TSTP Solution File: SWW474+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW474+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:58:58 EDT 2022
% Result : Theorem 1.13s 1.04s
% Output : Proof 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 69
% Syntax : Number of formulae : 139 ( 48 unt; 29 typ; 0 def)
% Number of atoms : 486 ( 79 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 483 ( 189 ~; 173 |; 0 &)
% ( 78 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 82 ( 82 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 16 >; 9 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 13 con; 0-2 aty)
% Number of variables : 170 ( 147 !; 0 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_f1760790145l_bool_type,type,
hAPP_f1760790145l_bool: ( $i * $i ) > $i ).
tff(hAPP_f921536533e_bool_type,type,
hAPP_f921536533e_bool: ( $i * $i ) > $i ).
tff(cOMBK_1079618832_state_type,type,
cOMBK_1079618832_state: $i > $i ).
tff(fFalse_type,type,
fFalse: $i ).
tff(collec727977250_state_type,type,
collec727977250_state: $i ).
tff(hAPP_f1583986009e_bool_type,type,
hAPP_f1583986009e_bool: ( $i * $i ) > $i ).
tff(hAPP_H727730819e_bool_type,type,
hAPP_H727730819e_bool: ( $i * $i ) > $i ).
tff(hAPP_c1546227244_state_type,type,
hAPP_c1546227244_state: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(hoare_Mirabelle_MGT_type,type,
hoare_Mirabelle_MGT: $i ).
tff(insert1835143293_state_type,type,
insert1835143293_state: $i ).
tff(semila447562797e_bool_type,type,
semila447562797e_bool: $i ).
tff(hoare_659004819_state_type,type,
hoare_659004819_state: $i > $i ).
tff(bot_bo1055319631e_bool_type,type,
bot_bo1055319631e_bool: $i ).
tff(hAPP_com_bool_type,type,
hAPP_com_bool: ( $i * $i ) > $i ).
tff(wt_type,type,
wt: $i ).
tff(some_com_type,type,
some_com: $i > $i ).
tff(hAPP_p799580910on_com_type,type,
hAPP_p799580910on_com: ( $i * $i ) > $i ).
tff(pn_type,type,
pn: $i ).
tff(body_type,type,
body: $i ).
tff(wT_bodies_type,type,
wT_bodies: $i ).
tff(hoare_298929751gleton_type,type,
hoare_298929751gleton: $i ).
tff(hAPP_f631639356e_bool_type,type,
hAPP_f631639356e_bool: ( $i * $i ) > $i ).
tff(dom_pname_com_type,type,
dom_pname_com: $i > $i ).
tff(image_275883510_state_type,type,
image_275883510_state: $i > $i ).
tff(hAPP_f1758910594_state_type,type,
hAPP_f1758910594_state: ( $i * $i ) > $i ).
tff(body_1_type,type,
body_1: $i ).
tff(cOMBB_422605457_pname_type,type,
cOMBB_422605457_pname: $i > $i ).
tff(1,plain,
^ [A: $i,A_1: $i] :
refl(
( ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) )
<=> ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) )
<=> ! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [A: $i,A_1: $i] :
rewrite(
( ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),A_1) )
<=> ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),A_1) )
<=> ! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),A_1) )
<=> ! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),A_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),A_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_insert__is__Un) ).
tff(7,plain,
! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),A_1) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [A: $i,A_1: $i] : ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),A_1) )
| ( hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))) = hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
^ [P_1: $i] :
refl(
( ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 )
<=> ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [P_1: $i] : ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 )
<=> ! [P_1: $i] : ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [P_1: $i] : ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 )
<=> ! [P_1: $i] : ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
! [P_1: $i] : ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Collect__def) ).
tff(18,plain,
! [P_1: $i] : ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [P_1: $i] : ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [P_1: $i] : ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [P_1: $i] : ( hAPP_f921536533e_bool(collec727977250_state,P_1) = P_1 )
| ( hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)) = cOMBK_1079618832_state(fFalse) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)) = cOMBK_1079618832_state(fFalse),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
cOMBK_1079618832_state(fFalse) = hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
hoare_659004819_state(cOMBK_1079618832_state(fFalse)) = hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
hAPP_f1760790145l_bool(hoare_659004819_state(cOMBK_1079618832_state(fFalse)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))) = hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),
inference(monotonicity,[status(thm)],[24,13]) ).
