TSTP Solution File: SWW470_3 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW470_3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 20:58:50 EDT 2022
% Result : Theorem 2.06s 1.68s
% Output : Proof 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 91
% Syntax : Number of formulae : 166 ( 55 unt; 44 typ; 0 def)
% Number of atoms : 567 ( 97 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 750 ( 339 ~; 251 |; 46 &)
% ( 78 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 34 ( 34 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 55 ( 24 >; 31 *; 0 +; 0 <<)
% Number of predicates : 38 ( 36 usr; 30 prp; 0-3 aty)
% Number of functors : 43 ( 43 usr; 20 con; 0-6 aty)
% Number of variables : 538 ( 437 !; 56 ?; 538 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_state_bool_type,type,
hAPP_state_bool: ( fun_state_bool * state ) > bool ).
tff(tptp_fun_S_2_30_type,type,
tptp_fun_S_2_30: ( fun_a_fun_state_bool * com * fun_Ho882550911a_bool * fun_a_fun_state_bool ) > state ).
tff(hAPP_f762886889e_bool_type,type,
hAPP_f762886889e_bool: ( fun_fu281355805e_bool * fun_state_bool ) > fun_a_fun_state_bool ).
tff(hAPP_f1759915619e_bool_type,type,
hAPP_f1759915619e_bool: ( fun_fu373216837e_bool * fun_state_bool ) > fun_state_bool ).
tff(b_type,type,
b: fun_state_bool ).
tff(hAPP_f2073279419e_bool_type,type,
hAPP_f2073279419e_bool: ( fun_fu88048803e_bool * fun_bool_bool ) > fun_fu373216837e_bool ).
tff(fNot_type,type,
fNot: fun_bool_bool ).
tff(cOMBB_160679318_state_type,type,
cOMBB_160679318_state: fun_fu88048803e_bool ).
tff(hAPP_f1261923407e_bool_type,type,
hAPP_f1261923407e_bool: ( fun_fu734682033e_bool * fun_a_2117018159e_bool ) > fun_fu281355805e_bool ).
tff(hAPP_f963367678e_bool_type,type,
hAPP_f963367678e_bool: ( fun_fu2008829792e_bool * fun_a_1632297036l_bool ) > fun_a_2117018159e_bool ).
tff(hAPP_f1509969235l_bool_type,type,
hAPP_f1509969235l_bool: ( fun_fu2118559873l_bool * fun_a_fun_state_bool ) > fun_a_1632297036l_bool ).
tff(p_type,type,
p: fun_a_fun_state_bool ).
tff(hAPP_f1178339559l_bool_type,type,
hAPP_f1178339559l_bool: ( fun_fu1340893257l_bool * fun_fu1658206819l_bool ) > fun_fu2118559873l_bool ).
tff(hAPP_f1561913689l_bool_type,type,
hAPP_f1561913689l_bool: ( fun_fu1873708859l_bool * fun_bo1549164019l_bool ) > fun_fu1658206819l_bool ).
tff(fconj_type,type,
fconj: fun_bo1549164019l_bool ).
tff(cOMBB_188601460_state_type,type,
cOMBB_188601460_state: fun_fu1873708859l_bool ).
tff(cOMBB_1355796797bool_a_type,type,
cOMBB_1355796797bool_a: fun_fu1340893257l_bool ).
tff(hAPP_f375255701e_bool_type,type,
hAPP_f375255701e_bool: ( fun_fu1631777789e_bool * fun_fu1047394976e_bool ) > fun_fu2008829792e_bool ).
tff(cOMBS_1378840469l_bool_type,type,
cOMBS_1378840469l_bool: fun_fu1047394976e_bool ).
tff(cOMBB_145932198bool_a_type,type,
cOMBB_145932198bool_a: fun_fu1631777789e_bool ).
tff(cOMBC_892787026e_bool_type,type,
cOMBC_892787026e_bool: fun_fu734682033e_bool ).
tff(g_type,type,
g: fun_Ho882550911a_bool ).
tff(c_type,type,
c: com ).
tff(hAPP_b2019457360e_bool_type,type,
hAPP_b2019457360e_bool: ( fun_bo1936561970e_bool * bool ) > fun_state_bool ).
