0.53 hoasinduction_lem3v2a_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2_lthm_type,type,
% 0.23/0.53 hoasinduction_lem2_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj2_gthm_type,type,
% 0.23/0.53 hoasapinj2_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_p_and_p_prime_type,type,
% 0.23/0.53 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1_lthm_type,type,
% 0.23/0.53 hoasinduction_lem1_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(lamnotap_type,type,
% 0.23/0.53 lamnotap: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj1_gthm_type,type,
% 0.23/0.53 hoasapinj1_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotvar_type,type,
% 0.23/0.53 hoaslamnotvar: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axidl_type,type,
% 0.23/0.53 axidl: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslaminj_gthm_type,type,
% 0.23/0.53 hoaslaminj_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(induction2_lthm_type,type,
% 0.23/0.53 induction2_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem0_lthm_type,type,
% 0.23/0.53 hoasinduction_lem0_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(substmonoid_lthm_type,type,
% 0.23/0.53 substmonoid_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_type,type,
% 0.23/0.53 pushprop: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3_gthm_type,type,
% 0.23/0.53 hoasinduction_lem3_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2_gthm_type,type,
% 0.23/0.53 hoasinduction_lem2_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3b_type,type,
% 0.23/0.53 hoasinduction_lem3b: $o ).
% 0.23/0.53
% 0.23/0.53 thf(substmonoid_type,type,
% 0.23/0.53 substmonoid: $o ).
% 0.23/0.53
% 0.23/0.53 thf(lamnotvar_type,type,
% 0.23/0.53 lamnotvar: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3a_type,type,
% 0.23/0.53 hoasinduction_lem3a: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1_gthm_type,type,
% 0.23/0.53 hoasinduction_lem1_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_no_psi_cond_type,type,
% 0.23/0.53 hoasinduction_no_psi_cond: $o ).
% 0.23/0.53
% 0.23/0.53 thf(induction2_gthm_type,type,
% 0.23/0.53 induction2_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem2v2_lthm_type,type,
% 0.23/0.53 pushprop_lem2v2_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasvar_type,type,
% 0.23/0.53 hoasvar: subst > term > subst > $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotap_type,type,
% 0.23/0.53 hoaslamnotap: $o ).
% 0.23/0.53
% 0.23/0.53 thf(substmonoid_gthm_type,type,
% 0.23/0.53 substmonoid_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(ulamvarsh_type,type,
% 0.23/0.53 ulamvarsh: $o ).
% 0.23/0.53
% 0.23/0.53 thf(induction2_type,type,
% 0.23/0.53 induction2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem3v2_type,type,
% 0.23/0.53 pushprop_lem3v2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem2v2_gthm_type,type,
% 0.23/0.53 pushprop_lem2v2_gthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1_lthm_type,type,
% 0.23/0.53 pushprop_lem1_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2_type,type,
% 0.23/0.53 hoasinduction_lem3v2: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axshiftcons_type,type,
% 0.23/0.53 axshiftcons: $o ).
% 0.23/0.53
% 0.23/0.53 thf(termmset_type,type,
% 0.23/0.53 termmset: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem0_lthm_type,type,
% 0.23/0.53 pushprop_lem0_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapnotvar_lthm_type,type,
% 0.23/0.53 hoasapnotvar_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2_lthm_type,type,
% 0.23/0.53 hoasinduction_lem3v2_lthm: $o ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_p_and_p_prime_type,type,
% 0.23/0.53 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.23/0.53
% 0.23/0.53 thf(axvarid_type,type,
% 0.23/0.53 axvarid: $o ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lthm_3_type,type,
% 0.23/0.53 hoasinduction_lthm_3: $o ).
% 0.23/0.53
% 0.23/0.53 thf(axapp,definition,
% 0.23/0.53 ( axapp
% 0.23/0.53 = ( ! [A: term,B: term,M: subst] :
% 0.23/0.53 ( ( sub @ ( ap @ A @ B ) @ M )
% 0.23/0.53 = ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axvarcons,definition,
% 0.23/0.53 ( axvarcons
% 0.23/0.53 = ( ! [A: term,M: subst] :
% 0.23/0.53 ( ( sub @ one @ ( push @ A @ M ) )
% 0.23/0.53 = A ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axvarid,definition,
% 0.23/0.53 ( axvarid
% 0.23/0.53 = ( ! [A: term] :
% 0.23/0.53 ( ( sub @ A @ id )
% 0.23/0.53 = A ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axabs,definition,
% 0.23/0.53 ( axabs
% 0.23/0.53 = ( ! [A: term,M: subst] :
% 0.23/0.53 ( ( sub @ ( lam @ A ) @ M )
% 0.23/0.53 = ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axclos,definition,
% 0.23/0.53 ( axclos
% 0.23/0.53 = ( ! [A: term,M: subst,N: subst] :
% 0.23/0.53 ( ( sub @ ( sub @ A @ M ) @ N )
% 0.23/0.53 = ( sub @ A @ ( comp @ M @ N ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axidl,definition,
% 0.23/0.53 ( axidl
% 0.23/0.53 = ( ! [M: subst] :
% 0.23/0.53 ( ( comp @ id @ M )
% 0.23/0.53 = M ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axshiftcons,definition,
% 0.23/0.53 ( axshiftcons
% 0.23/0.53 = ( ! [A: term,M: subst] :
% 0.23/0.53 ( ( comp @ sh @ ( push @ A @ M ) )
% 0.23/0.53 = M ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axassoc,definition,
% 0.23/0.53 ( axassoc
% 0.23/0.53 = ( ! [M: subst,N: subst,K: subst] :
% 0.23/0.53 ( ( comp @ ( comp @ M @ N ) @ K )
% 0.23/0.53 = ( comp @ M @ ( comp @ N @ K ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axmap,definition,
% 0.23/0.53 ( axmap
% 0.23/0.53 = ( ! [A: term,M: subst,N: subst] :
% 0.23/0.53 ( ( comp @ ( push @ A @ M ) @ N )
% 0.23/0.53 = ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axidr,definition,
