TSTP Solution File: ITP213_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ITP213_1 : TPTP v8.1.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n005.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 : Sat Sep 17 04:16:47 EDT 2022

% Result   : Theorem 11.51s 8.34s
% Output   : Proof 12.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   47
% Syntax   : Number of formulae    :   78 (  24 unt;  24 typ;   0 def)
%            Number of atoms       :  306 (  87 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  404 ( 180   ~; 166   |;   0   &)
%                                         (  37 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of FOOLs       :   28 (  28 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   20 (  11   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :   20 (  18 usr;  14 prp; 0-3 aty)
%            Number of functors    :   23 (  23 usr;  13 con; 0-3 aty)
%            Number of variables   :  145 ( 125   !;   0   ?; 145   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pp_type,type,
    pp: bool > $o ).

tff(aa_Pro2991721470636411351t_bool_type,type,
    aa_Pro2991721470636411351t_bool: ( fun_Pr6001797050664311790t_bool * produc3658429121746597890et_nat ) > bool ).

tff(produc7507926704131184380et_nat_type,type,
    produc7507926704131184380et_nat: ( heap_e7401611519738050253t_unit * set_nat ) > produc3658429121746597890et_nat ).

tff(aa_set_nat_set_nat_type,type,
    aa_set_nat_set_nat: ( fun_set_nat_set_nat * set_nat ) > set_nat ).

tff(as2_type,type,
    as2: set_nat ).

tff(aa_set2309701074089104077et_nat_type,type,
    aa_set2309701074089104077et_nat: ( fun_se1909708154429037836et_nat * set_nat ) > fun_set_nat_set_nat ).

tff(hoare_new_addrs_type,type,
    hoare_new_addrs: ( heap_e7401611519738050253t_unit * set_nat * heap_e7401611519738050253t_unit ) > set_nat ).

tff(h_type,type,
    h: heap_e7401611519738050253t_unit ).

tff(as1_type,type,
    as1: set_nat ).

tff(h2_type,type,
    h2: heap_e7401611519738050253t_unit ).

tff(sup_sup_set_nat_type,type,
    sup_sup_set_nat: fun_se1909708154429037836et_nat ).

tff(rep_assn_type,type,
    rep_assn: assn > fun_Pr6001797050664311790t_bool ).

tff(aa_assn_assn_type,type,
    aa_assn_assn: ( fun_assn_assn * assn ) > assn ).

tff(r_type,type,
    r: assn ).

tff(aa_ass954072293579886259n_assn_type,type,
    aa_ass954072293579886259n_assn: ( fun_as3983628580203722482n_assn * assn ) > fun_assn_assn ).

tff(aa_a_assn_type,type,
    aa_a_assn: ( fun_a_assn * a ) > assn ).

tff(r2_type,type,
    r2: a ).

tff(q_type,type,
    q: fun_a_assn ).

tff(times_times_assn_type,type,
    times_times_assn: fun_as3983628580203722482n_assn ).

tff(as_type,type,
    as: set_nat ).

tff(collect_nat_type,type,
    collect_nat: fun_nat_bool > set_nat ).

tff(aTP_Lamm_bg_type,type,
    aTP_Lamm_bg: fun_nat_bool ).

tff(inf_inf_set_nat_type,type,
    inf_inf_set_nat: fun_se1909708154429037836et_nat ).

tff(bot_bot_set_nat_type,type,
    bot_bot_set_nat: set_nat ).

tff(1,plain,
    ( ( hoare_new_addrs(h2,as,h) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2) )
  <=> ( hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ( hoare_new_addrs(h2,as,h) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2) )
  <=> ( hoare_new_addrs(h2,as,h) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    hoare_new_addrs(h2,as,h) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062new__addrs_Ah_Aas_Ah_H_A_061_Anew__addrs_Ah_Aas1_Ah_H_A_092_060union_062_Aas2_092_060close_062) ).

tff(4,plain,
    hoare_new_addrs(h2,as,h) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2),
    inference(modus_ponens,[status(thm)],[4,1]) ).

tff(6,plain,
    aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2) = hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h),
    inference(symmetry,[status(thm)],[5]) ).

tff(7,plain,
    produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2)) = produc7507926704131184380et_nat(h,hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h)),
    inference(monotonicity,[status(thm)],[6]) ).

tff(8,plain,
    aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))) = aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h))),
    inference(monotonicity,[status(thm)],[7]) ).

tff(9,plain,
    ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
  <=> pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h)))) ),
    inference(monotonicity,[status(thm)],[8]) ).

tff(10,plain,
    ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h))))
  <=> pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2)))) ),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    ( ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h))))
  <=> ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2)))) ),
    inference(monotonicity,[status(thm)],[10]) ).

tff(12,plain,
    ( ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as,h))))
  <=> ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ( ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as,h))))
  <=> ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as,h)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,axiom,
    ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as,h)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(15,plain,
    ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as,h)))),
    inference(modus_ponens,[status(thm)],[14,13]) ).

tff(16,plain,
    ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,as1),as2),h)))),
    inference(modus_ponens,[status(thm)],[15,12]) ).

tff(17,plain,
    ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2)))),
    inference(modus_ponens,[status(thm)],[16,11]) ).

tff(18,plain,
    ^ [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      refl(
        ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
          | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
      <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
          | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
        | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
  <=> ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
        | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ^ [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      trans(
        monotonicity(
          rewrite(
            ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) )
          <=> ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )),
          ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) ) )
        <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) ) )),
        rewrite(
          ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
        <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) ) )),
        ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
          | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) ) )
      <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
          | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) ) )),
    inference(bind,[status(th)],]) ).

tff(21,plain,
    ( ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
        | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) ) )
  <=> ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
        | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) ) ),
    inference(quant_intro,[status(thm)],[20]) ).