tff(fFalse_type,type,
fFalse: bool ).
tff(cOMBK_bool_state_type,type,
cOMBK_bool_state: fun_bo1936561970e_bool ).
tff(cOMBK_1458035955bool_a_type,type,
cOMBK_1458035955bool_a: fun_fu281355805e_bool ).
tff(hAPP_a2036067514e_bool_type,type,
hAPP_a2036067514e_bool: ( fun_a_fun_state_bool * x_a ) > fun_state_bool ).
tff(tptp_fun_Z_11_31_type,type,
tptp_fun_Z_11_31: ( fun_a_fun_state_bool * com * fun_Ho882550911a_bool * fun_a_fun_state_bool ) > x_a ).
tff(hAPP_H454055633a_bool_type,type,
hAPP_H454055633a_bool: ( fun_Ho882550911a_bool * hoare_2076525193iple_a ) > bool ).
tff(hoare_1876769875iple_a_type,type,
hoare_1876769875iple_a: ( fun_a_fun_state_bool * com * fun_a_fun_state_bool ) > hoare_2076525193iple_a ).
tff(hAPP_b1299643615a_bool_type,type,
hAPP_b1299643615a_bool: ( fun_bo840878273a_bool * bool ) > fun_Ho882550911a_bool ).
tff(cOMBK_861658160iple_a_type,type,
cOMBK_861658160iple_a: fun_bo840878273a_bool ).
tff(hAPP_f642208769a_bool_type,type,
hAPP_f642208769a_bool: ( fun_fu1663341283a_bool * fun_Ho882550911a_bool ) > fun_Ho882550911a_bool ).
tff(collec977865374iple_a_type,type,
collec977865374iple_a: fun_fu1663341283a_bool ).
tff(hAPP_f500854239l_bool_type,type,
hAPP_f500854239l_bool: ( fun_fu2026518849l_bool * fun_Ho882550911a_bool ) > bool ).
tff(hAPP_H1566092493l_bool_type,type,
hAPP_H1566092493l_bool: ( fun_Ho1910759733l_bool * hoare_2076525193iple_a ) > fun_fu2026518849l_bool ).
tff(member276146780iple_a_type,type,
member276146780iple_a: fun_Ho1910759733l_bool ).
tff(bot_bo214064617a_bool_type,type,
bot_bo214064617a_bool: fun_Ho882550911a_bool ).
tff(hAPP_H1940471919a_bool_type,type,
hAPP_H1940471919a_bool: ( fun_Ho112928087a_bool * hoare_2076525193iple_a ) > fun_fu1663341283a_bool ).
tff(insert1582918915iple_a_type,type,
insert1582918915iple_a: fun_Ho112928087a_bool ).
tff(tptp_fun_S_3_32_type,type,
tptp_fun_S_3_32: ( fun_a_fun_state_bool * fun_a_fun_state_bool * fun_a_fun_state_bool * com * fun_Ho882550911a_bool * fun_a_fun_state_bool ) > state ).
tff(hoare_572465367rivs_a_type,type,
hoare_572465367rivs_a: fun_Ho882550911a_bool > fun_fu2026518849l_bool ).
tff(1,plain,
^ [P: bool,Q: hoare_2076525193iple_a] :
refl(
( ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P )
<=> ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [P: bool,Q: hoare_2076525193iple_a] : ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P )
<=> ! [P: bool,Q: hoare_2076525193iple_a] : ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [P: bool,Q: hoare_2076525193iple_a] : ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P )
<=> ! [P: bool,Q: hoare_2076525193iple_a] : ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [P: bool,Q: hoare_2076525193iple_a] : ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____wdcyoqcnvy__) ).
tff(5,plain,
! [P: bool,Q: hoare_2076525193iple_a] : ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [P: bool,Q: hoare_2076525193iple_a] : ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [P: bool,Q: hoare_2076525193iple_a] : ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [P: bool,Q: hoare_2076525193iple_a] : ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,P),Q) = P )
| ( hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))) = fFalse ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))) = fFalse,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
fFalse = hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [P: bool,Q: state] :
refl(
( ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P )
<=> ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P )
<=> ! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P )
<=> ! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
tff(15,plain,
! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P )
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))) = fFalse ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))) = fFalse,
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [P: fun_state_bool,Q: x_a] :
refl(
( ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P )
<=> ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P )
<=> ! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P )
<=> ! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).