% 0.23/0.53 ( axidr
% 0.23/0.53 = ( ! [M: subst] :
% 0.23/0.53 ( ( comp @ M @ id )
% 0.23/0.53 = M ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axvarshift,definition,
% 0.23/0.53 ( axvarshift
% 0.23/0.53 = ( ( push @ one @ sh )
% 0.23/0.53 = id ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(axscons,definition,
% 0.23/0.53 ( axscons
% 0.23/0.53 = ( ! [M: subst] :
% 0.23/0.53 ( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
% 0.23/0.53 = M ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ulamvar1,definition,
% 0.23/0.53 ( ulamvar1
% 0.23/0.53 = ( var @ one ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ulamvarsh,definition,
% 0.23/0.53 ( ulamvarsh
% 0.23/0.53 = ( ! [A: term] :
% 0.23/0.53 ( ( var @ A )
% 0.23/0.53 => ( var @ ( sub @ A @ sh ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ulamvarind,definition,
% 0.23/0.53 ( ulamvarind
% 0.23/0.53 = ( ! [P: term > $o] :
% 0.23/0.53 ( ( P @ one )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( var @ A )
% 0.23/0.53 => ( ( P @ A )
% 0.23/0.53 => ( P @ ( sub @ A @ sh ) ) ) )
% 0.23/0.53 => ! [A: term] :
% 0.23/0.53 ( ( var @ A )
% 0.23/0.53 => ( P @ A ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(apinj1,definition,
% 0.23/0.53 ( apinj1
% 0.23/0.53 = ( ! [A: term,B: term,C: term,D: term] :
% 0.23/0.53 ( ( ( ap @ A @ C )
% 0.23/0.53 = ( ap @ B @ D ) )
% 0.23/0.53 => ( A = B ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(apinj2,definition,
% 0.23/0.53 ( apinj2
% 0.23/0.53 = ( ! [A: term,B: term,C: term,D: term] :
% 0.23/0.53 ( ( ( ap @ A @ C )
% 0.23/0.53 = ( ap @ B @ D ) )
% 0.23/0.53 => ( C = D ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(laminj,definition,
% 0.23/0.53 ( laminj
% 0.23/0.53 = ( ! [A: term,B: term] :
% 0.23/0.53 ( ( ( lam @ A )
% 0.23/0.53 = ( lam @ B ) )
% 0.23/0.53 => ( A = B ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(shinj,definition,
% 0.23/0.53 ( shinj
% 0.23/0.53 = ( ! [A: term,B: term] :
% 0.23/0.53 ( ( ( sub @ A @ sh )
% 0.23/0.53 = ( sub @ B @ sh ) )
% 0.23/0.53 => ( A = B ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(lamnotap,definition,
% 0.23/0.53 ( lamnotap
% 0.23/0.53 = ( ! [A: term,B: term,C: term] :
% 0.23/0.53 ( ( lam @ A )
% 0.23/0.53 != ( ap @ B @ C ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(apnotvar,definition,
% 0.23/0.53 ( apnotvar
% 0.23/0.53 = ( ! [A: term,B: term] :
% 0.23/0.53 ~ ( var @ ( ap @ A @ B ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(lamnotvar,definition,
% 0.23/0.53 ( lamnotvar
% 0.23/0.53 = ( ! [A: term] :
% 0.23/0.53 ~ ( var @ ( lam @ A ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(induction,definition,
% 0.23/0.53 ( induction
% 0.23/0.53 = ( ! [P: term > $o] :
% 0.23/0.53 ( ! [A: term] :
% 0.23/0.53 ( ( var @ A )
% 0.23/0.53 => ( P @ A ) )
% 0.23/0.53 => ( ! [A: term,B: term] :
% 0.23/0.53 ( ( P @ A )
% 0.23/0.53 => ( ( P @ B )
% 0.23/0.53 => ( P @ ( ap @ A @ B ) ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( P @ A )
% 0.23/0.53 => ( P @ ( lam @ A ) ) )
% 0.23/0.53 => ! [A: term] : ( P @ A ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_p_and_p_prime,definition,
% 0.23/0.53 ( pushprop_p_and_p_prime
% 0.23/0.53 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.23/0.53 ! [X: term] :
% 0.23/0.53 ( ( Q @ X )
% 0.23/0.53 <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem0,definition,
% 0.23/0.53 ( pushprop_lem0
% 0.23/0.53 = ( ! [P: term > $o,A: term,M: subst] :
% 0.23/0.53 ? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem0_gthm,definition,
% 0.23/0.53 ( pushprop_lem0_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => pushprop_lem0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem0_lthm,definition,
% 0.23/0.53 pushprop_lem0_lthm = pushprop_lem0 ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1,definition,
% 0.23/0.53 ( pushprop_lem1
% 0.23/0.53 = ( ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.23/0.53 ( ( P @ A )
% 0.23/0.53 => ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1_gthm,definition,
% 0.23/0.53 ( pushprop_lem1_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => pushprop_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1_lthm,definition,
% 0.23/0.53 ( pushprop_lem1_lthm
% 0.23/0.53 = ( axvarcons
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => pushprop_lem1 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1v2,definition,
% 0.23/0.53 ( pushprop_lem1v2
% 0.23/0.53 = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.23/0.53 ( ( P @ A )
% 0.23/0.53 => ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
% 0.23/0.53 => ( Q @ one ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1v2_gthm,definition,
% 0.23/0.53 ( pushprop_lem1v2_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => pushprop_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem1v2_lthm,definition,
% 0.23/0.53 ( pushprop_lem1v2_lthm
% 0.23/0.53 = ( axvarcons
% 0.23/0.53 => pushprop_lem1v2 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem2v2,definition,
% 0.23/0.53 ( pushprop_lem2v2
% 0.23/0.53 = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.23/0.53 ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
% 0.23/0.53 => ( ! [B: term] :
% 0.23/0.53 ( ( var @ B )
% 0.23/0.53 => ( P @ ( sub @ B @ M ) ) )
% 0.23/0.53 => ! [C: term] :
% 0.23/0.53 ( ( var @ C )
% 0.23/0.53 => ( ( Q @ C )
% 0.23/0.53 => ( Q @ ( sub @ C @ sh ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem2v2_gthm,definition,
% 0.23/0.53 ( pushprop_lem2v2_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => pushprop_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem2v2_lthm,definition,
% 0.23/0.53 ( pushprop_lem2v2_lthm
% 0.23/0.53 = ( axclos