tff(22,plain,
    ^ [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      trans(
        monotonicity(
          rewrite(
            ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
          <=> ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) ) )),
          ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) )
        <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) )
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) ) )),
        rewrite(
          ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) )
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) )
        <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) ) ) )),
        ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
          | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) )
      <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
          | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) ) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
        | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) )
  <=> ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
        | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) ) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

tff(24,plain,
    ( ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
        | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) )
  <=> ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
        | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ^ [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) = bot_bot_set_nat )
                 => pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) )
              <=> ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
                  | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) ) )),
              ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
               => ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) = bot_bot_set_nat )
                 => pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) ) )
            <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
               => ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
                  | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) ) ) )),
            rewrite(
              ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
               => ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
                  | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) ) )
            <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
                | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
                | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3))) ) )),
            ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
             => ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) = bot_bot_set_nat )
               => pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) ) )
          <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
              | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
              | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3))) ) )),
          ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
           => ( pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
             => ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) = bot_bot_set_nat )
               => pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) ) ) )
        <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
           => ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
              | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
              | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3))) ) ) )),
        rewrite(
          ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
           => ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
              | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
              | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3))) ) )
        <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) ) )),
        ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
         => ( pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
           => ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) = bot_bot_set_nat )
             => pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) ) ) )
      <=> ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
          | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) ) )),
    inference(bind,[status(th)],]) ).

tff(26,plain,
    ( ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
       => ( pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
         => ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) = bot_bot_set_nat )
           => pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) ) ) )
  <=> ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
        ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
        | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
        | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) ) ),
    inference(quant_intro,[status(thm)],[25]) ).

tff(27,axiom,
    ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      ( pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
     => ( pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
       => ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) = bot_bot_set_nat )
         => pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_star__assnI) ).

tff(28,plain,
    ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) ),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != bot_bot_set_nat )
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As))) ),
    inference(modus_ponens,[status(thm)],[28,24]) ).

tff(30,plain,
    ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) ) ),
    inference(modus_ponens,[status(thm)],[29,23]) ).

tff(31,plain,
    ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) ),
    inference(modus_ponens,[status(thm)],[30,21]) ).

tff(32,plain,
    ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) ),
    inference(skolemize,[status(sab)],[31]) ).

tff(33,plain,
    ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
      ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) ),
    inference(modus_ponens,[status(thm)],[32,19]) ).

tff(34,plain,
    ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
  <=> pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,axiom,
    pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_MDL) ).

tff(36,plain,
    pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h)))),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) )
  <=> ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = collect_nat(aTP_Lamm_bg) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(38,plain,
    ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = bot_bot_set_nat )
  <=> ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,plain,
    ( ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = bot_bot_set_nat )
  <=> ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = bot_bot_set_nat ) ),
    inference(rewrite,[status(thm)],]) ).

tff(40,axiom,
    aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = bot_bot_set_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_DJN) ).

tff(41,plain,
    aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = bot_bot_set_nat,
    inference(modus_ponens,[status(thm)],[40,39]) ).

tff(42,plain,
    aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,as1),as2),
    inference(modus_ponens,[status(thm)],[41,38]) ).

tff(43,plain,
    aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) = collect_nat(aTP_Lamm_bg),
    inference(modus_ponens,[status(thm)],[42,37]) ).

tff(44,plain,
    ( pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
  <=> pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2))) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,axiom,
    pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_Ih_H_M_Aas2_J_A_092_060Turnstile_062_AR_092_060close_062) ).

tff(46,plain,
    pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2))),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ( ( ~ ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
            ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
      | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) )
  <=> ( ~ ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
            ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
      | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(48,plain,
    ( ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) )
  <=> ( ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
      | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(49,plain,
    ( ( ~ ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
            ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
      | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) )
  <=> ( ~ ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
            ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
      | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) ) ),
    inference(monotonicity,[status(thm)],[48]) ).

tff(50,plain,
    ( ( ~ ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
            ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
      | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) )
  <=> ( ~ ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
            ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
            | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
            | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
      | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
      | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
      | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) ) ),
    inference(transitivity,[status(thm)],[49,47]) ).

tff(51,plain,
    ( ~ ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
          ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
          | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
    | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
    | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
    | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
    | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(52,plain,
    ( ~ ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
          ( pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(H,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,As),As3))))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(Q),produc7507926704131184380et_nat(H,As3)))
          | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(P),produc7507926704131184380et_nat(H,As)))
          | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,As),As3) != collect_nat(aTP_Lamm_bg) ) )
    | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2)))
    | ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h))))
    | pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2))))
    | ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != collect_nat(aTP_Lamm_bg) ) ),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    pp(aa_Pro2991721470636411351t_bool(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_a_assn(q,r2)),r)),produc7507926704131184380et_nat(h,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2)))),
    inference(unit_resolution,[status(thm)],[52,46,43,36,33]) ).

tff(54,plain,
    $false,
    inference(unit_resolution,[status(thm)],[53,17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem  : ITP213_1 : TPTP v8.1.0. Released v8.0.0.
% 0.06/0.15  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.36  % Computer : n005.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Sep  1 04:51:33 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.13/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36  Usage: tptp [options] [-file:]file
% 0.13/0.36    -h, -?       prints this message.
% 0.13/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.36    -m, -model   generate model.
% 0.13/0.36    -p, -proof   generate proof.
% 0.13/0.36    -c, -core    generate unsat core of named formulas.
% 0.13/0.36    -st, -statistics display statistics.
% 0.13/0.36    -t:timeout   set timeout (in second).
% 0.13/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36    -<param>:<value> configuration parameter and value.
% 0.13/0.36    -o:<output-file> file to place output in.
% 11.51/8.34  % SZS status Theorem
% 11.51/8.34  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------