TSTP Solution File: ALG248^2 by Refute---2015
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%------------------------------------------------------------------------------
% File : Refute---2015
% Problem : ALG248^2 : TPTP v6.4.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : isabelle tptp_refute %d %s
% Computer : n135.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.75MB
% OS : Linux 3.10.0-327.10.1.el7.x86_64
% CPULimit : 300s
% DateTime : Tue Apr 12 11:20:28 EDT 2016
% Result : CounterSatisfiable 59.02s
% Output : Assurance 0s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG248^2 : TPTP v6.4.0. Bugfixed v5.2.0.
% 0.02/0.04 % Command : isabelle tptp_refute %d %s
% 0.03/0.23 % Computer : n135.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.75MB
% 0.03/0.23 % OS : Linux 3.10.0-327.10.1.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Sat Apr 9 04:33:24 CDT 2016
% 0.03/0.23 % CPUTime :
% 6.38/5.90 > val it = (): unit
% 6.88/6.47 Trying to find a model that refutes: bnd_pushprop_lem1_lthm
% 14.00/13.54 Unfolded term: [| bnd_hoasinduction_no_psi_cond_lthm =
% 14.00/13.54 (bnd_hoasinduction_lem0 -->
% 14.00/13.54 bnd_induction2 -->
% 14.00/13.54 bnd_axvarid -->
% 14.00/13.54 bnd_hoasinduction_lem3v2a --> bnd_hoasinduction_no_psi_cond);
% 14.00/13.54 bnd_hoasinduction_no_psi_cond =
% 14.00/13.54 (ALL P.
% 14.00/13.54 (ALL A B.
% 14.00/13.54 P bnd_id A bnd_id -->
% 14.00/13.54 P bnd_id B bnd_id -->
% 14.00/13.54 P bnd_id (bnd_hoasap bnd_id A bnd_id B) bnd_id) -->
% 14.00/13.54 (ALL F.
% 14.00/13.54 (ALL M A N.
% 14.00/13.54 bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.00/13.54 (ALL A. P bnd_id A bnd_id --> P bnd_id (F bnd_id A) bnd_id) -->
% 14.00/13.54 P bnd_id (bnd_hoaslam bnd_id F) bnd_id) -->
% 14.00/13.54 (ALL A. P bnd_id A bnd_id));
% 14.00/13.54 bnd_hoasinduction_lthm_3 =
% 14.00/13.54 (bnd_hoasinduction_lem0 -->
% 14.00/13.54 bnd_induction2 -->
% 14.00/13.54 bnd_axvarid --> bnd_hoasinduction_lem3v2a --> bnd_hoasinduction);
% 14.00/13.54 bnd_hoasinduction_lthm =
% 14.00/13.54 (bnd_induction2 -->
% 14.00/13.54 bnd_hoasinduction_lem1 -->
% 14.00/13.54 bnd_hoasinduction_lem2 -->
% 14.00/13.54 bnd_hoasinduction_lem3 --> bnd_hoasinduction);
% 14.00/13.54 bnd_hoasinduction_gthm =
% 14.00/13.54 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar -->
% 14.19/13.78 bnd_hoasapnotvar -->
% 14.19/13.78 bnd_hoasinduction_lem1 -->
% 14.19/13.78 bnd_hoasinduction_lem2 -->
% 14.19/13.78 bnd_hoasinduction_lem3 --> bnd_hoasinduction);
% 14.19/13.78 bnd_hoasinduction =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P M A (bnd_comp K N) --> P (bnd_comp M K) (bnd_sub A K) N) -->
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P (bnd_comp M K) (bnd_sub A K) N --> P M A (bnd_comp K N)) -->
% 14.19/13.78 (ALL A. bnd_hoasvar bnd_id A bnd_id --> P bnd_id A bnd_id) -->
% 14.19/13.78 (ALL A B.
% 14.19/13.78 P bnd_id A bnd_id -->
% 14.19/13.78 P bnd_id B bnd_id -->
% 14.19/13.78 P bnd_id (bnd_hoasap bnd_id A bnd_id B) bnd_id) -->
% 14.19/13.78 (ALL F.
% 14.19/13.78 (ALL M A N.
% 14.19/13.78 bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 (ALL A. P bnd_id A bnd_id --> P bnd_id (F bnd_id A) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_hoaslam bnd_id F) bnd_id) -->
% 14.19/13.78 (ALL A. P bnd_id A bnd_id));
% 14.19/13.78 bnd_hoasinduction_lem3b_lthm = bnd_hoasinduction_lem3b;
% 14.19/13.78 bnd_hoasinduction_lem3b_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar -->
% 14.19/13.78 bnd_hoasapnotvar -->
% 14.19/13.78 bnd_hoasinduction_lem1 -->
% 14.19/13.78 bnd_hoasinduction_lem2 --> bnd_hoasinduction_lem3b);
% 14.19/13.78 bnd_hoasinduction_lem3b =
% 14.19/13.78 (ALL B. EX F. bnd_sub B (bnd_push bnd_one bnd_sh) = F bnd_sh bnd_one);
% 14.19/13.78 bnd_hoasinduction_lem3a_lthm =
% 14.19/13.78 (bnd_axvarid -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_hoasinduction_lem3aa --> bnd_hoasinduction_lem3a);
% 14.19/13.78 bnd_hoasinduction_lem3a_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar -->
% 14.19/13.78 bnd_hoasapnotvar -->
% 14.19/13.78 bnd_hoasinduction_lem1 -->
% 14.19/13.78 bnd_hoasinduction_lem2 --> bnd_hoasinduction_lem3a);
% 14.19/13.78 bnd_hoasinduction_lem3a =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL F.