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => pushprop_lem2v2 ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem3v2,definition,
% 0.23/0.53 ( pushprop_lem3v2
% 0.23/0.53 = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.23/0.53 ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
% 0.23/0.53 => ( ! [B: term] :
% 0.23/0.53 ( ( var @ B )
% 0.23/0.53 => ( Q @ B ) )
% 0.23/0.53 => ! [B: term] :
% 0.23/0.53 ( ( var @ B )
% 0.23/0.53 => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lem3v2_lthm,definition,
% 0.23/0.53 pushprop_lem3v2_lthm = pushprop_lem3v2 ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop,definition,
% 0.23/0.53 ( pushprop
% 0.23/0.53 = ( ! [P: term > $o,A: term,M: subst] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( var @ B )
% 0.23/0.53 => ( P @ ( sub @ B @ M ) ) )
% 0.23/0.53 => ( ( P @ A )
% 0.23/0.53 => ! [B: term] :
% 0.23/0.53 ( ( var @ B )
% 0.23/0.53 => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_gthm,definition,
% 0.23/0.53 ( pushprop_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lthm_orig,definition,
% 0.23/0.53 ( pushprop_lthm_orig
% 0.23/0.53 = ( ulamvar1
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => pushprop ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(pushprop_lthm,definition,
% 0.23/0.53 ( pushprop_lthm
% 0.23/0.53 = ( pushprop_lem0
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => pushprop ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(induction2lem,definition,
% 0.23/0.53 ( induction2lem
% 0.23/0.53 = ( ! [P: term > $o] :
% 0.23/0.53 ( ! [A: term,B: term] :
% 0.23/0.53 ( ( P @ A )
% 0.23/0.53 => ( ( P @ B )
% 0.23/0.53 => ( P @ ( ap @ A @ B ) ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( P @ B )
% 0.23/0.53 => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.23/0.53 => ( P @ ( lam @ A ) ) )
% 0.23/0.53 => ! [A: term,M: subst] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( var @ B )
% 0.23/0.53 => ( P @ ( sub @ B @ M ) ) )
% 0.23/0.53 => ( P @ ( sub @ A @ M ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(induction2lem_gthm,definition,
% 0.23/0.53 ( induction2lem_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => induction2lem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(induction2lem_lthm,definition,
% 0.23/0.53 ( induction2lem_lthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => induction2lem ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(induction2,definition,
% 0.23/0.53 ( induction2
% 0.23/0.53 = ( ! [P: term > $o] :
% 0.23/0.53 ( ! [A: term] :
% 0.23/0.53 ( ( var @ A )
% 0.23/0.53 => ( P @ A ) )
% 0.23/0.53 => ( ! [A: term,B: term] :
% 0.23/0.53 ( ( P @ A )
% 0.23/0.53 => ( ( P @ B )
% 0.23/0.53 => ( P @ ( ap @ A @ B ) ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( P @ B )
% 0.23/0.53 => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.23/0.53 => ( P @ ( lam @ A ) ) )
% 0.23/0.53 => ! [A: term] : ( P @ A ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(induction2_gthm,definition,
% 0.23/0.53 ( induction2_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(induction2_lthm,definition,
% 0.23/0.53 ( induction2_lthm
% 0.23/0.53 = ( axvarid
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => induction2 ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(substmonoid,definition,
% 0.23/0.53 ( substmonoid
% 0.23/0.53 = ( ! [M: subst,N: subst,K: subst] :
% 0.23/0.53 ( ( comp @ ( comp @ M @ N ) @ K )
% 0.23/0.53 = ( comp @ M @ ( comp @ N @ K ) ) )
% 0.23/0.53 & ! [M: subst] :
% 0.23/0.53 ( ( comp @ id @ M )
% 0.23/0.53 = M )
% 0.23/0.53 & ! [M: subst] :
% 0.23/0.53 ( ( comp @ M @ id )
% 0.23/0.53 = M ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(substmonoid_gthm,definition,
% 0.23/0.53 ( substmonoid_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => substmonoid ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(substmonoid_lthm,definition,
% 0.23/0.53 ( substmonoid_lthm
% 0.23/0.53 = ( axidl
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axidr
% 0.23/0.53 => substmonoid ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(termmset,definition,
% 0.23/0.53 ( termmset
% 0.23/0.53 = ( ! [A: term,M: subst,N: subst] :
% 0.23/0.53 ( ( sub @ ( sub @ A @ M ) @ N )
% 0.23/0.53 = ( sub @ A @ ( comp @ M @ N ) ) )
% 0.23/0.53 & ! [A: term] :
% 0.23/0.53 ( ( sub @ A @ id )
% 0.23/0.53 = A ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(termmset_gthm,definition,
% 0.23/0.53 ( termmset_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(termmset_lthm,definition,
% 0.23/0.53 ( termmset_lthm
% 0.23/0.53 = ( axvarid
% 0.23/0.53 => ( axclos
% 0.23/0.53 => termmset ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasap,definition,
% 0.23/0.53 ( hoasap
% 0.23/0.53 = ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslam,definition,
% 0.23/0.53 ( hoaslam
% 0.23/0.53 = ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasvar,definition,
% 0.23/0.53 ( hoasvar
% 0.23/0.53 = ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj1,definition,
% 0.23/0.53 ( hoasapinj1
% 0.23/0.53 = ( ! [A: term,B: term,C: term,D: term] :
% 0.23/0.53 ( ( ( hoasap @ id @ A @ id @ C )
% 0.23/0.53 = ( hoasap @ id @ B @ id @ D ) )
% 0.23/0.53 => ( A = B ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj1_gthm,definition,
% 0.23/0.53 ( hoasapinj1_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => hoasapinj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj1_lthm,definition,
% 0.23/0.53 ( hoasapinj1_lthm
% 0.23/0.53 = ( axvarid
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => hoasapinj1 ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj2,definition,
% 0.23/0.53 ( hoasapinj2
% 0.23/0.53 = ( ! [A: term,B: term,C: term,D: term] :
% 0.23/0.53 ( ( ( hoasap @ id @ A @ id @ C )
