%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW470_3 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:37:05 AM UTC 2025
% Result : Theorem 1.98s 2.17s
% Output : Proof 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 53 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 356 ( 28 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 523 ( 244 ~; 185 |; 31 &)
% ( 30 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 36 ( 34 usr; 28 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 17 con; 0-6 aty)
% Number of variables : 355 ( 285 !; 46 ?; 355 :)
% 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(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(hAPP_f500854239l_bool_type,type,
hAPP_f500854239l_bool: ( fun_fu2026518849l_bool * fun_Ho882550911a_bool ) > bool ).
tff(hAPP_f642208769a_bool_type,type,
hAPP_f642208769a_bool: ( fun_fu1663341283a_bool * fun_Ho882550911a_bool ) > fun_Ho882550911a_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(hoare_1876769875iple_a_type,type,
hoare_1876769875iple_a: ( fun_a_fun_state_bool * com * fun_a_fun_state_bool ) > hoare_2076525193iple_a ).
tff(insert1582918915iple_a_type,type,
insert1582918915iple_a: fun_Ho112928087a_bool ).
tff(hoare_572465367rivs_a_type,type,
hoare_572465367rivs_a: fun_Ho882550911a_bool > fun_fu2026518849l_bool ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
tff(5,plain,
! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [P: bool,Q: state] : ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,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)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).
tff(14,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)],[13,12]) ).
tff(15,plain,
! [P: fun_state_bool,Q: x_a] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,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)],[15,11]) ).
tff(17,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(18,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)],[17,16]) ).
tff(19,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)],[18]) ).
tff(20,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)))) = fFalse,
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,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(fFalse) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( hBOOL(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))))) ),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ~ hBOOL(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))))) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ~ hBOOL(fFalse)
<=> ~ hBOOL(fFalse) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
tff(26,plain,
~ hBOOL(fFalse),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,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)],[26,23]) ).
tff(28,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(29,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(30,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)],[29,28]) ).
tff(31,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)),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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(32,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)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)],[31]) ).
tff(33,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)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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(34,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)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)],[33]) ).
tff(35,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)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)],[34,32]) ).
tff(36,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)))
| ( 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)),bot_bo214064617a_bool)))
| ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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(37,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)))
| ( 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)),bot_bo214064617a_bool)))
| ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)],[36]) ).
tff(38,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(39,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(40,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)],[39]) ).
tff(41,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/sandbox/benchmark/theBenchmark.p',fact_123_conseq) ).
tff(42,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)],[41,40]) ).
tff(43,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)],[42,38]) ).
tff(44,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)))
| ( 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)),bot_bo214064617a_bool)))
| ( ~ 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)],[43]) ).
tff(45,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)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)],[44,37]) ).
tff(46,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)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)],[45,35]) ).
tff(47,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)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)))),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)))),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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(48,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)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)))),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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(49,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)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)))),bot_bo214064617a_bool)))
| ~ ( ~ 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)),bot_bo214064617a_bool)))
| ~ ( 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)],[48,47]) ).
tff(50,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)),bot_bo214064617a_bool)))
| ~ ( 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)],[49,46,30]) ).
tff(51,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)),bot_bo214064617a_bool)))
| ~ ( 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(52,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)],[51,50]) ).
tff(53,plain,
$false,
inference(unit_resolution,[status(thm)],[52,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW470_3 : TPTP v9.0.0. Released v5.3.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 11:49:12 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.98/2.17 % SZS status Theorem
% 1.98/2.17 % SZS output start Proof
% See solution above
% 2.07/2.28 % E exiting
%------------------------------------------------------------------------------