% 14.19/13.78 (ALL M A N.
% 14.19/13.78 bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 (ALL A. P bnd_id A bnd_id --> P bnd_id (F bnd_id A) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_hoaslam bnd_id F) bnd_id) -->
% 14.19/13.78 (ALL A.
% 14.19/13.78 (ALL B.
% 14.19/13.78 P bnd_id B bnd_id -->
% 14.19/13.78 P bnd_id (bnd_sub A (bnd_push B bnd_id)) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_lam A) bnd_id));
% 14.19/13.78 bnd_hoasinduction_lem3_lthm =
% 14.19/13.78 (bnd_axvarid -->
% 14.19/13.78 bnd_axvarshift --> bnd_hoasinduction_lem3aa --> bnd_hoasinduction_lem3);
% 14.19/13.78 bnd_hoasinduction_lem3_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar -->
% 14.19/13.78 bnd_hoasapnotvar -->
% 14.19/13.78 bnd_hoasinduction_lem1 -->
% 14.19/13.78 bnd_hoasinduction_lem2 --> bnd_hoasinduction_lem3);
% 14.19/13.78 bnd_hoasinduction_lem3 =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P M A (bnd_comp K N) --> P (bnd_comp M K) (bnd_sub A K) N) -->
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P (bnd_comp M K) (bnd_sub A K) N --> P M A (bnd_comp K N)) -->
% 14.19/13.78 (ALL F.
% 14.19/13.78 (ALL M A N.
% 14.19/13.78 bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 (ALL A. P bnd_id A bnd_id --> P bnd_id (F bnd_id A) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_hoaslam bnd_id F) bnd_id) -->
% 14.19/13.78 (ALL A.
% 14.19/13.78 (ALL B.
% 14.19/13.78 P bnd_id B bnd_id -->
% 14.19/13.78 P bnd_id (bnd_sub A (bnd_push B bnd_id)) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_lam A) bnd_id));
% 14.19/13.78 bnd_hoasinduction_lem3aaa =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL F.
% 14.19/13.78 (EX C. ALL M A N.
% 14.19/13.78 bnd_sub (F M A) N =
% 14.19/13.78 bnd_sub (bnd_sub C (bnd_push A M)) N &
% 14.19/13.78 bnd_sub C (bnd_push (bnd_sub A N) (bnd_comp M N)) =
% 14.19/13.78 F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 (ALL A. P bnd_id A bnd_id --> P bnd_id (F bnd_id A) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_hoaslam bnd_id F) bnd_id) -->
% 14.19/13.78 (ALL A.
% 14.19/13.78 (ALL B.
% 14.19/13.78 P bnd_id B bnd_id -->
% 14.19/13.78 P bnd_id (bnd_sub A (bnd_push B bnd_id)) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_lam (bnd_sub A (bnd_push bnd_one bnd_sh)))
% 14.19/13.78 bnd_id));
% 14.19/13.78 bnd_hoasinduction_lem3aa_lthm =
% 14.19/13.78 (bnd_axclos --> bnd_axmap --> bnd_hoasinduction_lem3aa);
% 14.19/13.78 bnd_hoasinduction_lem3aa =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL F.
% 14.19/13.78 (ALL M A N.
% 14.19/13.78 bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 (ALL A. P bnd_id A bnd_id --> P bnd_id (F bnd_id A) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_hoaslam bnd_id F) bnd_id) -->
% 14.19/13.78 (ALL A.
% 14.19/13.78 (ALL B.
% 14.19/13.78 P bnd_id B bnd_id -->
% 14.19/13.78 P bnd_id (bnd_sub A (bnd_push B bnd_id)) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_lam (bnd_sub A (bnd_push bnd_one bnd_sh)))
% 14.19/13.78 bnd_id));
% 14.19/13.78 bnd_hoasinduction_lem2_lthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar --> bnd_hoasapnotvar --> bnd_hoasinduction_lem2);
% 14.19/13.78 bnd_hoasinduction_lem2_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar --> bnd_hoasapnotvar --> bnd_hoasinduction_lem2);
% 14.19/13.78 bnd_hoasinduction_lem2 =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P M A (bnd_comp K N) --> P (bnd_comp M K) (bnd_sub A K) N) -->
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P (bnd_comp M K) (bnd_sub A K) N --> P M A (bnd_comp K N)) -->
% 14.19/13.78 (ALL A B.
% 14.19/13.78 P bnd_id A bnd_id -->
% 14.19/13.78 P bnd_id B bnd_id -->
% 14.19/13.78 P bnd_id (bnd_hoasap bnd_id A bnd_id B) bnd_id) -->
% 14.19/13.78 (ALL A B.