% 0.23/0.53 = ( hoasap @ id @ B @ id @ D ) )
% 0.23/0.53 => ( C = D ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj2_gthm,definition,
% 0.23/0.53 ( hoasapinj2_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => hoasapinj2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapinj2_lthm,definition,
% 0.23/0.53 ( hoasapinj2_lthm
% 0.23/0.53 = ( apinj2
% 0.23/0.53 => hoasapinj2 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslaminj,definition,
% 0.23/0.53 ( hoaslaminj
% 0.23/0.53 = ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ! [G: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( G @ M @ A ) @ N )
% 0.23/0.53 = ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ( ( ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 = ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
% 0.23/0.53 => ! [M: subst,A: term] :
% 0.23/0.53 ( ( F @ M @ A )
% 0.23/0.53 = ( G @ M @ A ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslaminj_gthm,definition,
% 0.23/0.53 ( hoaslaminj_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslaminj_lthm,definition,
% 0.23/0.53 ( hoaslaminj_lthm
% 0.23/0.53 = ( axvarcons
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( laminj
% 0.23/0.53 => hoaslaminj ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotap,definition,
% 0.23/0.53 ( hoaslamnotap
% 0.23/0.53 = ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ! [A: term,B: term] :
% 0.23/0.53 ( ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,C: term] : ( F @ M @ C ) )
% 0.23/0.53 != ( hoasap @ id @ A @ id @ B ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotap_gthm,definition,
% 0.23/0.53 ( hoaslamnotap_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotap_lthm,definition,
% 0.23/0.53 ( hoaslamnotap_lthm
% 0.23/0.53 = ( lamnotap
% 0.23/0.53 => hoaslamnotap ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotvar,definition,
% 0.23/0.53 ( hoaslamnotvar
% 0.23/0.53 = ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ~ ( hoasvar @ id
% 0.23/0.53 @ ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 @ id ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotvar_gthm,definition,
% 0.23/0.53 ( hoaslamnotvar_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoaslamnotvar_lthm,definition,
% 0.23/0.53 ( hoaslamnotvar_lthm
% 0.23/0.53 = ( axvarid
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => hoaslamnotvar ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapnotvar,definition,
% 0.23/0.53 ( hoasapnotvar
% 0.23/0.53 = ( ! [A: term,B: term] :
% 0.23/0.53 ~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapnotvar_gthm,definition,
% 0.23/0.53 ( hoasapnotvar_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasapnotvar_lthm,definition,
% 0.23/0.53 ( hoasapnotvar_lthm
% 0.23/0.53 = ( axvarid
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => hoasapnotvar ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_p_and_p_prime,definition,
% 0.23/0.53 ( hoasinduction_p_and_p_prime
% 0.23/0.53 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.23/0.53 ! [X: term] :
% 0.23/0.53 ( ( Q @ X )
% 0.23/0.53 <=> ( P @ id @ X @ id ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem0,definition,
% 0.23/0.53 ( hoasinduction_lem0
% 0.23/0.53 = ( ! [P: subst > term > subst > $o] :
% 0.23/0.53 ? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem0_lthm,definition,
% 0.23/0.53 hoasinduction_lem0_lthm = hoasinduction_lem0 ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1v2,definition,
% 0.23/0.53 ( hoasinduction_lem1v2
% 0.23/0.53 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.23/0.53 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.23/0.53 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.23/0.53 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( hoasvar @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ A @ id ) )
% 0.23/0.53 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.23/0.53 => ! [A: term] :
% 0.23/0.53 ( ( var @ A )
% 0.23/0.53 => ( Q @ A ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1v2_gthm,definition,
% 0.23/0.53 ( hoasinduction_lem1v2_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2v2,definition,
% 0.23/0.53 ( hoasinduction_lem2v2
% 0.23/0.53 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.23/0.53 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.23/0.53 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.23/0.53 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.23/0.53 => ( ! [A: term,B: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( ( P @ id @ B @ id )
% 0.23/0.53 => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
% 0.23/0.53 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.23/0.53 => ! [A: term,B: term] :
% 0.23/0.53 ( ( Q @ A )
% 0.23/0.53 => ( ( Q @ B )
% 0.23/0.53 => ( Q @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2v2_gthm,definition,
% 0.23/0.53 ( hoasinduction_lem2v2_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2_f,definition,
% 0.23/0.53 ( hoasinduction_lem3v2_f
% 0.23/0.53 = ( ! [B: term] :
% 0.23/0.53 ? [F: subst > term > term] :
% 0.23/0.53 ! [A: term,M: subst] :
% 0.23/0.53 ( ( F @ M @ A )
% 0.23/0.53 = ( sub @ B @ ( push @ A @ M ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2_f_lthm,definition,
% 0.23/0.53 hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2,definition,
% 0.23/0.53 ( hoasinduction_lem3v2
% 0.23/0.53 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.23/0.53 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.23/0.53 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.23/0.53 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.23/0.53 => ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.23/0.53 => ( P @ id
% 0.23/0.53 @ ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 @ id ) ) )
