%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP213_1 : TPTP v9.0.0. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 Jun 21 05:12:01 AM UTC 2025
% Result : Theorem 5.74s 5.94s
% Output : Proof 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 40 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 56 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 275 ( 119 ~; 112 |; 0 &)
% ( 23 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-3 aty)
% Number of variables : 105 ( 95 !; 0 ?; 105 :)
% 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(bot_bot_set_nat_type,type,
bot_bot_set_nat: set_nat ).
tff(inf_inf_set_nat_type,type,
inf_inf_set_nat: fun_se1909708154429037836et_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,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(2,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(3,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)],[2,1]) ).
tff(4,plain,
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),
inference(symmetry,[status(thm)],[3]) ).
tff(5,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,as,h)),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,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,as,h))),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,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,as,h)))) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,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,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2)))) ),
inference(symmetry,[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,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,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2)))) ),
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,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(11,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(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)))),
inference(modus_ponens,[status(thm)],[11,10]) ).
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,aa_set_nat_set_nat(aa_set2309701074089104077et_nat(sup_sup_set_nat,hoare_new_addrs(h2,as1,h)),as2)))),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,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))))
| ( 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) != 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(15,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(quant_intro,[status(thm)],[14]) ).
tff(16,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(17,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(18,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)],[17]) ).
tff(19,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(20,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)],[19,18]) ).
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))))
| ( 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)],[20,16]) ).
tff(22,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(skolemize,[status(sab)],[21]) ).
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))) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,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(25,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(26,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)],[25,24]) ).
tff(27,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(28,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(29,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)],[28,27]) ).
tff(30,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(31,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(32,plain,
pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(h,as2))),
inference(modus_ponens,[status(thm)],[31,30]) ).
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))))
| ( 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))) )
| ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != bot_bot_set_nat )
| ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(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,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_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h)))) )
<=> ( ~ ! [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))) )
| ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != bot_bot_set_nat )
| ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(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,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_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,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))))
| ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != bot_bot_set_nat )
| ~ 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) != bot_bot_set_nat )
| ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(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,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_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,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))) )
| 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) != bot_bot_set_nat )
| ~ 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)))) )
<=> ( ~ ! [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))) )
| ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != bot_bot_set_nat )
| ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(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,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_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h)))) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,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))) )
| 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) != bot_bot_set_nat )
| ~ 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)))) )
<=> ( ~ ! [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))) )
| ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != bot_bot_set_nat )
| ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(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,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_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h)))) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,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))) )
| 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) != bot_bot_set_nat )
| ~ 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)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,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))) )
| ( aa_set_nat_set_nat(aa_set2309701074089104077et_nat(inf_inf_set_nat,hoare_new_addrs(h2,as1,h)),as2) != bot_bot_set_nat )
| ~ pp(aa_Pro2991721470636411351t_bool(rep_assn(r),produc7507926704131184380et_nat(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,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_a_assn(q,r2)),produc7507926704131184380et_nat(h,hoare_new_addrs(h2,as1,h)))) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,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)],[38,32,29,26,23]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP213_1 : TPTP v9.0.0. Released v8.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Jun 19 18:31:04 EDT 2025
% 0.10/0.32 % CPUTime :
% 5.74/5.94 % SZS status Theorem
% 5.74/5.94 % SZS output start Proof
% See solution above
% 6.46/6.71 % E exiting
%------------------------------------------------------------------------------