% 14.19/13.78 P bnd_id A bnd_id -->
% 14.19/13.78 P bnd_id B bnd_id --> P bnd_id (bnd_ap A B) bnd_id));
% 14.19/13.78 bnd_hoasinduction_lem1_lthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar --> bnd_hoasapnotvar --> bnd_hoasinduction_lem1);
% 14.19/13.78 bnd_hoasinduction_lem1_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar --> bnd_hoasapnotvar --> bnd_hoasinduction_lem1);
% 14.19/13.78 bnd_hoasinduction_lem1 =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P M A (bnd_comp K N) --> P (bnd_comp M K) (bnd_sub A K) N) -->
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P (bnd_comp M K) (bnd_sub A K) N --> P M A (bnd_comp K N)) -->
% 14.19/13.78 (ALL A. bnd_hoasvar bnd_id A bnd_id --> P bnd_id A bnd_id) -->
% 14.19/13.78 (ALL A. bnd_var A --> P bnd_id A bnd_id));
% 14.19/13.78 bnd_hoasinduction_lem3v2a_lthm =
% 14.19/13.78 (bnd_hoasinduction_lem3v2_f -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axclos --> bnd_axmap --> bnd_hoasinduction_lem3v2a);
% 14.19/13.78 bnd_hoasinduction_lem3v2a =
% 14.19/13.78 (ALL P Q.
% 14.19/13.78 (ALL F.
% 14.19/13.78 (ALL M A N.
% 14.19/13.78 bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 (ALL A. P bnd_id A bnd_id --> P bnd_id (F bnd_id A) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_hoaslam bnd_id F) bnd_id) -->
% 14.19/13.78 bnd_hoasinduction_p_and_p_prime P Q -->
% 14.19/13.78 (ALL A.
% 14.19/13.78 (ALL B. Q B --> Q (bnd_sub A (bnd_push B bnd_id))) -->
% 14.19/13.78 Q (bnd_lam A)));
% 14.19/13.78 bnd_hoasinduction_lem3v2_lthm =
% 14.19/13.78 (bnd_axvarid -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axclos --> bnd_axmap --> bnd_hoasinduction_lem3v2);
% 14.19/13.78 bnd_hoasinduction_lem3v2_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar --> bnd_hoasapnotvar --> bnd_hoasinduction_lem3v2);
% 14.19/13.78 bnd_hoasinduction_lem3v2 =
% 14.19/13.78 (ALL P Q.
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P M A (bnd_comp K N) --> P (bnd_comp M K) (bnd_sub A K) N) -->
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P (bnd_comp M K) (bnd_sub A K) N --> P M A (bnd_comp K N)) -->
% 14.19/13.78 (ALL F.
% 14.19/13.78 (ALL M A N.
% 14.19/13.78 bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 (ALL A. P bnd_id A bnd_id --> P bnd_id (F bnd_id A) bnd_id) -->
% 14.19/13.78 P bnd_id (bnd_hoaslam bnd_id F) bnd_id) -->
% 14.19/13.78 bnd_hoasinduction_p_and_p_prime P Q -->
% 14.19/13.78 (ALL A.
% 14.19/13.78 (ALL B. Q B --> Q (bnd_sub A (bnd_push B bnd_id))) -->
% 14.19/13.78 Q (bnd_lam A)));
% 14.19/13.78 bnd_hoasinduction_lem3v2_f_lthm = bnd_hoasinduction_lem3v2_f;
% 14.19/13.78 bnd_hoasinduction_lem3v2_f =
% 14.19/13.78 (ALL B. EX F. ALL A M. F M A = bnd_sub B (bnd_push A M));
% 14.19/13.78 bnd_hoasinduction_lem2v2_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar --> bnd_hoasapnotvar --> bnd_hoasinduction_lem2v2);
% 14.19/13.78 bnd_hoasinduction_lem2v2 =
% 14.19/13.78 (ALL P Q.
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P M A (bnd_comp K N) --> P (bnd_comp M K) (bnd_sub A K) N) -->
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P (bnd_comp M K) (bnd_sub A K) N --> P M A (bnd_comp K N)) -->
% 14.19/13.78 (ALL A B.
% 14.19/13.78 P bnd_id A bnd_id -->
% 14.19/13.78 P bnd_id B bnd_id -->
% 14.19/13.78 P bnd_id (bnd_hoasap bnd_id A bnd_id B) bnd_id) -->
% 14.19/13.78 bnd_hoasinduction_p_and_p_prime P Q -->
% 14.19/13.78 (ALL A B. Q A --> Q B --> Q (bnd_ap A B)));
% 14.19/13.78 bnd_hoasinduction_lem1v2_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap -->
% 14.19/13.78 bnd_hoaslamnotvar --> bnd_hoasapnotvar --> bnd_hoasinduction_lem1v2);
% 14.19/13.78 bnd_hoasinduction_lem1v2 =
% 14.19/13.78 (ALL P Q.
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P M A (bnd_comp K N) --> P (bnd_comp M K) (bnd_sub A K) N) -->
% 14.19/13.78 (ALL M A N K.