% 0.23/0.53 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.23/0.53 => ! [A: term] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( Q @ B )
% 0.23/0.53 => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.23/0.53 => ( Q @ ( lam @ A ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2_gthm,definition,
% 0.23/0.53 ( hoasinduction_lem3v2_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => hoasinduction_lem3v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2_lthm,definition,
% 0.23/0.53 ( hoasinduction_lem3v2_lthm
% 0.23/0.53 = ( axvarid
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axmap
% 0.23/0.53 => hoasinduction_lem3v2 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2a,definition,
% 0.23/0.53 ( hoasinduction_lem3v2a
% 0.23/0.53 = ( ! [P: subst > term > subst > $o,Q: term > $o] :
% 0.23/0.53 ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.23/0.53 => ( P @ id
% 0.23/0.53 @ ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 @ id ) ) )
% 0.23/0.53 => ( ( hoasinduction_p_and_p_prime @ P @ Q )
% 0.23/0.53 => ! [A: term] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( Q @ B )
% 0.23/0.53 => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.23/0.53 => ( Q @ ( lam @ A ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3v2a_lthm,definition,
% 0.23/0.53 ( hoasinduction_lem3v2a_lthm
% 0.23/0.53 = ( hoasinduction_lem3v2_f
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axmap
% 0.23/0.53 => hoasinduction_lem3v2a ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1,definition,
% 0.23/0.53 ( hoasinduction_lem1
% 0.23/0.53 = ( ! [P: subst > term > subst > $o] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.23/0.53 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.23/0.53 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.23/0.53 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( hoasvar @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ A @ id ) )
% 0.23/0.53 => ! [A: term] :
% 0.23/0.53 ( ( var @ A )
% 0.23/0.53 => ( P @ id @ A @ id ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1_gthm,definition,
% 0.23/0.53 ( hoasinduction_lem1_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem1_lthm,definition,
% 0.23/0.53 ( hoasinduction_lem1_lthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2,definition,
% 0.23/0.53 ( hoasinduction_lem2
% 0.23/0.53 = ( ! [P: subst > term > subst > $o] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.23/0.53 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.23/0.53 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.23/0.53 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.23/0.53 => ( ! [A: term,B: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( ( P @ id @ B @ id )
% 0.23/0.53 => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
% 0.23/0.53 => ! [A: term,B: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( ( P @ id @ B @ id )
% 0.23/0.53 => ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2_gthm,definition,
% 0.23/0.53 ( hoasinduction_lem2_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem2_lthm,definition,
% 0.23/0.53 ( hoasinduction_lem2_lthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3aa,definition,
% 0.23/0.53 ( hoasinduction_lem3aa
% 0.23/0.53 = ( ! [P: subst > term > subst > $o] :
% 0.23/0.53 ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.23/0.53 => ( P @ id
% 0.23/0.53 @ ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 @ id ) ) )
% 0.23/0.53 => ! [A: term] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( P @ id @ B @ id )
% 0.23/0.53 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.23/0.53 => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3aa_lthm,definition,
% 0.23/0.53 ( hoasinduction_lem3aa_lthm
% 0.23/0.53 = ( axclos
% 0.23/0.53 => ( axmap
% 0.23/0.53 => hoasinduction_lem3aa ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3aaa,definition,
% 0.23/0.53 ( hoasinduction_lem3aaa
% 0.23/0.53 = ( ! [P: subst > term > subst > $o] :
% 0.23/0.53 ( ! [F: subst > term > term] :
% 0.23/0.53 ( ? [C: term] :
% 0.23/0.53 ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
% 0.23/0.53 & ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.23/0.53 => ( P @ id
% 0.23/0.53 @ ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 @ id ) ) )
% 0.23/0.53 => ! [A: term] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( P @ id @ B @ id )
% 0.23/0.53 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.23/0.53 => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3,definition,
% 0.23/0.53 ( hoasinduction_lem3
% 0.23/0.53 = ( ! [P: subst > term > subst > $o] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.23/0.53 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.23/0.53 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.23/0.53 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.23/0.53 => ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.23/0.53 => ( P @ id
% 0.23/0.53 @ ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 @ id ) ) )
% 0.23/0.53 => ! [A: term] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( P @ id @ B @ id )
% 0.23/0.53 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.23/0.53 => ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3_gthm,definition,
% 0.23/0.53 ( hoasinduction_lem3_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => ( hoasinduction_lem1
% 0.23/0.53 => ( hoasinduction_lem2
% 0.23/0.53 => hoasinduction_lem3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3_lthm,definition,
% 0.23/0.53 ( hoasinduction_lem3_lthm
% 0.23/0.53 = ( axvarid
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( hoasinduction_lem3aa
% 0.23/0.53 => hoasinduction_lem3 ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3a,definition,