tff(24,plain,
! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P )
| ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))) = hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))) = hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))) = hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))) = hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),
inference(transitivity,[status(thm)],[29,19,10]) ).
tff(31,plain,
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
<=> hBOOL(hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( hBOOL(hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
<=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ hBOOL(hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
<=> ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
^ [Pa: fun_Ho882550911a_bool] :
refl(
( ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa )
<=> ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [Pa: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa )
<=> ! [Pa: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [Pa: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa )
<=> ! [Pa: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
! [Pa: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Collect__def) ).
tff(38,plain,
! [Pa: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Pa: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Pa: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Pa: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(collec977865374iple_a,Pa) = Pa )
| ( hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) = hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) = hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))) = hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
<=> hBOOL(hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ~ hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
<=> ~ hBOOL(hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
^ [X_2: hoare_2076525193iple_a] :
refl(
( ( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) )
<=> ( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) )
<=> ! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
^ [X_2: hoare_2076525193iple_a] :
rewrite(
( ( hBOOL(hAPP_H454055633a_bool(bot_bo214064617a_bool,X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),bot_bo214064617a_bool)) )
<=> ( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(bot_bo214064617a_bool,X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),bot_bo214064617a_bool)) )
<=> ! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(bot_bo214064617a_bool,X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),bot_bo214064617a_bool)) )
<=> ! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(bot_bo214064617a_bool,X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),bot_bo214064617a_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(bot_bo214064617a_bool,X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),bot_bo214064617a_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_bot__empty__eq) ).
tff(52,plain,
! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(bot_bo214064617a_bool,X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),bot_bo214064617a_bool)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ),
inference(modus_ponens,[status(thm)],[52,49]) ).
tff(54,plain,
! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ~ ! [X_2: hoare_2076525193iple_a] :
( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),X_2))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,X_2),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) )
| ( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
^ [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
refl(
( ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) )
<=> ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) )
<=> ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
^ [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
rewrite(
( ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != bot_bo214064617a_bool )
<=> ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != bot_bo214064617a_bool )
<=> ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != bot_bo214064617a_bool )
<=> ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != bot_bo214064617a_bool ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,axiom,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != bot_bo214064617a_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_insert__not__empty) ).
tff(64,plain,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != bot_bo214064617a_bool ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ),
inference(modus_ponens,[status(thm)],[64,61]) ).
tff(66,plain,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ~ ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] : ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) )
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))) != hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
^ [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
refl(
( ( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) )
<=> ( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) )
<=> ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) )
<=> ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
^ [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
rewrite(
( ( hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
=> ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) )
<=> ( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
=> ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) )
<=> ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,axiom,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
=> ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_insert__absorb) ).
tff(76,plain,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) ),
inference(modus_ponens,[status(thm)],[78,71]) ).
tff(80,plain,
( ( ~ ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) )
| ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))) = hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ) )
<=> ( ~ ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) )
| ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))) = hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ~ ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) )
| ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))) = hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [A_13: hoare_2076525193iple_a,A: fun_Ho882550911a_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,A_13),A))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,A_13),A) = A ) )
| ~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))))
| ( hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))) = hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))),
inference(unit_resolution,[status(thm)],[82,79,69]) ).
tff(84,plain,
( ~ ( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) )
| ~ hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
( ~ ( hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
<=> hBOOL(hAPP_f500854239l_bool(hAPP_H1566092493l_bool(member276146780iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))) )
| ~ hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
~ hBOOL(hAPP_H454055633a_bool(hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))),
inference(unit_resolution,[status(thm)],[85,57]) ).
tff(87,plain,
~ hBOOL(hAPP_H454055633a_bool(hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse),hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))),
inference(modus_ponens,[status(thm)],[86,45]) ).
tff(88,plain,
~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))),
inference(modus_ponens,[status(thm)],[87,33]) ).
tff(89,plain,
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool)))
<=> ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))))) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool)))
<=> ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool))) ),
inference(rewrite,[status(thm)],]) ).
tff(91,axiom,
~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(92,plain,
~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),bot_bo214064617a_bool))),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse))))),
inference(modus_ponens,[status(thm)],[92,89]) ).