% 14.19/13.78 P (bnd_comp M K) (bnd_sub A K) N --> P M A (bnd_comp K N)) -->
% 14.19/13.78 (ALL A. bnd_hoasvar bnd_id A bnd_id --> P bnd_id A bnd_id) -->
% 14.19/13.78 bnd_hoasinduction_p_and_p_prime P Q --> (ALL A. bnd_var A --> Q A));
% 14.19/13.78 bnd_hoasinduction_lem0_lthm = bnd_hoasinduction_lem0;
% 14.19/13.78 bnd_hoasinduction_lem0 = (ALL P. Ex (bnd_hoasinduction_p_and_p_prime P));
% 14.19/13.78 bnd_hoasinduction_p_and_p_prime = (%P Q. ALL X. Q X = P bnd_id X bnd_id);
% 14.19/13.78 bnd_hoasapnotvar_lthm =
% 14.19/13.78 (bnd_axvarid --> bnd_apnotvar --> bnd_hoasapnotvar);
% 14.19/13.78 bnd_hoasapnotvar_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj -->
% 14.19/13.78 bnd_hoaslamnotap --> bnd_hoaslamnotvar --> bnd_hoasapnotvar);
% 14.19/13.78 bnd_hoasapnotvar =
% 14.19/13.78 (ALL A B. ~ bnd_hoasvar bnd_id (bnd_hoasap bnd_id A bnd_id B) bnd_id);
% 14.19/13.78 bnd_hoaslamnotvar_lthm =
% 14.19/13.78 (bnd_axvarid --> bnd_lamnotvar --> bnd_hoaslamnotvar);
% 14.19/13.78 bnd_hoaslamnotvar_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 -->
% 14.19/13.78 bnd_hoaslaminj --> bnd_hoaslamnotap --> bnd_hoaslamnotvar);
% 14.19/13.78 bnd_hoaslamnotvar =
% 14.19/13.78 (ALL F.
% 14.19/13.78 (ALL M A N. bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 ~ bnd_hoasvar bnd_id (bnd_hoaslam bnd_id F) bnd_id);
% 14.19/13.78 bnd_hoaslamnotap_lthm = (bnd_lamnotap --> bnd_hoaslamnotap);
% 14.19/13.78 bnd_hoaslamnotap_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset -->
% 14.19/13.78 bnd_hoasapinj1 -->
% 14.19/13.78 bnd_hoasapinj2 --> bnd_hoaslaminj --> bnd_hoaslamnotap);
% 14.19/13.78 bnd_hoaslamnotap =
% 14.19/13.78 (ALL F.
% 14.19/13.78 (ALL M A N. bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 (ALL A B. ~ bnd_hoaslam bnd_id F = bnd_hoasap bnd_id A bnd_id B));
% 14.19/13.78 bnd_hoaslaminj_lthm =
% 14.19/13.78 (bnd_axvarcons --> bnd_axshiftcons --> bnd_laminj --> bnd_hoaslaminj);
% 14.19/13.78 bnd_hoaslaminj_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid -->
% 14.19/13.78 bnd_termmset --> bnd_hoasapinj1 --> bnd_hoasapinj2 --> bnd_hoaslaminj);
% 14.19/13.78 bnd_hoaslaminj =
% 14.19/13.78 (ALL F.
% 14.19/13.78 (ALL M A N. bnd_sub (F M A) N = F (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 (ALL G.
% 14.19/13.78 (ALL M A N.
% 14.19/13.78 bnd_sub (G M A) N = G (bnd_comp M N) (bnd_sub A N)) -->
% 14.19/13.78 bnd_hoaslam bnd_id F = bnd_hoaslam bnd_id G -->
% 14.19/13.78 (ALL M A. F M A = G M A)));
% 14.19/13.78 bnd_hoasapinj2_lthm = (bnd_apinj2 --> bnd_hoasapinj2);
% 14.19/13.78 bnd_hoasapinj2_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 -->
% 14.19/13.78 bnd_substmonoid --> bnd_termmset --> bnd_hoasapinj1 --> bnd_hoasapinj2);
% 14.19/13.78 bnd_hoasapinj2 =
% 14.19/13.78 (ALL A B C D.
% 14.19/13.78 bnd_hoasap bnd_id A bnd_id C = bnd_hoasap bnd_id B bnd_id D -->
% 14.19/13.78 C = D);
% 14.19/13.78 bnd_hoasapinj1_lthm = (bnd_axvarid --> bnd_apinj1 --> bnd_hoasapinj1);
% 14.19/13.78 bnd_hoasapinj1_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 --> bnd_substmonoid --> bnd_termmset --> bnd_hoasapinj1);
% 14.19/13.78 bnd_hoasapinj1 =
% 14.19/13.78 (ALL A B C D.