% 0.23/0.53 ( hoasinduction_lem3a
% 0.23/0.53 = ( ! [P: subst > term > subst > $o] :
% 0.23/0.53 ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.23/0.53 => ( P @ id
% 0.23/0.53 @ ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 @ id ) ) )
% 0.23/0.53 => ! [A: term] :
% 0.23/0.53 ( ! [B: term] :
% 0.23/0.53 ( ( P @ id @ B @ id )
% 0.23/0.53 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.23/0.53 => ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3a_gthm,definition,
% 0.23/0.53 ( hoasinduction_lem3a_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => ( hoasinduction_lem1
% 0.23/0.53 => ( hoasinduction_lem2
% 0.23/0.53 => hoasinduction_lem3a ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3a_lthm,definition,
% 0.23/0.53 ( hoasinduction_lem3a_lthm
% 0.23/0.53 = ( axvarid
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( hoasinduction_lem3aa
% 0.23/0.53 => hoasinduction_lem3a ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3b,definition,
% 0.23/0.53 ( hoasinduction_lem3b
% 0.23/0.53 = ( ! [B: term] :
% 0.23/0.53 ? [F: subst > term > term] :
% 0.23/0.53 ( ( sub @ B @ ( push @ one @ sh ) )
% 0.23/0.53 = ( F @ sh @ one ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3b_gthm,definition,
% 0.23/0.53 ( hoasinduction_lem3b_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => ( hoasinduction_lem1
% 0.23/0.53 => ( hoasinduction_lem2
% 0.23/0.53 => hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lem3b_lthm,definition,
% 0.23/0.53 hoasinduction_lem3b_lthm = hoasinduction_lem3b ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction,definition,
% 0.23/0.53 ( hoasinduction
% 0.23/0.53 = ( ! [P: subst > term > subst > $o] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ M @ A @ ( comp @ K @ N ) )
% 0.23/0.53 => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.23/0.53 => ( ! [M: subst,A: term,N: subst,K: subst] :
% 0.23/0.53 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.23/0.53 => ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( hoasvar @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ A @ id ) )
% 0.23/0.53 => ( ! [A: term,B: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( ( P @ id @ B @ id )
% 0.23/0.53 => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
% 0.23/0.53 => ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.23/0.53 => ( P @ id
% 0.23/0.53 @ ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 @ id ) ) )
% 0.23/0.53 => ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_gthm,definition,
% 0.23/0.53 ( hoasinduction_gthm
% 0.23/0.53 = ( axapp
% 0.23/0.53 => ( axvarcons
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( axabs
% 0.23/0.53 => ( axclos
% 0.23/0.53 => ( axidl
% 0.23/0.53 => ( axshiftcons
% 0.23/0.53 => ( axassoc
% 0.23/0.53 => ( axmap
% 0.23/0.53 => ( axidr
% 0.23/0.53 => ( axvarshift
% 0.23/0.53 => ( axscons
% 0.23/0.53 => ( ulamvar1
% 0.23/0.53 => ( ulamvarsh
% 0.23/0.53 => ( ulamvarind
% 0.23/0.53 => ( apinj1
% 0.23/0.53 => ( apinj2
% 0.23/0.53 => ( laminj
% 0.23/0.53 => ( shinj
% 0.23/0.53 => ( lamnotap
% 0.23/0.53 => ( apnotvar
% 0.23/0.53 => ( lamnotvar
% 0.23/0.53 => ( induction
% 0.23/0.53 => ( pushprop
% 0.23/0.53 => ( induction2lem
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( substmonoid
% 0.23/0.53 => ( termmset
% 0.23/0.53 => ( hoasapinj1
% 0.23/0.53 => ( hoasapinj2
% 0.23/0.53 => ( hoaslaminj
% 0.23/0.53 => ( hoaslamnotap
% 0.23/0.53 => ( hoaslamnotvar
% 0.23/0.53 => ( hoasapnotvar
% 0.23/0.53 => ( hoasinduction_lem1
% 0.23/0.53 => ( hoasinduction_lem2
% 0.23/0.53 => ( hoasinduction_lem3
% 0.23/0.53 => hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lthm,definition,
% 0.23/0.53 ( hoasinduction_lthm
% 0.23/0.53 = ( induction2
% 0.23/0.53 => ( hoasinduction_lem1
% 0.23/0.53 => ( hoasinduction_lem2
% 0.23/0.53 => ( hoasinduction_lem3
% 0.23/0.53 => hoasinduction ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_lthm_3,definition,
% 0.23/0.53 ( hoasinduction_lthm_3
% 0.23/0.53 = ( hoasinduction_lem0
% 0.23/0.53 => ( induction2
% 0.23/0.53 => ( axvarid
% 0.23/0.53 => ( hoasinduction_lem3v2a
% 0.23/0.53 => hoasinduction ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_no_psi_cond,definition,
% 0.23/0.53 ( hoasinduction_no_psi_cond
% 0.23/0.53 = ( ! [P: subst > term > subst > $o] :
% 0.23/0.53 ( ! [A: term,B: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( ( P @ id @ B @ id )
% 0.23/0.53 => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
% 0.23/0.53 => ( ! [F: subst > term > term] :
% 0.23/0.53 ( ! [M: subst,A: term,N: subst] :
% 0.23/0.53 ( ( sub @ ( F @ M @ A ) @ N )
% 0.23/0.53 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.23/0.53 => ( ! [A: term] :
% 0.23/0.53 ( ( P @ id @ A @ id )
% 0.23/0.53 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.23/0.53 => ( P @ id
% 0.23/0.53 @ ( hoaslam @ id
% 0.23/0.53 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.23/0.53 @ id ) ) )
% 0.23/0.53 => ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(hoasinduction_no_psi_cond_lthm,definition,
% 0.23/0.58 ( hoasinduction_no_psi_cond_lthm
% 0.23/0.58 = ( hoasinduction_lem0
% 0.23/0.58 => ( induction2
% 0.23/0.58 => ( axvarid
% 0.23/0.58 => ( hoasinduction_lem3v2a
% 0.23/0.58 => hoasinduction_no_psi_cond ) ) ) ) ) ).
% 0.23/0.58
% 0.23/0.58 %------------------------------------------------------------------------------
% 0.23/0.58 %------------------------------------------------------------------------------
% 0.23/0.58 thf(thm,conjecture,
% 0.23/0.58 hoasinduction_lem3_gthm ).
% 0.23/0.58
% 0.23/0.58 %------------------------------------------------------------------------------
% 0.23/0.58 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.sbHHyoc3Hl/cvc5---1.0.5_2023.p...
