%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW474_2 : TPTP v9.0.0. Released v5.3.0.
% 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 05:37:10 AM UTC 2025
% Result : Theorem 3.04s 3.21s
% Output : Proof 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 38
% Syntax : Number of formulae : 102 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 470 ( 69 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 582 ( 246 ~; 239 |; 0 &)
% ( 54 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 25 ( 23 usr; 19 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 13 con; 0-2 aty)
% Number of variables : 144 ( 129 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_f1408815105l_bool_type,type,
hAPP_f1408815105l_bool: ( fun_fu689207471l_bool * fun_Ho1996104121e_bool ) > bool ).
tff(hAPP_f121055253e_bool_type,type,
hAPP_f121055253e_bool: ( fun_fu1296727421e_bool * fun_Ho1996104121e_bool ) > fun_Ho1996104121e_bool ).
tff(cOMBK_2086958736_state_type,type,
cOMBK_2086958736_state: bool > fun_Ho1996104121e_bool ).
tff(fFalse_type,type,
fFalse: bool ).
tff(collec1735317154_state_type,type,
collec1735317154_state: fun_fu1296727421e_bool ).
tff(hAPP_f1204759513e_bool_type,type,
hAPP_f1204759513e_bool: ( fun_fu947547457e_bool * fun_Ho1996104121e_bool ) > fun_fu1296727421e_bool ).
tff(bot_bo1715400655e_bool_type,type,
bot_bo1715400655e_bool: fun_Ho1996104121e_bool ).
tff(hAPP_H1625489667e_bool_type,type,
hAPP_H1625489667e_bool: ( fun_Ho1110608055e_bool * hoare_1875481847_state ) > fun_fu1296727421e_bool ).
tff(hAPP_c406083500_state_type,type,
hAPP_c406083500_state: ( fun_co2032091866_state * com ) > hoare_1875481847_state ).
tff(y_type,type,
y: com ).
tff(hoare_Mirabelle_MGT_type,type,
hoare_Mirabelle_MGT: fun_co2032091866_state ).
tff(insert694999549_state_type,type,
insert694999549_state: fun_Ho1110608055e_bool ).
tff(semila1107643821e_bool_type,type,
semila1107643821e_bool: fun_fu947547457e_bool ).
tff(hoare_2131502867_state_type,type,
hoare_2131502867_state: fun_Ho1996104121e_bool > fun_fu689207471l_bool ).
tff(hAPP_com_bool_type,type,
hAPP_com_bool: ( fun_com_bool * com ) > bool ).
tff(wt_type,type,
wt: fun_com_bool ).
tff(some_com_type,type,
some_com: com > option_com ).
tff(hAPP_p799580910on_com_type,type,
hAPP_p799580910on_com: ( fun_pname_option_com * pname ) > option_com ).
tff(pn_type,type,
pn: pname ).
tff(body_type,type,
body: fun_pname_option_com ).
tff(wT_bodies_type,type,
wT_bodies: bool ).
tff(hoare_1239590103gleton_type,type,
hoare_1239590103gleton: bool ).
tff(hAPP_f1291720380e_bool_type,type,
hAPP_f1291720380e_bool: ( fun_fu1176632176e_bool * fun_pname_bool ) > fun_Ho1996104121e_bool ).
tff(dom_pname_com_type,type,
dom_pname_com: fun_pname_option_com > fun_pname_bool ).
tff(image_1283223414_state_type,type,
image_1283223414_state: fun_pn664418900_state > fun_fu1176632176e_bool ).
tff(hAPP_f2031411714_state_type,type,
hAPP_f2031411714_state: ( fun_fu973320112_state * fun_pname_com ) > fun_pn664418900_state ).
tff(body_1_type,type,
body_1: fun_pname_com ).
tff(cOMBB_1364904209_pname_type,type,
cOMBB_1364904209_pname: fun_co2032091866_state > fun_fu973320112_state ).
tff(1,plain,
( ( bot_bo1715400655e_bool = hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)) )
<=> ( bot_bo1715400655e_bool = hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
bot_bo1715400655e_bool = hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_empty__def) ).