% 14.19/13.78 bnd_hoasap bnd_id A bnd_id C = bnd_hoasap bnd_id B bnd_id D -->
% 14.19/13.78 A = B);
% 14.19/13.78 bnd_hoasvar = (%M A N. bnd_var (bnd_sub A N));
% 14.19/13.78 bnd_hoaslam = (%M F. bnd_lam (F bnd_sh bnd_one));
% 14.19/13.78 bnd_hoasap = (%M A N. bnd_ap (bnd_sub A N));
% 14.19/13.78 bnd_termmset_lthm = (bnd_axvarid --> bnd_axclos --> bnd_termmset);
% 14.19/13.78 bnd_termmset_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem -->
% 14.19/13.78 bnd_induction2 --> bnd_substmonoid --> bnd_termmset);
% 14.19/13.78 bnd_termmset =
% 14.19/13.78 ((ALL A M N. bnd_sub (bnd_sub A M) N = bnd_sub A (bnd_comp M N)) &
% 14.19/13.78 (ALL A. bnd_sub A bnd_id = A));
% 14.19/13.78 bnd_substmonoid_lthm =
% 14.19/13.78 (bnd_axidl --> bnd_axassoc --> bnd_axidr --> bnd_substmonoid);
% 14.19/13.78 bnd_substmonoid_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop -->
% 14.19/13.78 bnd_induction2lem --> bnd_induction2 --> bnd_substmonoid);
% 14.19/13.78 bnd_substmonoid =
% 14.19/13.78 (((ALL M N K. bnd_comp (bnd_comp M N) K = bnd_comp M (bnd_comp N K)) &
% 14.19/13.78 (ALL M. bnd_comp bnd_id M = M)) &
% 14.19/13.78 (ALL M. bnd_comp M bnd_id = M));
% 14.19/13.78 bnd_induction2_lthm =
% 14.19/13.78 (bnd_axvarid --> bnd_induction2lem --> bnd_induction2);
% 14.19/13.78 bnd_induction2_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar -->
% 14.19/13.78 bnd_induction -->
% 14.19/13.78 bnd_pushprop --> bnd_induction2lem --> bnd_induction2);
% 14.19/13.78 bnd_induction2 =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL A. bnd_var A --> P A) -->
% 14.19/13.78 (ALL A B. P A --> P B --> P (bnd_ap A B)) -->
% 14.19/13.78 (ALL A.
% 14.19/13.78 (ALL B. P B --> P (bnd_sub A (bnd_push B bnd_id))) -->
% 14.19/13.78 P (bnd_lam A)) -->
% 14.19/13.78 All P);
% 14.19/13.78 bnd_induction2lem_lthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr --> bnd_induction --> bnd_pushprop --> bnd_induction2lem);
% 14.19/13.78 bnd_induction2lem_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar --> bnd_induction --> bnd_pushprop --> bnd_induction2lem);
% 14.19/13.78 bnd_induction2lem =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL A B. P A --> P B --> P (bnd_ap A B)) -->
% 14.19/13.78 (ALL A.
% 14.19/13.78 (ALL B. P B --> P (bnd_sub A (bnd_push B bnd_id))) -->
% 14.19/13.78 P (bnd_lam A)) -->
% 14.19/13.78 (ALL A M.
% 14.19/13.78 (ALL B. bnd_var B --> P (bnd_sub B M)) --> P (bnd_sub A M)));
% 14.19/13.78 bnd_pushprop_lthm =
% 14.19/13.78 (bnd_pushprop_lem0 -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axclos --> bnd_axshiftcons --> bnd_ulamvarind --> bnd_pushprop);
% 14.19/13.78 bnd_pushprop_lthm_orig =
% 14.19/13.78 (bnd_ulamvar1 -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axclos --> bnd_axshiftcons --> bnd_ulamvarind --> bnd_pushprop);
% 14.19/13.78 bnd_pushprop_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar --> bnd_lamnotvar --> bnd_induction --> bnd_pushprop);
% 14.19/13.78 bnd_pushprop =
% 14.19/13.78 (ALL P A M.
% 14.19/13.78 (ALL B. bnd_var B --> P (bnd_sub B M)) -->
% 14.19/13.78 P A --> (ALL B. bnd_var B --> P (bnd_sub B (bnd_push A M))));
% 14.19/13.78 bnd_pushprop_lem3v2_lthm = bnd_pushprop_lem3v2;
% 14.19/13.78 bnd_pushprop_lem3v2 =
% 14.19/13.78 (ALL P Q A M.
% 14.19/13.78 bnd_pushprop_p_and_p_prime A M P Q -->
% 14.19/13.78 (ALL B. bnd_var B --> Q B) -->
% 14.19/13.78 (ALL B. bnd_var B --> P (bnd_sub B (bnd_push A M))));
% 14.19/13.78 bnd_pushprop_lem2v2_lthm =
% 14.19/13.78 (bnd_axclos --> bnd_axshiftcons --> bnd_pushprop_lem2v2);
% 14.19/13.78 bnd_pushprop_lem2v2_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar --> bnd_induction --> bnd_pushprop_lem2v2);
% 14.19/13.78 bnd_pushprop_lem2v2 =
% 14.19/13.78 (ALL P Q A M.