% 0.23/0.58 (declare-sort $$unsorted 0)
% 0.23/0.58 (declare-sort tptp.term 0)
% 0.23/0.58 (declare-sort tptp.subst 0)
% 0.23/0.58 (declare-fun tptp.one () tptp.term)
% 0.23/0.58 (declare-fun tptp.ap (tptp.term tptp.term) tptp.term)
% 0.23/0.58 (declare-fun tptp.lam (tptp.term) tptp.term)
% 0.23/0.58 (declare-fun tptp.sub (tptp.term tptp.subst) tptp.term)
% 0.23/0.58 (declare-fun tptp.id () tptp.subst)
% 0.23/0.58 (declare-fun tptp.sh () tptp.subst)
% 0.23/0.58 (declare-fun tptp.push (tptp.term tptp.subst) tptp.subst)
% 0.23/0.58 (declare-fun tptp.comp (tptp.subst tptp.subst) tptp.subst)
% 0.23/0.58 (declare-fun tptp.var (tptp.term) Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem1v2 () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem1_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.axmap () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem0_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.shinj () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem1v2 () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem1v2_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasap (tptp.subst tptp.term tptp.subst tptp.term) tptp.term)
% 0.23/0.58 (declare-fun tptp.induction2lem () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3v2_f () Bool)
% 0.23/0.58 (declare-fun tptp.axvarshift () Bool)
% 0.23/0.58 (declare-fun tptp.hoasapinj2 () Bool)
% 0.23/0.58 (declare-fun tptp.hoasapnotvar_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasapinj1 () Bool)
% 0.23/0.58 (declare-fun tptp.ulamvar1 () Bool)
% 0.23/0.58 (declare-fun tptp.induction2lem_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3v2_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.apnotvar () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lthm_orig () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3v2_f_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_no_psi_cond_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoaslaminj () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3aaa () Bool)
% 0.23/0.58 (declare-fun tptp.induction2lem_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3aa_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3 () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem2 () Bool)
% 0.23/0.58 (declare-fun tptp.termmset_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem1 () Bool)
% 0.23/0.58 (declare-fun tptp.hoaslamnotap_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem1v2_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasapnotvar () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem0 () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.axapp () Bool)
% 0.23/0.58 (declare-fun tptp.hoaslamnotvar_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem3v2_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3b_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.ulamvarind () Bool)
% 0.23/0.58 (declare-fun tptp.induction () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3a_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.termmset_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3aa () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem1v2_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoaslamnotap_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoaslamnotvar_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3b_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem2v2 () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3a_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.axclos () Bool)
% 0.23/0.58 (declare-fun tptp.axassoc () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem2v2 () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.apinj2 () Bool)
% 0.23/0.58 (declare-fun tptp.apinj1 () Bool)
% 0.23/0.58 (declare-fun tptp.hoasapinj2_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3v2a () Bool)
% 0.23/0.58 (declare-fun tptp.hoasapinj1_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoaslaminj_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.axvarcons () Bool)
% 0.23/0.58 (declare-fun tptp.hoaslam (tptp.subst (-> tptp.subst tptp.term tptp.term)) tptp.term)
% 0.23/0.58 (declare-fun tptp.axscons () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem2v2_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.axidr () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem1 () Bool)
% 0.23/0.58 (declare-fun tptp.laminj () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem0 () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.axabs () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3v2a_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem2_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasapinj2_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_p_and_p_prime ((-> tptp.subst tptp.term tptp.subst Bool) (-> tptp.term Bool)) Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem1_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.lamnotap () Bool)
% 0.23/0.58 (declare-fun tptp.hoasapinj1_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoaslamnotvar () Bool)
% 0.23/0.58 (declare-fun tptp.axidl () Bool)
% 0.23/0.58 (declare-fun tptp.hoaslaminj_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.induction2_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem0_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.substmonoid_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem2_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3b () Bool)
% 0.23/0.58 (declare-fun tptp.substmonoid () Bool)
% 0.23/0.58 (declare-fun tptp.lamnotvar () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3a () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem1_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_no_psi_cond () Bool)
% 0.23/0.58 (declare-fun tptp.induction2_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem2v2_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasvar (tptp.subst tptp.term tptp.subst) Bool)
% 0.23/0.58 (declare-fun tptp.hoaslamnotap () Bool)
% 0.23/0.58 (declare-fun tptp.substmonoid_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.ulamvarsh () Bool)
% 0.23/0.58 (declare-fun tptp.induction2 () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem3v2 () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem2v2_gthm () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem1_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3v2 () Bool)
% 0.23/0.58 (declare-fun tptp.axshiftcons () Bool)
% 0.23/0.58 (declare-fun tptp.termmset () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_lem0_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasapnotvar_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lem3v2_lthm () Bool)
% 0.23/0.58 (declare-fun tptp.pushprop_p_and_p_prime (tptp.term tptp.subst (-> tptp.term Bool) (-> tptp.term Bool)) Bool)
% 0.23/0.58 (declare-fun tptp.axvarid () Bool)
% 0.23/0.58 (declare-fun tptp.hoasinduction_lthm_3 () Bool)
% 0.23/0.58 (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))))))
% 0.23/0.58 (assert (= tptp.axvarcons (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ tptp.sub tptp.one) (@ (@ tptp.push A) M)) A))))
% 0.23/0.58 (assert (= tptp.axvarid (forall ((A tptp.term)) (= (@ (@ tptp.sub A) tptp.id) A))))
% 0.23/0.58 (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))))))))
% 0.23/0.58 (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)))))))
% 0.23/0.58 (assert (= tptp.axidl (forall ((M tptp.subst)) (= (@ (@ tptp.comp tptp.id) M) M))))
% 0.23/0.58 (assert (= tptp.axshiftcons (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ tptp.comp tptp.sh) (@ (@ tptp.push A) M)) M))))
% 0.23/0.58 (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)))))))
% 0.23/0.58 (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))))))
