%------------------------------------------------------------------------------
% 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 : n001.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 1.95s 2.21s
% Output : Proof 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 61 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 395 ( 39 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 576 ( 267 ~; 208 |; 31 &)
% ( 34 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 17 con; 0-6 aty)
% Number of variables : 369 ( 297 !; 46 ?; 369 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_state_bool_type,type,
hAPP_state_bool: ( $i * $i ) > $i ).
tff(tptp_fun_S_2_30_type,type,
tptp_fun_S_2_30: ( $i * $i * $i * $i ) > $i ).
tff(hAPP_f762886889e_bool_type,type,
hAPP_f762886889e_bool: ( $i * $i ) > $i ).
tff(hAPP_f1759915619e_bool_type,type,
hAPP_f1759915619e_bool: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(hAPP_f2073279419e_bool_type,type,
hAPP_f2073279419e_bool: ( $i * $i ) > $i ).
tff(fNot_type,type,
fNot: $i ).
tff(cOMBB_160679318_state_type,type,
cOMBB_160679318_state: $i ).
tff(hAPP_f1261923407e_bool_type,type,
hAPP_f1261923407e_bool: ( $i * $i ) > $i ).
tff(hAPP_f963367678e_bool_type,type,
hAPP_f963367678e_bool: ( $i * $i ) > $i ).
tff(hAPP_f1509969235l_bool_type,type,
hAPP_f1509969235l_bool: ( $i * $i ) > $i ).
tff(p_type,type,
p: $i ).
tff(hAPP_f1178339559l_bool_type,type,
hAPP_f1178339559l_bool: ( $i * $i ) > $i ).
tff(hAPP_f1561913689l_bool_type,type,
hAPP_f1561913689l_bool: ( $i * $i ) > $i ).
tff(fconj_type,type,
fconj: $i ).
tff(cOMBB_188601460_state_type,type,
cOMBB_188601460_state: $i ).
tff(cOMBB_1355796797bool_a_type,type,
cOMBB_1355796797bool_a: $i ).
tff(hAPP_f375255701e_bool_type,type,
hAPP_f375255701e_bool: ( $i * $i ) > $i ).
tff(cOMBS_1378840469l_bool_type,type,
cOMBS_1378840469l_bool: $i ).
tff(cOMBB_145932198bool_a_type,type,
cOMBB_145932198bool_a: $i ).
tff(cOMBC_892787026e_bool_type,type,
cOMBC_892787026e_bool: $i ).
tff(g_type,type,
g: $i ).
tff(c_type,type,
c: $i ).
tff(hAPP_b2019457360e_bool_type,type,
hAPP_b2019457360e_bool: ( $i * $i ) > $i ).
tff(fFalse_type,type,
fFalse: $i ).
tff(cOMBK_bool_state_type,type,
cOMBK_bool_state: $i ).
tff(cOMBK_1458035955bool_a_type,type,
cOMBK_1458035955bool_a: $i ).
tff(hAPP_a2036067514e_bool_type,type,
hAPP_a2036067514e_bool: ( $i * $i ) > $i ).
tff(tptp_fun_Z_11_31_type,type,
tptp_fun_Z_11_31: ( $i * $i * $i * $i ) > $i ).
tff(is_bool_type,type,
is_bool: $i > $o ).
tff(tptp_fun_S_3_32_type,type,
tptp_fun_S_3_32: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(hAPP_f1695230391l_bool_type,type,
hAPP_f1695230391l_bool: ( $i * $i ) > $i ).
tff(hAPP_f20753329a_bool_type,type,
hAPP_f20753329a_bool: ( $i * $i ) > $i ).
tff(bot_bo797238721a_bool_type,type,
bot_bo797238721a_bool: $i ).
tff(hAPP_H1743777351a_bool_type,type,
hAPP_H1743777351a_bool: ( $i * $i ) > $i ).
tff(hoare_1916936827iple_a_type,type,
hoare_1916936827iple_a: ( $i * $i * $i ) > $i ).
tff(insert956547291iple_a_type,type,
insert956547291iple_a: $i ).
tff(hoare_2102800559rivs_a_type,type,
hoare_2102800559rivs_a: $i > $i ).
tff(1,plain,
^ [P: $i,Q: $i] :
refl(( ( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )
<=> ( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )
<=> ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )
<=> ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [P: $i,Q: $i] :
rewrite(( ( is_bool(P)
=> ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )
<=> ( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [P: $i,Q: $i] :
( is_bool(P)
=> ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )
<=> ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [P: $i,Q: $i] :
( is_bool(P)
=> ( 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(7,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( is_bool(fFalse)
<=> is_bool(fFalse) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
is_bool(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_fFalse) ).