% 14.19/13.78 bnd_pushprop_p_and_p_prime A M P Q -->
% 14.19/13.78 (ALL B. bnd_var B --> P (bnd_sub B M)) -->
% 14.19/13.78 (ALL C. bnd_var C --> Q C --> Q (bnd_sub C bnd_sh)));
% 14.19/13.78 bnd_pushprop_lem1v2_lthm = (bnd_axvarcons --> bnd_pushprop_lem1v2);
% 14.19/13.78 bnd_pushprop_lem1v2_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar -->
% 14.19/13.78 bnd_lamnotvar --> bnd_induction --> bnd_pushprop_lem1v2);
% 14.19/13.78 bnd_pushprop_lem1v2 =
% 14.19/13.78 (ALL P Q A M. P A --> bnd_pushprop_p_and_p_prime A M P Q --> Q bnd_one);
% 14.19/13.78 bnd_pushprop_lem1_lthm =
% 14.19/13.78 (bnd_axvarcons -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axshiftcons --> bnd_ulamvarind --> bnd_pushprop_lem1);
% 14.19/13.78 bnd_pushprop_lem1_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar --> bnd_lamnotvar --> bnd_induction --> bnd_pushprop_lem1);
% 14.19/13.78 bnd_pushprop_lem1 =
% 14.19/13.78 (ALL P K A M B. P A --> K (bnd_sub A (bnd_push B M)));
% 14.19/13.78 bnd_pushprop_lem0_lthm = bnd_pushprop_lem0;
% 14.19/13.78 bnd_pushprop_lem0_gthm =
% 14.19/13.78 (bnd_axapp -->
% 14.19/13.78 bnd_axvarcons -->
% 14.19/13.78 bnd_axvarid -->
% 14.19/13.78 bnd_axabs -->
% 14.19/13.78 bnd_axclos -->
% 14.19/13.78 bnd_axidl -->
% 14.19/13.78 bnd_axshiftcons -->
% 14.19/13.78 bnd_axassoc -->
% 14.19/13.78 bnd_axmap -->
% 14.19/13.78 bnd_axidr -->
% 14.19/13.78 bnd_axvarshift -->
% 14.19/13.78 bnd_axscons -->
% 14.19/13.78 bnd_ulamvar1 -->
% 14.19/13.78 bnd_ulamvarsh -->
% 14.19/13.78 bnd_ulamvarind -->
% 14.19/13.78 bnd_apinj1 -->
% 14.19/13.78 bnd_apinj2 -->
% 14.19/13.78 bnd_laminj -->
% 14.19/13.78 bnd_shinj -->
% 14.19/13.78 bnd_lamnotap -->
% 14.19/13.78 bnd_apnotvar --> bnd_lamnotvar --> bnd_induction --> bnd_pushprop_lem0);
% 14.19/13.78 bnd_pushprop_lem0 = (ALL P A M. Ex (bnd_pushprop_p_and_p_prime A M P));
% 14.19/13.78 bnd_pushprop_p_and_p_prime =
% 14.19/13.78 (%A M P Q. ALL X. Q X = P (bnd_sub X (bnd_push A M)));
% 14.19/13.78 bnd_induction =
% 14.19/13.78 (ALL P.
% 14.19/13.78 (ALL A. bnd_var A --> P A) -->
% 14.19/13.78 (ALL A B. P A --> P B --> P (bnd_ap A B)) -->
% 14.19/13.78 (ALL A. P A --> P (bnd_lam A)) --> All P);
% 14.19/13.78 bnd_lamnotvar = (ALL A. ~ bnd_var (bnd_lam A));
% 14.19/13.78 bnd_apnotvar = (ALL A B. ~ bnd_var (bnd_ap A B));
% 14.19/13.78 bnd_lamnotap = (ALL A B C. ~ bnd_lam A = bnd_ap B C);
% 14.19/13.78 bnd_shinj = (ALL A B. bnd_sub A bnd_sh = bnd_sub B bnd_sh --> A = B);
% 14.19/13.78 bnd_laminj = (ALL A B. bnd_lam A = bnd_lam B --> A = B);
% 14.19/13.78 bnd_apinj2 = (ALL A B C D. bnd_ap A C = bnd_ap B D --> C = D);
% 14.19/13.78 bnd_apinj1 = (ALL A B C D. bnd_ap A C = bnd_ap B D --> A = B);
% 14.19/13.78 bnd_ulamvarind =
% 14.19/13.78 (ALL P.
% 14.19/13.78 P bnd_one -->
% 14.19/13.78 (ALL A. bnd_var A --> P A --> P (bnd_sub A bnd_sh)) -->
% 14.19/13.78 (ALL A. bnd_var A --> P A));
% 14.19/13.78 bnd_ulamvarsh = (ALL A. bnd_var A --> bnd_var (bnd_sub A bnd_sh));
% 14.19/13.78 bnd_ulamvar1 = bnd_var bnd_one;
% 14.19/13.78 bnd_axscons =
% 14.19/13.78 (ALL M. bnd_push (bnd_sub bnd_one M) (bnd_comp bnd_sh M) = M);
% 14.19/13.78 bnd_axvarshift = (bnd_push bnd_one bnd_sh = bnd_id);
% 14.19/13.78 bnd_axidr = (ALL M. bnd_comp M bnd_id = M);
% 14.19/13.78 bnd_axmap =
% 14.19/13.78 (ALL A M N.
% 14.19/13.78 bnd_comp (bnd_push A M) N = bnd_push (bnd_sub A N) (bnd_comp M N));
% 14.19/13.78 bnd_axassoc =
% 14.19/13.78 (ALL M N K. bnd_comp (bnd_comp M N) K = bnd_comp M (bnd_comp N K));
% 14.19/13.78 bnd_axshiftcons = (ALL A M. bnd_comp bnd_sh (bnd_push A M) = M);
% 14.19/13.78 bnd_axidl = (ALL M. bnd_comp bnd_id M = M);
% 14.19/13.78 bnd_axclos =
% 14.19/13.78 (ALL A M N. bnd_sub (bnd_sub A M) N = bnd_sub A (bnd_comp M N));
% 14.19/13.78 bnd_axabs =
% 14.19/13.78 (ALL A M.