tff(94,plain,
^ [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
refl(
( ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
^ [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
rewrite(
( ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
^ [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
rewrite(
( ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
& ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
& ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
^ [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
rewrite(
( ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
& ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
& ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
& ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
<=> ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
& ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
^ [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
rewrite(
( ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool)))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) )
<=> ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool)))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) )
<=> ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
( ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool)))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) )
<=> ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool)))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
^ [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Z_11: x_a,S_2: state] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
rewrite(
( ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)) ) )
<=> ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ))),
( ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)) ) )
<=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) )),
( ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)) ) ) )
<=> ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) )),
rewrite(
( ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) )
<=> ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) )),
( ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)) ) ) )
<=> ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ))),
( ! [Z_11: x_a,S_2: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)) ) ) )
<=> ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) )),
( ( ! [Z_11: x_a,S_2: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)) ) ) )
=> hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool))) )
<=> ( ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) )
=> hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool))) ) )),
rewrite(
( ( ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) )
=> hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool))) )
<=> ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool)))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ) )),
( ( ! [Z_11: x_a,S_2: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)) ) ) )
=> hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool))) )
<=> ( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool)))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( ! [Z_11: x_a,S_2: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)) ) ) )
=> hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool))) )
<=> ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool)))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,axiom,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( ! [Z_11: x_a,S_2: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2))
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3)) )
=> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3)) ) ) )
=> hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_conseq) ).
tff(109,plain,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool)))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),bot_bo214064617a_bool)))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),bot_bo214064617a_bool)))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ! [Z_11: x_a,S_2: state] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
& ! [S_3: state] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),S_3))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),S_2)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[110,104]) ).
tff(112,plain,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
& ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
& ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
& ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[112,102]) ).
tff(114,plain,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[113,100]) ).
tff(115,plain,
! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[114,98]) ).
tff(116,plain,
( ( ~ ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
| hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,c,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ) ) ) ) )
<=> ( ~ ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
| hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,c,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ~ ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
| hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,c,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [Q_1: fun_a_fun_state_bool,Ga: fun_Ho882550911a_bool,Ca: com,Pa: fun_a_fun_state_bool] :
( hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(Pa,Ca,Q_1)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1)))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(Ga),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,Ca,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,tptp_fun_Z_11_31(Pa,Ca,Ga,Q_1)),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,Pa,Ca,Ga,Q_1)))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(Pa,Ca,Ga,Q_1))) ) ) ) ) )
| hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,c,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
~ ( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,c,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ) ) ) ),
inference(unit_resolution,[status(thm)],[118,115,93]) ).
tff(120,plain,
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [P_1: fun_a_fun_state_bool,Q_2: fun_a_fun_state_bool] :
( ~ hBOOL(hAPP_f500854239l_bool(hoare_572465367rivs_a(g),hAPP_f642208769a_bool(hAPP_H1940471919a_bool(insert1582918915iple_a,hoare_1876769875iple_a(P_1,c,Q_2)),hAPP_f642208769a_bool(collec977865374iple_a,hAPP_b1299643615a_bool(cOMBK_861658160iple_a,fFalse)))))
| ~ ( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ ! [Z_12: x_a] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_12),tptp_fun_S_3_32(Q_2,P_1,hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))))
| ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_12),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ) ) )
| hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))) ),
inference(tautology,[status(thm)],]) ).
tff(121,plain,
hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),tptp_fun_Z_11_31(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b)))),tptp_fun_S_2_30(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,hAPP_b2019457360e_bool(cOMBK_bool_state,fFalse)),c,g,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(hAPP_f375255701e_bool(cOMBB_145932198bool_a,cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(hAPP_f1178339559l_bool(cOMBB_1355796797bool_a,hAPP_f1561913689l_bool(cOMBB_188601460_state,fconj)),p))),hAPP_f1759915619e_bool(hAPP_f2073279419e_bool(cOMBB_160679318_state,fNot),b))))),
inference(unit_resolution,[status(thm)],[120,119]) ).
tff(122,plain,
$false,
inference(unit_resolution,[status(thm)],[121,88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW470_3 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.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 18:04:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 2.06/1.68 % SZS status Theorem
% 2.06/1.68 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------