tff(3,plain,
bot_bo1715400655e_bool = hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
^ [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] :
refl(( ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) )
<=> ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) )
<=> ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) )
<=> ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_insert__is__Un) ).
tff(10,plain,
! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ~ ! [A: hoare_1875481847_state,A_1: fun_Ho1996104121e_bool] : ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),A_1) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,A),bot_bo1715400655e_bool)),A_1) )
| ( hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(14,plain,
hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))) = hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),
inference(unit_resolution,[status(thm)],[13,12]) ).
tff(15,plain,
hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))) = hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool),
inference(transitivity,[status(thm)],[15,5]) ).
tff(17,plain,
hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)) = bot_bo1715400655e_bool,
inference(symmetry,[status(thm)],[3]) ).
tff(18,plain,
hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))) = hoare_2131502867_state(bot_bo1715400655e_bool),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))) = hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),
inference(monotonicity,[status(thm)],[18,16]) ).
tff(20,plain,
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
<=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)))
<=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))))) ),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ( hAPP_p799580910on_com(body,pn) = some_com(y) )
<=> ( hAPP_p799580910on_com(body,pn) = some_com(y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
hAPP_p799580910on_com(body,pn) = some_com(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
tff(24,plain,
hAPP_p799580910on_com(body,pn) = some_com(y),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( hBOOL(wT_bodies)
<=> hBOOL(wT_bodies) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
hBOOL(wT_bodies),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(27,plain,
hBOOL(wT_bodies),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [Pn: pname,B_4: com] :
refl(( ( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
<=> ( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
<=> ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
<=> ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [Pn: pname,B_4: com] :
trans(monotonicity(rewrite(( ( ( hAPP_p799580910on_com(body,Pn) = some_com(B_4) )
=> hBOOL(hAPP_com_bool(wt,B_4)) )
<=> ( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ) )),
( ( hBOOL(wT_bodies)
=> ( ( hAPP_p799580910on_com(body,Pn) = some_com(B_4) )
=> hBOOL(hAPP_com_bool(wt,B_4)) ) )
<=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ) ) )),
rewrite(( ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ) )
<=> ( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ) )),
( ( hBOOL(wT_bodies)
=> ( ( hAPP_p799580910on_com(body,Pn) = some_com(B_4) )
=> hBOOL(hAPP_com_bool(wt,B_4)) ) )
<=> ( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [Pn: pname,B_4: com] :
( hBOOL(wT_bodies)
=> ( ( hAPP_p799580910on_com(body,Pn) = some_com(B_4) )
=> hBOOL(hAPP_com_bool(wt,B_4)) ) )
<=> ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [Pn: pname,B_4: com] :
( hBOOL(wT_bodies)
=> ( ( hAPP_p799580910on_com(body,Pn) = some_com(B_4) )
=> hBOOL(hAPP_com_bool(wt,B_4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_WT__bodiesD) ).
tff(34,plain,
! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
| ~ hBOOL(wT_bodies)
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) )
<=> ( ~ ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
| ~ hBOOL(wT_bodies)
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) )
| ~ hBOOL(wT_bodies) )
<=> ( ~ hBOOL(wT_bodies)
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( ~ ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) )
| ~ hBOOL(wT_bodies) )
<=> ( ~ ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
| ~ hBOOL(wT_bodies)
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) )
| ~ hBOOL(wT_bodies) )
<=> ( ~ ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
| ~ hBOOL(wT_bodies)
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) )
| ~ hBOOL(wT_bodies) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Pn: pname,B_4: com] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
| ~ hBOOL(wT_bodies)
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
hBOOL(hAPP_com_bool(wt,y)),
inference(unit_resolution,[status(thm)],[43,37,27,24]) ).