% 14.19/13.78 bnd_sub (bnd_lam A) M =
% 14.19/13.78 bnd_lam (bnd_sub A (bnd_push bnd_one (bnd_comp M bnd_sh))));
% 14.19/13.78 bnd_axvarid = (ALL A. bnd_sub A bnd_id = A);
% 14.19/13.78 bnd_axvarcons = (ALL A M. bnd_sub bnd_one (bnd_push A M) = A);
% 14.19/13.78 bnd_axapp =
% 14.19/13.78 (ALL A B M.
% 14.19/13.78 bnd_sub (bnd_ap A B) M = bnd_ap (bnd_sub A M) (bnd_sub B M)) |]
% 14.19/13.78 ==> bnd_pushprop_lem1_lthm
% 14.19/13.78 Adding axioms...
% 14.19/13.78 Typedef.type_definition_def
% 14.19/13.78 Typedef.type_definition_def
% 35.65/35.12 ...done.
% 35.65/35.14 Ground types: ?'b, bnd_subst, bnd_term
% 35.65/35.14 Translating term (sizes: 1, 1, 1) ...
% 58.30/57.79 Invoking SAT solver...
% 59.02/58.42 Model found:
% 59.02/58.42 Size of types: ?'b: 1, bnd_subst: 1, bnd_term: 1
% 59.02/58.42 bnd_pushprop_lem0_gthm: True
% 59.02/58.42 bnd_pushprop_lem0_lthm: True
% 59.02/58.42 bnd_pushprop_lem1_gthm: True
% 59.02/58.42 bnd_pushprop_lem1: False
% 59.02/58.42 bnd_pushprop_lem1_lthm: False
% 59.02/58.42 bnd_pushprop_lem1v2_gthm: True
% 59.02/58.42 bnd_pushprop_lem1v2: True
% 59.02/58.42 bnd_pushprop_lem1v2_lthm: True
% 59.02/58.42 bnd_pushprop_lem2v2_gthm: True
% 59.02/58.42 bnd_pushprop_lem2v2: True
% 59.02/58.42 bnd_pushprop_lem2v2_lthm: True
% 59.02/58.42 bnd_pushprop_p_and_p_prime: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 {({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 True)},
% 59.02/58.42 {({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 True)},
% 59.02/58.42 True),
% 59.02/58.42 ({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 False)},
% 59.02/58.42 False)}),
% 59.02/58.42 ({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 False)},
% 59.02/58.42 {({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 True)},
% 59.02/58.42 False),
% 59.02/58.42 ({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 False)},
% 59.02/58.42 True)})})})}
% 59.02/58.42 bnd_pushprop_lem3v2: True
% 59.02/58.42 bnd_pushprop_lem3v2_lthm: True
% 59.02/58.42 bnd_pushprop_gthm: True
% 59.02/58.42 bnd_pushprop_lthm_orig: True
% 59.02/58.42 bnd_pushprop_lem0: True
% 59.02/58.42 bnd_pushprop_lthm: True
% 59.02/58.42 bnd_induction2lem_gthm: True
% 59.02/58.42 bnd_induction2lem_lthm: True
% 59.02/58.42 bnd_induction2_gthm: True
% 59.02/58.42 bnd_induction2_lthm: True
% 59.02/58.42 bnd_substmonoid_gthm: True
% 59.02/58.42 bnd_substmonoid_lthm: True
% 59.02/58.42 bnd_termmset_gthm: True
% 59.02/58.42 bnd_termmset_lthm: True
% 59.02/58.42 bnd_hoasapinj1_gthm: True
% 59.02/58.42 bnd_hoasapinj1_lthm: True
% 59.02/58.42 bnd_hoasapinj2_gthm: True
% 59.02/58.42 bnd_hoasapinj2_lthm: True
% 59.02/58.42 bnd_hoaslaminj_gthm: True
% 59.02/58.42 bnd_hoaslaminj_lthm: True
% 59.02/58.42 bnd_hoaslamnotap_gthm: True
% 59.02/58.42 bnd_hoaslamnotap_lthm: True
% 59.02/58.42 bnd_hoaslamnotvar_gthm: True
% 59.02/58.42 bnd_hoaslamnotvar_lthm: True
% 59.02/58.42 bnd_hoasapnotvar_gthm: True
% 59.02/58.42 bnd_hoasapnotvar_lthm: True
% 59.02/58.42 bnd_hoasinduction_lem0_lthm: True
% 59.02/58.42 bnd_hoasinduction_lem1v2: True
% 59.02/58.42 bnd_hoasinduction_lem1v2_gthm: True
% 59.02/58.42 bnd_hoasinduction_lem2v2: True
% 59.02/58.42 bnd_hoasinduction_lem2v2_gthm: True
% 59.02/58.42 bnd_hoasinduction_lem3v2_f_lthm: True
% 59.02/58.42 bnd_hoasinduction_lem3v2_gthm: True
% 59.02/58.42 bnd_hoasinduction_lem3v2: True
% 59.02/58.42 bnd_hoasinduction_lem3v2_lthm: True
% 59.02/58.42 bnd_hoasinduction_p_and_p_prime: {({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 True)})})},
% 59.02/58.42 {({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0, True)},
% 59.02/58.42 True),
% 59.02/58.42 ({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 False)},
% 59.02/58.42 False)}),
% 59.02/58.42 ({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 False)})})},
% 59.02/58.42 {({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0, True)},
% 59.02/58.42 False),