tff(13,plain,
is_bool(fFalse),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )
| ~ is_bool(fFalse)
| ( 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 ) )
<=> ( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )
| ~ is_bool(fFalse)
| ( 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(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )
| ~ is_bool(fFalse)
| ( 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(16,plain,
( ~ ! [P: $i,Q: $i] :
( ~ is_bool(P)
| ( hAPP_state_bool(hAPP_b2019457360e_bool(cOMBK_bool_state,P),Q) = P ) )
| ~ is_bool(fFalse)
| ( 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(modus_ponens,[status(thm)],[15,14]) ).
tff(17,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)],[16,13,10]) ).
tff(18,plain,
^ [P: $i,Q: $i] :
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(19,plain,
( ! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P )
<=> ! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P )
<=> ! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [P: $i,Q: $i] : ( 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(22,plain,
! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [P: $i,Q: $i] : ( hAPP_a2036067514e_bool(hAPP_f762886889e_bool(cOMBK_1458035955bool_a,P),Q) = P ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [P: $i,Q: $i] : ( 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(26,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)],[25,24]) ).
tff(27,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)],[26]) ).
tff(28,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)],[27,17]) ).
tff(29,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)],[28]) ).
tff(30,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)],[29]) ).
tff(31,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)],[30]) ).
tff(32,plain,
( ~ hBOOL(fFalse)
<=> ~ hBOOL(fFalse) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
tff(34,plain,
~ hBOOL(fFalse),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,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)],[34,31]) ).
tff(36,plain,
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_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_bo797238721a_bool)))
<=> ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_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_bo797238721a_bool))) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_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_bo797238721a_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(38,plain,
~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_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_bo797238721a_bool))),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
refl(( ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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(40,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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)],[39]) ).
tff(41,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
rewrite(( ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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(42,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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)],[41]) ).
tff(43,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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)],[42,40]) ).
tff(44,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
rewrite(( ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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(45,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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)],[44]) ).
tff(46,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))
| ~ ! [Z_11: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))
| ~ ! [Z_11: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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(47,plain,
^ [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [Z_11: $i,S_2: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [P_1: $i,Q_2: $i] :
rewrite(( ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( ! [Z_12: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( ! [Z_12: $i] :
( 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: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( ! [Z_12: $i] :
( 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: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( ! [Z_12: $i] :
( 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: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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: $i,S_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( ! [Z_12: $i] :
( 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: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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: $i,S_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( ! [Z_12: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool))) )
<=> ( ! [Z_11: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool))) ) )),
rewrite(( ( ! [Z_11: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool))) )
<=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))
| ~ ! [Z_11: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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: $i,S_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( ! [Z_12: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool))) )
<=> ( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))
| ~ ! [Z_11: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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(48,plain,
( ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( ! [Z_11: $i,S_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( ! [Z_12: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool))) )
<=> ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))
| ~ ! [Z_11: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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)],[47]) ).
tff(49,axiom,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( ! [Z_11: $i,S_2: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
=> ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( ! [Z_12: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_conseq) ).
tff(50,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))
| ~ ! [Z_11: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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)],[49,48]) ).
tff(51,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_bool)))
| ~ ! [Z_11: $i,S_2: $i] :
( ~ hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_11),S_2))
| ? [P_1: $i,Q_2: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_bool)))
& ! [S_3: $i] :
( hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_11),S_3))
| ~ ! [Z_12: $i] :
( 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)],[50,46]) ).
tff(52,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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)],[51]) ).
tff(53,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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)],[52,45]) ).
tff(54,plain,
! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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)],[53,43]) ).
tff(55,plain,
( ( ~ ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_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_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,c,Q_2)),bot_bo797238721a_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: $i] :
( 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: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_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_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,c,Q_2)),bot_bo797238721a_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: $i] :
( 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(56,plain,
( ~ ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_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_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,c,Q_2)),bot_bo797238721a_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: $i] :
( 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(57,plain,
( ~ ! [Q_1: $i,Ga: $i,Ca: $i,Pa: $i] :
( hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(Pa,Ca,Q_1)),bot_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(Ga),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,Ca,Q_2)),bot_bo797238721a_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: $i] :
( 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_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_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_bo797238721a_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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,c,Q_2)),bot_bo797238721a_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: $i] :
( 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)],[56,55]) ).
tff(58,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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,c,Q_2)),bot_bo797238721a_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: $i] :
( 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)],[57,54,38]) ).
tff(59,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: $i,Q_2: $i] :
( ~ hBOOL(hAPP_f1695230391l_bool(hoare_2102800559rivs_a(g),hAPP_f20753329a_bool(hAPP_H1743777351a_bool(insert956547291iple_a,hoare_1916936827iple_a(P_1,c,Q_2)),bot_bo797238721a_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: $i] :
( 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(60,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)],[59,58]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW470+3 : TPTP v9.0.0. Released v5.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 11:51:35 EDT 2025
% 0.11/0.34 % CPUTime :
% 1.95/2.21 % SZS status Theorem
% 1.95/2.21 % SZS output start Proof
% See solution above
% 2.12/2.31 % E exiting
%------------------------------------------------------------------------------