tff(45,plain,
( hBOOL(hoare_1239590103gleton)
<=> hBOOL(hoare_1239590103gleton) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
hBOOL(hoare_1239590103gleton),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(47,plain,
hBOOL(hoare_1239590103gleton),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
^ [C: com] :
refl(( ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
<=> ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
<=> ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
^ [C: com] :
trans(monotonicity(trans(monotonicity(rewrite(( ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) )
<=> ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) )),
( ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) )
<=> ( hBOOL(wT_bodies)
=> ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) ) )),
rewrite(( ( hBOOL(wT_bodies)
=> ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies) ) )),
( ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies) ) )),
( ( hBOOL(hoare_1239590103gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) ) )
<=> ( hBOOL(hoare_1239590103gleton)
=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies) ) ) )),
rewrite(( ( hBOOL(hoare_1239590103gleton)
=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies) ) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ) )),
( ( hBOOL(hoare_1239590103gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) ) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [C: com] :
( hBOOL(hoare_1239590103gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) ) )
<=> ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [C: com] :
( hBOOL(hoare_1239590103gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_MGF) ).
tff(54,plain,
! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ~ ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton)
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) )
<=> ( ~ ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton)
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,y))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
<=> ( ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton)
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( ~ ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,y))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
<=> ( ~ ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton)
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,y))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
<=> ( ~ ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton)
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,y))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [C: com] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,C)),bot_bo1715400655e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton) )
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1239590103gleton)
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ),
inference(unit_resolution,[status(thm)],[63,57,47,27]) ).
tff(65,plain,
hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(bot_bo1715400655e_bool),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))),
inference(unit_resolution,[status(thm)],[64,44]) ).
tff(66,plain,
hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))))),
inference(modus_ponens,[status(thm)],[65,21]) ).
tff(67,plain,
hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))) = hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),bot_bo1715400655e_bool),
inference(monotonicity,[status(thm)],[17]) ).
tff(68,plain,
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))))
<=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),bot_bo1715400655e_bool)) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),bot_bo1715400655e_bool))
<=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))) ),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
^ [G_1: fun_Ho1996104121e_bool] :
refl(( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool))
<=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool)) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool))
<=> ! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool)) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool))
<=> ! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).
tff(74,plain,
! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool)),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool)),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool)),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [G_1: fun_Ho1996104121e_bool] : hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),bot_bo1715400655e_bool))
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),bot_bo1715400655e_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),bot_bo1715400655e_bool)),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))),
inference(modus_ponens,[status(thm)],[78,69]) ).
tff(80,plain,
hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))) = hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),
inference(monotonicity,[status(thm)],[16]) ).
tff(81,plain,
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
<=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)))
<=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))))) ),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
( ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)))
<=> ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))))) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)))
<=> ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_7) ).
tff(86,plain,
~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool))),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))))),
inference(modus_ponens,[status(thm)],[86,83]) ).
tff(88,plain,
^ [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
refl(( ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) )
<=> ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) )
<=> ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
^ [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ) )),
( ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) ) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ) ) )),
rewrite(( ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ) )),
( ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) ) )
<=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) ) )
<=> ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
=> ( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2))
=> hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cut) ).
tff(94,plain,
! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
( ( ~ ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) )
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))) )
<=> ( ~ ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) )
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) )
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [G_1: fun_Ho1996104121e_bool,G_2: fun_Ho1996104121e_bool,Ts: fun_Ho1996104121e_bool] :
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_2),Ts))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(G_1),G_2)) )
| hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
( hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse))),hAPP_f121055253e_bool(hAPP_f1204759513e_bool(semila1107643821e_bool,hAPP_f121055253e_bool(hAPP_H1625489667e_bool(insert694999549_state,hAPP_c406083500_state(hoare_Mirabelle_MGT,y)),bot_bo1715400655e_bool)),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))))
| ~ hBOOL(hAPP_f1408815105l_bool(hoare_2131502867_state(hAPP_f1291720380e_bool(image_1283223414_state(hAPP_f2031411714_state(cOMBB_1364904209_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f121055253e_bool(collec1735317154_state,cOMBK_2086958736_state(fFalse)))) ),
inference(unit_resolution,[status(thm)],[100,97]) ).
tff(102,plain,
$false,
inference(unit_resolution,[status(thm)],[101,87,79,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW474_2 : TPTP v9.0.0. Released v5.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 11:52:48 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.04/3.21 % SZS status Theorem
% 3.04/3.21 % SZS output start Proof
% See solution above
% 3.10/3.30 % E exiting
%------------------------------------------------------------------------------