% 59.02/58.42 ({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 False)},
% 59.02/58.42 True)})}
% 59.02/58.42 bnd_hoasinduction_lem3v2_f: True
% 59.02/58.42 bnd_hoasinduction_lem3v2a_lthm: True
% 59.02/58.42 bnd_var: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0, True)}
% 59.02/58.42 bnd_hoasinduction_lem1_gthm: True
% 59.02/58.42 bnd_hoasinduction_lem1_lthm: True
% 59.02/58.42 bnd_ap: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0)})}
% 59.02/58.42 bnd_hoasinduction_lem2_gthm: True
% 59.02/58.42 bnd_hoasinduction_lem2_lthm: True
% 59.02/58.42 bnd_hoasinduction_lem3aa_lthm: True
% 59.02/58.42 bnd_hoasinduction_lem3aaa: True
% 59.02/58.42 bnd_hoasinduction_lem3_gthm: True
% 59.02/58.42 bnd_hoasinduction_lem3_lthm: True
% 59.02/58.42 bnd_lam: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0)}
% 59.02/58.42 bnd_hoasinduction_lem3a_gthm: True
% 59.02/58.42 bnd_hoasinduction_lem3a: True
% 59.02/58.42 bnd_hoasinduction_lem3aa: True
% 59.02/58.42 bnd_hoasinduction_lem3a_lthm: True
% 59.02/58.42 bnd_sh: ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0
% 59.02/58.42 bnd_one: ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0
% 59.02/58.42 bnd_push: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0)})}
% 59.02/58.42 bnd_hoasinduction_lem3b_gthm: True
% 59.02/58.42 bnd_hoasinduction_lem3b: True
% 59.02/58.42 bnd_hoasinduction_lem3b_lthm: True
% 59.02/58.42 bnd_hoasvar: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 True)})})}
% 59.02/58.42 bnd_hoasapnotvar: False
% 59.02/58.42 bnd_hoaslamnotvar: False
% 59.02/58.42 bnd_hoaslamnotap: False
% 59.02/58.42 bnd_hoaslaminj: True
% 59.02/58.42 bnd_hoasapinj2: True
% 59.02/58.42 bnd_hoasapinj1: True
% 59.02/58.42 bnd_termmset: True
% 59.02/58.42 bnd_substmonoid: True
% 59.02/58.42 bnd_induction2lem: True
% 59.02/58.42 bnd_pushprop: True
% 59.02/58.42 bnd_induction: True
% 59.02/58.42 bnd_lamnotvar: False
% 59.02/58.42 bnd_apnotvar: False
% 59.02/58.42 bnd_lamnotap: False
% 59.02/58.42 bnd_shinj: True
% 59.02/58.42 bnd_laminj: True
% 59.02/58.42 bnd_apinj2: True
% 59.02/58.42 bnd_apinj1: True
% 59.02/58.42 bnd_ulamvarind: True
% 59.02/58.42 bnd_ulamvarsh: True
% 59.02/58.42 bnd_ulamvar1: True
% 59.02/58.42 bnd_axscons: True
% 59.02/58.42 bnd_axvarshift: True
% 59.02/58.42 bnd_axidr: True
% 59.02/58.42 bnd_axmap: True
% 59.02/58.42 bnd_axassoc: True
% 59.02/58.42 bnd_axshiftcons: True
% 59.02/58.42 bnd_axidl: True
% 59.02/58.42 bnd_axclos: True
% 59.02/58.42 bnd_axabs: True
% 59.02/58.42 bnd_axvarcons: True
% 59.02/58.42 bnd_axapp: True
% 59.02/58.42 bnd_hoasinduction_gthm: True
% 59.02/58.42 bnd_hoasinduction_lem3: True
% 59.02/58.42 bnd_hoasinduction_lem2: True
% 59.02/58.42 bnd_hoasinduction_lem1: True
% 59.02/58.42 bnd_hoasinduction_lthm: True
% 59.02/58.42 bnd_hoasinduction: True
% 59.02/58.42 bnd_hoasinduction_lthm_3: True
% 59.02/58.42 bnd_hoaslam: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 {({(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0)})},
% 59.02/58.42 ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0)})}
% 59.02/58.42 bnd_comp: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0)})}
% 59.02/58.42 bnd_sub: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0)})}
% 59.02/58.42 bnd_hoasap: {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0,
% 59.02/58.42 {(??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0,
% 59.02/58.42 ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_term0)})})})}
% 59.02/58.42 bnd_id: ??.Scratch_tptp_refute_20804_24173.theBenchmark_46p.bnd_subst0
% 59.02/58.42 bnd_hoasinduction_no_psi_cond: True
% 59.02/58.42 bnd_hoasinduction_lem3v2a: True
% 59.02/58.42 bnd_axvarid: True
% 59.02/58.42 bnd_induction2: True
% 59.02/58.42 bnd_hoasinduction_lem0: True
% 59.02/58.42 bnd_hoasinduction_no_psi_cond_lthm: True
% 59.02/58.42
% 59.02/58.42 % SZS status CounterSatisfiable
%------------------------------------------------------------------------------