tff(26,plain,
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(cOMBK_1079618832_state(fFalse)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
<=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
<=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(cOMBK_1079618832_state(fFalse)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ( hAPP_p799580910on_com(body,pn) = some_com(y) )
<=> ( hAPP_p799580910on_com(body,pn) = some_com(y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
hAPP_p799580910on_com(body,pn) = some_com(y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
tff(30,plain,
hAPP_p799580910on_com(body,pn) = some_com(y),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
^ [Pn: $i,B_4: $i] :
refl(
( ( 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) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) )
<=> ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) )
<=> ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
^ [Pn: $i,B_4: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(asserted(hBOOL(wT_bodies)),
( hBOOL(wT_bodies)
<=> $true )),
( ~ hBOOL(wT_bodies)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ hBOOL(wT_bodies)
<=> $false )),
( ( 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) )
| $false ) )),
rewrite(
( ( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| $false )
<=> ( 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(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) )
<=> ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [Pn: $i,B_4: $i] :
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(37,plain,
( ! [Pn: $i,B_4: $i] :
( hBOOL(wT_bodies)
=> ( ( hAPP_p799580910on_com(body,Pn) = some_com(B_4) )
=> hBOOL(hAPP_com_bool(wt,B_4)) ) )
<=> ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [Pn: $i,B_4: $i] :
( hBOOL(wT_bodies)
=> ( ( hAPP_p799580910on_com(body,Pn) = some_com(B_4) )
=> hBOOL(hAPP_com_bool(wt,B_4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_WT__bodiesD) ).
tff(39,plain,
! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) )
| ~ hBOOL(wT_bodies) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) ),
inference(modus_ponens,[status(thm)],[42,32]) ).
tff(44,plain,
( ( ~ ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) )
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) )
<=> ( ~ ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) )
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) )
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [Pn: $i,B_4: $i] :
( hBOOL(hAPP_com_bool(wt,B_4))
| ( hAPP_p799580910on_com(body,Pn) != some_com(B_4) ) )
| hBOOL(hAPP_com_bool(wt,y))
| ( hAPP_p799580910on_com(body,pn) != some_com(y) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
hBOOL(hAPP_com_bool(wt,y)),
inference(unit_resolution,[status(thm)],[46,43,30]) ).
tff(48,plain,
^ [C: $i] :
refl(
( ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) )
<=> ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) )
<=> ! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
^ [C: $i] :
trans(
monotonicity(
rewrite(
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
<=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) )),
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_com_bool(wt,C)) ) )),
rewrite(
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_com_bool(wt,C)) )
<=> ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ) )),
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) )
<=> ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [C: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) )
<=> ! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [C: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) )
<=> ! [C: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
^ [C: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(asserted(hBOOL(wT_bodies)),
( hBOOL(wT_bodies)
<=> $true )),
( ~ hBOOL(wT_bodies)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ hBOOL(wT_bodies)
<=> $false )),
trans(
monotonicity(
iff_true(asserted(hBOOL(hoare_298929751gleton)),
( hBOOL(hoare_298929751gleton)
<=> $true )),
( ~ hBOOL(hoare_298929751gleton)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ hBOOL(hoare_298929751gleton)
<=> $false )),
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_298929751gleton) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| $false
| $false ) )),
rewrite(
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| $false
| $false )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) ) )),
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_298929751gleton) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [C: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_298929751gleton) )
<=> ! [C: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) )
<=> ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) )),
( ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) )
<=> ( hBOOL(wT_bodies)
=> ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) ) )),
rewrite(
( ( hBOOL(wT_bodies)
=> ( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies) ) )),
( ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies) ) )),
( ( hBOOL(hoare_298929751gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) ) )
<=> ( hBOOL(hoare_298929751gleton)
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies) ) ) )),
rewrite(
( ( hBOOL(hoare_298929751gleton)
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies) ) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_298929751gleton) ) )),
( ( hBOOL(hoare_298929751gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) ) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_298929751gleton) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [C: $i] :
( hBOOL(hoare_298929751gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) ) )
<=> ! [C: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_298929751gleton) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [C: $i] :
( hBOOL(hoare_298929751gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP_com_bool(wt,C))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_MGF) ).