% 0.23/0.58 (assert (= tptp.axidr (forall ((M tptp.subst)) (= (@ (@ tptp.comp M) tptp.id) M))))
% 0.23/0.58 (assert (= tptp.axvarshift (= (@ (@ tptp.push tptp.one) tptp.sh) tptp.id)))
% 0.23/0.58 (assert (= tptp.axscons (forall ((M tptp.subst)) (= (@ (@ tptp.push (@ (@ tptp.sub tptp.one) M)) (@ (@ tptp.comp tptp.sh) M)) M))))
% 0.23/0.58 (assert (= tptp.ulamvar1 (@ tptp.var tptp.one)))
% 0.23/0.58 (assert (= tptp.ulamvarsh (forall ((A tptp.term)) (=> (@ tptp.var A) (@ tptp.var (@ (@ tptp.sub A) tptp.sh))))))
% 0.23/0.58 (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))))))))
% 0.23/0.58 (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)))))
% 0.23/0.58 (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)))))
% 0.23/0.58 (assert (= tptp.laminj (forall ((A tptp.term) (B tptp.term)) (=> (= (@ tptp.lam A) (@ tptp.lam B)) (= A B)))))
% 0.23/0.58 (assert (= tptp.shinj (forall ((A tptp.term) (B tptp.term)) (=> (= (@ (@ tptp.sub A) tptp.sh) (@ (@ tptp.sub B) tptp.sh)) (= A B)))))
% 0.23/0.58 (assert (= tptp.lamnotap (forall ((A tptp.term) (B tptp.term) (C tptp.term)) (not (= (@ tptp.lam A) (@ (@ tptp.ap B) C))))))
% 0.23/0.58 (assert (= tptp.apnotvar (forall ((A tptp.term) (B tptp.term)) (not (@ tptp.var (@ (@ tptp.ap A) B))))))
% 0.23/0.58 (assert (= tptp.lamnotvar (forall ((A tptp.term)) (not (@ tptp.var (@ tptp.lam A))))))
% 0.23/0.58 (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))))))))
% 0.23/0.58 (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))))))))
% 0.23/0.58 (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)))))
% 0.23/0.58 (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)))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0))
% 0.23/0.58 (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)))))))
% 0.23/0.58 (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)))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1))))))
% 0.23/0.58 (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))))))
% 0.23/0.58 (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)))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2)))
% 0.23/0.58 (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))))))))))
% 0.23/0.58 (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)))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2))))
% 0.23/0.58 (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))))))))))
% 0.23/0.58 (assert (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2))
% 0.23/0.58 (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))))))))))
% 0.23/0.58 (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)))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.pushprop_lthm_orig (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))))
% 0.23/0.58 (assert (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop))))))))
% 0.23/0.58 (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)))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))
% 0.23/0.58 (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))))))))))))
% 0.23/0.58 (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))))))))
% 0.23/0.58 (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)))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.induction2_lthm (=> tptp.axvarid (=> tptp.induction2lem tptp.induction2))))
% 0.23/0.58 (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)))))
% 0.23/0.58 (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))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid)))))
% 0.23/0.58 (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)))))
% 0.23/0.58 (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)))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset))))
% 0.23/0.58 (assert (= tptp.hoasap (lambda ((M tptp.subst) (A tptp.term) (N tptp.subst) (B tptp.term)) (@ (@ tptp.ap (@ (@ tptp.sub A) N)) B))))
% 0.23/0.58 (assert (= tptp.hoaslam (lambda ((M tptp.subst) (F (-> tptp.subst tptp.term tptp.term))) (@ tptp.lam (@ (@ F tptp.sh) tptp.one)))))
% 0.23/0.58 (assert (= tptp.hoasvar (lambda ((M tptp.subst) (A tptp.term) (N tptp.subst)) (@ tptp.var (@ (@ tptp.sub A) N)))))
% 0.23/0.58 (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))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1))))
% 0.23/0.58 (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))))))
% 0.23/0.58 (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)))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2)))
% 0.23/0.58 (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)))))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj)))))
% 0.23/0.58 (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))))))))
% 0.23/0.58 (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)))))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap)))
% 0.23/0.58 (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))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar))))
% 0.23/0.58 (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)))))
% 0.23/0.58 (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)))))))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar))))
% 0.23/0.58 (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))))))
% 0.23/0.58 (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)))))
% 0.23/0.58 (assert (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0))
% 0.23/0.58 (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))))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (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))))))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (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))))))))
% 0.23/0.58 (assert (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f))
% 0.23/0.58 (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)))))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2))))))
% 0.23/0.58 (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)))))))))
% 0.23/0.58 (assert (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a)))))))
% 0.23/0.58 (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)))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (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)))))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (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)))))))
% 0.23/0.58 (assert (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa))))
% 0.23/0.58 (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)))))))
% 0.23/0.58 (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)))))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3)))))
% 0.23/0.58 (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)))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a)))))
% 0.23/0.58 (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))))))
% 0.23/0.58 (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))))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b))
% 0.23/0.58 (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))))))))))
% 0.23/0.58 (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)))))))))))))))))))))))))))))))))))))))
% 0.23/0.58 (assert (= tptp.hoasinduction_lthm (=> tptp.induction2 (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> t/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 2613 Alarm clock ( read result; case "$result" in
% 299.88/300.20 unsat)
% 299.88/300.20 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.88/300.20 ;;
% 299.88/300.20 sat)
% 299.88/300.20 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.88/300.20 ;;
% 299.88/300.20 esac; exit 1 )
% 299.88/300.21 Alarm clock
% 299.88/300.21 % cvc5---1.0.5 exiting
% 299.88/300.21 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------