tff(58,plain,
! [C: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_298929751gleton) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [C: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [C: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(bot_bo1055319631e_bool),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),bot_bo1055319631e_bool)))
| ~ hBOOL(hAPP_com_bool(wt,C)) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(modus_ponens,[status(thm)],[60,51]) ).
tff(62,plain,
! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(modus_ponens,[status(thm)],[62,49]) ).
tff(64,plain,
( ( ~ ! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) )
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) )
<=> ( ~ ! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) )
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) )
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [C: $i] :
( ~ hBOOL(hAPP_com_bool(wt,C))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,C)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) )
| ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ hBOOL(hAPP_com_bool(wt,y))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(unit_resolution,[status(thm)],[66,63]) ).
tff(68,plain,
hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))),
inference(unit_resolution,[status(thm)],[67,47]) ).
tff(69,plain,
hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(cOMBK_1079618832_state(fFalse)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))),
inference(modus_ponens,[status(thm)],[68,27]) ).
tff(70,plain,
hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),cOMBK_1079618832_state(fFalse)) = hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))),
inference(monotonicity,[status(thm)],[23]) ).
tff(71,plain,
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),cOMBK_1079618832_state(fFalse)))
<=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))
<=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),cOMBK_1079618832_state(fFalse))) ),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
^ [G_1: $i] :
refl(
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))
<=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))
<=> ! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [G_1: $i] :
rewrite(
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool))
<=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool))
<=> ! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool))
<=> ! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool)) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).
tff(79,plain,
! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),bot_bo1055319631e_bool)),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),
inference(modus_ponens,[status(thm)],[79,76]) ).
tff(81,plain,
! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
( ~ ! [G_1: $i] : hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),cOMBK_1079618832_state(fFalse))),
inference(modus_ponens,[status(thm)],[84,72]) ).
tff(86,plain,
hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))) = hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),
inference(monotonicity,[status(thm)],[13]) ).
tff(87,plain,
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
<=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
<=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
<=> ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),bot_bo1055319631e_bool)))
<=> ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),bot_bo1055319631e_bool)))
<=> ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),bot_bo1055319631e_bool))) ),
inference(rewrite,[status(thm)],]) ).
tff(92,axiom,
~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),bot_bo1055319631e_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_7) ).
tff(93,plain,
~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),bot_bo1055319631e_bool))),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))),
inference(modus_ponens,[status(thm)],[93,90]) ).
tff(95,plain,
~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse))))),
inference(modus_ponens,[status(thm)],[94,89]) ).
tff(96,plain,
^ [G_1: $i,G_2: $i,Ts: $i] :
refl(
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) )
<=> ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) )
<=> ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
^ [G_1: $i,G_2: $i,Ts: $i] :
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ) )),
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) ) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ) ) )),
rewrite(
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ) )),
( ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) ) )
<=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) ) )
<=> ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
=> ( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2))
=> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_cut) ).
tff(102,plain,
! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( ( ~ ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) )
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(cOMBK_1079618832_state(fFalse)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),cOMBK_1079618832_state(fFalse))) )
<=> ( ~ ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) )
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(cOMBK_1079618832_state(fFalse)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),cOMBK_1079618832_state(fFalse))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ~ ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) )
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(cOMBK_1079618832_state(fFalse)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),cOMBK_1079618832_state(fFalse))) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [G_1: $i,G_2: $i,Ts: $i] :
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),G_2)) )
| hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(cOMBK_1079618832_state(fFalse)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),cOMBK_1079618832_state(fFalse))) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(cOMBK_1079618832_state(fFalse)),hAPP_f921536533e_bool(hAPP_f1583986009e_bool(semila447562797e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hAPP_c1546227244_state(hoare_Mirabelle_MGT,y)),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))),hAPP_f921536533e_bool(collec727977250_state,cOMBK_1079618832_state(fFalse)))))
| ~ hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(hAPP_f631639356e_bool(image_275883510_state(hAPP_f1758910594_state(cOMBB_422605457_pname(hoare_Mirabelle_MGT),body_1)),dom_pname_com(body))),cOMBK_1079618832_state(fFalse))) ),
inference(unit_resolution,[status(thm)],[108,105]) ).
tff(110,plain,
$false,
inference(unit_resolution,[status(thm)],[109,95,85,69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW474+2 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 18:39:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.13/1.04 % SZS status Theorem
% 1.13/1.04 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------